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Sample records for classical nucleation theory

  1. Classical nucleation theory in the phase-field crystal model.

    Science.gov (United States)

    Jreidini, Paul; Kocher, Gabriel; Provatas, Nikolas

    2018-04-01

    A full understanding of polycrystalline materials requires studying the process of nucleation, a thermally activated phase transition that typically occurs at atomistic scales. The numerical modeling of this process is problematic for traditional numerical techniques: commonly used phase-field methods' resolution does not extend to the atomic scales at which nucleation takes places, while atomistic methods such as molecular dynamics are incapable of scaling to the mesoscale regime where late-stage growth and structure formation takes place following earlier nucleation. Consequently, it is of interest to examine nucleation in the more recently proposed phase-field crystal (PFC) model, which attempts to bridge the atomic and mesoscale regimes in microstructure simulations. In this work, we numerically calculate homogeneous liquid-to-solid nucleation rates and incubation times in the simplest version of the PFC model, for various parameter choices. We show that the model naturally exhibits qualitative agreement with the predictions of classical nucleation theory (CNT) despite a lack of some explicit atomistic features presumed in CNT. We also examine the early appearance of lattice structure in nucleating grains, finding disagreement with some basic assumptions of CNT. We then argue that a quantitatively correct nucleation theory for the PFC model would require extending CNT to a multivariable theory.

  2. Classical nucleation theory in the phase-field crystal model

    Science.gov (United States)

    Jreidini, Paul; Kocher, Gabriel; Provatas, Nikolas

    2018-04-01

    A full understanding of polycrystalline materials requires studying the process of nucleation, a thermally activated phase transition that typically occurs at atomistic scales. The numerical modeling of this process is problematic for traditional numerical techniques: commonly used phase-field methods' resolution does not extend to the atomic scales at which nucleation takes places, while atomistic methods such as molecular dynamics are incapable of scaling to the mesoscale regime where late-stage growth and structure formation takes place following earlier nucleation. Consequently, it is of interest to examine nucleation in the more recently proposed phase-field crystal (PFC) model, which attempts to bridge the atomic and mesoscale regimes in microstructure simulations. In this work, we numerically calculate homogeneous liquid-to-solid nucleation rates and incubation times in the simplest version of the PFC model, for various parameter choices. We show that the model naturally exhibits qualitative agreement with the predictions of classical nucleation theory (CNT) despite a lack of some explicit atomistic features presumed in CNT. We also examine the early appearance of lattice structure in nucleating grains, finding disagreement with some basic assumptions of CNT. We then argue that a quantitatively correct nucleation theory for the PFC model would require extending CNT to a multivariable theory.

  3. A two-parameter extension of classical nucleation theory

    Science.gov (United States)

    Lutsko, James F.; Durán-Olivencia, Miguel A.

    2015-06-01

    A two-variable stochastic model for diffusion-limited nucleation is developed using a formalism derived from fluctuating hydrodynamics. The model is a direct generalization of the standard classical nucleation theory (CNT). The nucleation rate and pathway are calculated in the weak-noise approximation and are shown to be in good agreement with direct numerical simulations for the weak-solution/strong-solution transition in globular proteins. We find that CNT underestimates the time needed for the formation of a critical cluster by two orders of magnitude and that this discrepancy is due to the more complex dynamics of the two variable model and not, as often is assumed, a result of errors in the estimation of the free energy barrier.

  4. A two-parameter extension of classical nucleation theory

    International Nuclear Information System (INIS)

    Lutsko, James F; Durán-Olivencia, Miguel A

    2015-01-01

    A two-variable stochastic model for diffusion-limited nucleation is developed using a formalism derived from fluctuating hydrodynamics. The model is a direct generalization of the standard classical nucleation theory (CNT). The nucleation rate and pathway are calculated in the weak-noise approximation and are shown to be in good agreement with direct numerical simulations for the weak-solution/strong-solution transition in globular proteins. We find that CNT underestimates the time needed for the formation of a critical cluster by two orders of magnitude and that this discrepancy is due to the more complex dynamics of the two variable model and not, as often is assumed, a result of errors in the estimation of the free energy barrier. (paper)

  5. The Lack of Chemical Equilibrium does not Preclude the Use of the Classical Nucleation Theory in Circumstellar Outflows

    Science.gov (United States)

    Paquette, John A.; Nuth, Joseph A., III

    2011-01-01

    Classical nucleation theory has been used in models of dust nucleation in circumstellar outflows around oxygen-rich asymptotic giant branch stars. One objection to the application of classical nucleation theory (CNT) to astrophysical systems of this sort is that an equilibrium distribution of clusters (assumed by CNT) is unlikely to exist in such conditions due to a low collision rate of condensable species. A model of silicate grain nucleation and growth was modified to evaluate the effect of a nucleation flux orders of magnitUde below the equilibrium value. The results show that a lack of chemical equilibrium has only a small effect on the ultimate grain distribution.

  6. A classical density functional investigation of nucleation

    International Nuclear Information System (INIS)

    Ghosh, Satinath; Ghosh, Swapan K.

    2009-01-01

    Study of nucleation and growth phenomena in condensation is of prime importance in various applications such as crystal growth, nanoparticle synthesis, pattern formation etc. The knowledge of nucleation barrier in condensation is necessary to control the nucleation kinetics, size of the nanoparticles etc. Classical nucleation theory (CNT) assumes the density of the drop as bulk density irrespective of the size of the drop and overestimates the nucleation barrier. Here we are interested in solving the problem analytically using density functional theory (DFT) with square gradient approximation along the lines of Cahn and Hilliard. Nucleation barrier and density profile obtained in this work are consistent with other works based on nonclassical theory. (author)

  7. A nanoscale temperature-dependent heterogeneous nucleation theory

    International Nuclear Information System (INIS)

    Cao, Y. Y.; Yang, G. W.

    2015-01-01

    Classical nucleation theory relies on the hypothetical equilibrium of the whole nucleation system, and neglects the thermal fluctuations of the surface; this is because the high entropic gains of the (thermodynamically extensive) surface would lead to multiple stable states. In fact, at the nanometer scale, the entropic gains of the surface are high enough to destroy the stability of the thermal equilibrium during nucleation, comparing with the whole system. We developed a temperature-dependent nucleation theory to elucidate the heterogeneous nucleation process, by considering the thermal fluctuations based on classical nucleation theory. It was found that the temperature not only affected the phase transformation, but also influenced the surface energy of the nuclei. With changes in the Gibbs free energy barrier, nucleation behaviors, such as the nucleation rate and the critical radius of the nuclei, showed temperature-dependent characteristics that were different from those predicted by classical nucleation theory. The temperature-dependent surface energy density of a nucleus was deduced based on our theoretical model. The agreement between the theoretical and experimental results suggested that the developed nucleation theory has the potential to contribute to the understanding and design of heterogeneous nucleation at the nanoscale

  8. Thermodynamics and Kinetics of Prenucleation Clusters, Classical and Non-Classical Nucleation.

    Science.gov (United States)

    Zahn, Dirk

    2015-07-20

    Recent observations of prenucleation species and multi-stage crystal nucleation processes challenge the long-established view on the thermodynamics of crystal formation. Here, we review and generalize extensions to classical nucleation theory. Going beyond the conventional implementation as has been used for more than a century now, nucleation inhibitors, precursor clusters and non-classical nucleation processes are rationalized as well by analogous concepts based on competing interface and bulk energy terms. This is illustrated by recent examples of species formed prior to/instead of crystal nucleation and multi-step nucleation processes. Much of the discussed insights were obtained from molecular simulation using advanced sampling techniques, briefly summarized herein for both nucleation-controlled and diffusion-controlled aggregate formation. © 2015 The Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA. This is an open access article under the terms of the Creative Commons Attribution Non-Commercial NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.

  9. A dynamical theory of nucleation

    Science.gov (United States)

    Lutsko, James F.

    2013-05-01

    A dynamical theory of nucleation based on fluctuating hydrodynamics is described. It is developed in detail for the case of diffusion-limited nucleation appropriate to colloids and macro-molecules in solution. By incorporating fluctuations, realistic fluid-transport and realistic free energy models the theory is able to give a unified treatment of both the pre-critical development of fluctuations leading to a critical cluster as well as of post-critical growth. Standard results from classical nucleation theory are shown to follow in the weak noise limit while the generality of the theory allows for many extensions including the description of very high supersaturations (small clusters), multiple order parameters and strong-noise effects to name a few. The theory is applied to homogeneous and heterogeneous nucleation of a model globular protein in a confined volume and it is found that nucleation depends critically on the existence of long-wavelength, small-amplitude density fluctuations.

  10. Simple improvements to classical bubble nucleation models.

    Science.gov (United States)

    Tanaka, Kyoko K; Tanaka, Hidekazu; Angélil, Raymond; Diemand, Jürg

    2015-08-01

    We revisit classical nucleation theory (CNT) for the homogeneous bubble nucleation rate and improve the classical formula using a correct prefactor in the nucleation rate. Most of the previous theoretical studies have used the constant prefactor determined by the bubble growth due to the evaporation process from the bubble surface. However, the growth of bubbles is also regulated by the thermal conduction, the viscosity, and the inertia of liquid motion. These effects can decrease the prefactor significantly, especially when the liquid pressure is much smaller than the equilibrium one. The deviation in the nucleation rate between the improved formula and the CNT can be as large as several orders of magnitude. Our improved, accurate prefactor and recent advances in molecular dynamics simulations and laboratory experiments for argon bubble nucleation enable us to precisely constrain the free energy barrier for bubble nucleation. Assuming the correction to the CNT free energy is of the functional form suggested by Tolman, the precise evaluations of the free energy barriers suggest the Tolman length is ≃0.3σ independently of the temperature for argon bubble nucleation, where σ is the unit length of the Lennard-Jones potential. With this Tolman correction and our prefactor one gets accurate bubble nucleation rate predictions in the parameter range probed by current experiments and molecular dynamics simulations.

  11. A novel approach to the theory of homogeneous and heterogeneous nucleation.

    Science.gov (United States)

    Ruckenstein, Eli; Berim, Gersh O; Narsimhan, Ganesan

    2015-01-01

    A new approach to the theory of nucleation, formulated relatively recently by Ruckenstein, Narsimhan, and Nowakowski (see Refs. [7-16]) and developed further by Ruckenstein and other colleagues, is presented. In contrast to the classical nucleation theory, which is based on calculating the free energy of formation of a cluster of the new phase as a function of its size on the basis of macroscopic thermodynamics, the proposed theory uses the kinetic theory of fluids to calculate the condensation (W(+)) and dissociation (W(-)) rates on and from the surface of the cluster, respectively. The dissociation rate of a monomer from a cluster is evaluated from the average time spent by a surface monomer in the potential well as obtained from the solution of the Fokker-Planck equation in the phase space of position and momentum for liquid-to-solid transition and the phase space of energy for vapor-to-liquid transition. The condensation rates are calculated using traditional expressions. The knowledge of those two rates allows one to calculate the size of the critical cluster from the equality W(+)=W(-) as well as the rate of nucleation. The developed microscopic approach allows one to avoid the controversial application of classical thermodynamics to the description of nuclei which contain a few molecules. The new theory was applied to a number of cases, such as the liquid-to-solid and vapor-to-liquid phase transitions, binary nucleation, heterogeneous nucleation, nucleation on soluble particles and protein folding. The theory predicts higher nucleation rates at high saturation ratios (small critical clusters) than the classical nucleation theory for both solid-to-liquid as well as vapor-to-liquid transitions. As expected, at low saturation ratios for which the size of the critical cluster is large, the results of the new theory are consistent with those of the classical one. The present approach was combined with the density functional theory to account for the density

  12. Nucleation theory - Is replacement free energy needed?. [error analysis of capillary approximation

    Science.gov (United States)

    Doremus, R. H.

    1982-01-01

    It has been suggested that the classical theory of nucleation of liquid from its vapor as developed by Volmer and Weber (1926) needs modification with a factor referred to as the replacement free energy and that the capillary approximation underlying the classical theory is in error. Here, the classical nucleation equation is derived from fluctuation theory, Gibb's result for the reversible work to form a critical nucleus, and the rate of collision of gas molecules with a surface. The capillary approximation is not used in the derivation. The chemical potential of small drops is then considered, and it is shown that the capillary approximation can be derived from thermodynamic equations. The results show that no corrections to Volmer's equation are needed.

  13. New mechanism for bubble nucleation: Classical transitions

    International Nuclear Information System (INIS)

    Easther, Richard; Giblin, John T. Jr; Hui Lam; Lim, Eugene A.

    2009-01-01

    Given a scalar field with metastable minima, bubbles nucleate quantum mechanically. When bubbles collide, energy stored in the bubble walls is converted into kinetic energy of the field. This kinetic energy can facilitate the classical nucleation of new bubbles in minima that lie below those of the 'parent' bubbles. This process is efficient and classical, and changes the dynamics and statistics of bubble formation in models with multiple vacua, relative to that derived from quantum tunneling.

  14. Acoustic Effects in Classical Nucleation Theory

    Science.gov (United States)

    Baird, J. K.; Su, C.-H.

    2017-01-01

    The effect of sound wave oscillations on the rate of nucleation in a parent phase can be calculated by expanding the free energy of formation of a nucleus of the second phase in powers of the acoustic pressure. Since the period of sound wave oscillation is much shorter than the time scale for nucleation, the acoustic effect can be calculated as a time average of the free energy of formation of the nucleus. The leading non-zero term in the time average of the free energy is proportional to the square of the acoustic pressure. The Young-Laplace equation for the surface tension of the nucleus can be used to link the time average of the square of the pressure in the parent phase to its time average in the nucleus of the second phase. Due to the surface tension, the pressure in the nuclear phase is higher than the pressure in the parent phase. The effect is to lower the free energy of formation of the nucleus and increase the rate of nucleation.

  15. Dynamics of homogeneous nucleation

    DEFF Research Database (Denmark)

    Toxværd, Søren

    2015-01-01

    The classical nucleation theory for homogeneous nucleation is formulated as a theory for a density fluctuation in a supersaturated gas at a given temperature. But molecular dynamics simulations reveal that it is small cold clusters which initiates the nucleation. The temperature in the nucleating...

  16. Nucleation theory in Langevin's approach and lifetime of a Brownian particle in potential wells.

    Science.gov (United States)

    Alekseechkin, N V

    2008-07-14

    The multivariable theory of nucleation suggested by Alekseechkin [J. Chem. Phys. 124, 124512 (2006)] is further developed in the context of Langevin's approach. The use of this approach essentially enhances the capability of the nucleation theory, because it makes possible to consider the cases of small friction which are not taken into account by the classical Zel'dovich-Frenkel theory and its multivariable extensions. The procedure for the phenomenological determination of the nucleation parameters is described. Using the similarity of the Kramers model with that of nucleation, the lifetime of a Brownian particle in potential wells in various dimensionalities is calculated with the help of the expression for the steady state nucleation rate.

  17. Recent developments in the kinetic theory of nucleation.

    Science.gov (United States)

    Ruckenstein, E; Djikaev, Y S

    2005-12-30

    , but the hierarchy of time scales does allow one to reduce it to the Fokker-Plank equation in the energy space. The new theory provides an equation for the critical radius of a new-phase particle which in the limit of large clusters (low supersaturations) yields the Kelvin equation and hence an expression for the macroscopic surface tension. The theory was illustrated with numerical calculations for a molecular pair interaction potential combining the dispersive attraction with the hard-sphere repulsion. The results for the liquid-to-solid nucleation clearly show that at given supersaturation the nucleation rate depends on the cluster structure (for three cluster structures considered-amorphous, fcc, and icosahedral). For both the liquid-to-solid and vapor-to-liquid nucleation, the predictions of the theory are consistent with the results of classical nucleation theory (CNT) in the limit of large critical clusters (low supersaturations). For small critical clusters the new theory provides higher nucleation rates than CNT. This can be accounted for by the fact that CNT uses the macroscopic interfacial tension which presumably overpredicts the surface tension of small clusters, and hence underpredicts nucleation rates.

  18. A classical view on nonclassical nucleation.

    Science.gov (United States)

    Smeets, Paul J M; Finney, Aaron R; Habraken, Wouter J E M; Nudelman, Fabio; Friedrich, Heiner; Laven, Jozua; De Yoreo, James J; Rodger, P Mark; Sommerdijk, Nico A J M

    2017-09-19

    Understanding and controlling nucleation is important for many crystallization applications. Calcium carbonate (CaCO 3 ) is often used as a model system to investigate nucleation mechanisms. Despite its great importance in geology, biology, and many industrial applications, CaCO 3 nucleation is still a topic of intense discussion, with new pathways for its growth from ions in solution proposed in recent years. These new pathways include the so-called nonclassical nucleation mechanism via the assembly of thermodynamically stable prenucleation clusters, as well as the formation of a dense liquid precursor phase via liquid-liquid phase separation. Here, we present results from a combined experimental and computational investigation on the precipitation of CaCO 3 in dilute aqueous solutions. We propose that a dense liquid phase (containing 4-7 H 2 O per CaCO 3 unit) forms in supersaturated solutions through the association of ions and ion pairs without significant participation of larger ion clusters. This liquid acts as the precursor for the formation of solid CaCO 3 in the form of vaterite, which grows via a net transfer of ions from solution according to z Ca 2+ + z CO 3 2- → z CaCO 3 The results show that all steps in this process can be explained according to classical concepts of crystal nucleation and growth, and that long-standing physical concepts of nucleation can describe multistep, multiphase growth mechanisms.

  19. On the usage of classical nucleation theory in predicting the impact of bacteria on weather and climate

    Science.gov (United States)

    Sahyoun, Maher; Woetmann Nielsen, Niels; Havskov Sørensen, Jens; Finster, Kai; Bay Gosewinkel Karlson, Ulrich; Šantl-Temkiv, Tina; Smith Korsholm, Ulrik

    2014-05-01

    Bacteria, e.g. Pseudomonas syringae, have previously been found efficient in nucleating ice heterogeneously at temperatures close to -2°C in laboratory tests. Therefore, ice nucleation active (INA) bacteria may be involved in the formation of precipitation in mixed phase clouds, and could potentially influence weather and climate. Investigations into the impact of INA bacteria on climate have shown that emissions were too low to significantly impact the climate (Hoose et al., 2010). The goal of this study is to clarify the reason for finding the marginal impact on climate when INA bacteria were considered, by investigating the usability of ice nucleation rate parameterization based on classical nucleation theory (CNT). For this purpose, two parameterizations of heterogeneous ice nucleation were compared. Both parameterizations were implemented and tested in a 1-d version of the operational weather model (HIRLAM) (Lynch et al., 2000; Unden et al., 2002) in two different meteorological cases. The first parameterization is based on CNT and denoted CH08 (Chen et al., 2008). This parameterization is a function of temperature and the size of the IN. The second parameterization, denoted HAR13, was derived from nucleation measurements of SnomaxTM (Hartmann et al., 2013). It is a function of temperature and the number of protein complexes on the outer membranes of the cell. The fraction of cloud droplets containing each type of IN as percentage in the cloud droplets population were used and the sensitivity of cloud ice production in each parameterization was compared. In this study, HAR13 produces more cloud ice and precipitation than CH08 when the bacteria fraction increases. In CH08, the increase of the bacteria fraction leads to decreasing the cloud ice mixing ratio. The ice production using HAR13 was found to be more sensitive to the change of the bacterial fraction than CH08 which did not show a similar sensitivity. As a result, this may explain the marginal impact of

  20. Nucleation in the atmosphere

    International Nuclear Information System (INIS)

    Hegg, D A; Baker, M B

    2009-01-01

    Small particles play major roles in modulating radiative and hydrological fluxes in the atmosphere and thus they impact both climate (IPCC 2007) and weather. Most atmospheric particles outside clouds are created in situ through nucleation from gas phase precursors and most ice particles within clouds are formed by nucleation, usually from the liquid. Thus, the nucleation process is of great significance in the Earth's atmosphere. The theoretical examination of nucleation in the atmosphere has been based mostly on classical nucleation theory. While diagnostically very useful, the prognostic skill demonstrated by this approach has been marginal. Microscopic approaches such as molecular dynamics and density functional theory have also proven useful in elucidating various aspects of the process but are not yet sufficiently refined to offer a significant prognostic advantage to the classical approach, due primarily to the heteromolecular nature of atmospheric nucleation. An important aspect of the nucleation process in the atmosphere is that the degree of metastability of the parent phase for the nucleation is modulated by a number of atmospheric processes such as condensation onto pre-existing particles, updraft velocities that are the main driving force for supersaturation of water (a major factor in all atmospheric nucleation), and photochemical production rates of nucleation precursors. Hence, atmospheric nucleation is both temporally and spatially inhomogeneous

  1. Superheating in nucleate boiling calculated by the heterogeneous nucleation theory

    International Nuclear Information System (INIS)

    Gerum, E.; Straub, J.; Grigull, U.

    1979-01-01

    With the heterogeneous nucleation theory the superheating of the liquid boundary layer in nucleate boiling is described not only for the onset of nuclear boiling but also for the boiling crisis. The rate of superheat depends on the thermodynamic stability of the metastable liquid, which is influenced by the statistical fluctuations in the liquid and the nucleation at the solid surface. Because of the fact that the cavities acting as nuclei are too small for microscopic observation, the size and distribution function of the nuclei on the surface necessary for the determination of the probability of bubble formation cannot be detected by measuring techniques. The work of bubble formation reduced by the nuclei can be represented by a simple empirical function whose coefficients are determined from boiling experiments. Using this the heterogeneous nucleation theory describes the superheating of the liquid. Several fluids including refrigerants, liquid gases, organic liquids and water were used to check the theory. (author)

  2. Role of stacking disorder in ice nucleation.

    Science.gov (United States)

    Lupi, Laura; Hudait, Arpa; Peters, Baron; Grünwald, Michael; Gotchy Mullen, Ryan; Nguyen, Andrew H; Molinero, Valeria

    2017-11-08

    The freezing of water affects the processes that determine Earth's climate. Therefore, accurate weather and climate forecasts hinge on good predictions of ice nucleation rates. Such rate predictions are based on extrapolations using classical nucleation theory, which assumes that the structure of nanometre-sized ice crystallites corresponds to that of hexagonal ice, the thermodynamically stable form of bulk ice. However, simulations with various water models find that ice nucleated and grown under atmospheric temperatures is at all sizes stacking-disordered, consisting of random sequences of cubic and hexagonal ice layers. This implies that stacking-disordered ice crystallites either are more stable than hexagonal ice crystallites or form because of non-equilibrium dynamical effects. Both scenarios challenge central tenets of classical nucleation theory. Here we use rare-event sampling and free energy calculations with the mW water model to show that the entropy of mixing cubic and hexagonal layers makes stacking-disordered ice the stable phase for crystallites up to a size of at least 100,000 molecules. We find that stacking-disordered critical crystallites at 230 kelvin are about 14 kilojoules per mole of crystallite more stable than hexagonal crystallites, making their ice nucleation rates more than three orders of magnitude higher than predicted by classical nucleation theory. This effect on nucleation rates is temperature dependent, being the most pronounced at the warmest conditions, and should affect the modelling of cloud formation and ice particle numbers, which are very sensitive to the temperature dependence of ice nucleation rates. We conclude that classical nucleation theory needs to be corrected to include the dependence of the crystallization driving force on the size of the ice crystallite when interpreting and extrapolating ice nucleation rates from experimental laboratory conditions to the temperatures that occur in clouds.

  3. Effects of shear flow on phase nucleation and crystallization.

    Science.gov (United States)

    Mura, Federica; Zaccone, Alessio

    2016-04-01

    Classical nucleation theory offers a good framework for understanding the common features of new phase formation processes in metastable homogeneous media at rest. However, nucleation processes in liquids are ubiquitously affected by hydrodynamic flow, and there is no satisfactory understanding of whether shear promotes or slows down the nucleation process. We developed a classical nucleation theory for sheared systems starting from the molecular level of the Becker-Doering master kinetic equation and we analytically derived a closed-form expression for the nucleation rate. The theory accounts for the effect of flow-mediated transport of molecules to the nucleus of the new phase, as well as for the mechanical deformation imparted to the nucleus by the flow field. The competition between flow-induced molecular transport, which accelerates nucleation, and flow-induced nucleus straining, which lowers the nucleation rate by increasing the nucleation energy barrier, gives rise to a marked nonmonotonic dependence of the nucleation rate on the shear rate. The theory predicts an optimal shear rate at which the nucleation rate is one order of magnitude larger than in the absence of flow.

  4. Nucleation in ZBLAN glasses

    NARCIS (Netherlands)

    de Leede, G.L.A.; Waal, de H.

    1989-01-01

    Nucleation rates were detd. in a ZrF4-BaF2-NaF-LaF3-AlF3 glass (ZBLAN) using an optical method. The results were compared with a similar glass having a slightly different compn. The difference in the nucleation rate is explained by classical nucleation theory using calcd. free-energy differences

  5. Study of homogeneous bubble nucleation in liquid carbon dioxide by a hybrid approach combining molecular dynamics simulation and density gradient theory

    Science.gov (United States)

    Langenbach, K.; Heilig, M.; Horsch, M.; Hasse, H.

    2018-03-01

    A new method for predicting homogeneous bubble nucleation rates of pure compounds from vapor-liquid equilibrium (VLE) data is presented. It combines molecular dynamics simulation on the one side with density gradient theory using an equation of state (EOS) on the other. The new method is applied here to predict bubble nucleation rates in metastable liquid carbon dioxide (CO2). The molecular model of CO2 is taken from previous work of our group. PC-SAFT is used as an EOS. The consistency between the molecular model and the EOS is achieved by adjusting the PC-SAFT parameters to VLE data obtained from the molecular model. The influence parameter of density gradient theory is fitted to the surface tension of the molecular model. Massively parallel molecular dynamics simulations are performed close to the spinodal to compute bubble nucleation rates. From these simulations, the kinetic prefactor of the hybrid nucleation theory is estimated, whereas the nucleation barrier is calculated from density gradient theory. This enables the extrapolation of molecular simulation data to the whole metastable range including technically relevant densities. The results are tested against available experimental data and found to be in good agreement. The new method does not suffer from typical deficiencies of classical nucleation theory concerning the thermodynamic barrier at the spinodal and the bubble size dependence of surface tension, which is typically neglected in classical nucleation theory. In addition, the density in the center of critical bubbles and their surface tension is determined as a function of their radius. The usual linear Tolman correction to the capillarity approximation is found to be invalid.

  6. Study of homogeneous bubble nucleation in liquid carbon dioxide by a hybrid approach combining molecular dynamics simulation and density gradient theory.

    Science.gov (United States)

    Langenbach, K; Heilig, M; Horsch, M; Hasse, H

    2018-03-28

    A new method for predicting homogeneous bubble nucleation rates of pure compounds from vapor-liquid equilibrium (VLE) data is presented. It combines molecular dynamics simulation on the one side with density gradient theory using an equation of state (EOS) on the other. The new method is applied here to predict bubble nucleation rates in metastable liquid carbon dioxide (CO 2 ). The molecular model of CO 2 is taken from previous work of our group. PC-SAFT is used as an EOS. The consistency between the molecular model and the EOS is achieved by adjusting the PC-SAFT parameters to VLE data obtained from the molecular model. The influence parameter of density gradient theory is fitted to the surface tension of the molecular model. Massively parallel molecular dynamics simulations are performed close to the spinodal to compute bubble nucleation rates. From these simulations, the kinetic prefactor of the hybrid nucleation theory is estimated, whereas the nucleation barrier is calculated from density gradient theory. This enables the extrapolation of molecular simulation data to the whole metastable range including technically relevant densities. The results are tested against available experimental data and found to be in good agreement. The new method does not suffer from typical deficiencies of classical nucleation theory concerning the thermodynamic barrier at the spinodal and the bubble size dependence of surface tension, which is typically neglected in classical nucleation theory. In addition, the density in the center of critical bubbles and their surface tension is determined as a function of their radius. The usual linear Tolman correction to the capillarity approximation is found to be invalid.

  7. Homogeneous nucleation of water in synthetic air

    NARCIS (Netherlands)

    Fransen, M.A.L.J.; Sachteleben, E.; Hruby, J.; Smeulders, D.M.J.; DeMott, P.J.; O'Dowd, C.D.

    2013-01-01

    Homogeneous nucleation rates for water vapor in synthetic air are measured by means of a Pulse-Expansion Wave Tube (PEWT). A comparison of the experimental nucleation rates with the Classical Nucleation Theory (CNT) shows that a more elaborated model is necessary to describe supercooled water

  8. Non stationary nucleation: the model with minimal environment

    OpenAIRE

    Kurasov, Victor

    2013-01-01

    A new model to calculate the rate of nucleation is formulated. This model is based on the classical nucleation theory but considers also vapor depletion around the formed embryo. As the result the free energy has to be recalculated which brings a new expression for the nucleation rate.

  9. Predicting glass-to-glass and liquid-to-liquid phase transitions in supercooled water using classical nucleation theory

    Science.gov (United States)

    Tournier, Robert F.

    2018-01-01

    Glass-to-glass and liquid-to-liquid phase transitions are observed in bulk and confined water, with or without applied pressure. They result from the competition of two liquid phases separated by an enthalpy difference depending on temperature. The classical nucleation equation of these phases is completed by this quantity existing at all temperatures, a pressure contribution, and an enthalpy excess. This equation leads to two homogeneous nucleation temperatures in each liquid phase; the first one (Tn- below Tm) being the formation temperature of an "ordered" liquid phase and the second one corresponding to the overheating temperature (Tn+ above Tm). Thermodynamic properties, double glass transition temperatures, sharp enthalpy and volume changes are predicted in agreement with experimental results. The first-order transition line at TLL = 0.833 × Tm between fragile and strong liquids joins two critical points. Glass phase above Tg becomes "ordered" liquid phase disappearing at TLL at low pressure and at Tn+ = 1.302 × Tm at high pressure.

  10. Nucleation of voids in materials supersaturated with mobile interstitials, vacancies and divacancies

    International Nuclear Information System (INIS)

    Wolfer, W.G.; Si-Ahmed, A.

    1982-01-01

    In previous void nucleation theories, the void size has been allowed to change only by one atomic volume through vacancy or interstitial absorption or through vacancy emission. To include the absorption of divacancies, the classical nucleation theory is here extended to include double-step transitions between clusters. The new nucleation theory is applied to study the effect of divacancies on void formation. It is found that the steady-state void nucleation rate is enhanced by several orders of magnitude as compared to results with previous void nucleation theories. However, to obtain void nucleation rates comparable to measured ones, the effect of impurities, segregation and insoluble gases must still be invoked. (author)

  11. Theories of nucleation and growth of bubbles and voids

    International Nuclear Information System (INIS)

    Speight, M.V.

    1977-01-01

    The application of classical nucleation theory to the formation of voids from a supersaturated concentration of vacancies is reviewed. The effect of a dissolved concentration of barley soluble gas on the nucleation rate of voids is emphasized. Exposure to a damaging flux of irradiation is the most effective way of introducing a vacancy supersaturation, but interstitials are produced at an equal rate. The concentration of interstitials inhibits the nucleation of voids which can occur only in the presence of dislocations since they preferentially absorb interstitials. It is well known that a definite value of internal gas pressure is necessary to stabilize a bubble so that it shows no tendencies to either shrink or grow. The arguments are reviewed which conclude that this pressure is determined by the specific surface free energy of the solid rather than the surface tension. While the former property refers to the energy necessary to create new surface, the latter is a measure of the work done in elastically stretching a a given surface. The presence of an equilibrium gas bubble leaves the stresses in the surrounding solid unperturbed only when surface energy and surface tension are numerically equal. A bubble with internal pressure greater than the restraint offered by surface energy tends to grow to relieve the excess pressure. The mechanism of growth can involve the migration of vacancies from remote sources to the bubble surface or the plastic straining of the solid surrounding the bubble. The kinetics of both mechanisms are developed and compared. The theory of growth of grain-boundary voids by vacancy condensation under an applied stress is also considered. (author)

  12. Homogeneous crystal nucleation in polymers.

    Science.gov (United States)

    Schick, C; Androsch, R; Schmelzer, J W P

    2017-11-15

    The pathway of crystal nucleation significantly influences the structure and properties of semi-crystalline polymers. Crystal nucleation is normally heterogeneous at low supercooling, and homogeneous at high supercooling, of the polymer melt. Homogeneous nucleation in bulk polymers has been, so far, hardly accessible experimentally, and was even doubted to occur at all. This topical review summarizes experimental findings on homogeneous crystal nucleation in polymers. Recently developed fast scanning calorimetry, with cooling and heating rates up to 10 6 K s -1 , allows for detailed investigations of nucleation near and even below the glass transition temperature, including analysis of nuclei stability. As for other materials, the maximum homogeneous nucleation rate for polymers is located close to the glass transition temperature. In the experiments discussed here, it is shown that polymer nucleation is homogeneous at such temperatures. Homogeneous nucleation in polymers is discussed in the framework of the classical nucleation theory. The majority of our observations are consistent with the theory. The discrepancies may guide further research, particularly experiments to progress theoretical development. Progress in the understanding of homogeneous nucleation is much needed, since most of the modelling approaches dealing with polymer crystallization exclusively consider homogeneous nucleation. This is also the basis for advancing theoretical approaches to the much more complex phenomena governing heterogeneous nucleation.

  13. Modelling the effect of acoustic waves on nucleation

    Energy Technology Data Exchange (ETDEWEB)

    Haqshenas, S. R., E-mail: seyyed.haqshenas.12@ucl.ac.uk; Saffari, N., E-mail: n.saffari@ucl.ac.uk [Department of Mechanical Engineering, University College London, Gower Street, London WC1E 7JE (United Kingdom); Ford, I. J., E-mail: i.ford@ucl.ac.uk [Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT (United Kingdom)

    2016-07-14

    A phase transformation in a metastable phase can be affected when it is subjected to a high intensity ultrasound wave. In this study we determined the effect of oscillation in pressure and temperature on a phase transformation using the Gibbs droplet model in a generic format. The developed model is valid for both equilibrium and non-equilibrium clusters formed through a stationary or non-stationary process. We validated the underlying model by comparing the predicted kinetics of water droplet formation from the gas phase against experimental data in the absence of ultrasound. Our results demonstrated better agreement with experimental data in comparison with classical nucleation theory. Then, we determined the thermodynamics and kinetics of nucleation and the early stage of growth of clusters in an isothermal sonocrystallisation process. This new contribution shows that the effect of pressure on the kinetics of nucleation is cluster size-dependent in contrast to classical nucleation theory.

  14. Effect of ions on sulfuric acid-water binary particle formation: 2. Experimental data and comparison with QC-normalized classical nucleation theory

    CERN Document Server

    Duplissy, J.; Franchin, A.; Tsagkogeorgas, G.; Kangasluoma, J.; Wimmer, D.; Vuollekoski, H.; Schobesberger, S.; Lehtipalo, K.; Flagan, R. C.; Brus, D.; Donahue, N. M.; Vehkamäki, H.; Almeida, J.; Amorim, A.; Barmet, P.; Bianchi, F.; Breitenlechner, M.; Dunne, E. M.; Guida, R.; Henschel, H.; Junninen, H.; Kirkby, J.; Kürten, A.; Kupc, A.; Määttänen, A.; Makhmutov, V.; Mathot, S.; Nieminen, T.; Onnela, A.; Praplan, A. P.; Riccobono, F.; Rondo, L.; Steiner, G.; Tome, A.; Walther, H.; Baltensperger, U.; Carslaw, K. S.; Dommen, J.; Hansel, A.; Petäjä, T.; Sipilä, M.; Stratmann, F.; Vrtala, A.; Wagner, P. E.; Worsnop, D. R.; Curtius, J.; Kulmala, M.

    2015-09-04

    We report comprehensive, demonstrably contaminant‐free measurements of binary particle formation rates by sulfuric acid and water for neutral and ion‐induced pathways conducted in the European Organization for Nuclear Research Cosmics Leaving Outdoor Droplets chamber. The recently developed Atmospheric Pressure interface‐time of flight‐mass spectrometer was used to detect contaminants in charged clusters and to identify runs free of any contaminants. Four parameters were varied to cover ambient conditions: sulfuric acid concentration (105 to 109 mol cm−3), relative humidity (11% to 58%), temperature (207 K to 299 K), and total ion concentration (0 to 6800 ions cm−3). Formation rates were directly measured with novel instruments at sizes close to the critical cluster size (mobility size of 1.3 nm to 3.2 nm). We compare our results with predictions from Classical Nucleation Theory normalized by Quantum Chemical calculation (QC‐normalized CNT), which is described in a companion pape...

  15. Heterogeneous nucleation of calcium oxalate on native oxide surfaces

    International Nuclear Information System (INIS)

    Song, L.; Pattillo, M.J.; Graff, G.L.; Campbell, A.A.; Bunker, B.C.

    1994-04-01

    The aqueous deposition of calcium oxalate onto colloidal oxides has been studied as a model system for understanding heterogeneous nucleation processes of importance in biomimetic synthesis of ceramic thin films. Calcium oxalate nucleation has been monitored by measuring induction times for nucleation using Constant Composition techniques and by measuring nucleation densities on extended oxide surfaces using an atomic force microscope. Results show that the dependence of calcium oxalate nucleation on solution supersaturation fits the functional form predicted by classical nucleation theories. Anionic surfaces appear to promote nucleation better than cationic surfaces, lowering the effective energy barrier to heterogeneous nucleation

  16. Homogeneous nucleation, growth and recrystallization of discharge products on electrodes

    Energy Technology Data Exchange (ETDEWEB)

    Kappus, W.

    1983-11-01

    The early stage of discharge of electrodes with an electrodissolution/precipitation mechanism is investigated. A theory is proposed for quasi-classical homogeneous nucleation and the subsequent growth. Based on this theory the radii distribution function was calculated for the diffusion-controlled growth of crystallites. Recrystallization was included. The nucleation overpotential was calculated as a function of time for discharges under various conditions.

  17. A classical view on nonclassical nucleation

    NARCIS (Netherlands)

    Smeets, P.J.M.; Finney, A.R.; Habraken, W.J.E.M.; Nudelman, F.; Friedrich, H.; Laven, J.; De Yoreo, J.J.; Rodger, P.M.; Sommerdijk, N.A.J.M.

    2017-01-01

    Understanding and controlling nucleation is important for many crystallization applications. Calcium carbonate (CaCO3) is often used as a model system to investigate nucleation mechanisms. Despite its great importance in geology, biology, and many industrial applications, CaCO3 nucleation is still a

  18. Forward flux sampling calculation of homogeneous nucleation rates from aqueous NaCl solutions.

    Science.gov (United States)

    Jiang, Hao; Haji-Akbari, Amir; Debenedetti, Pablo G; Panagiotopoulos, Athanassios Z

    2018-01-28

    We used molecular dynamics simulations and the path sampling technique known as forward flux sampling to study homogeneous nucleation of NaCl crystals from supersaturated aqueous solutions at 298 K and 1 bar. Nucleation rates were obtained for a range of salt concentrations for the Joung-Cheatham NaCl force field combined with the Extended Simple Point Charge (SPC/E) water model. The calculated nucleation rates are significantly lower than the available experimental measurements. The estimates for the nucleation rates in this work do not rely on classical nucleation theory, but the pathways observed in the simulations suggest that the nucleation process is better described by classical nucleation theory than an alternative interpretation based on Ostwald's step rule, in contrast to some prior simulations of related models. In addition to the size of NaCl nucleus, we find that the crystallinity of a nascent cluster plays an important role in the nucleation process. Nuclei with high crystallinity were found to have higher growth probability and longer lifetimes, possibly because they are less exposed to hydration water.

  19. Nonclassical nucleation pathways in protein crystallization.

    Science.gov (United States)

    Zhang, Fajun

    2017-11-08

    Classical nucleation theory (CNT), which was established about 90 years ago, has been very successful in many research fields, and continues to be the most commonly used theory in describing the nucleation process. For a fluid-to-solid phase transition, CNT states that the solute molecules in a supersaturated solution reversibly form small clusters. Once the cluster size reaches a critical value, it becomes thermodynamically stable and favored for further growth. One of the most important assumptions of CNT is that the nucleation process is described by one reaction coordinate and all order parameters proceed simultaneously. Recent studies in experiments, computer simulations and theory have revealed nonclassical features in the early stage of nucleation. In particular, the decoupling of order parameters involved during a fluid-to-solid transition leads to the so-called two-step nucleation mechanism, in which a metastable intermediate phase (MIP) exists between the initial supersaturated solution and the final crystals. Depending on the exact free energy landscapes, the MIPs can be a high density liquid phase, mesoscopic clusters, or a pre-ordered state. In this review, we focus on the studies of nonclassical pathways in protein crystallization and discuss the applications of the various scenarios of two-step nucleation theory. In particular, we focus on protein solutions in the presence of multivalent salts, which serve as a model protein system to study the nucleation pathways. We wish to point out the unique features of proteins as model systems for further studies.

  20. Nonclassical nucleation pathways in protein crystallization

    Science.gov (United States)

    Zhang, Fajun

    2017-11-01

    Classical nucleation theory (CNT), which was established about 90 years ago, has been very successful in many research fields, and continues to be the most commonly used theory in describing the nucleation process. For a fluid-to-solid phase transition, CNT states that the solute molecules in a supersaturated solution reversibly form small clusters. Once the cluster size reaches a critical value, it becomes thermodynamically stable and favored for further growth. One of the most important assumptions of CNT is that the nucleation process is described by one reaction coordinate and all order parameters proceed simultaneously. Recent studies in experiments, computer simulations and theory have revealed nonclassical features in the early stage of nucleation. In particular, the decoupling of order parameters involved during a fluid-to-solid transition leads to the so-called two-step nucleation mechanism, in which a metastable intermediate phase (MIP) exists between the initial supersaturated solution and the final crystals. Depending on the exact free energy landscapes, the MIPs can be a high density liquid phase, mesoscopic clusters, or a pre-ordered state. In this review, we focus on the studies of nonclassical pathways in protein crystallization and discuss the applications of the various scenarios of two-step nucleation theory. In particular, we focus on protein solutions in the presence of multivalent salts, which serve as a model protein system to study the nucleation pathways. We wish to point out the unique features of proteins as model systems for further studies.

  1. Molecular-dynamics simulations of urea nucleation from aqueous solution

    Science.gov (United States)

    Salvalaglio, Matteo; Perego, Claudio; Giberti, Federico; Mazzotti, Marco; Parrinello, Michele

    2015-01-01

    Despite its ubiquitous character and relevance in many branches of science and engineering, nucleation from solution remains elusive. In this framework, molecular simulations represent a powerful tool to provide insight into nucleation at the molecular scale. In this work, we combine theory and molecular simulations to describe urea nucleation from aqueous solution. Taking advantage of well-tempered metadynamics, we compute the free-energy change associated to the phase transition. We find that such a free-energy profile is characterized by significant finite-size effects that can, however, be accounted for. The description of the nucleation process emerging from our analysis differs from classical nucleation theory. Nucleation of crystal-like clusters is in fact preceded by large concentration fluctuations, indicating a predominant two-step process, whereby embryonic crystal nuclei emerge from dense, disordered urea clusters. Furthermore, in the early stages of nucleation, two different polymorphs are seen to compete. PMID:25492932

  2. Molecular-dynamics simulations of urea nucleation from aqueous solution.

    Science.gov (United States)

    Salvalaglio, Matteo; Perego, Claudio; Giberti, Federico; Mazzotti, Marco; Parrinello, Michele

    2015-01-06

    Despite its ubiquitous character and relevance in many branches of science and engineering, nucleation from solution remains elusive. In this framework, molecular simulations represent a powerful tool to provide insight into nucleation at the molecular scale. In this work, we combine theory and molecular simulations to describe urea nucleation from aqueous solution. Taking advantage of well-tempered metadynamics, we compute the free-energy change associated to the phase transition. We find that such a free-energy profile is characterized by significant finite-size effects that can, however, be accounted for. The description of the nucleation process emerging from our analysis differs from classical nucleation theory. Nucleation of crystal-like clusters is in fact preceded by large concentration fluctuations, indicating a predominant two-step process, whereby embryonic crystal nuclei emerge from dense, disordered urea clusters. Furthermore, in the early stages of nucleation, two different polymorphs are seen to compete.

  3. Systematic coarse-graining in nucleation theory

    Science.gov (United States)

    Schweizer, M.; Sagis, L. M. C.

    2015-08-01

    In this work, we show that the standard method to obtain nucleation rate-predictions with the aid of atomistic Monte Carlo simulations leads to nucleation rate predictions that deviate 3 - 5 orders of magnitude from the recent brute-force molecular dynamics simulations [Diemand et al., J. Chem. Phys. 139, 074309 (2013)] conducted in the experimental accessible supersaturation regime for Lennard-Jones argon. We argue that this is due to the truncated state space the literature mostly relies on, where the number of atoms in a nucleus is considered the only relevant order parameter. We here formulate the nonequilibrium statistical mechanics of nucleation in an extended state space, where the internal energy and momentum of the nuclei are additionally incorporated. We show that the extended model explains the lack in agreement between the molecular dynamics simulations by Diemand et al. and the truncated state space. We demonstrate additional benefits of using the extended state space; in particular, the definition of a nucleus temperature arises very naturally and can be shown without further approximation to obey the fluctuation law of McGraw and LaViolette. In addition, we illustrate that our theory conveniently allows to extend existing theories to richer sets of order parameters.

  4. Ice nucleation rates near ˜225 K

    Science.gov (United States)

    Amaya, Andrew J.; Wyslouzil, Barbara E.

    2018-02-01

    We have measured the ice nucleation rates, Jice, in supercooled nano-droplets with radii ranging from 6.6 nm to 10 nm and droplet temperatures, Td, ranging from 225 K to 204 K. The initial temperature of the 10 nm water droplets is ˜250 K, i.e., well above the homogeneous nucleation temperature for micron sized water droplets, TH ˜235 K. The nucleation rates increase systematically from ˜1021 cm-3 s-1 to ˜1022 cm-3 s-1 in this temperature range, overlap with the nucleation rates of Manka et al. [Phys. Chem. Chem. Phys. 14, 4505 (2012)], and suggest that experiments with larger droplets would extrapolate smoothly the rates of Hagen et al. [J. Atmos. Sci. 38, 1236 (1981)]. The sharp corner in the rate data as temperature drops is, however, difficult to match with available theory even if we correct classical nucleation theory and the physical properties of water for the high internal pressure of the nanodroplets.

  5. Classical field theory

    CERN Document Server

    Franklin, Joel

    2017-01-01

    Classical field theory, which concerns the generation and interaction of fields, is a logical precursor to quantum field theory, and can be used to describe phenomena such as gravity and electromagnetism. Written for advanced undergraduates, and appropriate for graduate level classes, this book provides a comprehensive introduction to field theories, with a focus on their relativistic structural elements. Such structural notions enable a deeper understanding of Maxwell's equations, which lie at the heart of electromagnetism, and can also be applied to modern variants such as Chern–Simons and Born–Infeld. The structure of field theories and their physical predictions are illustrated with compelling examples, making this book perfect as a text in a dedicated field theory course, for self-study, or as a reference for those interested in classical field theory, advanced electromagnetism, or general relativity. Demonstrating a modern approach to model building, this text is also ideal for students of theoretic...

  6. Viscosity of interfacial water regulates ice nucleation

    International Nuclear Information System (INIS)

    Li, Kaiyong; Chen, Jing; Zhang, Qiaolan; Zhang, Yifan; Xu, Shun; Zhou, Xin; Cui, Dapeng; Wang, Jianjun; Song, Yanlin

    2014-01-01

    Ice formation on solid surfaces is an important phenomenon in many fields, such as cloud formation and atmospheric icing, and a key factor for applications in preventing freezing. Here, we report temperature-dependent nucleation rates of ice for hydrophilic and hydrophobic surfaces. The results show that hydrophilic surface presents a lower ice nucleation rate. We develop a strategy to extract the thermodynamic parameters, J 0 and Γ, in the context of classical nucleation theory. From the extracted J 0 and Γ, we reveal the dominant role played by interfacial water. The results provide an insight into freezing mechanism on solid surfaces

  7. High performance computations using dynamical nucleation theory

    International Nuclear Information System (INIS)

    Windus, T L; Crosby, L D; Kathmann, S M

    2008-01-01

    Chemists continue to explore the use of very large computations to perform simulations that describe the molecular level physics of critical challenges in science. In this paper, we describe the Dynamical Nucleation Theory Monte Carlo (DNTMC) model - a model for determining molecular scale nucleation rate constants - and its parallel capabilities. The potential for bottlenecks and the challenges to running on future petascale or larger resources are delineated. A 'master-slave' solution is proposed to scale to the petascale and will be developed in the NWChem software. In addition, mathematical and data analysis challenges are described

  8. Random electrodynamics: the theory of classical electrodynamics with classical electromagnetic zero-point radiation

    International Nuclear Information System (INIS)

    Boyer, T.H.

    1975-01-01

    The theory of classical electrodynamics with classical electromagnetic zero-point radiation is outlined here under the title random electrodynamics. The work represents a reanalysis of the bounds of validity of classical electron theory which should sharpen the understanding of the connections and distinctions between classical and quantum theories. The new theory of random electrodynamics is a classical electron theory involving Newton's equations for particle motion due to the Lorentz force, and Maxwell's equations for the electromagnetic fields with point particles as sources. However, the theory departs from the classical electron theory of Lorentz in that it adopts a new boundary condition on Maxwell's equations. It is assumed that the homogeneous boundary condition involves random classical electromagnetic radiation with a Lorentz-invariant spectrum, classical electromagnetic zero-point radiation. The implications of random electrodynamics for atomic structure, atomic spectra, and particle-interference effects are discussed on an order-of-magnitude or heuristic level. Some detailed mathematical connections and some merely heuristic connections are noted between random electrodynamics and quantum theory. (U.S.)

  9. Crystal Nucleation in Liquids: Open Questions and Future Challenges in Molecular Dynamics Simulations.

    Science.gov (United States)

    Sosso, Gabriele C; Chen, Ji; Cox, Stephen J; Fitzner, Martin; Pedevilla, Philipp; Zen, Andrea; Michaelides, Angelos

    2016-06-22

    The nucleation of crystals in liquids is one of nature's most ubiquitous phenomena, playing an important role in areas such as climate change and the production of drugs. As the early stages of nucleation involve exceedingly small time and length scales, atomistic computer simulations can provide unique insights into the microscopic aspects of crystallization. In this review, we take stock of the numerous molecular dynamics simulations that, in the past few decades, have unraveled crucial aspects of crystal nucleation in liquids. We put into context the theoretical framework of classical nucleation theory and the state-of-the-art computational methods by reviewing simulations of such processes as ice nucleation and the crystallization of molecules in solutions. We shall see that molecular dynamics simulations have provided key insights into diverse nucleation scenarios, ranging from colloidal particles to natural gas hydrates, and that, as a result, the general applicability of classical nucleation theory has been repeatedly called into question. We have attempted to identify the most pressing open questions in the field. We believe that, by improving (i) existing interatomic potentials and (ii) currently available enhanced sampling methods, the community can move toward accurate investigations of realistic systems of practical interest, thus bringing simulations a step closer to experiments.

  10. Overview: Nucleation of clathrate hydrates.

    Science.gov (United States)

    Warrier, Pramod; Khan, M Naveed; Srivastava, Vishal; Maupin, C Mark; Koh, Carolyn A

    2016-12-07

    Molecular level knowledge of nucleation and growth of clathrate hydrates is of importance for advancing fundamental understanding on the nature of water and hydrophobic hydrate formers, and their interactions that result in the formation of ice-like solids at temperatures higher than the ice-point. The stochastic nature and the inability to probe the small length and time scales associated with the nucleation process make it very difficult to experimentally determine the molecular level changes that lead to the nucleation event. Conversely, for this reason, there have been increasing efforts to obtain this information using molecular simulations. Accurate knowledge of how and when hydrate structures nucleate will be tremendously beneficial for the development of sustainable hydrate management strategies in oil and gas flowlines, as well as for their application in energy storage and recovery, gas separation, carbon sequestration, seawater desalination, and refrigeration. This article reviews various aspects of hydrate nucleation. First, properties of supercooled water and ice nucleation are reviewed briefly due to their apparent similarity to hydrates. Hydrate nucleation is then reviewed starting from macroscopic observations as obtained from experiments in laboratories and operations in industries, followed by various hydrate nucleation hypotheses and hydrate nucleation driving force calculations based on the classical nucleation theory. Finally, molecular simulations on hydrate nucleation are discussed in detail followed by potential future research directions.

  11. Overview: Nucleation of clathrate hydrates

    Science.gov (United States)

    Warrier, Pramod; Khan, M. Naveed; Srivastava, Vishal; Maupin, C. Mark; Koh, Carolyn A.

    2016-12-01

    Molecular level knowledge of nucleation and growth of clathrate hydrates is of importance for advancing fundamental understanding on the nature of water and hydrophobic hydrate formers, and their interactions that result in the formation of ice-like solids at temperatures higher than the ice-point. The stochastic nature and the inability to probe the small length and time scales associated with the nucleation process make it very difficult to experimentally determine the molecular level changes that lead to the nucleation event. Conversely, for this reason, there have been increasing efforts to obtain this information using molecular simulations. Accurate knowledge of how and when hydrate structures nucleate will be tremendously beneficial for the development of sustainable hydrate management strategies in oil and gas flowlines, as well as for their application in energy storage and recovery, gas separation, carbon sequestration, seawater desalination, and refrigeration. This article reviews various aspects of hydrate nucleation. First, properties of supercooled water and ice nucleation are reviewed briefly due to their apparent similarity to hydrates. Hydrate nucleation is then reviewed starting from macroscopic observations as obtained from experiments in laboratories and operations in industries, followed by various hydrate nucleation hypotheses and hydrate nucleation driving force calculations based on the classical nucleation theory. Finally, molecular simulations on hydrate nucleation are discussed in detail followed by potential future research directions.

  12. A variational approach to nucleation simulation.

    Science.gov (United States)

    Piaggi, Pablo M; Valsson, Omar; Parrinello, Michele

    2016-12-22

    We study by computer simulation the nucleation of a supersaturated Lennard-Jones vapor into the liquid phase. The large free energy barriers to transition make the time scale of this process impossible to study by ordinary molecular dynamics simulations. Therefore we use a recently developed enhanced sampling method [Valsson and Parrinello, Phys. Rev. Lett.113, 090601 (2014)] based on the variational determination of a bias potential. We differ from previous applications of this method in that the bias is constructed on the basis of the physical model provided by the classical theory of nucleation. We examine the technical problems associated with this approach. Our results are very satisfactory and will pave the way for calculating the nucleation rates in many systems.

  13. Droplet and bubble nucleation modeled by density gradient theory – cubic equation of state versus saft model

    Directory of Open Access Journals (Sweden)

    Hrubý Jan

    2012-04-01

    Full Text Available The study presents some preliminary results of the density gradient theory (GT combined with two different equations of state (EoS: the classical cubic equation by van der Waals and a recent approach based on the statistical associating fluid theory (SAFT, namely its perturbed-chain (PC modification. The results showed that the cubic EoS predicted for a given surface tension the density profile with a noticeable defect. Bulk densities predicted by the cubic EoS differed as much as by 100 % from the reference data. On the other hand, the PC-SAFT EoS provided accurate results for density profile and both bulk densities in the large range of temperatures. It has been shown that PC-SAFT is a promising tool for accurate modeling of nucleation using the GT. Besides the basic case of a planar phase interface, the spherical interface was analyzed to model a critical cluster occurring either for nucleation of droplets (condensation or bubbles (boiling, cavitation. However, the general solution for the spherical interface will require some more attention due to its numerical difficulty.

  14. Predictions of homogeneous nucleation rates for n-alkanes accounting for the diffuse phase interface and capillary waves

    Czech Academy of Sciences Publication Activity Database

    Planková, Barbora; Vinš, Václav; Hrubý, Jan

    2017-01-01

    Roč. 147, č. 16 (2017), č. článku 164702. ISSN 0021-9606 R&D Projects: GA MŠk(CZ) 7F14466; GA ČR(CZ) GJ15-07129Y Institutional support: RVO:61388998 Keywords : nucleation * classical nucleation theory * density gradient theory Subject RIV: BJ - Thermodynamics OBOR OECD: Thermodynamics Impact factor: 2.965, year: 2016

  15. A computational fluid dynamics approach to nucleation in the water-sulfuric acid system.

    Science.gov (United States)

    Herrmann, E; Brus, D; Hyvärinen, A-P; Stratmann, F; Wilck, M; Lihavainen, H; Kulmala, M

    2010-08-12

    This study presents a computational fluid dynamics modeling approach to investigate the nucleation in the water-sulfuric acid system in a flow tube. On the basis of an existing experimental setup (Brus, D.; Hyvärinen, A.-P.; Viisanen, Y.; Kulmala, M.; Lihavainen, H. Atmos. Chem. Phys. 2010, 10, 2631-2641), we first establish the effect of convection on the flow profile. We then proceed to simulate nucleation for relative humidities of 10, 30, and 50% and for sulfuric acid concentration between 10(9) to 3 x 10(10) cm(-3). We describe the nucleation zone in detail and determine how flow rate and relative humidity affect its characteristics. Experimental nucleation rates are compared to rates gained from classical binary and kinetic nucleation theory as well as cluster activation theory. For low RH values, kinetic theory yields the best agreement with experimental results while binary nucleation best reproduces the experimental nucleation behavior at 50% relative humidity. Particle growth is modeled for an example case at 50% relative humidity. The final simulated diameter is very close to the experimental result.

  16. Nucleation behavior of glutathione polymorphs in water

    International Nuclear Information System (INIS)

    Chen, Zhi; Dang, Leping; Li, Shuai; Wei, Hongyuan

    2013-01-01

    Nucleation behavior of glutathione (GSH) polymorphs in water was investigated by experimental method combined with classical nucleation theory. The solubility of α and β forms GSH in water at different temperatures, and the nucleation induction period at various supersaturations and temperatures were determined experimentally. The results show that, in a certain range of supersaturation, the nucleation of β form predominates at relatively higher temperature, while α form will be obtained at lower temperature. The nucleation kinetics parameters of α and β form were then calculated. To understand the crucial role of temperature on crystal forms, “hypothetic” nucleation parameters of β form at 283.15 K were deduced based on extrapolation method. The results show that the interfacial tension, critical free energy, critical nucleus radius and nucleus number of α form are smaller than that of β form in the same condition at 283.15 K, which implies that α form nucleates easier than β form at low temperature. This work may be useful for the control and optimization of GSH crystallization process in industry

  17. The emergence of modern nucleation theory

    International Nuclear Information System (INIS)

    Cahn, J.W.

    1987-01-01

    A series of important papers by David Turnbull and his collaborators in the late 1940's and early 1950's laid the experimental and theoretical foundation of modern nucleation theory. The elegance, versatility, and generality of the phenomenological approach, coupled with brilliant and insightful experimental confirmation, sparked widespread application which continues today. Much of David Turnbull's subsequent work in other subjects grew directly or indirectly from this work

  18. Classical and semi-classical solutions of the Yang--Mills theory

    International Nuclear Information System (INIS)

    Jackiw, R.; Nohl, C.; Rebbi, C.

    1977-12-01

    This review summarizes what is known at present about classical solutions to Yang-Mills theory both in Euclidean and Minkowski space. The quantal meaning of these solutions is also discussed. Solutions in Euclidean space expose multiple vacua and tunnelling of the quantum theory. Those in Minkowski space-time provide a semi-classical spectrum for a conformal generator

  19. Parametrization of the homogeneous ice nucleation rate for the numerical simulation of multiphase flow

    Czech Academy of Sciences Publication Activity Database

    Němec, Tomáš; Eisenschmidt, K.; Rauschenberger, P.; Weigand, B.

    2012-01-01

    Roč. 12, č. 1 (2012), s. 533-534 ISSN 1617-7061 R&D Projects: GA ČR GAP101/10/1819 Institutional research plan: CEZ:AV0Z20760514 Keywords : ice nucleation * ice-water surface energy * classical nucleation theory Subject RIV: BJ - Thermodynamics http://onlinelibrary.wiley.com/doi/10.1002/pamm.201210255/abstract

  20. Analysis of the Effect of Water Activity on Ice Formation Using a New Theory of Nucleation

    Science.gov (United States)

    Barahona, Donifan

    2013-01-01

    In this work a new theory of nucleation is developed and used to investigate the effect of water activity on the formation of ice within super-cooled droplets. The new theory is based on a novel concept where the interface is assumed to be made of liquid molecules trapped by the solid matrix. Using this concept new expressions are developed for the critical ice germ size and the nucleation work, with explicit dependencies on temperature and water activity. However unlike previous approaches, the new theory does not depend on the interfacial tension between liquid and ice. Comparison against experimental results shows that the new theory is able to reproduce the observed effect of water activity on nucleation rate and freezing temperature. It allows for the first time a theoretical derivation of the constant shift in water activity between melting and nucleation. The new theory offers a consistent thermodynamic view of ice nucleation, simple enough to be applied in atmospheric models of cloud formation.

  1. Protein Polymerization into Fibrils from the Viewpoint of Nucleation Theory.

    Science.gov (United States)

    Kashchiev, Dimo

    2015-11-17

    The assembly of various proteins into fibrillar aggregates is an important phenomenon with wide implications ranging from human disease to nanoscience. Using general kinetic results of nucleation theory, we analyze the polymerization of protein into linear or helical fibrils in the framework of the Oosawa-Kasai (OK) model. We show that while within the original OK model of linear polymerization the process does not involve nucleation, within a modified OK model it is nucleation-mediated. Expressions are derived for the size of the fibril nucleus, the work for fibril formation, the nucleation barrier, the equilibrium and stationary fibril size distributions, and the stationary fibril nucleation rate. Under otherwise equal conditions, this rate decreases considerably when the short (subnucleus) fibrils lose monomers much more frequently than the long (supernucleus) fibrils, a feature that should be born in mind when designing a strategy for stymying or stimulating fibril nucleation. The obtained dependence of the nucleation rate on the concentration of monomeric protein is convenient for experimental verification and for use in rate equations accounting for nucleation-mediated fibril formation. The analysis and the results obtained for linear fibrils are fully applicable to helical fibrils whose formation is describable by a simplified OK model. Copyright © 2015 Biophysical Society. Published by Elsevier Inc. All rights reserved.

  2. Principles of nucleation theory

    International Nuclear Information System (INIS)

    Clement, C.F.; Wood, M.H.

    1980-01-01

    The nucleation of small stable species is described in the problem of void growth by discrete rate equations. When gas is being produced the problem reduces to one of calculating the incubation dose for the gas bubble to void transition. A general expression for the steady state nucleation rate is derived for the case when voids are formed by vacancy fluctuations which enable an effective nucleation barrier to be crossed. (author)

  3. The classical theory of fields electromagnetism

    CERN Document Server

    Helrich, Carl S

    2012-01-01

    The study of classical electromagnetic fields is an adventure. The theory is complete mathematically and we are able to present it as an example of classical Newtonian experimental and mathematical philosophy. There is a set of foundational experiments, on which most of the theory is constructed. And then there is the bold theoretical proposal of a field-field interaction from James Clerk Maxwell. This textbook presents the theory of classical fields as a mathematical structure based solidly on laboratory experiments. Here the student is introduced to the beauty of classical field theory as a gem of theoretical physics. To keep the discussion fluid, the history is placed in a beginning chapter and some of the mathematical proofs in the appendices. Chapters on Green’s Functions and Laplace’s Equation and a discussion of Faraday’s Experiment further deepen the understanding. The chapter on Einstein’s relativity is an integral necessity to the text. Finally, chapters on particle motion and waves in a dis...

  4. Experimental investigation of the role of ions in aerosol nucleation

    DEFF Research Database (Denmark)

    Enghoff, Martin Andreas Bødker

    The role of ions in producing aerosols in Earth’s atmosphere is an area of very active research. Atmospheric and experimental observations have shown that the nucleation of aerosol particles can occur under conditions that cannot be explained by classical nucleation theory. Several ideas have been...... put forward to solve this nucleation problem, e.g. Ion-Induced Nucleation and Ternary Nucleation. Experimental investigations exploring the role of ions in particle production are scarce, and often at conditions far removed from those relevant for the lower part of the atmosphere. Recent experimental...... were grown using photochemically produced sulphuric acid and ionization levels were controlled with a Cs-137 gamma-source. An increase in nucleation was observed when the chamber was exposed to the radioactive source. The results were analyzed using a model based on the General Dynamic Equation...

  5. Nucleation barrier reconstruction via the seeding method in a lattice model with competing nucleation pathways.

    Science.gov (United States)

    Lifanov, Yuri; Vorselaars, Bart; Quigley, David

    2016-12-07

    We study a three-species analogue of the Potts lattice gas model of nucleation from solution in a regime where partially disordered solute is a viable thermodynamic phase. Using a multicanonical sampling protocol, we compute phase diagrams for the system, from which we determine a parameter regime where the partially disordered phase is metastable almost everywhere in the temperature-fugacity plane. The resulting model shows non-trivial nucleation and growth behaviour, which we examine via multidimensional free energy calculations. We consider the applicability of the model in capturing the multi-stage nucleation mechanisms of polymorphic biominerals (e.g., CaCO 3 ). We then quantitatively explore the kinetics of nucleation in our model using the increasingly popular "seeding" method. We compare the resulting free energy barrier heights to those obtained via explicit free energy calculations over a wide range of temperatures and fugacities, carefully considering the propagation of statistical error. We find that the ability of the "seeding" method to reproduce accurate free energy barriers is dependent on the degree of supersaturation, and severely limited by the use of a nucleation driving force Δμ computed for bulk phases. We discuss possible reasons for this in terms of underlying kinetic assumptions, and those of classical nucleation theory.

  6. Charged and Neutral Binary Nucleation of Sulfuric Acid in Free Troposphere Conditions

    OpenAIRE

    Duplissy, Jonathan; Merikanto, Joonas; Sellegri, Karine; Rose, Clemence; Asmi, Eija; Freney, Evelyn; Juninen, Heikki; Sipilä, Mikko; Vehkamaki, Hanna; Kulmala, Markku

    2013-01-01

    We present a data set of binary nucleation of sulfuric acid and water, measured in the CLOUD chamber at CERN during the CLOUD3 and CLOUD5 campaigns. Four parameters have been varied to cover neutral and ion-induced binary nucleation processes: Sulfuric acid concentration (1e5 to 1e8 molecules per cm^(−3)), relative humidity (10% to 80%), temperature (208-293K) and ion concentration (0-4000 ions per cm^(−3)). In addition, classical nucleation theory implemented with hydrates and ion induced nu...

  7. Pseudo-classical theory of Majorana-Weyl particle

    International Nuclear Information System (INIS)

    Grigoryan, G.V.; Grigoryan, R.P.; Tyutin, I.V.

    1996-01-01

    A pseudo-classical theory of Weyl particle in the space-time dimensions D = 2 n is constructed. The canonical quantization of that pseudo-classical theory is carried out and it results in the theory of the D = 2 n dimensional Weyl particle in the Foldy-Wouthuysen representation. 28 refs

  8. Modelling the role of compositional fluctuations in nucleation kinetics

    International Nuclear Information System (INIS)

    Ženíšek, J.; Kozeschnik, E.; Svoboda, J.; Fischer, F.D.

    2015-01-01

    The classical nucleation theory of precipitate nucleation in interstitial/substitutional alloys is applied to account for the influence of spatial A–B composition fluctuations in an A–B–C matrix on the kinetics of nucleation of (A,B) 3 C precipitates. A and B are substitutional elements in the matrix and C is an interstitial component, assumed to preferentially bind to B atoms. All lattice sites are considered as potential nucleation sites. The fluctuations of chemical composition result in a local variation of the nucleation probability. The nucleation sites are eliminated from the system if they are located in a C-depleted diffusion zone belonging to an already nucleated and growing precipitate. The chemistry is that of an Fe–Cr–C system, and the specific interface energy is treated as a free parameter. Random, regular and homogeneous A–B distributions in the matrix are simulated and compared for various values of the interface energy. An increasing enhancement of the role of compositional fluctuations on nucleation kinetics with increasing interface energy and decreasing chemical driving force is observed

  9. Nonrelativistic Schroedinger equation in quasi-classical theory

    International Nuclear Information System (INIS)

    Wignall, J.W.G.

    1987-01-01

    The author has recently proposed a quasi-classical theory of particles and interactions in which particles are pictured as extended periodic disturbances in a universal field chi(x,t), interacting with each other via nonlinearity in the equation of motion for chi. The present paper explores the relationship of this theory to nonrelativistic quantum mechanics; as a first step, it is shown how it is possible to construct from chi a configuration-space wave function Psi(x 1 , X 2 , t), and that the theory requires that Psi satisfy the two-particle Schroedinger equation in the case where the two particles are well separated from each other. This suggests that the multiparticle Schroedinger equation can be obtained as a direct consequence of the quasi-classical theory without any use of the usual formalism (Hilbert space, quantization rules, etc.) of conventional quantum theory and in particular without using the classical canonical treatment of a system as a crutch theory which has subsequently to be quantized. The quasi-classical theory also suggests the existence of a preferred absolute gauge for the electromagnetic potentials

  10. Wetting of heterogeneous substrates. A classical density-functional-theory approach

    Science.gov (United States)

    Yatsyshin, Peter; Parry, Andrew O.; Rascón, Carlos; Duran-Olivencia, Miguel A.; Kalliadasis, Serafim

    2017-11-01

    Wetting is a nucleation of a third phase (liquid) on the interface between two different phases (solid and gas). In many experimentally accessible cases of wetting, the interplay between the substrate structure, and the fluid-fluid and fluid-substrate intermolecular interactions leads to the appearance of a whole ``zoo'' of exciting interface phase transitions, associated with the formation of nano-droplets/bubbles, and thin films. Practical applications of wetting at small scales are numerous and include the design of lab-on-a-chip devices and superhydrophobic surfaces. In this talk, we will use a fully microscopic approach to explore the phase space of a planar wall, decorated with patches of different hydrophobicity, and demonstrate the highly non-trivial behaviour of the liquid-gas interface near the substrate. We will present fluid density profiles, adsorption isotherms and wetting phase diagrams. Our analysis is based on a formulation of statistical mechanics, commonly known as classical density-functional theory. It provides a computationally-friendly and rigorous framework, suitable for probing small-scale physics of classical fluids and other soft-matter systems. EPSRC Grants No. EP/L027186,EP/K503733;ERC Advanced Grant No. 247031.

  11. Steady-state molecular dynamics simulation of vapor to liquid nucleation with Mc Donald's demon

    International Nuclear Information System (INIS)

    Horsch, M.; Miroshnichenko, S.; Vrabec, J.

    2009-01-01

    Grand canonical MD with McDonald's demon is discussed in the present contribution and applied for sampling both nucleation kinetics and steady-state properties of a supersaturated vapor. The idea behind the new approach is to simulate the production of clusters up to a given size for a specified supersaturation. The classical nucleation theory is found to overestimate the free energy of cluster formation and deviate by two orders of magnitude from the nucleation rate below the triple point at high supersaturations.

  12. Classical theory of algebraic numbers

    CERN Document Server

    Ribenboim, Paulo

    2001-01-01

    Gauss created the theory of binary quadratic forms in "Disquisitiones Arithmeticae" and Kummer invented ideals and the theory of cyclotomic fields in his attempt to prove Fermat's Last Theorem These were the starting points for the theory of algebraic numbers, developed in the classical papers of Dedekind, Dirichlet, Eisenstein, Hermite and many others This theory, enriched with more recent contributions, is of basic importance in the study of diophantine equations and arithmetic algebraic geometry, including methods in cryptography This book has a clear and thorough exposition of the classical theory of algebraic numbers, and contains a large number of exercises as well as worked out numerical examples The Introduction is a recapitulation of results about principal ideal domains, unique factorization domains and commutative fields Part One is devoted to residue classes and quadratic residues In Part Two one finds the study of algebraic integers, ideals, units, class numbers, the theory of decomposition, iner...

  13. Predictions of homogeneous nucleation rates for n-alkanes accounting for the diffuse phase interface and capillary waves.

    Science.gov (United States)

    Planková, Barbora; Vinš, Václav; Hrubý, Jan

    2017-10-28

    Homogeneous droplet nucleation has been studied for almost a century but has not yet been fully understood. In this work, we used the density gradient theory (DGT) and considered the influence of capillary waves (CWs) on the predicted size-dependent surface tensions and nucleation rates for selected n-alkanes. The DGT model was completed by an equation of state (EoS) based on the perturbed-chain statistical associating fluid theory and compared to the classical nucleation theory and the Peng-Robinson EoS. It was found that the critical clusters are practically free of CWs because they are so small that even the smallest wavelengths of CWs do not fit into their finite dimensions. The CWs contribute to the entropy of the system and thus decrease the surface tension. A correction for the effect of CWs on the surface tension is presented. The effect of the different EoSs is relatively small because by a fortuitous coincidence their predictions are similar in the relevant range of critical cluster sizes. The difference of the DGT predictions to the classical nucleation theory computations is important but not decisive. Of the effects investigated, the most pronounced is the suppression of CWs which causes a sizable decrease of the predicted nucleation rates. The major difference between experimental nucleation rate data and theoretical predictions remains in the temperature dependence. For normal alkanes, this discrepancy is much stronger than observed, e.g., for water. Theoretical corrections developed here have a minor influence on the temperature dependency. We provide empirical equations correcting the predicted nucleation rates to values comparable with experiments.

  14. Predictions of homogeneous nucleation rates for n-alkanes accounting for the diffuse phase interface and capillary waves

    Science.gov (United States)

    Planková, Barbora; Vinš, Václav; Hrubý, Jan

    2017-10-01

    Homogeneous droplet nucleation has been studied for almost a century but has not yet been fully understood. In this work, we used the density gradient theory (DGT) and considered the influence of capillary waves (CWs) on the predicted size-dependent surface tensions and nucleation rates for selected n-alkanes. The DGT model was completed by an equation of state (EoS) based on the perturbed-chain statistical associating fluid theory and compared to the classical nucleation theory and the Peng-Robinson EoS. It was found that the critical clusters are practically free of CWs because they are so small that even the smallest wavelengths of CWs do not fit into their finite dimensions. The CWs contribute to the entropy of the system and thus decrease the surface tension. A correction for the effect of CWs on the surface tension is presented. The effect of the different EoSs is relatively small because by a fortuitous coincidence their predictions are similar in the relevant range of critical cluster sizes. The difference of the DGT predictions to the classical nucleation theory computations is important but not decisive. Of the effects investigated, the most pronounced is the suppression of CWs which causes a sizable decrease of the predicted nucleation rates. The major difference between experimental nucleation rate data and theoretical predictions remains in the temperature dependence. For normal alkanes, this discrepancy is much stronger than observed, e.g., for water. Theoretical corrections developed here have a minor influence on the temperature dependency. We provide empirical equations correcting the predicted nucleation rates to values comparable with experiments.

  15. Quantum scattering from classical field theory

    International Nuclear Information System (INIS)

    Gould, T.M.; Poppitz, E.R.

    1995-01-01

    We show that scattering amplitudes between initial wave packet states and certain coherent final states can be computed in a systematic weak coupling expansion about classical solutions satisfying initial-value conditions. The initial-value conditions are such as to make the solution of the classical field equations amenable to numerical methods. We propose a practical procedure for computing classical solutions which contribute to high energy two-particle scattering amplitudes. We consider in this regard the implications of a recent numerical simulation in classical SU(2) Yang-Mills theory for multiparticle scattering in quantum gauge theories and speculate on its generalization to electroweak theory. We also generalize our results to the case of complex trajectories and discuss the prospects for finding a solution to the resulting complex boundary value problem, which would allow the application of our method to any wave packet to coherent state transition. Finally, we discuss the relevance of these results to the issues of baryon number violation and multiparticle scattering at high energies. ((orig.))

  16. Texture control and seeded nucleation of nanosize structures of ferroelectric thin films

    Science.gov (United States)

    Muralt, Paul

    2006-09-01

    An overview is given on nucleation phenomena of Pb(Zr ,Ti)O3 (PZT) thin films on Pt(111)-based substrates. Emphasis is given on in situ growth methods, particularly in situ reactive sputtering from three metallic targets. Growth of PZT thin films is discussed from the point of view of the PbOx-TiO2 phase diagram, PbO vapor pressure, and classical nucleation theory. The role of thin TiO2 affinity layers and spots is explained in the frame of this theory. Activation energies for desorption and chemisorption are adapted to comply with the fact that nucleation rates on TiO2 are much larger than the ones on bare Pt(111). The model reproduces well the PbO surface flux from bare Pt(111) to the affinity spots in the case of PbTiO3 nucleation and the reversed tendency in the case of PZT 40/60 nucleation, explaining experimental observations. The critical size of nuclei was calculated to contain 8-10unit cells for PbTiO3/Pt nucleation and 14-17 for PZT/Pt nucleation.

  17. A Classical Introduction to Galois Theory

    CERN Document Server

    Newman, Stephen C

    2012-01-01

    This book provides an introduction to Galois theory and focuses on one central theme - the solvability of polynomials by radicals. Both classical and modern approaches to the subject are described in turn in order to have the former (which is relatively concrete and computational) provide motivation for the latter (which can be quite abstract). The theme of the book is historically the reason that Galois theory was created, and it continues to provide a platform for exploring both classical and modern concepts. This book examines a number of problems arising in the area of classical mathematic

  18. A theory-based parameterization for heterogeneous ice nucleation and implications for the simulation of ice processes in atmospheric models

    Science.gov (United States)

    Savre, J.; Ekman, A. M. L.

    2015-05-01

    A new parameterization for heterogeneous ice nucleation constrained by laboratory data and based on classical nucleation theory is introduced. Key features of the parameterization include the following: a consistent and modular modeling framework for treating condensation/immersion and deposition freezing, the possibility to consider various potential ice nucleating particle types (e.g., dust, black carbon, and bacteria), and the possibility to account for an aerosol size distribution. The ice nucleating ability of each aerosol type is described using a contact angle (θ) probability density function (PDF). A new modeling strategy is described to allow the θ PDF to evolve in time so that the most efficient ice nuclei (associated with the lowest θ values) are progressively removed as they nucleate ice. A computationally efficient quasi Monte Carlo method is used to integrate the computed ice nucleation rates over both size and contact angle distributions. The parameterization is employed in a parcel model, forced by an ensemble of Lagrangian trajectories extracted from a three-dimensional simulation of a springtime low-level Arctic mixed-phase cloud, in order to evaluate the accuracy and convergence of the method using different settings. The same model setup is then employed to examine the importance of various parameters for the simulated ice production. Modeling the time evolution of the θ PDF is found to be particularly crucial; assuming a time-independent θ PDF significantly overestimates the ice nucleation rates. It is stressed that the capacity of black carbon (BC) to form ice in the condensation/immersion freezing mode is highly uncertain, in particular at temperatures warmer than -20°C. In its current version, the parameterization most likely overestimates ice initiation by BC.

  19. Beam structures classical and advanced theories

    CERN Document Server

    Carrera, Erasmo; Petrolo, Marco

    2011-01-01

    Beam theories are exploited worldwide to analyze civil, mechanical, automotive, and aerospace structures. Many beam approaches have been proposed during the last centuries by eminent scientists such as Euler, Bernoulli, Navier, Timoshenko, Vlasov, etc.  Most of these models are problem dependent: they provide reliable results for a given problem, for instance a given section and cannot be applied to a different one. Beam Structures: Classical and Advanced Theories proposes a new original unified approach to beam theory that includes practically all classical and advanced models for be

  20. Classical field theory on electrodynamics, non-Abelian gauge theories and gravitation

    CERN Document Server

    Scheck, Florian

    2012-01-01

    The book describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams. Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary of semi-Riemannian geometry as the framework for the classical field theory of gravitation. The chapter concludes wit...

  1. Atomic Scale Imaging of Nucleation and Growth Trajectories of an Interfacial Bismuth Nanodroplet.

    Science.gov (United States)

    Li, Yingxuan; Bunes, Benjamin R; Zang, Ling; Zhao, Jie; Li, Yan; Zhu, Yunqing; Wang, Chuanyi

    2016-02-23

    Because of the lack of experimental evidence, much confusion still exists on the nucleation and growth dynamics of a nanostructure, particularly of metal. The situation is even worse for nanodroplets because it is more difficult to induce the formation of a nanodroplet while imaging the dynamic process with atomic resolution. Here, taking advantage of an electron beam to induce the growth of Bi nanodroplets on a SrBi2Ta2O9 platelet under a high resolution transmission electron microscope (HRTEM), we directly observed the detailed growth pathways of Bi nanodroplets from the earliest stage of nucleation that were previously inaccessible. Atomic scale imaging reveals that the dynamics of nucleation involves a much more complex trajectory than previously predicted based on classical nucleation theory (CNT). The monatomic Bi layer was first formed in the nucleation process, which induced the formation of the prenucleated clusters. Following that, critical nuclei for the nanodroplets formed both directly from the addition of atoms to the prenucleated clusters by the classical growth process and indirectly through transformation of an intermediate liquid film based on the Stranski-Krastanov growth mode, in which the liquid film was induced by the self-assembly of the prenucleated clusters. Finally, the growth of the Bi nanodroplets advanced through the classical pathway and sudden droplet coalescence. This study allows us to visualize the critical steps in the nucleation process of an interfacial nanodroplet, which suggests a revision of the perspective of CNT.

  2. Lagrangian formulation of classical BMT-theory

    International Nuclear Information System (INIS)

    Pupasov-Maksimov, Andrey; Deriglazov, Alexei; Guzman, Walberto

    2013-01-01

    Full text: The most popular classical theory of electron has been formulated by Bargmann, Michel and Telegdi (BMT) in 1959. The BMT equations give classical relativistic description of a charged particle with spin and anomalous magnetic momentum moving in homogeneous electro-magnetic field. This allows to study spin dynamics of polarized beams in uniform fields. In particular, first experimental measurements of muon anomalous magnetic momentum were done using changing of helicity predicted by BMT equations. Surprisingly enough, a systematic formulation and the analysis of the BMT theory are absent in literature. In the present work we particularly fill this gap by deducing Lagrangian formulation (variational problem) for BMT equations. Various equivalent forms of Lagrangian will be discussed in details. An advantage of the obtained classical model is that the Lagrangian action describes a relativistic spinning particle without Grassmann variables, for both free and interacting cases. This implies also the possibility of canonical quantization. In the interacting case, an arbitrary electromagnetic background may be considered, which generalizes the BMT theory formulated to the case of homogeneous fields. The classical model has two local symmetries, which gives an interesting example of constrained classical dynamics. It is surprising, that the case of vanishing anomalous part of the magnetic momentum is naturally highlighted in our construction. (author)

  3. Ice nucleation properties of mineral dust particles: determination of onset RHi, IN active fraction, nucleation time-lag, and the effect of active sites on contact angles

    Directory of Open Access Journals (Sweden)

    S. Dobbie

    2010-01-01

    Full Text Available A newly developed ice nucleation experimental set up was used to investigate the heterogeneous ice nucleation properties of three Saharan and one Spanish dust particle samples. It was observed that the spread in the onset relative humidities with respect to ice (RHi for Saharan dust particles varied from 104% to 110%, whereas for the Spanish dust from 106% to 110%. The elemental composition analysis shows a prominent Ca feature in the Spanish dust sample which could potentially explain the differences in nucleation threshold. Although the spread in the onset RHi for the three Saharan dust samples were in agreement, the active fractions and nucleation time-lags calculated at various temperature and RHi conditions were found to differ. This could be due to the subtle variation in the elemental composition of the dust samples, and surface irregularities like steps, cracks, cavities etc. A combination of classical nucleation theory and active site theory is used to understand the importance of these surface irregularities on the nucleability parameter, contact angle that is widely used in ice cloud modeling. These calculations show that the surface irregularities can reduce the contact angle by approximately 10 degrees.

  4. Differential formalism aspects of the gauge classical theories

    International Nuclear Information System (INIS)

    Stedile, E.

    1982-01-01

    The classical aspects of the gauge theories are shown using differential geometry as fundamental tool. Somme comments are done about Maxwell Electro-dynamics, classical Yang-Mills and gravitation theories. (L.C.) [pt

  5. Nucleation, growth and transport modelling of helium bubbles under nuclear irradiation in lead–lithium with the self-consistent nucleation theory and surface tension corrections

    International Nuclear Information System (INIS)

    Fradera, J.; Cuesta-López, S.

    2013-01-01

    Highlights: • The work presented in this manuscript provides a reliable computational tool to quantify the He complex phenomena in a HCLL. • A model based on the self-consistent nucleation theory (SCT) is exposed. It includes radiation induced nucleation modelling and surface tension corrections. • Results informed reinforce the necessity of conducting experiments to determine nucleation conditions and bubble transport parameters in LM breeders. • Our findings and model provide a good qualitative insight into the helium nucleation phenomenon in LM systems for fusion technology and can be used to identify key system parameters. -- Abstract: Helium (He) nucleation in liquid metal breeding blankets of a DT fusion reactor may have a significant impact regarding system design, safety and operation. Large He production rates are expected due to tritium (T) fuel self-sufficiency requirement, as both, He and T, are produced at the same rate. Low He solubility, local high concentrations, radiation damage and fluid discontinuities, among other phenomena, may yield the necessary conditions for He nucleation. Hence, He nucleation may have a significant impact on T inventory and may lower the T breeding ratio. A model based on the self-consistent nucleation theory (SCT) with a surface tension curvature correction model has been implemented in OpenFOAM ® CFD code. A modification through a single parameter of the necessary nucleation condition is proposed in order to take into account all the nucleation triggering phenomena, specially radiation induced nucleation. Moreover, the kinetic growth model has been adapted so as to allow for the transition from a critical cluster to a macroscopic bubble with a diffusion growth process. Limitations and capabilities of the models are shown by means of zero-dimensional simulations and sensitivity analyses to key parameters under HCLL breeding unit conditions. Results provide a good qualitative insight into the helium nucleation

  6. Nucleation, growth and transport modelling of helium bubbles under nuclear irradiation in lead–lithium with the self-consistent nucleation theory and surface tension corrections

    Energy Technology Data Exchange (ETDEWEB)

    Fradera, J., E-mail: jfradera@ubu.es; Cuesta-López, S., E-mail: scuesta@ubu.es

    2013-12-15

    Highlights: • The work presented in this manuscript provides a reliable computational tool to quantify the He complex phenomena in a HCLL. • A model based on the self-consistent nucleation theory (SCT) is exposed. It includes radiation induced nucleation modelling and surface tension corrections. • Results informed reinforce the necessity of conducting experiments to determine nucleation conditions and bubble transport parameters in LM breeders. • Our findings and model provide a good qualitative insight into the helium nucleation phenomenon in LM systems for fusion technology and can be used to identify key system parameters. -- Abstract: Helium (He) nucleation in liquid metal breeding blankets of a DT fusion reactor may have a significant impact regarding system design, safety and operation. Large He production rates are expected due to tritium (T) fuel self-sufficiency requirement, as both, He and T, are produced at the same rate. Low He solubility, local high concentrations, radiation damage and fluid discontinuities, among other phenomena, may yield the necessary conditions for He nucleation. Hence, He nucleation may have a significant impact on T inventory and may lower the T breeding ratio. A model based on the self-consistent nucleation theory (SCT) with a surface tension curvature correction model has been implemented in OpenFOAM{sup ®} CFD code. A modification through a single parameter of the necessary nucleation condition is proposed in order to take into account all the nucleation triggering phenomena, specially radiation induced nucleation. Moreover, the kinetic growth model has been adapted so as to allow for the transition from a critical cluster to a macroscopic bubble with a diffusion growth process. Limitations and capabilities of the models are shown by means of zero-dimensional simulations and sensitivity analyses to key parameters under HCLL breeding unit conditions. Results provide a good qualitative insight into the helium

  7. Investigating heterogeneous nucleation in peritectic materials via the phase-field method

    International Nuclear Information System (INIS)

    Emmerich, Heike; Siquieri, Ricardo

    2006-01-01

    Here we propose a phase-field approach to investigate the influence of convection on peritectic growth as well as the heterogeneous nucleation kinetics of peritectic systems. For this purpose we derive a phase-field model for peritectic growth taking into account fluid flow in the melt, which is convergent to the underlying sharp interface problem in the thin interface limit (Karma and Rappel 1996 Phys. Rev. E 53 R3017). Moreover, we employ our new phase-field model to study the heterogeneous nucleation kinetics of peritectic material systems. Our approach is based on a similar approach towards homogeneous nucleation in Granasy et al (2003 Interface and Transport Dynamics (Springer Lecture Notes in Computational Science and Engineering vol 32) ed Emmerich et al (Berlin: Springer) p 190). We applied our model successfully to extend the nucleation rate predicted by classical nucleation theory for an additional morphological term relevant for peritectic growth. Further applications to understand the mechanisms and consequences of heterogeneous nucleation kinetics in more detail are discussed

  8. Quantifying the Effect of Stress on Sn Whisker Nucleation Kinetics

    Science.gov (United States)

    Chason, Eric; Vasquez, Justin; Pei, Fei; Jain, Nupur; Hitt, Andrew

    2018-01-01

    Although Sn whiskers have been studied extensively, there is still a need to understand the driving forces behind whisker nucleation and growth. Many studies point to the role of stress, but confirming this requires a quantitative comparison between controlled stress and the resulting whisker evolution. Recent experimental studies applied stress to a Sn layer via thermal cycling and simultaneously monitored the evolution of the temperature, stress and number of nuclei. In this work, we analyze these nucleation kinetics in terms of classical nucleation theory to relate the observed behavior to underlying mechanisms including a stress dependent activation energy and a temperature and stress-dependent whisker growth rate. Non-linear least squares fitting of the data taken at different temperatures and strain rates to the model shows that the results can be understood in terms of stress decreasing the barrier for whisker nucleation.

  9. Homogeneous nucleation in liquid nitrogen at negative pressures

    Energy Technology Data Exchange (ETDEWEB)

    Baidakov, V. G., E-mail: baidakov@itp.uran.ru; Vinogradov, V. E.; Pavlov, P. A. [Russian Academy of Sciences, Institute of Thermal Physics, Ural Branch (Russian Federation)

    2016-10-15

    The kinetics of spontaneous cavitation in liquid nitrogen at positive and negative pressures has been studied in a tension wave formed by a compression pulse reflected from the liquid–vapor interface on a thin platinum wire heated by a current pulse. The limiting tensile stresses (Δp = p{sub s}–p, where p{sub s} is the saturation pressure), the corresponding bubble nucleation frequencies J (10{sup 20}–10{sup 22} s{sup –1} m{sup –3}), and temperature induced nucleation frequency growth rate G{sub T} = dlnJ/dT have been experimentally determined. At T = 90 K, the limiting tensile stress was Δp = 8.3 MPa, which was 4.9 MPa lower than the value corresponding to the boundary of thermodynamic stability of the liquid phase (spinodal). The measurement results were compared to classical (homogeneous) nucleation theory (CNT) with and without neglect of the dependence of the surface tension of critical bubbles on their dimensions. In the latter case, the properties of new phase nuclei were described in terms of the Van der Waals theory of capillarity. The experimental data agree well with the CNT theory when it takes into account the “size effect.”.

  10. Nonlinear classical theory of electromagnetism

    International Nuclear Information System (INIS)

    Pisello, D.

    1977-01-01

    A topological theory of electric charge is given. Einstein's criteria for the completion of classical electromagnetic theory are summarized and their relation to quantum theory and the principle of complementarity is indicated. The inhibiting effect that this principle has had on the development of physical thought is discussed. Developments in the theory of functions on nonlinear spaces provide the conceptual framework required for the completion of electromagnetism. The theory is based on an underlying field which is a continuous mapping of space-time into points on the two-sphere. (author)

  11. Thermokinetics of heterogeneous droplet nucleation on conically textured substrates.

    Science.gov (United States)

    Singha, Sanat K; Das, Prasanta K; Maiti, Biswajit

    2015-11-28

    Within the framework of the classical theory of heterogeneous nucleation, a thermokinetic model is developed for line-tension-associated droplet nucleation on conical textures considering growth or shrinkage of the formed cluster due to both interfacial and peripheral monomer exchange and by considering different geometric configurations. Along with the principle of free energy extremization, Katz kinetic approach has been employed to study the effect of substrate conicity and wettability on the thermokinetics of heterogeneous water droplet nucleation. Not only the peripheral tension is found to have a considerable effect on the free energy barrier but also the substrate hydrophobicity and hydrophilicity are observed to switch over their roles between conical crest and trough for different growth rates of the droplet. Besides, the rate of nucleation increases and further promotes nucleation for negative peripheral tension as it diminishes the free energy barrier appreciably. Moreover, nucleation inhibition can be achievable for positive peripheral tension due to the enhancement of the free energy barrier. Analyzing all possible geometric configurations, the hydrophilic narrower conical cavity is found to be the most preferred nucleation site. These findings suggest a physical insight into the context of surface engineering for the promotion or the suppression of nucleation on real or engineered substrates.

  12. Dynamics of ice nucleation on water repellent surfaces.

    Science.gov (United States)

    Alizadeh, Azar; Yamada, Masako; Li, Ri; Shang, Wen; Otta, Shourya; Zhong, Sheng; Ge, Liehui; Dhinojwala, Ali; Conway, Ken R; Bahadur, Vaibhav; Vinciquerra, A Joseph; Stephens, Brian; Blohm, Margaret L

    2012-02-14

    Prevention of ice accretion and adhesion on surfaces is relevant to many applications, leading to improved operation safety, increased energy efficiency, and cost reduction. Development of passive nonicing coatings is highly desirable, since current antiicing strategies are energy and cost intensive. Superhydrophobicity has been proposed as a lead passive nonicing strategy, yet the exact mechanism of delayed icing on these surfaces is not clearly understood. In this work, we present an in-depth analysis of ice formation dynamics upon water droplet impact on surfaces with different wettabilities. We experimentally demonstrate that ice nucleation under low-humidity conditions can be delayed through control of surface chemistry and texture. Combining infrared (IR) thermometry and high-speed photography, we observe that the reduction of water-surface contact area on superhydrophobic surfaces plays a dual role in delaying nucleation: first by reducing heat transfer and second by reducing the probability of heterogeneous nucleation at the water-substrate interface. This work also includes an analysis (based on classical nucleation theory) to estimate various homogeneous and heterogeneous nucleation rates in icing situations. The key finding is that ice nucleation delay on superhydrophobic surfaces is more prominent at moderate degrees of supercooling, while closer to the homogeneous nucleation temperature, bulk and air-water interface nucleation effects become equally important. The study presented here offers a comprehensive perspective on the efficacy of textured surfaces for nonicing applications.

  13. Phase nucleation and evolution mechanisms in heterogeneous solids

    Science.gov (United States)

    Udupa, Anirudh

    Phase nucleation and evolution is a problem of critical importance in many applications. As the length scales are reduced, it becomes increasingly important to consider interfacial and micro-structural effects that can be safely ignored at larger length scales owing to randomness. The theory of phase nucleation has been addressed usually by the classical nucleation theory, which was originally derived for single component fluid systems, after making an assumption of equilibrium. The criterion has not been rigorously derived for solids, which are far from equilibrium due to dissipation by multiple physical drivers. In this thesis, a thermodynamically sound nucleation criterion is derived for systems with multiple interacting physical phenomena and multiple dissipating mechanisms. This is done, using the tools of continuum mechanics, by determining the change in free energy upon the introduction of a new nucleus into the system. The developed theory is demonstrated to be a generalization of the classical nucleation theory (CNT). The developed theory is then applied to the problem of electromigration driven void nucleation, a serious reliability concern for the microelectronics industry. The void grows and eventually severs the line making the chip nonfunctional. There are two classes of theories at present in the electromigration literature to address the problem of void nucleation, the vacancy supersaturation theory and the entropic dissipation theory, both of which are empirical and based on intuition developed from experimental observations. When the developed theory was applied to the problem of electromigration, it was found to be consistent with the vacancy supersaturation theory, but provided the correct energetic quantity, the chemical potential, which has contribution from both the vacancy concentration as well as the hydrostatic stress. An experiment, consisting of electromigration tests on serpentine lines, was developed to validate the developed

  14. Perturbation theory via Feynman diagrams in classical mechanics

    OpenAIRE

    Penco, R.; Mauro, D.

    2006-01-01

    In this paper we show how Feynman diagrams, which are used as a tool to implement perturbation theory in quantum field theory, can be very useful also in classical mechanics, provided we introduce also at the classical level concepts like path integrals and generating functionals.

  15. Theory and Simulation of Nucleation

    NARCIS (Netherlands)

    Kuipers, J.|info:eu-repo/dai/nl/304832049

    2009-01-01

    Nucleation is the process where a stable nucleus spontaneously emerges in a metastable environment. Examples of nucleation abound, for instance the formation of droplets in undercooled gasses and of crystals in undercooled liquids. The process is thermally activated and is key to understanding

  16. Hydration Effects on the Stability of Calcium Carbonate Pre-Nucleation Species

    Directory of Open Access Journals (Sweden)

    Alejandro Burgos-Cara

    2017-07-01

    Full Text Available Recent experimental evidence and computer modeling have shown that the crystallization of a range of minerals does not necessarily follow classical models and theories. In several systems, liquid precursors, stable pre-nucleation clusters and amorphous phases precede the nucleation and growth of stable mineral phases. However, little is known on the effect of background ionic species on the formation and stability of pre-nucleation species formed in aqueous solutions. Here, we present a systematic study on the effect of a range of background ions on the crystallization of solid phases in the CaCO3-H2O system, which has been thoroughly studied due to its technical and mineralogical importance, and is known to undergo non-classical crystallization pathways. The induction time for the onset of calcium carbonate nucleation and effective critical supersaturation are systematically higher in the presence of background ions with decreasing ionic radii. We propose that the stabilization of water molecules in the pre-nucleation clusters by background ions can explain these results. The stabilization of solvation water hinders cluster dehydration, which is an essential step for precipitation. This hypothesis is corroborated by the observed correlation between parameters such as the macroscopic equilibrium constant for the formation of calcium/carbonate ion associates, the induction time, and the ionic radius of the background ions in the solution. Overall, these results provide new evidence supporting the hypothesis that pre-nucleation cluster dehydration is the rate-controlling step for calcium carbonate precipitation.

  17. Homogeneous nucleation: a problem in nonequilibrium quantum statistical mechanics

    International Nuclear Information System (INIS)

    1978-08-01

    The master equation for cluster growth and evaporation is derived for many-body quantum mechanics and from a modified version of quantum damping theory used in laser physics. For application to nucleation theory, the quantum damping theory is generalized to include system and reservoir states that are not separate entities. Formulas for rate constants are obtained. Solutions of the master equation yield equations of state and system-averaged quantities recognized as thermodynamic variables. Formulas for Helmholtz free energies of clusters in a Debye approximation are derived. Coexistence-line equations for pressure, volume, and number of clusters are obtained from equations-of-state analysis. Coexistence-line and surface-tension data are used to obtain values of parameters for the Debye approximation. These data are employed in calculating both the nucleation current in diffusion cloud chamber experiments and the onset of condensation in expansion nozzle experiments. Theoretical and experimental results are similar for both cloud chamber and nozzle experiments, which measure water. Comparison with other theories reveals that classical theory only accidently agrees with experiment and that the Helmholtz free-energy formula used in the Lothe--Pound theory is incomplete. 27 figures, 3 tables, 149 references

  18. Free energy landscape and molecular pathways of gas hydrate nucleation

    Energy Technology Data Exchange (ETDEWEB)

    Bi, Yuanfei; Porras, Anna; Li, Tianshu, E-mail: tsli@gwu.edu [Department of Civil and Environmental Engineering, George Washington University, Washington DC 20052 (United States)

    2016-12-07

    Despite the significance of gas hydrates in diverse areas, a quantitative knowledge of hydrate formation at a molecular level is missing. The impediment to acquiring this understanding is primarily attributed to the stochastic nature and ultra-fine scales of nucleation events, posing a great challenge for both experiment and simulation to explore hydrate nucleation. Here we employ advanced molecular simulation methods, including forward flux sampling (FFS), p{sub B} histogram analysis, and backward flux sampling, to overcome the limit of direct molecular simulation for exploring both the free energy landscape and molecular pathways of hydrate nucleation. First we test the half-cage order parameter (H-COP) which we developed for driving FFS, through conducting the p{sub B} histogram analysis. Our results indeed show that H-COP describes well the reaction coordinates of hydrate nucleation. Through the verified order parameter, we then directly compute the free energy landscape for hydrate nucleation by combining both forward and backward flux sampling. The calculated stationary distribution density, which is obtained independently of nucleation theory, is found to fit well against the classical nucleation theory (CNT). Subsequent analysis of the obtained large ensemble of hydrate nucleation trajectories show that although on average, hydrate formation is facilitated by a two-step like mechanism involving a gradual transition from an amorphous to a crystalline structure, there also exist nucleation pathways where hydrate crystallizes directly, without going through the amorphous stage. The CNT-like free energy profile and the structural diversity suggest the existence of multiple active transition pathways for hydrate nucleation, and possibly also imply the near degeneracy in their free energy profiles among different pathways. Our results thus bring a new perspective to the long standing question of how hydrates crystallize.

  19. Free energy landscape and molecular pathways of gas hydrate nucleation

    International Nuclear Information System (INIS)

    Bi, Yuanfei; Porras, Anna; Li, Tianshu

    2016-01-01

    Despite the significance of gas hydrates in diverse areas, a quantitative knowledge of hydrate formation at a molecular level is missing. The impediment to acquiring this understanding is primarily attributed to the stochastic nature and ultra-fine scales of nucleation events, posing a great challenge for both experiment and simulation to explore hydrate nucleation. Here we employ advanced molecular simulation methods, including forward flux sampling (FFS), p B histogram analysis, and backward flux sampling, to overcome the limit of direct molecular simulation for exploring both the free energy landscape and molecular pathways of hydrate nucleation. First we test the half-cage order parameter (H-COP) which we developed for driving FFS, through conducting the p B histogram analysis. Our results indeed show that H-COP describes well the reaction coordinates of hydrate nucleation. Through the verified order parameter, we then directly compute the free energy landscape for hydrate nucleation by combining both forward and backward flux sampling. The calculated stationary distribution density, which is obtained independently of nucleation theory, is found to fit well against the classical nucleation theory (CNT). Subsequent analysis of the obtained large ensemble of hydrate nucleation trajectories show that although on average, hydrate formation is facilitated by a two-step like mechanism involving a gradual transition from an amorphous to a crystalline structure, there also exist nucleation pathways where hydrate crystallizes directly, without going through the amorphous stage. The CNT-like free energy profile and the structural diversity suggest the existence of multiple active transition pathways for hydrate nucleation, and possibly also imply the near degeneracy in their free energy profiles among different pathways. Our results thus bring a new perspective to the long standing question of how hydrates crystallize.

  20. Free energy landscape and molecular pathways of gas hydrate nucleation.

    Science.gov (United States)

    Bi, Yuanfei; Porras, Anna; Li, Tianshu

    2016-12-07

    Despite the significance of gas hydrates in diverse areas, a quantitative knowledge of hydrate formation at a molecular level is missing. The impediment to acquiring this understanding is primarily attributed to the stochastic nature and ultra-fine scales of nucleation events, posing a great challenge for both experiment and simulation to explore hydrate nucleation. Here we employ advanced molecular simulation methods, including forward flux sampling (FFS), p B histogram analysis, and backward flux sampling, to overcome the limit of direct molecular simulation for exploring both the free energy landscape and molecular pathways of hydrate nucleation. First we test the half-cage order parameter (H-COP) which we developed for driving FFS, through conducting the p B histogram analysis. Our results indeed show that H-COP describes well the reaction coordinates of hydrate nucleation. Through the verified order parameter, we then directly compute the free energy landscape for hydrate nucleation by combining both forward and backward flux sampling. The calculated stationary distribution density, which is obtained independently of nucleation theory, is found to fit well against the classical nucleation theory (CNT). Subsequent analysis of the obtained large ensemble of hydrate nucleation trajectories show that although on average, hydrate formation is facilitated by a two-step like mechanism involving a gradual transition from an amorphous to a crystalline structure, there also exist nucleation pathways where hydrate crystallizes directly, without going through the amorphous stage. The CNT-like free energy profile and the structural diversity suggest the existence of multiple active transition pathways for hydrate nucleation, and possibly also imply the near degeneracy in their free energy profiles among different pathways. Our results thus bring a new perspective to the long standing question of how hydrates crystallize.

  1. Classical and non-classical effective medium theories: New perspectives

    International Nuclear Information System (INIS)

    Tsukerman, Igor

    2017-01-01

    Highlights: • Advanced non-asymptotic and nonlocal homogenization theories of metamaterials, valid in electrostatics and electrodynamics. • Classical theories (Clausius–Mossotti, Lorenz–Lorentz, Maxwell Garnett) fit well into the proposed framework. • Nonlocal effects can be included in the model, making order-of-magnitude accuracy improvements possible. • A challenging problem for future research is to determine what effective tensors are attainable for given constituents of a metamaterial. - Abstract: Future research in electrodynamics of periodic electromagnetic composites (metamaterials) can be expected to produce sophisticated homogenization theories valid for any composition and size of the lattice cell. The paper outlines a promising path in that direction, leading to non-asymptotic and nonlocal homogenization models, and highlights aspects of homogenization that are often overlooked: the finite size of the sample and the role of interface boundaries. Classical theories (e.g. Clausius–Mossotti, Maxwell Garnett), while originally derived from a very different set of ideas, fit well into the proposed framework. Nonlocal effects can be included in the model, making an order-of-magnitude accuracy improvements possible. One future challenge is to determine what effective parameters can or cannot be obtained for a given set of constituents of a metamaterial lattice cell, thereby delineating the possible from the impossible in metamaterial design.

  2. Classical and non-classical effective medium theories: New perspectives

    Energy Technology Data Exchange (ETDEWEB)

    Tsukerman, Igor, E-mail: igor@uakron.edu

    2017-05-18

    Highlights: • Advanced non-asymptotic and nonlocal homogenization theories of metamaterials, valid in electrostatics and electrodynamics. • Classical theories (Clausius–Mossotti, Lorenz–Lorentz, Maxwell Garnett) fit well into the proposed framework. • Nonlocal effects can be included in the model, making order-of-magnitude accuracy improvements possible. • A challenging problem for future research is to determine what effective tensors are attainable for given constituents of a metamaterial. - Abstract: Future research in electrodynamics of periodic electromagnetic composites (metamaterials) can be expected to produce sophisticated homogenization theories valid for any composition and size of the lattice cell. The paper outlines a promising path in that direction, leading to non-asymptotic and nonlocal homogenization models, and highlights aspects of homogenization that are often overlooked: the finite size of the sample and the role of interface boundaries. Classical theories (e.g. Clausius–Mossotti, Maxwell Garnett), while originally derived from a very different set of ideas, fit well into the proposed framework. Nonlocal effects can be included in the model, making an order-of-magnitude accuracy improvements possible. One future challenge is to determine what effective parameters can or cannot be obtained for a given set of constituents of a metamaterial lattice cell, thereby delineating the possible from the impossible in metamaterial design.

  3. Homogeneous nucleation of water in argon. Nucleation rate computation from molecular simulations of TIP4P and TIP4P/2005 water model.

    Science.gov (United States)

    Dumitrescu, Lucia R; Smeulders, David M J; Dam, Jacques A M; Gaastra-Nedea, Silvia V

    2017-02-28

    Molecular dynamics (MD) simulations were conducted to study nucleation of water at 350 K in argon using TIP4P and TIP4P/2005 water models. We found that the stability of any cluster, even if large, strongly depends on the energetic interactions with its vicinity, while the stable clusters change their composition almost entirely during nucleation. Using the threshold method, direct nucleation rates are obtained. Our nucleation rates are found to be 1.08×10 27 cm -3 s -1 for TIP4P and 2.30×10 27 cm -3 s -1 for TIP4P/2005. The latter model prescribes a faster dynamics than the former, with a nucleation rate two times larger due to its higher electrostatic charges. The non-equilibrium water densities derived from simulations and state-of-art equilibrium parameters from Vega and de Miguel [J. Chem. Phys. 126, 154707 (2007)] are used for the classical nucleation theory (CNT) prediction. The CNT overestimates our results for both water models, where TIP4P/2005 shows largest discrepancy. Our results complement earlier data at high nucleation rates and supersaturations in the Hale plot [Phys. Rev. A 33, 4156 (1986)], and are consistent with MD data on the SPC/E and the TIP4P/2005 model.

  4. Heterogeneous Nucleation of Colloidal Crystals on a Glass Substrate with Depletion Attraction.

    Science.gov (United States)

    Guo, Suxia; Nozawa, Jun; Hu, Sumeng; Koizumi, Haruhiko; Okada, Junpei; Uda, Satoshi

    2017-10-10

    The heterogeneous nucleation of colloidal crystals with attractive interactions has been investigated via in situ observations. We have found two types of nucleation processes: a cluster that overcomes the critical size for nucleation with a monolayer, and a method that occurs with two layers. The Gibbs free energy changes (ΔG) for these two types of nucleation processes are evaluated by taking into account the effect of various interfacial energies. In contrast to homogeneous nucleation, the change in interfacial free energy, Δσ, is generated for colloidal nucleation on a foreign substrate such as a cover glass in the present study. The Δσ and step free energy of the first layer, γ 1 , are obtained experimentally based on the equation deduced from classical nucleation theory (CNT). It is concluded that the ΔG of q-2D nuclei is smaller than of monolayer nuclei, provided that the same number of particles are used, which explains the experimental result that the critical size in q-2D nuclei is smaller than that in monolayer nuclei.

  5. Homogeneous SPC/E water nucleation in large molecular dynamics simulations.

    Science.gov (United States)

    Angélil, Raymond; Diemand, Jürg; Tanaka, Kyoko K; Tanaka, Hidekazu

    2015-08-14

    We perform direct large molecular dynamics simulations of homogeneous SPC/E water nucleation, using up to ∼ 4 ⋅ 10(6) molecules. Our large system sizes allow us to measure extremely low and accurate nucleation rates, down to ∼ 10(19) cm(-3) s(-1), helping close the gap between experimentally measured rates ∼ 10(17) cm(-3) s(-1). We are also able to precisely measure size distributions, sticking efficiencies, cluster temperatures, and cluster internal densities. We introduce a new functional form to implement the Yasuoka-Matsumoto nucleation rate measurement technique (threshold method). Comparison to nucleation models shows that classical nucleation theory over-estimates nucleation rates by a few orders of magnitude. The semi-phenomenological nucleation model does better, under-predicting rates by at worst a factor of 24. Unlike what has been observed in Lennard-Jones simulations, post-critical clusters have temperatures consistent with the run average temperature. Also, we observe that post-critical clusters have densities very slightly higher, ∼ 5%, than bulk liquid. We re-calibrate a Hale-type J vs. S scaling relation using both experimental and simulation data, finding remarkable consistency in over 30 orders of magnitude in the nucleation rate range and 180 K in the temperature range.

  6. Lectures on classical and quantum theory of fields

    International Nuclear Information System (INIS)

    Arodz, Henryk; Hadasz, Leszek

    2010-01-01

    This textbook on classical and quantum theory of fields addresses graduate students starting to specialize in theoretical physics. It provides didactic introductions to the main topics in the theory of fields, while taking into account the contemporary view of the subject. The student will find concise explanations of basic notions essential for applications of the theory of fields as well as for frontier research in theoretical physics. One third of the book is devoted to classical fields. Each chapter contains exercises of varying degree of difficulty with hints or solutions, plus summaries and worked examples as useful. The textbook is based on lectures delivered to students of theoretical physics at Jagiellonian University. It aims to deliver a unique combination of classical and quantum field theory in one compact course. (orig.)

  7. Lectures on Classical and Quantum Theory of Fields

    CERN Document Server

    Arodź, Henryk

    2010-01-01

    This textbook on classical and quantum theory of fields addresses graduate students starting to specialize in theoretical physics. It provides didactic introductions to the main topics in the theory of fields, while taking into account the contemporary view of the subject. The student will find concise explanations of basic notions essential for applications of the theory of fields as well as for frontier research in theoretical physics. One third of the book is devoted to classical fields. Each chapter contains exercises of varying degree of difficulty with hints or solutions, plus summaries and worked examples as useful. The textbook is based on lectures delivered to students of theoretical physics at Jagiellonian University. It aims to deliver a unique combination of classical and quantum field theory in one compact course.

  8. Lectures on classical and quantum theory of fields

    Energy Technology Data Exchange (ETDEWEB)

    Arodz, Henryk; Hadasz, Leszek [Jagiellonian Univ., Krakow (Poland). Inst. Physics

    2010-07-01

    This textbook on classical and quantum theory of fields addresses graduate students starting to specialize in theoretical physics. It provides didactic introductions to the main topics in the theory of fields, while taking into account the contemporary view of the subject. The student will find concise explanations of basic notions essential for applications of the theory of fields as well as for frontier research in theoretical physics. One third of the book is devoted to classical fields. Each chapter contains exercises of varying degree of difficulty with hints or solutions, plus summaries and worked examples as useful. The textbook is based on lectures delivered to students of theoretical physics at Jagiellonian University. It aims to deliver a unique combination of classical and quantum field theory in one compact course. (orig.)

  9. A Theory of Immersion Freezing

    Science.gov (United States)

    Barahona, Donifan

    2017-01-01

    Immersion freezing is likely involved in the initiation of precipitation and determines to large extent the phase partitioning in convective clouds. Theoretical models commonly used to describe immersion freezing in atmospheric models are based on the classical nucleation theory which however neglects important interactions near the immersed particle that may affect nucleation rates. This work introduces a new theory of immersion freezing based on two premises. First, immersion ice nucleation is mediated by the modification of the properties of water near the particle-liquid interface, rather than by the geometry of the ice germ. Second, the same mechanism that leads to the decrease in the work of germ formation also decreases the mobility of water molecules near the immersed particle. These two premises allow establishing general thermodynamic constraints to the ice nucleation rate. Analysis of the new theory shows that active sites likely trigger ice nucleation, but they do not control the overall nucleation rate nor the probability of freezing. It also suggests that materials with different ice nucleation efficiency may exhibit similar freezing temperatures under similar conditions but differ in their sensitivity to particle surface area and cooling rate. Predicted nucleation rates show good agreement with observations for a diverse set of materials including dust, black carbon and bacterial ice nucleating particles. The application of the new theory within the NASA Global Earth System Model (GEOS-5) is also discussed.

  10. Classical theory of radiating strings

    Science.gov (United States)

    Copeland, Edmund J.; Haws, D.; Hindmarsh, M.

    1990-01-01

    The divergent part of the self force of a radiating string coupled to gravity, an antisymmetric tensor and a dilaton in four dimensions are calculated to first order in classical perturbation theory. While this divergence can be absorbed into a renormalization of the string tension, demanding that both it and the divergence in the energy momentum tensor vanish forces the string to have the couplings of compactified N = 1 D = 10 supergravity. In effect, supersymmetry cures the classical infinities.

  11. Fundamental theories of waves and particles formulated without classical mass

    Science.gov (United States)

    Fry, J. L.; Musielak, Z. E.

    2010-12-01

    Quantum and classical mechanics are two conceptually and mathematically different theories of physics, and yet they do use the same concept of classical mass that was originally introduced by Newton in his formulation of the laws of dynamics. In this paper, physical consequences of using the classical mass by both theories are explored, and a novel approach that allows formulating fundamental (Galilean invariant) theories of waves and particles without formally introducing the classical mass is presented. In this new formulation, the theories depend only on one common parameter called 'wave mass', which is deduced from experiments for selected elementary particles and for the classical mass of one kilogram. It is shown that quantum theory with the wave mass is independent of the Planck constant and that higher accuracy of performing calculations can be attained by such theory. Natural units in connection with the presented approach are also discussed and justification beyond dimensional analysis is given for the particular choice of such units.

  12. Nucleation and microstructure development in Cr-Mo-V tool steel during gas atomization

    Science.gov (United States)

    Behúlová, M.; Grgač, P.; Čička, R.

    2017-11-01

    Nucleation studies of undercooled metallic melts are of essential interest for the understanding of phase selection, growth kinetics and microstructure development during their rapid non-equilibrium solidification. The paper deals with the modelling of nucleation processes and microstructure development in the hypoeutectic tool steel Ch12MF4 with the chemical composition of 2.37% C, 12.06 % Cr, 1.2% Mo, 4.0% V and balance Fe [wt. %] in the process of nitrogen gas atomization. Based on the classical theory of homogeneous nucleation, the nucleation temperature of molten rapidly cooled spherical particles from this alloy with diameter from 40 μm to 600 μm in the gas atomization process is calculated using various estimations of parameters influencing the nucleation process - the Gibbs free energy difference between solid and liquid phases and the solid/liquid interfacial energy. Results of numerical calculations are compared with experimentally measured nucleation temperatures during levitation experiments and microstructures developed in rapidly solidified powder particles from the investigated alloy.

  13. Molecular dynamics simulations of bubble nucleation in dark matter detectors.

    Science.gov (United States)

    Denzel, Philipp; Diemand, Jürg; Angélil, Raymond

    2016-01-01

    Bubble chambers and droplet detectors used in dosimetry and dark matter particle search experiments use a superheated metastable liquid in which nuclear recoils trigger bubble nucleation. This process is described by the classical heat spike model of F. Seitz [Phys. Fluids (1958-1988) 1, 2 (1958)PFLDAS0031-917110.1063/1.1724333], which uses classical nucleation theory to estimate the amount and the localization of the deposited energy required for bubble formation. Here we report on direct molecular dynamics simulations of heat-spike-induced bubble formation. They allow us to test the nanoscale process described in the classical heat spike model. 40 simulations were performed, each containing about 20 million atoms, which interact by a truncated force-shifted Lennard-Jones potential. We find that the energy per length unit needed for bubble nucleation agrees quite well with theoretical predictions, but the allowed spike length and the required total energy are about twice as large as predicted. This could be explained by the rapid energy diffusion measured in the simulation: contrary to the assumption in the classical model, we observe significantly faster heat diffusion than the bubble formation time scale. Finally we examine α-particle tracks, which are much longer than those of neutrons and potential dark matter particles. Empirically, α events were recently found to result in louder acoustic signals than neutron events. This distinction is crucial for the background rejection in dark matter searches. We show that a large number of individual bubbles can form along an α track, which explains the observed larger acoustic amplitudes.

  14. Molecular dynamics studies of crystalline nucleation in one-component Yukawa plasmas

    International Nuclear Information System (INIS)

    Ravelo, R.; Hammerberg, J.E.; Holian, B.L.

    1992-01-01

    We report on molecular dynamics studies of one-component Yukawa plasmas undergoing rapid quenches from a fluid state with a Coulomb parameter Γ = 40 to solid states in the range 350 < Γ < 800. The detailed dynamical structure of ordering appears more complicated than results from classical theories of nucleation, with planar formation being observed before fully 3-dimensional ordering appears

  15. Classical theory of electric and magnetic fields

    CERN Document Server

    Good, Roland H

    1971-01-01

    Classical Theory of Electric and Magnetic Fields is a textbook on the principles of electricity and magnetism. This book discusses mathematical techniques, calculations, with examples of physical reasoning, that are generally applied in theoretical physics. This text reviews the classical theory of electric and magnetic fields, Maxwell's Equations, Lorentz Force, and Faraday's Law of Induction. The book also focuses on electrostatics and the general methods for solving electrostatic problems concerning images, inversion, complex variable, or separation of variables. The text also explains ma

  16. Classical diffusion: theory and simulation codes

    International Nuclear Information System (INIS)

    Grad, H.; Hu, P.N.

    1978-03-01

    A survey is given of the development of classical diffusion theory which arose from the observation of Grad and Hogan that the Pfirsch-Schluter and Neoclassical theories are very special and frequently inapplicable because they require that plasma mass flow be treated as transport rather than as a state variable of the plasma. The subsequent theory, efficient numerical algorithms, and results of various operating codes are described

  17. The significance of classical structures in quantum theories

    International Nuclear Information System (INIS)

    Lowe, M.J.

    1978-09-01

    The implications for the quantum theory of the presence of non-linear classical solutions of the equations of motion are investigated in various model systems under the headings: (1) Canonical quantisation of the soliton in lambdaphi 4 theory in two dimensions. (2) Bound for soliton masses in two dimensional field theories. (3) The canonical quantisation of a soliton like solution in the non-linear schrodinger equation. (4) The significance of the instanton classical solution in a quantum mechanical system. (U.K.)

  18. Using the thermal diffusion cloud chamber to study the ion-induced nucleation by radon decay

    International Nuclear Information System (INIS)

    Wu, Yefei.

    1991-01-01

    Thermal diffusion cloud chamber is steady-state device and has been extensively used for nucleation research. In order to study the ion-induced nucleation by radon decay, a new chamber was designed with improved both upper and bottom plates, the system of circulating fluid, the gasketting, the temperature measurement and the insulation. An alternative method of using oxygen as carrier gas was examined. Therefore, the heavy carrier gas including nitrogen, oxygen, neon, argon and air can be used to study radon radiolysis-induced nucleation for the water or organic compounds in the TDCC. The effects of the pressure and temperature ranges on the density, supersaturation, temperature and partial pressure profile for the water-oxygen-helium in the TDCC have been examined. Based on the classical theory, the rate profile of ion-induced nucleation by radon decays was calculated and compared with the homogeneous nucleation. From measured indoor concentrations of Volatile Organic Compounds (VOC), thermodynamic theory models were used to assess the possibility that these compounds will form ultrafine particles in indoor air by ion-induced nucleation. The energy, number of molecules and equilibrium radius of clusters have been calculated based on Such and Thomson theories. These two sets of values have been compared. Ion cluster radii corresponding to 1--3 VOC molecules are in range of 3--5 x 10 -8 cm. 43 refs., 18 figs., 5 tabs

  19. Gauge-fields and integrated quantum-classical theory

    International Nuclear Information System (INIS)

    Stapp, H.P.

    1986-01-01

    Physical situations in which quantum systems communicate continuously to their classically described environment are not covered by contemporary quantum theory, which requires a temporary separation of quantum degrees of freedom from classical ones. A generalization would be needed to cover these situations. An incomplete proposal is advanced for combining the quantum and classical degrees of freedom into a unified objective description. It is based on the use of certain quantum-classical structures of light that arise from gauge invariance to coordinate the quantum and classical degrees of freedom. Also discussed is the question of where experimenters should look to find phenomena pertaining to the quantum-classical connection. 17 refs

  20. A Model of Silicate Grain Nucleation and Growth in Circumstellar Outflows

    Science.gov (United States)

    Paquette, John A.; Ferguson, Frank T.; Nuth, Joseph A., III

    2011-01-01

    Based on its abundance, high bond energy, and recent measurements of its vapor pressure SiO is a natural candidate for dust nucleation in circumstellar outflows around asymptotic giant branch stars. In this paper, we describe a model of the nucleation and growth of silicate dust in such outflows. The sensitivity of the model to varying choices of poorly constrained chemical parameters is explored, and the merits of using scaled rather than classical nucleation theory are briefly considered, An elaboration of the model that includes magnesium and iron as growth species is then presented and discussed. The composition of the bulk of the grains derived from the model is consistent with olivines and pyroxenes, but somewhat metal-rich grains and very small, nearly pure SiO grains are also produced,

  1. Classical field theory. On electrodynamics, non-Abelian gauge theories and gravitation. 2. ed.

    Energy Technology Data Exchange (ETDEWEB)

    Scheck, Florian

    2018-04-01

    Scheck's successful textbook presents a comprehensive treatment, ideally suited for a one-semester course. The textbook describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell's theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell's theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams. Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell's theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary of semi-Riemannian geometry as the framework for the classical field theory of gravitation. The chapter concludes with a discussion of the Schwarzschild solution of Einstein's equations and the classical tests of general relativity. The new concept of this edition presents the content divided into two tracks: the fast track for master's students, providing the essentials, and the intensive track for all wanting to get in depth knowledge of the field. Cleary labeled material and sections guide students through the preferred level of treatment. Numerous problems and worked examples will provide successful access to Classical Field Theory.

  2. Chance, determinism and the classical theory of probability.

    Science.gov (United States)

    Vasudevan, Anubav

    2018-02-01

    This paper situates the metaphysical antinomy between chance and determinism in the historical context of some of the earliest developments in the mathematical theory of probability. Since Hacking's seminal work on the subject, it has been a widely held view that the classical theorists of probability were guilty of an unwitting equivocation between a subjective, or epistemic, interpretation of probability, on the one hand, and an objective, or statistical, interpretation, on the other. While there is some truth to this account, I argue that the tension at the heart of the classical theory of probability is not best understood in terms of the duality between subjective and objective interpretations of probability. Rather, the apparent paradox of chance and determinism, when viewed through the lens of the classical theory of probability, manifests itself in a much deeper ambivalence on the part of the classical probabilists as to the rational commensurability of causal and probabilistic reasoning. Copyright © 2017 Elsevier Ltd. All rights reserved.

  3. Structuring effects in binary nucleation : Molecular dynamics simulatons and coarse-grained nucleation theory

    NARCIS (Netherlands)

    Braun, S.; Kraska, T.; Kalikmanov, V.I.

    2013-01-01

    Binary clusters formed by vapor-liquid nucleation are frequently nonhomogeneous objects in which components are not well mixed. The structure of a cluster plays an important role in nucleation and cluster growth. We demonstrate structuring effects by studying high-pressure nucleation and cluster

  4. Heterogeneous ice nucleation

    Energy Technology Data Exchange (ETDEWEB)

    Bogdan, A. [Helsinki Univ. (Finland). Dept. of Physics

    1994-12-31

    The classical theory of heterogenous ice nucleation is reviewed in detail. The modelling of ice nucleation in the adsorbed water films on natural particles by analogous ice nucleation in adsorbed water films on the walls of porous media is discussed. Ice nucleation in adsorbed films of purewater and the HNO{sub 3}/H{sub 2}0 binary system on the surface of porous aerosol (SiO{sub 2}) was investigated using the method of NMR spectroscopy. The median freezing temperature and freezing temperature region were shown to be highly sensitive both to the average thickness of the adsorbed films and to the amount of adsorbed nitric acid. The character of the ice phase formation tends to approach that of bulk liquid with increasing adsorbed film thickness. Under the given conditions the thickness of the adsorbed films decreases with an increasing amount of adsorbed nitric acid molecules The molar concentration of nitric acid in the adsorbed films is very small (of the order of 10{sup -}3 10{sup -}2 (M/l)). Nitric acid molecules tend to adsorb on the surface of aerosol to a greater extent than in subsequent layers. The concentration is greatest in layers situated close to the surface and sharply decreases with the distance from the surface. The difference between the median freezing temperatures for adsorbed pure water and for the binary system was found to be about 9 K for films of equal thickness. This is about 150 times greater than the difference between the median freezing temperatures of bulk pure water and a solution with the same concentration of nitric acid. (orig.)

  5. Current state of aerosol nucleation parameterizations for air-quality and climate modeling

    Science.gov (United States)

    Semeniuk, Kirill; Dastoor, Ashu

    2018-04-01

    Aerosol nucleation parameterization models commonly used in 3-D air quality and climate models have serious limitations. This includes classical nucleation theory based variants, empirical models and other formulations. Recent work based on detailed and extensive laboratory measurements and improved quantum chemistry computation has substantially advanced the state of nucleation parameterizations. In terms of inorganic nucleation involving BHN and THN including ion effects these new models should be considered as worthwhile replacements for the old models. However, the contribution of organic species to nucleation remains poorly quantified. New particle formation consists of a distinct post-nucleation growth regime which is characterized by a strong Kelvin curvature effect and is thus dependent on availability of very low volatility organic species or sulfuric acid. There have been advances in the understanding of the multiphase chemistry of biogenic and anthropogenic organic compounds which facilitate to overcome the initial aerosol growth barrier. Implementation of processes influencing new particle formation is challenging in 3-D models and there is a lack of comprehensive parameterizations. This review considers the existing models and recent innovations.

  6. The role of confined collagen geometry in decreasing nucleation energy barriers to intrafibrillar mineralization.

    Science.gov (United States)

    Kim, Doyoon; Lee, Byeongdu; Thomopoulos, Stavros; Jun, Young-Shin

    2018-03-06

    Mineralization of collagen is critical for the mechanical functions of bones and teeth. Calcium phosphate nucleation in collagenous structures follows distinctly different patterns in highly confined gap regions (nanoscale confinement) than in less confined extrafibrillar spaces (microscale confinement). Although the mechanism(s) driving these differences are still largely unknown, differences in the free energy for nucleation may explain these two mineralization behaviors. Here, we report on experimentally obtained nucleation energy barriers to intra- and extrafibrillar mineralization, using in situ X-ray scattering observations and classical nucleation theory. Polyaspartic acid, an extrafibrillar nucleation inhibitor, increases interfacial energies between nuclei and mineralization fluids. In contrast, the confined gap spaces inside collagen fibrils lower the energy barrier by reducing the reactive surface area of nuclei, decreasing the surface energy penalty. The confined gap geometry, therefore, guides the two-dimensional morphology and structure of bioapatite and changes the nucleation pathway by reducing the total energy barrier.

  7. Nucleation behavior of melted Bi films at cooling rates from 101 to 104 K/s studied by combining scanning AC and DC nano-calorimetry techniques

    International Nuclear Information System (INIS)

    Xiao, Kechao; Vlassak, Joost J.

    2015-01-01

    Highlights: • We proposed a general data reduction scheme that combines scanning AC and DC calorimetry results for the study of reaction kinetics. • Calorimetry measurements at cooling rates ranging from 30 K/s to 20,000 K/s were achieved. • Upon initial melting, the Bi thin-film sample breaks up into thousands of isolated islands, and highly repeatable nucleation behavior is observed. • The nucleation rate of melted Bi is calculated, which can be well described by classical nucleation theory over a wide range of cooling rates. - Abstract: We study the nucleation behavior of undercooled liquid Bi at cooling rates ranging from 10 1 to 10 4 K/s using a combination of scanning DC and AC nano-calorimetry techniques. Upon initial melting, the Bi thin-film sample breaks up into silicon nitride-coated isolated islands. The number of islands in a typical sample is sufficiently large that highly repeatable nucleation behavior is observed, despite the stochastic nature of the nucleation process. We establish a data reduction technique to evaluate the nucleation rate from DC and AC calorimetry results. The results show that the driving force for the nucleation of melted Bi is well described by classical nucleation theory over a wide range of cooling rates. The proposed technique provides a unique and efficient way to examine nucleation kinetics with cooling rates over several orders of magnitude. The technique is quite general and can be used to evaluate reaction kinetics in other materials

  8. Classical field theory on electrodynamics, non-abelian gauge theories and gravitation

    CERN Document Server

    Scheck, Florian

    2018-01-01

    Scheck’s successful textbook presents a comprehensive treatment, ideally suited for a one-semester course. The textbook describes Maxwell's equations first in their integral, directly testable form, then moves on to their local formulation. The first two chapters cover all essential properties of Maxwell's equations, including their symmetries and their covariance in a modern notation. Chapter 3 is devoted to Maxwell's theory as a classical field theory and to solutions of the wave equation. Chapter 4 deals with important applications of Maxwell's theory. It includes topical subjects such as metamaterials with negative refraction index and solutions of Helmholtz' equation in paraxial approximation relevant for the description of laser beams. Chapter 5 describes non-Abelian gauge theories from a classical, geometric point of view, in analogy to Maxwell's theory as a prototype, and culminates in an application to the U(2) theory relevant for electroweak interactions. The last chapter 6 gives a concise summary...

  9. Experimental assessment of unvalidated assumptions in classical plasticity theory.

    Energy Technology Data Exchange (ETDEWEB)

    Brannon, Rebecca Moss (University of Utah, Salt Lake City, UT); Burghardt, Jeffrey A. (University of Utah, Salt Lake City, UT); Bauer, Stephen J.; Bronowski, David R.

    2009-01-01

    This report investigates the validity of several key assumptions in classical plasticity theory regarding material response to changes in the loading direction. Three metals, two rock types, and one ceramic were subjected to non-standard loading directions, and the resulting strain response increments were displayed in Gudehus diagrams to illustrate the approximation error of classical plasticity theories. A rigorous mathematical framework for fitting classical theories to the data, thus quantifying the error, is provided. Further data analysis techniques are presented that allow testing for the effect of changes in loading direction without having to use a new sample and for inferring the yield normal and flow directions without having to measure the yield surface. Though the data are inconclusive, there is indication that classical, incrementally linear, plasticity theory may be inadequate over a certain range of loading directions. This range of loading directions also coincides with loading directions that are known to produce a physically inadmissible instability for any nonassociative plasticity model.

  10. Heterogeneous nucleation on convex spherical substrate surfaces: A rigorous thermodynamic formulation of Fletcher's classical model and the new perspectives derived.

    Science.gov (United States)

    Qian, Ma; Ma, Jie

    2009-06-07

    Fletcher's spherical substrate model [J. Chem. Phys. 29, 572 (1958)] is a basic model for understanding the heterogeneous nucleation phenomena in nature. However, a rigorous thermodynamic formulation of the model has been missing due to the significant complexities involved. This has not only left the classical model deficient but also likely obscured its other important features, which would otherwise have helped to better understand and control heterogeneous nucleation on spherical substrates. This work presents a rigorous thermodynamic formulation of Fletcher's model using a novel analytical approach and discusses the new perspectives derived. In particular, it is shown that the use of an intermediate variable, a selected geometrical angle or pseudocontact angle between the embryo and spherical substrate, revealed extraordinary similarities between the first derivatives of the free energy change with respect to embryo radius for nucleation on spherical and flat substrates. Enlightened by the discovery, it was found that there exists a local maximum in the difference between the equivalent contact angles for nucleation on spherical and flat substrates due to the existence of a local maximum in the difference between the shape factors for nucleation on spherical and flat substrate surfaces. This helps to understand the complexity of the heterogeneous nucleation phenomena in a practical system. Also, it was found that the unfavorable size effect occurs primarily when R<5r( *) (R: radius of substrate and r( *): critical embryo radius) and diminishes rapidly with increasing value of R/r( *) beyond R/r( *)=5. This finding provides a baseline for controlling the size effects in heterogeneous nucleation.

  11. A nucleation theory of cell surface capping

    International Nuclear Information System (INIS)

    Coutsias, E.A.; Wester, M.J.; Perelson, A.S.

    1997-01-01

    We propose a new theory of cell surface capping based on the principles of nucleation. When antibody interacts with cell surface molecules, the molecules initially form small aggregates called patches that later coalesce into a large aggregate called a cap. While a cap can form by patches being pulled together by action of the cell''s cytoskeleton, in the case of some molecules, disruption of the cytoskeleton does not prevent cap formation. Diffusion of large aggregates on a cell surface is slow, and thus we propose that a cap can form solely through the diffusion of small aggregates containing just one or a few cell surface molecules. Here we consider the extreme case in which single molecules are mobile, but aggregates of all larger sizes are immobile. We show that a set of patches in equilibrium with a open-quotes seaclose quotes of free cell surface molecules can undergo a nucleation-type phase transition in which the largest patch will bind free cell surface molecules, deplete the concentration of such molecules in the open-quotes seaclose quotes and thus cause the other patches to shrink in size. We therefore show that a cap can form without patches having to move, collide with each other, and aggregate

  12. Overview: Understanding nucleation phenomena from simulations of lattice gas models

    International Nuclear Information System (INIS)

    Binder, Kurt; Virnau, Peter

    2016-01-01

    Monte Carlo simulations of homogeneous and heterogeneous nucleation in Ising/lattice gas models are reviewed with an emphasis on the general insight gained on the mechanisms by which metastable states decay. Attention is paid to the proper distinction of particles that belong to a cluster (droplet), that may trigger a nucleation event, from particles in its environment, a problem crucial near the critical point. Well below the critical point, the lattice structure causes an anisotropy of the interface tension, and hence nonspherical droplet shapes result, making the treatment nontrivial even within the conventional classical theory of homogeneous nucleation. For temperatures below the roughening transition temperature facetted crystals rather than spherical droplets result. The possibility to find nucleation barriers from a thermodynamic analysis avoiding a cluster identification on the particle level is discussed, as well as the question of curvature corrections to the interfacial tension. For the interpretation of heterogeneous nucleation at planar walls, knowledge of contact angles and line tensions is desirable, and methods to extract these quantities from simulations will be mentioned. Finally, also the problem of nucleation near the stability limit of metastable states and the significance of the spinodal curve will be discussed, in the light of simulations of Ising models with medium range interactions.

  13. Correlation between thermodynamic anomalies and pathways of ice nucleation in supercooled water

    International Nuclear Information System (INIS)

    Singh, Rakesh S.; Bagchi, Biman

    2014-01-01

    The well-known classical nucleation theory (CNT) for the free energy barrier towards formation of a nucleus of critical size of the new stable phase within the parent metastable phase fails to take into account the influence of other metastable phases having density/order intermediate between the parent metastable phase and the final stable phase. This lacuna can be more serious than capillary approximation or spherical shape assumption made in CNT. This issue is particularly significant in ice nucleation because liquid water shows rich phase diagram consisting of two (high and low density) liquid phases in supercooled state. The explanations of thermodynamic and dynamic anomalies of supercooled water often invoke the possible influence of a liquid-liquid transition between two metastable liquid phases. To investigate both the role of thermodynamic anomalies and presence of distinct metastable liquid phases in supercooled water on ice nucleation, we employ density functional theoretical approach to find nucleation free energy barrier in different regions of phase diagram. The theory makes a number of striking predictions, such as a dramatic lowering of nucleation barrier due to presence of a metastable intermediate phase and crossover in the dependence of free energy barrier on temperature near liquid-liquid critical point. These predictions can be tested by computer simulations as well as by controlled experiments

  14. The contrasting roles of Planck's constant in classical and quantum theories

    Science.gov (United States)

    Boyer, Timothy H.

    2018-04-01

    We trace the historical appearance of Planck's constant in physics, and we note that initially the constant did not appear in connection with quanta. Furthermore, we emphasize that Planck's constant can appear in both classical and quantum theories. In both theories, Planck's constant sets the scale of atomic phenomena. However, the roles played in the foundations of the theories are sharply different. In quantum theory, Planck's constant is crucial to the structure of the theory. On the other hand, in classical electrodynamics, Planck's constant is optional, since it appears only as the scale factor for the (homogeneous) source-free contribution to the general solution of Maxwell's equations. Since classical electrodynamics can be solved while taking the homogenous source-free contribution in the solution as zero or non-zero, there are naturally two different theories of classical electrodynamics, one in which Planck's constant is taken as zero and one where it is taken as non-zero. The textbooks of classical electromagnetism present only the version in which Planck's constant is taken to vanish.

  15. A survey on classical minimal surface theory

    CERN Document Server

    Meeks, William H

    2012-01-01

    Meeks and Pérez present a survey of recent spectacular successes in classical minimal surface theory. The classification of minimal planar domains in three-dimensional Euclidean space provides the focus of the account. The proof of the classification depends on the work of many currently active leading mathematicians, thus making contact with much of the most important results in the field. Through the telling of the story of the classification of minimal planar domains, the general mathematician may catch a glimpse of the intrinsic beauty of this theory and the authors' perspective of what is happening at this historical moment in a very classical subject. This book includes an updated tour through some of the recent advances in the theory, such as Colding-Minicozzi theory, minimal laminations, the ordering theorem for the space of ends, conformal structure of minimal surfaces, minimal annular ends with infinite total curvature, the embedded Calabi-Yau problem, local pictures on the scale of curvature and t...

  16. Lectures on classical and quantum theory of fields

    CERN Document Server

    Arodz, Henryk

    2017-01-01

    This textbook addresses graduate students starting to specialize in theoretical physics. It provides didactic introductions to the main topics in the theory of fields, while taking into account the contemporary view of the subject. The student will find concise explanations of basic notions essential for applications of the theory of fields as well as for frontier research in theoretical physics. One third of the book is devoted to classical fields. Each chapter contains exercises of varying degree of difficulty with hints or solutions, plus summaries and worked examples as useful. It aims to deliver a unique combination of classical and quantum field theory in one compact course.

  17. Two-Dimensional Nucleation on the Terrace of Colloidal Crystals with Added Polymers.

    Science.gov (United States)

    Nozawa, Jun; Uda, Satoshi; Guo, Suxia; Hu, Sumeng; Toyotama, Akiko; Yamanaka, Junpei; Okada, Junpei; Koizumi, Haruhiko

    2017-04-04

    Understanding nucleation dynamics is important both fundamentally and technologically in materials science and other scientific fields. Two-dimensional (2D) nucleation is the predominant growth mechanism in colloidal crystallization, in which the particle interaction is attractive, and has recently been regarded as a promising method to fabricate varieties of complex nanostructures possessing innovative functionality. Here, polymers are added to a colloidal suspension to generate a depletion attractive force, and the detailed 2D nucleation process on the terrace of the colloidal crystals is investigated. In the system, we first measured the nucleation rate at various area fractions of particles on the terrace, ϕ area . In situ observations at single-particle resolution revealed that nucleation behavior follows the framework of classical nucleation theory (CNT), such as single-step nucleation pathway and existence of critical size. Characteristic nucleation behavior is observed in that the nucleation and growth stage are clearly differentiated. When many nuclei form in a small area of the terrace, a high density of kink sites of once formed islands makes growth more likely to occur than further nucleation because nucleation has a higher energy barrier than growth. The steady-state homogeneous 2D nucleation rate, J, and the critical size of nuclei, r*, are measured by in situ observations based on the CNT, which enable us to obtain the step free energy, γ, which is an important parameter for characterizing the nucleation process. The γ value is found to change according to the strength of attraction, which is tuned by the concentration of the polymer as a depletant.

  18. Assessment of the theoretical basis of the Rule of Additivity for the nucleation incubation time during continuous cooling

    International Nuclear Information System (INIS)

    Zhu, Y.T.; Lowe, T.C.; Asaro, R.J.

    1997-01-01

    The rule of additivity was first proposed by Scheil and Steinberg for predicting the incubation time for nucleation of solid phases during continuous-cooling phase transformations, and has since been widely used for both the nucleation incubation and the entire process of phase transformation. While having been successfully used to calculate the transformed volume fraction during continuous cooling in many steel alloy systems, there is experimental evidence that shows rule of additivity to be invalid for describing the incubation time for nucleation. Attempts to prove the validity of the rule of additivity for the incubation time have not met with much success, and much confusion still exists about its applicability to the incubation time. This article investigates the additivity of the consumption of the incubation time for nucleation during continuous cooling through an analysis based upon classical nucleation theory. It is rigorously demonstrated that the rule of additivity is invalid for the incubation time for nucleation. However, in practice, the relative error caused by using the rule of additivity could be very small in many cases due to the resolution limit of current experimental techniques. The present theory provides an explanation for the failure of the rule of additivity in predicting the incubation time for nucleation during continuous cooling. copyright 1997 American Institute of Physics

  19. Electrocrystallisation of zinc from acidic sulphate baths; A nucleation and crystal growth process

    International Nuclear Information System (INIS)

    Vasilakopoulos, D.; Bouroushian, M.; Spyrellis, N.

    2009-01-01

    The electrochemical nucleation and growth of zinc on low-carbon steel from acidic (pH 2.0-4.5) baths containing ZnSO 4 , NaCl, and H 3 BO 3 , was studied by means of chronoamperometry at various cathodic potentials under a charge-transfer controlled regime. It is shown that at overpotentials in the range 0.30-0.55 V (negative to the Zn 2+ /Zn redox value) the electrodeposition proceeds by instantaneous three-dimensional nucleation, which turns to progressive at higher overpotentials and/or very acidic baths. At low cathodic overpotentials (<0.30 V), a two-dimensional contribution limited by the incorporation of Zn ad-atoms in the developing lattice becomes significant at the early stages of deposition, and is more progressive in type the more acidic is the bath pH. Nucleation rate constants were calculated and correlated analytically with the respective potentials, using the classical theory of heterogeneous nucleation, which though fails to lead to reasonable values for the critical nucleus size

  20. Deviation from equilibrium conditions in molecular dynamic simulations of homogeneous nucleation.

    Science.gov (United States)

    Halonen, Roope; Zapadinsky, Evgeni; Vehkamäki, Hanna

    2018-04-28

    We present a comparison between Monte Carlo (MC) results for homogeneous vapour-liquid nucleation of Lennard-Jones clusters and previously published values from molecular dynamics (MD) simulations. Both the MC and MD methods sample real cluster configuration distributions. In the MD simulations, the extent of the temperature fluctuation is usually controlled with an artificial thermostat rather than with more realistic carrier gas. In this study, not only a primarily velocity scaling thermostat is considered, but also Nosé-Hoover, Berendsen, and stochastic Langevin thermostat methods are covered. The nucleation rates based on a kinetic scheme and the canonical MC calculation serve as a point of reference since they by definition describe an equilibrated system. The studied temperature range is from T = 0.3 to 0.65 ϵ/k. The kinetic scheme reproduces well the isothermal nucleation rates obtained by Wedekind et al. [J. Chem. Phys. 127, 064501 (2007)] using MD simulations with carrier gas. The nucleation rates obtained by artificially thermostatted MD simulations are consistently lower than the reference nucleation rates based on MC calculations. The discrepancy increases up to several orders of magnitude when the density of the nucleating vapour decreases. At low temperatures, the difference to the MC-based reference nucleation rates in some cases exceeds the maximal nonisothermal effect predicted by classical theory of Feder et al. [Adv. Phys. 15, 111 (1966)].

  1. Thermodynamic Derivation of the Activation Energy for Ice Nucleation

    Science.gov (United States)

    Barahona, D.

    2015-01-01

    Cirrus clouds play a key role in the radiative and hydrological balance of the upper troposphere. Their correct representation in atmospheric models requires an understanding of the microscopic processes leading to ice nucleation. A key parameter in the theoretical description of ice nucleation is the activation energy, which controls the flux of water molecules from the bulk of the liquid to the solid during the early stages of ice formation. In most studies it is estimated by direct association with the bulk properties of water, typically viscosity and self-diffusivity. As the environment in the ice-liquid interface may differ from that of the bulk, this approach may introduce bias in calculated nucleation rates. In this work a theoretical model is proposed to describe the transfer of water molecules across the ice-liquid interface. Within this framework the activation energy naturally emerges from the combination of the energy required to break hydrogen bonds in the liquid, i.e., the bulk diffusion process, and the work dissipated from the molecular rearrangement of water molecules within the ice-liquid interface. The new expression is introduced into a generalized form of classical nucleation theory. Even though no nucleation rate measurements are used to fit any of the parameters of the theory the predicted nucleation rate is in good agreement with experimental results, even at temperature as low as 190 K, where it tends to be underestimated by most models. It is shown that the activation energy has a strong dependency on temperature and a weak dependency on water activity. Such dependencies are masked by thermodynamic effects at temperatures typical of homogeneous freezing of cloud droplets; however, they may affect the formation of ice in haze aerosol particles. The new model provides an independent estimation of the activation energy and the homogeneous ice nucleation rate, and it may help to improve the interpretation of experimental results and the

  2. k-Cosymplectic Classical Field Theories: Tulczyjew and Skinner-Rusk Formulations

    Science.gov (United States)

    Rey, Angel M.; Román-Roy, Narciso; Salgado, Modesto; Vilariño, Silvia

    2012-06-01

    The k-cosymplectic Lagrangian and Hamiltonian formalisms of first-order classical field theories are reviewed and completed. In particular, they are stated for singular and almost-regular systems. Subsequently, several alternative formulations for k-cosymplectic first-order field theories are developed: First, generalizing the construction of Tulczyjew for mechanics, we give a new interpretation of the classical field equations. Second, the Lagrangian and Hamiltonian formalisms are unified by giving an extension of the Skinner-Rusk formulation on classical mechanics.

  3. k-Cosymplectic Classical Field Theories: Tulczyjew and Skinner–Rusk Formulations

    International Nuclear Information System (INIS)

    Rey, Angel M.; Román-Roy, Narciso; Salgado, Modesto; Vilariño, Silvia

    2012-01-01

    The k-cosymplectic Lagrangian and Hamiltonian formalisms of first-order classical field theories are reviewed and completed. In particular, they are stated for singular and almost-regular systems. Subsequently, several alternative formulations for k-cosymplectic first-order field theories are developed: First, generalizing the construction of Tulczyjew for mechanics, we give a new interpretation of the classical field equations. Second, the Lagrangian and Hamiltonian formalisms are unified by giving an extension of the Skinner–Rusk formulation on classical mechanics.

  4. Evaluation of surface tension and Tolman length as a function of droplet radius from experimental nucleation rate and supersaturation ratio: metal vapor homogeneous nucleation.

    Science.gov (United States)

    Onischuk, A A; Purtov, P A; Baklanov, A M; Karasev, V V; Vosel, S V

    2006-01-07

    Zinc and silver vapor homogeneous nucleations are studied experimentally at the temperature from 600 to 725 and 870 K, respectively, in a laminar flow diffusion chamber with Ar as a carrier gas at atmospheric pressure. The size, shape, and concentration of aerosol particles outcoming the diffusion chamber are analyzed by a transmission electron microscope and an automatic diffusion battery. The wall deposit is studied by a scanning electron microscope (SEM). Using SEM data the nucleation rate for both Zn and Ag is estimated as 10(10) cm(-3) s(-1). The dependence of critical supersaturation on temperature for Zn and Ag measured in this paper as well as Li, Na, Cs, Ag, Mg, and Hg measured elsewhere is analyzed. To this aim the classical nucleation theory is extended by the dependence of surface tension on the nucleus radius. The preexponent in the formula for the vapor nucleation rate is derived using the formula for the work of formation of noncritical embryo [obtained by Nishioka and Kusaka [J. Chem. Phys. 96, 5370 (1992)] and later by Debenedetti and Reiss [J. Chem. Phys. 108, 5498 (1998)

  5. Nucleation and dissociation of nano-particles in gas phase; Nucleation et evaporation de nanoparticules en phase gazeuse

    Energy Technology Data Exchange (ETDEWEB)

    Feiden, P

    2007-09-15

    This work deals with the study of nano-particles formation in gas phase and their dissociation pathways after an optical excitation. The clusters formation decomposes in two steps: a seed is formed (nucleation phase) and sticks atoms during its propagation in a sodium atomic vapor (growth phase). Those two steps have been observed separately for homogeneous Na{sub n} and heterogeneous Na{sub n}X particles (X = (NaOH){sub 2} or (Na{sub 2}O){sub 2}). The growth mechanism is well interpreted by a Monte Carlo simulation taking into account an accretion mechanism with hard-sphere cross section. The homogeneous nucleation mechanism has been highlighted by a direct comparison with the Classical Nucleation Theory predictions. The clusters fragmentation of ionic Na{sup +}(NaOH){sub p} et Na{sup +}(NaF){sub p} particles is studied in the second part. The way clusters fragment with size when they are excited optically is compared with theoretical previsions: this highlights the existence of an energetic barrier for special size of clusters. Finally, the fragmentation of doubly charged Na{sup +} Na{sup +} (NaOH){sub p} clusters shows a competition between the fission into two single charged fragments and the unimolecular evaporation of a neutral fragment. (author)

  6. The influence of ion hydration on nucleation and growth of LiF crystals in aqueous solution.

    Science.gov (United States)

    Lanaro, G; Patey, G N

    2018-01-14

    Molecular dynamics (MD) simulations are employed to investigate crystal nucleation and growth in oversaturated aqueous LiF solutions. Results obtained for a range of temperatures provide evidence that the rate of crystal growth is determined by a substantial energy barrier (∼49 kJ mol -1 ) related to the loss of water from the ion hydration shells. Employing direct MD simulations, we do not observe spontaneous nucleation of LiF crystals at 300 K, but nucleation is easily observable in NVT simulations at 500 K. This contrasts with the NaCl case, where crystal nucleation is directly observed in similar simulations at 300 K. Based on these observations, together with a detailed analysis of ion clustering in metastable LiF solutions, we argue that the ion dehydration barrier also plays a key role in crystal nucleation. The hydration of the relatively small Li + and F - ions strongly influences the probability of forming large, crystal-like ion clusters, which are a necessary precursor to nucleation. This important factor is not accounted for in classical nucleation theory.

  7. Numeric implementation of a nucleation, growth and transport model for helium bubbles in lead-lithium HCLL breeding blanket channels: Theory and code development

    Energy Technology Data Exchange (ETDEWEB)

    Batet, L., E-mail: lluis.batet@upc.edu [Technical University of Catalonia (UPC), Energy and Radiation Studies Research Group (GREENER), Technology for Fusion T4F, Barcelona (Spain); UPC, Department of Physics and Nuclear Engineering (DFEN), ETSEIB, Av. Diagonal 647, 08028 Barcelona (Spain); Fradera, J. [Technical University of Catalonia (UPC), Energy and Radiation Studies Research Group (GREENER), Technology for Fusion T4F, Barcelona (Spain); UPC, Department of Physics and Nuclear Engineering (DFEN), ETSEIB, Av. Diagonal 647, 08028 Barcelona (Spain); Valls, E. Mas de les [Technical University of Catalonia (UPC), Energy and Radiation Studies Research Group (GREENER), Technology for Fusion T4F, Barcelona (Spain); UPC, Department of Heat Engines (DMMT), ETSEIB, Av. Diagonal 647, 08028 Barcelona (Spain); Sedano, L.A. [EURATOM-CIEMAT Association, Fusion Technology Division, Av. Complutense 22, 28040 Madrid (Spain)

    2011-06-15

    Large helium (He) production rates in liquid metal breeding blankets of a DT fusion reactor might have a significant influence in the system design. Low He solubility together with high local concentrations may create the conditions for He cavitation, which would have an impact in the components performance. The paper states that such a possibility is not remote in a helium cooled lithium-lead breeding blanket design. A model based on the Classical Nucleation Theory (CNT) has been developed and implemented in order to have a specific tool able to simulate HCLL systems and identify the key parameters and sensitivities. The nucleation and growth model has been implemented in the open source CFD code OpenFOAM so that transport of dissolved atomic He and nucleated He bubbles can be simulated. At the current level of development it is assumed that void fraction is small enough not to affect either the hydrodynamics or the properties of the liquid metal; thus, bubbles can be represented by means of a passive scalar. He growth and transport has been implemented using the mean radius approach in order to save computational time. Limitations and capabilities of the model are shown by means of zero-dimensional simulation and sensitivity analysis under HCLL breeding unit conditions.

  8. Optimal search behavior and classic foraging theory

    International Nuclear Information System (INIS)

    Bartumeus, F; Catalan, J

    2009-01-01

    Random walk methods and diffusion theory pervaded ecological sciences as methods to analyze and describe animal movement. Consequently, statistical physics was mostly seen as a toolbox rather than as a conceptual framework that could contribute to theory on evolutionary biology and ecology. However, the existence of mechanistic relationships and feedbacks between behavioral processes and statistical patterns of movement suggests that, beyond movement quantification, statistical physics may prove to be an adequate framework to understand animal behavior across scales from an ecological and evolutionary perspective. Recently developed random search theory has served to critically re-evaluate classic ecological questions on animal foraging. For instance, during the last few years, there has been a growing debate on whether search behavior can include traits that improve success by optimizing random (stochastic) searches. Here, we stress the need to bring together the general encounter problem within foraging theory, as a mean for making progress in the biological understanding of random searching. By sketching the assumptions of optimal foraging theory (OFT) and by summarizing recent results on random search strategies, we pinpoint ways to extend classic OFT, and integrate the study of search strategies and its main results into the more general theory of optimal foraging.

  9. Bulk liquid undercooling and nucleation in nickel

    Energy Technology Data Exchange (ETDEWEB)

    Bokeloh, Joachim; Moros, Anna; Wilde, Gerhard [Institut fuer Materialphysik, Westfaelische Wilhelms-Universitaet Muenster (Germany)

    2010-07-01

    While classical nucleation theory is widely accepted textbook knowledge, it is somewhat lacking with regard to the atomistic details of the nucleation and growth mechanisms. Right now, there are many efforts in exploring these details with computational methods. However, only few experimental methods that can corroborate these results are available. The best known of these experimental methods are containerless processing in levitation melting and the investigation of fine droplet dispersions. We present here data on the liquid undercooling behaviour of Ni obtained by repeated melting and crystallization in a DTA. This method allows to acquire a statistically meaningful data set under clean and reproducible conditions, while still allowing reasonable sample sizes, thus combining several advantages of the two methods mentioned above. Ni was chosen as a model system because it shows good levels of undercooling and because it is well suited for computer simulations due to its relatively low number of electrons.

  10. New trends in the nucleation research

    Science.gov (United States)

    Anisimov, M. P.; Hopke, P. K.

    2017-09-01

    During the last half of century the most of efforts have been directed towards small molecule system modeling using intermolecular potentials. Summarizing the nucleation theory, it can be concluded that the nowadays theory is far from complete. The vapor-gas nucleation theory can produce values that deviate from the experimental results by several orders of magnitude currently. Experiments on the vapor-gas nucleation rate measurements using different devices show significant inconsistencies in the measured rates as well. Theoretical results generally are quite reasonable for sufficiently low vapor nucleation rates where the capillary approximation is applicable. In the present research the advantages and current problems of the vapor-gas nucleation experiments are discussed briefly and a view of the future studies is presented. Using the brake points of the first derivative for the nucleation rate surface as markers of the critical embryos phase change is fresh idea to show the gas-pressure effect for the nucleating vapor-gas systems. To test the accuracy of experimental techniques, it is important to have a standard system that can be measured over a range of nucleation conditions. Several results illustrate that high-pressure techniques are needed to study multi-channel nucleation. In practical applications, parametric theories can be used for the systems of interest. However, experimental measurements are still the best source of information on nucleation rates. Experiments are labor intensive and costly, and thus, it is useful to extend the value of limited experimental measurements to a broader range of nucleation conditions. Only limited experimental data one needs for use in normalizing the slopes of the linearized nucleation rate surfaces. The nucleation rate surface is described in terms of steady-state nucleation rates. It is supposed that several new measuring systems, such as High Pressure Flow Diffusion Chamber for pressure limit up to 150 bar will be

  11. NUCLEATION STUDIES OF GOLD ON CARBON ELECTRODES

    Directory of Open Access Journals (Sweden)

    S. SOBRI

    2008-04-01

    Full Text Available Interest has grown in developing non-toxic electrolytes for gold electrodeposition to replace the conventional cyanide-based bath for long term sustainability of gold electroplating. A solution containing thiosulphate and sulphite has been developed specially for microelectronics applications. However, at the end of the electrodeposition process, the spent electrolyte can contain a significant amount of gold in solution. This study has been initiated to investigate the feasibility of gold recovery from a spent thiosulphate-sulphite electrolyte. We have used flat-plate glassy carbon and graphite electrodes to study the mechanism of nucleation and crystal growth of gold deposition from the spent electrolyte. It was found that at the early stages of reduction process, the deposition of gold on glassy carbon exhibits an instantaneous nucleation of non-overlapping particles. At longer times, the particles begin to overlap and the deposition follows a classic progressive nucleation phenomenon. On the other hand, deposition of gold on graphite does not follow the classical nucleation phenomena.

  12. Classical geometry from the quantum Liouville theory

    Science.gov (United States)

    Hadasz, Leszek; Jaskólski, Zbigniew; Piaţek, Marcin

    2005-09-01

    Zamolodchikov's recursion relations are used to analyze the existence and approximations to the classical conformal block in the case of four parabolic weights. Strong numerical evidence is found that the saddle point momenta arising in the classical limit of the DOZZ quantum Liouville theory are simply related to the geodesic length functions of the hyperbolic geometry on the 4-punctured Riemann sphere. Such relation provides new powerful methods for both numerical and analytical calculations of these functions. The consistency conditions for the factorization of the 4-point classical Liouville action in different channels are numerically verified. The factorization yields efficient numerical methods to calculate the 4-point classical action and, by the Polyakov conjecture, the accessory parameters of the Fuchsian uniformization of the 4-punctured sphere.

  13. Classical geometry from the quantum Liouville theory

    International Nuclear Information System (INIS)

    Hadasz, Leszek; Jaskolski, Zbigniew; Piatek, Marcin

    2005-01-01

    Zamolodchikov's recursion relations are used to analyze the existence and approximations to the classical conformal block in the case of four parabolic weights. Strong numerical evidence is found that the saddle point momenta arising in the classical limit of the DOZZ quantum Liouville theory are simply related to the geodesic length functions of the hyperbolic geometry on the 4-punctured Riemann sphere. Such relation provides new powerful methods for both numerical and analytical calculations of these functions. The consistency conditions for the factorization of the 4-point classical Liouville action in different channels are numerically verified. The factorization yields efficient numerical methods to calculate the 4-point classical action and, by the Polyakov conjecture, the accessory parameters of the Fuchsian uniformization of the 4-punctured sphere

  14. How important is biological ice nucleation in clouds on a global scale?

    International Nuclear Information System (INIS)

    Hoose, C; Kristjansson, J E; Burrows, S M

    2010-01-01

    The high ice nucleating ability of some biological particles has led to speculations about living and dead organisms being involved in cloud ice and precipitation formation, exerting a possibly significant influence on weather and climate. In the present study, the role of primary biological aerosol particles (PBAPs) as heterogeneous ice nuclei is investigated with a global model. Emission parametrizations for bacteria, fungal spores and pollen based on recent literature are introduced, as well as an immersion freezing parametrization based on classical nucleation theory and laboratory measurements. The simulated contribution of PBAPs to the global average ice nucleation rate is only 10 -5 %, with an uppermost estimate of 0.6%. At the same time, observed PBAP concentrations in air and biological ice nucleus concentrations in snow are reasonably well captured by the model. This implies that 'bioprecipitation' processes (snow and rain initiated by PBAPs) are of minor importance on the global scale.

  15. Morphology-dependent crossover effects in heterogeneous nucleation of peritectic materials studied via the phase-field method for Al-Ni

    International Nuclear Information System (INIS)

    Siquieri, R; Emmerich, H

    2009-01-01

    The application of phase-field modeling to nucleation as a phenomenon at the nanoscale is justified, if one takes into account the great success of continuum approaches in nanofluidics as proven by the many comparisons to experiments. Employed in this manner it provides an approach allowing us to account for effects of the physical diffuseness of a nucleus' interface and thereby go beyond classical nucleation theory (Granasy and James 2000 J. Chem. Phys. 113 9810; Emmerich and Siquieri 2006 J. Phys.: Condens. Matter 18 11121). Here we extend the focus of previous work in this field and address the question of how far the phase-field method can also be applied to gain further insight into nucleation statistics, in particular the nucleation prefactor appearing in the nucleation rate. In this context we describe in detail a morphology-dependent crossover effect noticeable for the nucleation rate at small driving forces.

  16. The evolving Planck mass in classically scale-invariant theories

    Energy Technology Data Exchange (ETDEWEB)

    Kannike, K.; Raidal, M.; Spethmann, C.; Veermäe, H. [National Institute of Chemical Physics and Biophysics,Rävala 10, 10143 Tallinn (Estonia)

    2017-04-05

    We consider classically scale-invariant theories with non-minimally coupled scalar fields, where the Planck mass and the hierarchy of physical scales are dynamically generated. The classical theories possess a fixed point, where scale invariance is spontaneously broken. In these theories, however, the Planck mass becomes unstable in the presence of explicit sources of scale invariance breaking, such as non-relativistic matter and cosmological constant terms. We quantify the constraints on such classical models from Big Bang Nucleosynthesis that lead to an upper bound on the non-minimal coupling and require trans-Planckian field values. We show that quantum corrections to the scalar potential can stabilise the fixed point close to the minimum of the Coleman-Weinberg potential. The time-averaged motion of the evolving fixed point is strongly suppressed, thus the limits on the evolving gravitational constant from Big Bang Nucleosynthesis and other measurements do not presently constrain this class of theories. Field oscillations around the fixed point, if not damped, contribute to the dark matter density of the Universe.

  17. The evolving Planck mass in classically scale-invariant theories

    Science.gov (United States)

    Kannike, K.; Raidal, M.; Spethmann, C.; Veermäe, H.

    2017-04-01

    We consider classically scale-invariant theories with non-minimally coupled scalar fields, where the Planck mass and the hierarchy of physical scales are dynamically generated. The classical theories possess a fixed point, where scale invariance is spontaneously broken. In these theories, however, the Planck mass becomes unstable in the presence of explicit sources of scale invariance breaking, such as non-relativistic matter and cosmological constant terms. We quantify the constraints on such classical models from Big Bang Nucleosynthesis that lead to an upper bound on the non-minimal coupling and require trans-Planckian field values. We show that quantum corrections to the scalar potential can stabilise the fixed point close to the minimum of the Coleman-Weinberg potential. The time-averaged motion of the evolving fixed point is strongly suppressed, thus the limits on the evolving gravitational constant from Big Bang Nucleosynthesis and other measurements do not presently constrain this class of theories. Field oscillations around the fixed point, if not damped, contribute to the dark matter density of the Universe.

  18. First Measurements of Time-Dependent Nucleation as a Function of Composition in Na2O.2CaO.3SiO2 Glasses

    Science.gov (United States)

    Kelton, K. F.; Narayan, K. Lakshmi

    1996-01-01

    The first measurements in any system of the composition dependence of the time-dependent nucleation rate are presented Nucleation rates of the stoichiometric crystalline phase, Na2O.2CaO.3SiO2, from quenched glasses made with different SiO2 concentrations were determined as a function of temperature and glass composition. A strong compositional dependence of the nucleation rates and a weak dependence for the induction times are observed. Using measured values of the liquidus temperatures and growth velocities as a function of glass composition, these data are shown to be consistent with predictions from the classical theory of nucleation, assuming a composition-dependent interfacial energy.

  19. Classical quantum theory of wobbling modes

    International Nuclear Information System (INIS)

    Onishi, Naoki

    1986-01-01

    Wobbling modes are studied extensively in terms of time-dependent variational theory. Quantum states and their energies are determined by the Bohr-Sommerfeld rule of classical quantization. Numerical calculations are performed for states of 166 Er with vertical strokejvertical stroke=30-40 (h/2π). (orig.)

  20. Tensor algebra over Hilbert space: Field theory in classical phase space

    International Nuclear Information System (INIS)

    Matos Neto, A.; Vianna, J.D.M.

    1984-01-01

    It is shown using tensor algebras, namely Symmetric and Grassmann algebras over Hilbert Space that it is possible to introduce field operators, associated to the Liouville equation of classical statistical mechanics, which are characterized by commutation (for Symmetric) and anticommutation (for Grassmann) rules. The procedure here presented shows by construction that many-particle classical systems admit an algebraic structure similar to that of quantum field theory. It is considered explicitly the case of n-particle systems interacting with an external potential. A new derivation of Schoenberg's result about the equivalence between his field theory in classical phase space and the usual classical statistical mechanics is obtained as a consequence of the algebraic structure of the theory as introduced by our method. (Author) [pt

  1. Characterization of particle states in relativistic classical quantum theory

    International Nuclear Information System (INIS)

    Horwitz, L.P.; Rabin, Y.

    1977-02-01

    Classical and quantum relativistic mechanics are studied. The notion of a ''particle'' is defined in the classical case and the interpretation of mechanics in space-time is clarified. These notions are carried over to the quantum theory, as much as possible. The relation between the results of Feyman's path integral approach and the theory of Horwitz and Piron is discussed. The ''particle'' interpretation is shown to imply an asymptotic condition for scattering. A general method of constructing the dynamical mass spectrum of composite ''particle'' states is discussed. An interference experiment is proposed to affirm the interpretation and applicability of Stueckelberg type wave functions for actual physical phenomena. Some discussion of the relation of this relativistic quantum theory to Feynman's approach to quantum field theory is also given

  2. Classical geometry from the quantum Liouville theory

    Energy Technology Data Exchange (ETDEWEB)

    Hadasz, Leszek [M. Smoluchowski Institute of Physics, Jagellonian University, Reymonta 4, 30-059 Cracow (Poland)]. E-mail: hadasz@th.if.uj.edu.pl; Jaskolski, Zbigniew [Institute of Theoretical Physics, University of WrocIaw, pl. M. Borna, 950-204 WrocIaw (Poland)]. E-mail: jask@ift.uni.wroc.pl; Piatek, Marcin [Institute of Theoretical Physics, University of WrocIaw, pl. M. Borna, 950-204 WrocIaw (Poland)]. E-mail: piatek@ift.uni.wroc.pl

    2005-09-26

    Zamolodchikov's recursion relations are used to analyze the existence and approximations to the classical conformal block in the case of four parabolic weights. Strong numerical evidence is found that the saddle point momenta arising in the classical limit of the DOZZ quantum Liouville theory are simply related to the geodesic length functions of the hyperbolic geometry on the 4-punctured Riemann sphere. Such relation provides new powerful methods for both numerical and analytical calculations of these functions. The consistency conditions for the factorization of the 4-point classical Liouville action in different channels are numerically verified. The factorization yields efficient numerical methods to calculate the 4-point classical action and, by the Polyakov conjecture, the accessory parameters of the Fuchsian uniformization of the 4-punctured sphere.

  3. Classical solutions in lattice gauge theories

    International Nuclear Information System (INIS)

    Mitrjushkin, V.K.

    1996-08-01

    The solutions of the classical equations of motion on a periodic lattice are found which correspond to abelian single and double Dirac sheets. These solutions exist also in non-abelian theories. Possible applications of these solutions to the calculation of gauge dependent and gauge invariant observables are discussed. (orig.)

  4. Assessing difference between classical test theory and item ...

    African Journals Online (AJOL)

    Assessing difference between classical test theory and item response theory methods in scoring primary four multiple choice objective test items. ... All research participants were ranked on the CTT number correct scores and the corresponding IRT item pattern scores from their performance on the PRISMADAT. Wilcoxon ...

  5. Hilbert space theory of classical electrodynamics

    Indian Academy of Sciences (India)

    Hilbert space; Koopman–von Neumann theory; classical electrodynamics. PACS No. 03.50. ... The paper is divided into four sections. Section 2 .... construction of Sudarshan is to be contrasted with that of Koopman and von Neumann. ..... ture from KvN and [16] in this formulation is to define new momentum and coordinate.

  6. The semi classical laser theory and some applications of laser

    International Nuclear Information System (INIS)

    Abdalla, Abbaker Ali

    1995-04-01

    The semi classical laser theory is concerned with the interaction between light and matter in such a way that the matter is treated quantum-mechanically whereas light is treated in terms of the classical electromagnetic equations. In this work the Maxwell-Bloch equations are employed to describe the interaction between light and matter. Applications of the theory as well as different types of lasers are reviewed. (Author)

  7. Atmospheric nucleation: highlights of the EUCAARI project and future directions

    Directory of Open Access Journals (Sweden)

    V.-M. Kerminen

    2010-11-01

    Full Text Available Within the project EUCAARI (European Integrated project on Aerosol Cloud Climate and Air Quality interactions, atmospheric nucleation was studied by (i developing and testing new air ion and cluster spectrometers, (ii conducting homogeneous nucleation experiments for sulphate and organic systems in the laboratory, (iii investigating atmospheric nucleation mechanism under field conditions, and (iv applying new theoretical and modelling tools for data interpretation and development of parameterisations. The current paper provides a synthesis of the obtained results and identifies the remaining major knowledge gaps related to atmospheric nucleation. The most important technical achievement of the project was the development of new instruments for measuring sub-3 nm particle populations, along with the extensive application of these instruments in both the laboratory and the field. All the results obtained during EUCAARI indicate that sulphuric acid plays a central role in atmospheric nucleation. However, also vapours other than sulphuric acid are needed to explain the nucleation and the subsequent growth processes, at least in continental boundary layers. Candidate vapours in this respect are some organic compounds, ammonia, and especially amines. Both our field and laboratory data demonstrate that the nucleation rate scales to the first or second power of the nucleating vapour concentration(s. This agrees with the few earlier field observations, but is in stark contrast with classical thermodynamic nucleation theories. The average formation rates of 2-nm particles were found to vary by almost two orders of magnitude between the different EUCAARI sites, whereas the formation rates of charged 2-nm particles varied very little between the sites. Overall, our observations are indicative of frequent, yet moderate, ion-induced nucleation usually outweighed by much stronger neutral nucleation events in the continental lower troposphere. The most concrete

  8. a Classical Isodual Theory of Antimatter and its Prediction of Antigravity

    Science.gov (United States)

    Santilli, Ruggero Maria

    An inspection of the contemporary physics literature reveals that, while matter is treated at all levels of study, from Newtonian mechanics to quantum field theory, antimatter is solely treated at the level of second quantization. For the purpose of initiating the restoration of full equivalence in the treatment of matter and antimatter in due time, and as the classical foundations of an axiomatically consistent inclusion of gravitation in unified gauge theories recently appeared elsewhere, in this paper we present a classical representation of antimatter which begins at the primitive Newtonian level with corresponding formulations at all subsequent levels. By recalling that charge conjugation of particles into antiparticles is antiautomorphic, the proposed theory of antimatter is based on a new map, called isoduality, which is also antiautomorphic (and more generally, antiisomorphic), yet it is applicable beginning at the classical level and then persists at the quantum level where it becomes equivalent to charge conjugation. We therefore present, apparently for the first time, the classical isodual theory of antimatter, we identify the physical foundations of the theory as being the novel isodual Galilean, special and general relativities, and we show the compatibility of the theory with all available classical experimental data on antimatter. We identify the classical foundations of the prediction of antigravity for antimatter in the field of matter (or vice-versa) without any claim on its validity, and defer its resolution to specifically identified experiments. We identify the novel, classical, isodual electromagnetic waves which are predicted to be emitted by antimatter, the so-called space-time machine based on a novel non-Newtonian geometric propulsion, and other implications of the theory. We also introduce, apparently for the first time, the isodual space and time inversions and show that they are nontrivially different than the conventional ones, thus

  9. Nucleation in As2Se3 glass studied by DSC

    International Nuclear Information System (INIS)

    Svoboda, Roman; Málek, Jiří

    2014-01-01

    Highlights: • Nucleation behavior of As 2 Se 3 glass was studied by DSC in dependence on particle size. • Correlation between the enthalpies of fusion and crystallization were confirmed. • Apart from classical heterogeneous nucleation a second nucleation mechanism was found. • Rapid formation of crystallization centers from a damaged glassy structure occurs. • Mechanical defects seem to partially suppress the CNT nucleation process. - Abstract: Differential scanning calorimetry was used to study nucleation behavior in As 2 Se 3 glass, dependent on particle size. The nucleation process was examined for a series of different coarse powders; the nucleation rate was estimated from the proportion of the crystalline material fraction. The enthalpy of fusion was utilized in this respect, and a correlation between ΔH m and ΔH c was confirmed. Two mechanisms of nucleus formation were found: classical heterogeneous nucleation (following CNT) and so-called “activation” of mechanically-induced defects. The latter appears to represent rapid formation of crystallization centers from a damaged glassy structure, where complete saturation occurs for fine powders in the range of 195–235 °C. A high amount of mechanical defects, on the other hand, was found to partially suppress the CNT nucleation process

  10. Nucleus-size pinning for determination of nucleation free-energy barriers and nucleus geometry

    Science.gov (United States)

    Sharma, Abhishek K.; Escobedo, Fernando A.

    2018-05-01

    Classical Nucleation Theory (CNT) has recently been used in conjunction with a seeding approach to simulate nucleation phenomena at small-to-moderate supersaturation conditions when large free-energy barriers ensue. In this study, the conventional seeding approach [J. R. Espinosa et al., J. Chem. Phys. 144, 034501 (2016)] is improved by a novel, more robust method to estimate nucleation barriers. Inspired by the interfacial pinning approach [U. R. Pedersen, J. Chem. Phys. 139, 104102 (2013)] used before to determine conditions where two phases coexist, the seed of the incipient phase is pinned to a preselected size to iteratively drive the system toward the conditions where the seed becomes a critical nucleus. The proposed technique is first validated by estimating the critical nucleation conditions for the disorder-to-order transition in hard spheres and then applied to simulate and characterize the highly non-trivial (prolate) morphology of the critical crystal nucleus in hard gyrobifastigia. A generalization of CNT is used to account for nucleus asphericity and predict nucleation free-energy barriers for gyrobifastigia. These predictions of nuclei shape and barriers are validated by independent umbrella sampling calculations.

  11. Homogeneous nucleation in supersaturated vapors of methane, ethane, and carbon dioxide predicted by brute force molecular dynamics.

    Science.gov (United States)

    Horsch, Martin; Vrabec, Jadran; Bernreuther, Martin; Grottel, Sebastian; Reina, Guido; Wix, Andrea; Schaber, Karlheinz; Hasse, Hans

    2008-04-28

    Molecular dynamics (MD) simulation is applied to the condensation process of supersaturated vapors of methane, ethane, and carbon dioxide. Simulations of systems with up to a 10(6) particles were conducted with a massively parallel MD program. This leads to reliable statistics and makes nucleation rates down to the order of 10(30) m(-3) s(-1) accessible to the direct simulation approach. Simulation results are compared to the classical nucleation theory (CNT) as well as the modification of Laaksonen, Ford, and Kulmala (LFK) which introduces a size dependence of the specific surface energy. CNT describes the nucleation of ethane and carbon dioxide excellently over the entire studied temperature range, whereas LFK provides a better approach to methane at low temperatures.

  12. Classic Grounded Theory to Analyse Secondary Data: Reality and Reflections

    Directory of Open Access Journals (Sweden)

    Lorraine Andrews

    2012-06-01

    Full Text Available This paper draws on the experiences of two researchers and discusses how they conducted a secondary data analysis using classic grounded theory. The aim of the primary study was to explore first-time parents’ postnatal educational needs. A subset of the data from the primary study (eight transcripts from interviews with fathers was used for the secondary data analysis. The objectives of the secondary data analysis were to identify the challenges of using classic grounded theory with secondary data and to explore whether the re-analysis of primary data using a different methodology would yield a different outcome. Through the process of re-analysis a tentative theory emerged on ‘developing competency as a father’. Challenges encountered during this re-analysis included the small dataset, the pre-framed data, and limited ability for theoretical sampling. This re-analysis proved to be a very useful learning tool for author 1(LA, who was a novice with classic grounded theory.

  13. On the Foundational Equations of the Classical Theory of ...

    Indian Academy of Sciences (India)

    IAS Admin

    ... Equations of the Classical. Theory of Electrodynamics ... most cherished notions of the Maxwell{Lorentz theory .... dia in the presence of the fields, in which case a self- consistent ..... could benefit from further experimental verification, we.

  14. Comparison of Classical Test Theory and Item Response Theory in Individual Change Assessment

    NARCIS (Netherlands)

    Jabrayilov, Ruslan; Emons, Wilco H. M.; Sijtsma, Klaas

    2016-01-01

    Clinical psychologists are advised to assess clinical and statistical significance when assessing change in individual patients. Individual change assessment can be conducted using either the methodologies of classical test theory (CTT) or item response theory (IRT). Researchers have been optimistic

  15. Ultrasound assisted nucleation and growth characteristics of glycine polymorphs--a combined experimental and analytical approach.

    Science.gov (United States)

    Renuka Devi, K; Raja, A; Srinivasan, K

    2015-05-01

    For the first time, the effect of ultrasound in the diagnostic frequency range of 1-10 MHz on the nucleation and growth characteristics of glycine has been explored. The investigation employing the ultrasonic interferometer was carried out at a constant insonation time over a wide range of relative supersaturation from σ=-0.09 to 0.76 in the solution. Ultrasound promotes only α nucleation and completely inhibits both the β and γ nucleation in the system. The propagation of ultrasound assisted mass transport facilitates nucleation even at very low supersaturation levels in the solution. The presence of ultrasound exhibits a profound effect on nucleation and growth characteristics in terms of decrease in induction period, increase in nucleation rate and decrease in crystal size than its absence in the solution. With an increase in the frequency of ultrasound, a further decrease in induction period, increase in nucleation rate and decrease in the size of the crystal is noticed even at the same relative supersaturation levels. The increase in the nucleation rate explains the combined dominating effects of both the ultrasound frequency and the supersaturation in the solution. Analytically, the nucleation parameters of the nucleated polymorph have been deduced at different ultrasonic frequencies based on the classical nucleation theory and correlations with the experimental results have been obtained. Structural affirmation of the nucleated polymorph has been ascertained by powder X-ray diffraction. Copyright © 2014 Elsevier B.V. All rights reserved.

  16. Gravitation in the 'quasi-classical' theory

    International Nuclear Information System (INIS)

    Wignall, J.W.G.; Zangari, M.

    1990-01-01

    The 'quasi-classical' picture of particles as extendend periodic disturbances in a classical nonlinear field, previously shown to imply all the equations of Maxwell electrodynamics with very little formal input, is here applied to the other known long-range force, gravitation. It is shown that the picture's absolute interpretation of inertial mass and four-potential as measures of the local spacing between equal-phase hypersurfaces, together with the empirically established proportionality of gravitational 'charge' to inertial mass, leads naturally to the gravitational red-shift formula, and it thus provides a physical basis for the spacetime curvature that is the central idea of Einstein's general theory of relativity. 16 refs., 1 fig

  17. On the Relationship between Classical Test Theory and Item Response Theory: From One to the Other and Back

    Science.gov (United States)

    Raykov, Tenko; Marcoulides, George A.

    2016-01-01

    The frequently neglected and often misunderstood relationship between classical test theory and item response theory is discussed for the unidimensional case with binary measures and no guessing. It is pointed out that popular item response models can be directly obtained from classical test theory-based models by accounting for the discrete…

  18. Nucleation and dissociation of nano-particles in gas phase

    International Nuclear Information System (INIS)

    Feiden, P.

    2007-09-01

    This work deals with the study of nano-particles formation in gas phase and their dissociation pathways after an optical excitation. The clusters formation decomposes in two steps: a seed is formed (nucleation phase) and sticks atoms during its propagation in a sodium atomic vapor (growth phase). Those two steps have been observed separately for homogeneous Na n and heterogeneous Na n X particles (X = (NaOH) 2 or (Na 2 O) 2 ). The growth mechanism is well interpreted by a Monte Carlo simulation taking into account an accretion mechanism with hard-sphere cross section. The homogeneous nucleation mechanism has been highlighted by a direct comparison with the Classical Nucleation Theory predictions. The clusters fragmentation of ionic Na + (NaOH) p et Na + (NaF) p particles is studied in the second part. The way clusters fragment with size when they are excited optically is compared with theoretical previsions: this highlights the existence of an energetic barrier for special size of clusters. Finally, the fragmentation of doubly charged Na + Na + (NaOH) p clusters shows a competition between the fission into two single charged fragments and the unimolecular evaporation of a neutral fragment. (author)

  19. An inverse modeling procedure to determine particle growth and nucleation rates from measured aerosol size distributions

    Directory of Open Access Journals (Sweden)

    B. Verheggen

    2006-01-01

    Full Text Available Classical nucleation theory is unable to explain the ubiquity of nucleation events observed in the atmosphere. This shows a need for an empirical determination of the nucleation rate. Here we present a novel inverse modeling procedure to determine particle nucleation and growth rates based on consecutive measurements of the aerosol size distribution. The particle growth rate is determined by regression analysis of the measured change in the aerosol size distribution over time, taking into account the effects of processes such as coagulation, deposition and/or dilution. This allows the growth rate to be determined with a higher time-resolution than can be deduced from inspecting contour plots ('banana-plots''. Knowing the growth rate as a function of time enables the evaluation of the time of nucleation of measured particles of a certain size. The nucleation rate is then obtained by integrating the particle losses from time of measurement to time of nucleation. The regression analysis can also be used to determine or verify the optimum value of other parameters of interest, such as the wall loss or coagulation rate constants. As an example, the method is applied to smog chamber measurements. This program offers a powerful interpretive tool to study empirical aerosol population dynamics in general, and nucleation and growth in particular.

  20. "Scars" connect classical and quantum theory

    CERN Multimedia

    Monteiro, T

    1990-01-01

    Chaotic systems are unstable and extremely sensitive to initial condititions. So far, scientists have been unable to demonstrate that the same kind of behaviour exists in quantum or microscopic systems. New connections have been discovered though between classical and quantum theory. One is the phenomena of 'scars' which cut through the wave function of a particle (1 page).

  1. Classical open-string field theory: A∞-algebra, renormalization group and boundary states

    International Nuclear Information System (INIS)

    Nakatsu, Toshio

    2002-01-01

    We investigate classical bosonic open-string field theory from the perspective of the Wilson renormalization group of world-sheet theory. The microscopic action is identified with Witten's covariant cubic action and the short-distance cut-off scale is introduced by length of open-string strip which appears in the Schwinger representation of open-string propagator. Classical open-string field theory in the title means open-string field theory governed by a classical part of the low energy action. It is obtained by integrating out suitable tree interactions of open-strings and is of non-polynomial type. We study this theory by using the BV formalism. It turns out to be deeply related with deformation theory of A ∞ -algebra. We introduce renormalization group equation of this theory and discuss it from several aspects. It is also discussed that this theory is interpreted as a boundary open-string field theory. Closed-string BRST charge and boundary states of closed-string field theory in the presence of open-string field play important roles

  2. Aspects of a representation of quantum theory in terms of classical probability theory by means of integration in Hilbert space

    International Nuclear Information System (INIS)

    Bach, A.

    1981-01-01

    A representation of quantum mechanics in terms of classical probability theory by means of integration in Hilbert space is discussed. This formal hidden-variables representation is analysed in the context of impossibility proofs concerning hidden-variables theories. The structural analogy of this formulation of quantum theory with classical statistical mechanics is used to elucidate the difference between classical mechanics and quantum mechanics. (author)

  3. Kinetics of heterogeneous nucleation on intrinsic nucleants in pure fcc transition metals

    International Nuclear Information System (INIS)

    Wilde, G; Bokeloh, J; Santhaweesuk, C; Perepezko, J H; Sebright, J L

    2009-01-01

    Nucleation during solidification is heterogeneous in nature in an overwhelmingly large fraction of all solidification events. Yet, most often the identity of the heterogeneous nucleants that initiate nucleation remains a matter of speculation. In fact, a series of dedicated experiments needs to be designed in order to verify if nucleation of the material under study is based on one type of heterogeneous nucleant and if the potency of that nucleant is constant, e.g. for a population of individual droplets, or stays constant over time, e.g. throughout repeated melting/solidification cycles. In this work it is demonstrated that one way to circumvent ambiguities and analyze nucleation kinetics under well-defined conditions experimentally is given by performing statistically significant numbers of repeated single-droplet experiments. The application of proper statistics analyses based upon a non-homogeneous Poisson process is shown to yield nucleation rates that are independent of a specific nucleation model. Based upon this approach nucleation undercooling measurements on pure Au, Cu and Ni as model materials have confirmed that the experimental strategy and analysis method are valid. The results are comparable to those obtained by classical nucleation theory applied to experimental data that has been verified to comply with the assertions that are necessary for applying this model framework. However, the results reveal also other complex nucleant-sample interactions such as an initial transient undercooling behavior and impurity removal during repeated cycling treatments. The transient undercooling behavior has been analyzed by a nucleant refining model to provide new insight on the operation of melt fluxing treatments.

  4. Functional methods underlying classical mechanics, relativity and quantum theory

    International Nuclear Information System (INIS)

    Kryukov, A

    2013-01-01

    The paper investigates the physical content of a recently proposed mathematical framework that unifies the standard formalisms of classical mechanics, relativity and quantum theory. In the framework states of a classical particle are identified with Dirac delta functions. The classical space is ''made'' of these functions and becomes a submanifold in a Hilbert space of states of the particle. The resulting embedding of the classical space into the space of states is highly non-trivial and accounts for numerous deep relations between classical and quantum physics and relativity. One of the most striking results is the proof that the normal probability distribution of position of a macroscopic particle (equivalently, position of the corresponding delta state within the classical space submanifold) yields the Born rule for transitions between arbitrary quantum states.

  5. Critical Nuclei Size, Rate, and Activation Energy of H2 Gas Nucleation.

    Science.gov (United States)

    German, Sean R; Edwards, Martin A; Ren, Hang; White, Henry S

    2018-03-21

    Electrochemical measurements of the nucleation rate of individual H 2 bubbles at the surface of Pt nanoelectrodes (radius = 7-41 nm) are used to determine the critical size and geometry of H 2 nuclei leading to stable bubbles. Precise knowledge of the H 2 concentration at the electrode surface, C H 2 surf , is obtained by controlled current reduction of H + in a H 2 SO 4 solution. Induction times of single-bubble nucleation events are measured by stepping the current, to control C H 2 surf , while monitoring the voltage. We find that gas nucleation follows a first-order rate process; a bubble spontaneously nucleates after a stochastic time delay, as indicated by a sudden voltage spike that results from impeded transport of H + to the electrode. Hundreds of individual induction times, at different applied currents and using different Pt nanoelectrodes, are used to characterize the kinetics of phase nucleation. The rate of bubble nucleation increases by four orders of magnitude (0.3-2000 s -1 ) over a very small relative change in C H 2 surf (0.21-0.26 M, corresponding to a ∼0.025 V increase in driving force). Classical nucleation theory yields thermodynamic radii of curvature for critical nuclei of 4.4 to 5.3 nm, corresponding to internal pressures of 330 to 270 atm, and activation energies for nuclei formation of 14 to 26 kT, respectively. The dependence of nucleation rate on H 2 concentration indicates that nucleation occurs by a heterogeneous mechanism, where the nuclei have a contact angle of ∼150° with the electrode surface and contain between 35 and 55 H 2 molecules.

  6. Longitudinal vibration of isotropic solid rods: from classical to modern theories

    CSIR Research Space (South Africa)

    Shatalov, M

    2011-12-01

    Full Text Available Vibration of Isotropic Solid Rods: From Classical to Modern Theories Michael Shatalov1,2, Julian Marais2, Igor Fedotov2 and Michel Djouosseu Tenkam2 1Council for Scientific and Industrial Research 2Tshwane University of Technology South Africa 1...). The classical approximate theory of longitudinal vibration of rods was developed during the 18th century by J. D?Alembert, D. Bernoulli, L. Euler and J. Lagrange. This theory is based on the analysis of the one dimensional wave equation and is applicable...

  7. Constrained variational calculus for higher order classical field theories

    Energy Technology Data Exchange (ETDEWEB)

    Campos, Cedric M; De Leon, Manuel; De Diego, David MartIn, E-mail: cedricmc@icmat.e, E-mail: mdeleon@icmat.e, E-mail: david.martin@icmat.e [Instituto de Ciencias Matematicas, CSIC-UAM-UC3M-UCM, Serrano 123, 28006 Madrid (Spain)

    2010-11-12

    We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner-Rusk formalism. Some examples of applications are studied, in particular to the geometrical description of optimal control theory for partial differential equations.

  8. Constrained variational calculus for higher order classical field theories

    International Nuclear Information System (INIS)

    Campos, Cedric M; De Leon, Manuel; De Diego, David MartIn

    2010-01-01

    We develop an intrinsic geometrical setting for higher order constrained field theories. As a main tool we use an appropriate generalization of the classical Skinner-Rusk formalism. Some examples of applications are studied, in particular to the geometrical description of optimal control theory for partial differential equations.

  9. Emergence of classical theories from quantum mechanics

    International Nuclear Information System (INIS)

    Hájícek, P

    2012-01-01

    Three problems stand in the way of deriving classical theories from quantum mechanics: those of realist interpretation, of classical properties and of quantum measurement. Recently, we have identified some tacit assumptions that lie at the roots of these problems. Thus, a realist interpretation is hindered by the assumption that the only properties of quantum systems are values of observables. If one simply postulates the properties to be objective that are uniquely defined by preparation then all difficulties disappear. As for classical properties, the wrong assumption is that there are arbitrarily sharp classical trajectories. It turns out that fuzzy classical trajectories can be obtained from quantum mechanics by taking the limit of high entropy. Finally, standard quantum mechanics implies that any registration on a quantum system is disturbed by all quantum systems of the same kind existing somewhere in the universe. If one works out systematically how quantum mechanics must be corrected so that there is no such disturbance, one finds a new interpretation of von Neumann's 'first kind of dynamics', and so a new way to a solution of the quantum measurement problem. The present paper gives a very short review of this work.

  10. Non-monotonic variations of the nucleation free energy in a glass-forming ultra-soft particles fluid.

    Science.gov (United States)

    Desgranges, Caroline; Delhommelle, Jerome

    2018-06-18

    Using molecular dynamics simulation, we study the impact of the degree of supercooling on the crystal nucleation of ultra-soft particles, modeled with the Gaussian core potential. Focusing on systems with a high number density, our simulations reveal dramatically different behaviors as the degree of supercooling is varied. In the moderate supercooling regime, crystal nucleation proceeds as expected from classical nucleation theory, with a decrease in the free energy of nucleation, as well as in the size of the critical nucleus, as supercooling is increased. On the other hand, in the large supercooling regime, we observe an unusual reversal of behavior with an increase in the free energy of nucleation and in the critical size, as supercooling is increased. This unexpected result is analyzed in terms of the interplay between the glass transition and the crystal nucleation process. Specifically, medium range order crystal-like domains, with structural features different from that of the crystal nucleus, are found to form throughout the system when the supercooling is very large. These, in turn, play a pivotal role in the increase in the free energy of nucleation, as well as in the critical size, as the temperature gets closer to the glass transition.

  11. Attainment of unstable β nucleation of glycine in presence of L-tyrosine and its analytical interpretation-A combined approach

    Science.gov (United States)

    Renuka Devi, K.; Srinivasan, K.

    2015-05-01

    The ability of L-tyrosine molecules to act as a template and to facilitate the nucleation of unstable β polymorph in the solution has been revealed through in-situ nucleation study. This nucleation of β occurs along with the existing α nucleation at the critical concentration of additive in the solution. The presence of L-tyrosine molecules lowers the inherent barrier that exists for β nucleation in the solution. No nucleation of γ was observed over the entire range of concentrations studied. The molecular recognition capability and stereo selective inhibitory action of the added L-tyrosine molecules towards glycine molecule have been successfully revealed in terms of habit modification observed in the nucleated polymorphs. In the case of α polymorph, L-tyrosine induces a change in the morphology along the enantiopolar -b direction while in the case of β polymorph, habit modification from needle to plate like structure is observed. With the increase in time span, solution mediated phase transformation from β to α polymorph has been observed in the solution. Analytically the nucleation parameters of α and β polymorphs were estimated based on Classical Nucleation Theory. Form of crystallization of the nucleated polymorphs of glycine was confirmed by a powder x-ray diffraction analysis.

  12. Nucleation phenomena at Suzuki phases

    International Nuclear Information System (INIS)

    Acosta-Najarro, D.; Jose Y, M.

    1982-01-01

    Crystal of NaCl doped with Mn present regions with an increase in nucleation densities when observed by surface gold decoration; this increase is related to the nucleation of the Suzuki phases which are induced by cooling of the crystal matrix. Calculations based on atomistic nucleation theory are developed to explain the increased nucleation density. Experiments were made to compare with the theoretical results. In particular the density of nuclei was measured as a function of the rate or arrival of atoms to the surface. Therefore, the changes in the nucleation densities are explained in terms of change in migration energies between the Suzuki phase and the NaCl matrix excluding the possibility of nucleation induced by point defects. (author)

  13. Classical theory of atom-surface scattering: The rainbow effect

    Science.gov (United States)

    Miret-Artés, Salvador; Pollak, Eli

    2012-07-01

    The scattering of heavy atoms and molecules from surfaces is oftentimes dominated by classical mechanics. A large body of experiments have gathered data on the angular distributions of the scattered species, their energy loss distribution, sticking probability, dependence on surface temperature and more. For many years these phenomena have been considered theoretically in the framework of the “washboard model” in which the interaction of the incident particle with the surface is described in terms of hard wall potentials. Although this class of models has helped in elucidating some of the features it left open many questions such as: true potentials are clearly not hard wall potentials, it does not provide a realistic framework for phonon scattering, and it cannot explain the incident angle and incident energy dependence of rainbow scattering, nor can it provide a consistent theory for sticking. In recent years we have been developing a classical perturbation theory approach which has provided new insight into the dynamics of atom-surface scattering. The theory includes both surface corrugation as well as interaction with surface phonons in terms of harmonic baths which are linearly coupled to the system coordinates. This model has been successful in elucidating many new features of rainbow scattering in terms of frictions and bath fluctuations or noise. It has also given new insight into the origins of asymmetry in atomic scattering from surfaces. New phenomena deduced from the theory include friction induced rainbows, energy loss rainbows, a theory of super-rainbows, and more. In this review we present the classical theory of atom-surface scattering as well as extensions and implications for semiclassical scattering and the further development of a quantum theory of surface scattering. Special emphasis is given to the inversion of scattering data into information on the particle-surface interactions.

  14. Theoretical Studies Of Nucleation Kinetics And Nanodroplet Microstructure

    International Nuclear Information System (INIS)

    Wilemski, Gerald

    2009-01-01

    The goals of this project were to (1) explore ways of bridging the gap between fundamental molecular nucleation theories and phenomenological approaches based on thermodynamic reasoning, (2) test and improve binary nucleation theory, and (3) provide the theoretical underpinning for a powerful new experimental technique, small angle neutron scattering (SANS) from nanodroplet aerosols, that can probe the compositional structure of nanodroplets. This report summarizes the accomplishments of this project in realizing these goals. Publications supported by this project fall into three general categories: (1) theoretical work on nucleation theory (2) experiments and modeling of nucleation and condensation in supersonic nozzles, and (3) experimental and theoretical work on nanodroplet structure and neutron scattering. These publications are listed and briefly summarized in this report.

  15. Homogeneous ice nucleation from aqueous inorganic/organic particles representative of biomass burning: water activity, freezing temperatures, nucleation rates.

    Science.gov (United States)

    Knopf, Daniel A; Rigg, Yannick J

    2011-02-10

    Homogeneous ice nucleation plays an important role in the formation of cirrus clouds with subsequent effects on the global radiative budget. Here we report on homogeneous ice nucleation temperatures and corresponding nucleation rate coefficients of aqueous droplets serving as surrogates of biomass burning aerosol. Micrometer-sized (NH(4))(2)SO(4)/levoglucosan droplets with mass ratios of 10:1, 1:1, 1:5, and 1:10 and aqueous multicomponent organic droplets with and without (NH(4))(2)SO(4) under typical tropospheric temperatures and relative humidities are investigated experimentally using a droplet conditioning and ice nucleation apparatus coupled to an optical microscope with image analysis. Homogeneous freezing was determined as a function of temperature and water activity, a(w), which was set at droplet preparation conditions. The ice nucleation data indicate that minor addition of (NH(4))(2)SO(4) to the aqueous organic droplets renders the temperature dependency of water activity negligible in contrast to the case of aqueous organic solution droplets. The mean homogeneous ice nucleation rate coefficient derived from 8 different aqueous droplet compositions with average diameters of ∼60 μm for temperatures as low as 195 K and a(w) of 0.82-1 is 2.18 × 10(6) cm(-3) s(-1). The experimentally derived freezing temperatures and homogeneous ice nucleation rate coefficients are in agreement with predictions of the water activity-based homogeneous ice nucleation theory when taking predictive uncertainties into account. However, the presented ice nucleation data indicate that the water activity-based homogeneous ice nucleation theory overpredicts the freezing temperatures by up to 3 K and corresponding ice nucleation rate coefficients by up to ∼2 orders of magnitude. A shift of 0.01 in a(w), which is well within the uncertainty of typical field and laboratory relative humidity measurements, brings experimental and predicted freezing temperatures and homogeneous ice

  16. Cavitation in a metallic liquid: homogeneous nucleation and growth of nanovoids.

    Science.gov (United States)

    Cai, Y; Wu, H A; Luo, S N

    2014-06-07

    Large-scale molecular dynamics (MD) simulations are performed to investigate homogeneous nucleation and growth of nanovoids during cavitation in liquid Cu. We characterize in detail the atomistic cavitation processes by following the temporal evolution of cavities or voids, analyze the nucleation behavior with the mean first-passage time (MFPT) and survival probability (SP) methods, and discuss the results against classical nucleation theory (CNT), the Tolman equation for surface energy, independent calculation of surface tension via integrating the stress profiles, the Johnson-Mehl-Avrami (JMA) growth law, and the power law for nucleus size distributions. Cavitation in this representative metallic liquid is a high energy barrier Poisson processes, and the steady-state nucleation rates obtained from statistical runs with the MFPT and SP methods are in agreement. The MFPT method also yields the critical nucleus size and the Zeldovich factor. Fitting with the Tolman's equation to the MD simulations yields the surface energy of a planar interface (~0.9 J m⁻²) and the Tolman length (0.4-0.5 Å), and those values are in accord with those from integrating the stress profiles of a planar interface. Independent CNT predictions of the nucleation rate (10(33 - 34) s(-1) m(-3)) and critical size (3-4 Å in radius) are in agreement with the MFPT and SP results. The JMA law can reasonably describe the nucleation and growth process. The size distribution of subcritical nuclei appears to follow a power law with an exponent decreasing with increasing tension owing to coupled nucleation and growth, and that of the supercritical nuclei becomes flattened during further stress relaxation due to void coalescence.

  17. Cavitation in a metallic liquid: Homogeneous nucleation and growth of nanovoids

    International Nuclear Information System (INIS)

    Cai, Y.; Wu, H. A.; Luo, S. N.

    2014-01-01

    Large-scale molecular dynamics (MD) simulations are performed to investigate homogeneous nucleation and growth of nanovoids during cavitation in liquid Cu. We characterize in detail the atomistic cavitation processes by following the temporal evolution of cavities or voids, analyze the nucleation behavior with the mean first-passage time (MFPT) and survival probability (SP) methods, and discuss the results against classical nucleation theory (CNT), the Tolman equation for surface energy, independent calculation of surface tension via integrating the stress profiles, the Johnson-Mehl-Avrami (JMA) growth law, and the power law for nucleus size distributions. Cavitation in this representative metallic liquid is a high energy barrier Poisson processes, and the steady-state nucleation rates obtained from statistical runs with the MFPT and SP methods are in agreement. The MFPT method also yields the critical nucleus size and the Zeldovich factor. Fitting with the Tolman's equation to the MD simulations yields the surface energy of a planar interface (∼0.9 J m −2 ) and the Tolman length (0.4–0.5 Å), and those values are in accord with those from integrating the stress profiles of a planar interface. Independent CNT predictions of the nucleation rate (10 33−34 s −1  m −3 ) and critical size (3–4 Å in radius) are in agreement with the MFPT and SP results. The JMA law can reasonably describe the nucleation and growth process. The size distribution of subcritical nuclei appears to follow a power law with an exponent decreasing with increasing tension owing to coupled nucleation and growth, and that of the supercritical nuclei becomes flattened during further stress relaxation due to void coalescence

  18. Large stability and high catalytic activities of sub-nm metal (0) clusters: implications into the nucleation and growth theory.

    Science.gov (United States)

    Piñeiro, Yolanda; Buceta, David; Calvo, Javier; Huseyinova, Shahana; Cuerva, Miguel; Pérez, Ángel; Domínguez, Blanca; López-Quintela, M Arturo

    2015-07-01

    Clusters are stable catalytic species, which are produced during the synthesis of nanoparticles (NPs). Their existence contradicts the thermodynamic principles used to explain the formation of NPs by the classical nucleation and growth theories (NGTs). Using chemical and electrochemical methods we will show that depending on the experimental conditions one can produce either Ag clusters or Ag NPs. Moreover, using already prepared Ag clusters one can observe the disappearance of the usual induction period observed for the kinetics of NP formation, indicating that clusters catalyze the formation of NPs. Taking these data together with some previous examples of cluster-catalyzed anisotropic growth, we derived a qualitative approach to include the catalytic activities of clusters into the formation of NPs, which is incorporated into the NGT. Some qualitative conclusions about the main experimental parameters, which affect the formation of clusters versus NPs, as well as the catalytic mechanism versus the non-catalytic one, are also described. Copyright © 2015 Elsevier Inc. All rights reserved.

  19. Does general relativity theory possess the classical newtonian limit

    International Nuclear Information System (INIS)

    Denisov, V.I.; Logunov, A.A.

    1980-01-01

    A detailed comparison of newtonian approximation of the Einstein theory and the Newton theory of gravity is made. A difference of principle between these two theories is clarified at the stage of obtaining integrals of motion. Exact eqautions of motion and Einstein equations shows the existence only zero integrals of motion as well as in the newtonian approximation. A conclusion is that GRT has no classical newtonian limit, since the integrals of motion in the Newton theory of gravity and in the newtonian approximation of the Einstein theory do not coincide [ru

  20. Bubbles in Titan’s Seas: Nucleation, Growth, and RADAR Signature

    Science.gov (United States)

    Cordier, Daniel; Liger-Belair, Gérard

    2018-05-01

    In the polar regions of Titan, the main satellite of Saturn, hydrocarbon seas have been discovered by the Cassini–Huygens mission. RADAR observations have revealed surprising and transient bright areas over the Ligeia Mare surface. As suggested by recent research, bubbles could explain these strange features. However, the nucleation and growth of such bubbles, together with their RADAR reflectivity, have never been investigated. All of these aspects are critical to an actual observation. We have thus applied the classical nucleation theory to our context, and we developed a specific radiative transfer model that is appropriate for bubble streams in cryogenic liquids. According to our results, the sea bed appears to be the most plausible place for the generation of bubbles, leading to a signal comparable to observations. This conclusion is supported by thermodynamic arguments and by RADAR properties of a bubbly column. The latter are also valid in the case of bubble plumes, due to gas leaking from the sea floor.

  1. Analysis of isothermal and cooling-rate-dependent immersion freezing by a unifying stochastic ice nucleation model

    Science.gov (United States)

    Alpert, Peter A.; Knopf, Daniel A.

    2016-02-01

    Immersion freezing is an important ice nucleation pathway involved in the formation of cirrus and mixed-phase clouds. Laboratory immersion freezing experiments are necessary to determine the range in temperature, T, and relative humidity, RH, at which ice nucleation occurs and to quantify the associated nucleation kinetics. Typically, isothermal (applying a constant temperature) and cooling-rate-dependent immersion freezing experiments are conducted. In these experiments it is usually assumed that the droplets containing ice nucleating particles (INPs) all have the same INP surface area (ISA); however, the validity of this assumption or the impact it may have on analysis and interpretation of the experimental data is rarely questioned. Descriptions of ice active sites and variability of contact angles have been successfully formulated to describe ice nucleation experimental data in previous research; however, we consider the ability of a stochastic freezing model founded on classical nucleation theory to reproduce previous results and to explain experimental uncertainties and data scatter. A stochastic immersion freezing model based on first principles of statistics is presented, which accounts for variable ISA per droplet and uses parameters including the total number of droplets, Ntot, and the heterogeneous ice nucleation rate coefficient, Jhet(T). This model is applied to address if (i) a time and ISA-dependent stochastic immersion freezing process can explain laboratory immersion freezing data for different experimental methods and (ii) the assumption that all droplets contain identical ISA is a valid conjecture with subsequent consequences for analysis and interpretation of immersion freezing. The simple stochastic model can reproduce the observed time and surface area dependence in immersion freezing experiments for a variety of methods such as: droplets on a cold-stage exposed to air or surrounded by an oil matrix, wind and acoustically levitated droplets

  2. Antigravity and classical solutions of five-dimensional Kaluza-Klein theory

    Energy Technology Data Exchange (ETDEWEB)

    Pollard, D. (Imperial Coll. of Science and Technology, London (UK). Blackett Lab.)

    1983-02-21

    Classical solutions are exhibited of a graviton-graviphoton-graviscalar field theory which are antigravitating in the weak-field approximation. The theory itself is obtained by a Kaluza-Klein type reduction from five to four dimensions. The solutions are dyonic black holes with scalar charge. They share some similarities with the extreme Reissner-Nordstrom black holes of Einstein-Maxwell theory.

  3. Nucleation of voids - the impurity effect

    International Nuclear Information System (INIS)

    Chen, I-W; Taiwo, A.

    1984-01-01

    Nucleation of voids under irradiation in multicomponent alloys remains an unsolved theoretical problem. Of particular interest are the effects of nonequilibrium solute segregation phenomena on the critical nucleus and the nucleation rate. The resolution of the multicomponent nucleation in a dissipative system also has broader implication to the field of irreversible thermodynamics. The present paper describes a recent study of solute segregation effects in void nucleation. We begin with a thermodynamic model for a nonequilibrium void with interfacial segregation. The thermodynamic model is coupled with kinetic considerations of solute/solvent diffusion under a bias, which is itself related to segregation by the coating effect, to assess the stability of void embryos. To determine nucleation rate, we develop a novel technique by extending the most probable path method in statistical mechanics for nonequilibrium steady state to simulate large fluctuation with nonlinear dissipation. The path of nucleation is determined by solving an analogous problem on particle trajectory in classical dynamics. The results of both the stability analysis and the fluctuation analysis establish the paramount significance of the impurity effect via the mechanism of nonequilibrium segregation. We conclude that over-segregation is probably the most general cause for the apparently low nucleation barriers that are responsible for nearly ubiquitous occurrence of void swelling in common metals

  4. The Prediction of Item Parameters Based on Classical Test Theory and Latent Trait Theory

    Science.gov (United States)

    Anil, Duygu

    2008-01-01

    In this study, the prediction power of the item characteristics based on the experts' predictions on conditions try-out practices cannot be applied was examined for item characteristics computed depending on classical test theory and two-parameters logistic model of latent trait theory. The study was carried out on 9914 randomly selected students…

  5. Theoretical physics 3. Classical field theory. On electrodynamics, non-Abelian gauge theories, and gravitation. 3. ed.

    International Nuclear Information System (INIS)

    Scheck, Florian

    2010-01-01

    Stringent presentation of field theory, mediates the connection from the classicalelectrodynamics up to modern gauge theories. The compact presentation is ideal for the bachelor study. New chapter on general relativity theory. Deepens the learned by numerous application from laser physic, metamaterials and different more. Theoretical physics 3. Classical field theory. On electrodynamics, non-Abelian, and gravitation is the third of five volumes on theoretical physics by professor Scheck. The cycle theoretical physics comprehends: Volume 1: Mechanics. From Newtons law to the deterministic chaos. Volume 2: Nonrelativistic quantum theory. From the hydrogen atom to the many-particle systems. Volume 3: Classical field theory. From the electrodynamics to the gauge theories. Volume 5: From the laws of thermodynamics to the quantum statistics. This textbook mediates modern theoretical physics in string presentation illustrated by many examples. It contains numerous problems with solution hints ore exemplary, complete solutions. The third edition was revised in many single topics, especially the chapter on general relativity theory was supplemented by an extensive analysis of the Schwarzschild solution. [de

  6. Supersaturation-nucleation behavior of poorly soluble drugs and its impact on the oral absorption of drugs in thermodynamically high-energy forms.

    Science.gov (United States)

    Ozaki, Shunsuke; Minamisono, Takuma; Yamashita, Taro; Kato, Takashi; Kushida, Ikuo

    2012-01-01

    In order to better understand the oral absorption behavior of poorly water-soluble drugs, their supersaturation-nucleation behavior was characterized in fasted state simulated intestinal fluid. The induction time (t(ind)) for nucleation was measured for four model drugs: itraconazole, erlotinib, troglitazone, and PLX4032. Supersaturated solutions were prepared by solvent shift method, and nucleation initiation was monitored by ultraviolet detection. The relationship between t(ind) and degree of supersaturation was analyzed in terms of classical nucleation theory. The defined supersaturation stability proved to be compound specific. Clinical data on oral absorption were investigated for drugs in thermodynamically high-energy forms such as amorphous forms and salts and was compared with in vitro supersaturation-nucleation characteristics. Solubility-limited maximum absorbable dose was proportionate to intestinal effective drug concentrations, which are related to supersaturation stability and thermodynamic solubility. Supersaturation stability was shown to be an important factor in determining the effect of high-energy forms. The characterization of supersaturation-nucleation behavior by the presented method is, therefore, valuable for assessing the potential absorbability of poorly water-soluble drugs. Copyright © 2011 Wiley-Liss, Inc.

  7. Comment on theories for helium-assisted void nucleation

    International Nuclear Information System (INIS)

    Russell, K.C.

    1976-01-01

    Voids form by agglomeration of irradiation-induced vacancies which remain after preferential absorption of self interstitials at dislocation lines. Helium which is formed by (n,α) transmutations and, in simulation studies, may be ion-implanted, often plays an important, but puzzling role. In some materials, very few voids form in the absence of helium, even after intense irradiation. In many other materials , voids form readily under a variety of irradiation conditions, even in the absence of helium. Why some materials require helium - typically in the 10 -6 apa (atom per atom) range - and others do not, and the reason for that particular level are by no means clear. The physics of void nucleation, particularly the role of helium, have been the subject of several theoretical papers. This note presents a critique of these theories, and then briefly outlines a new analysis which is not subject to their limitations. (Auth.)

  8. Quantum fermions and quantum field theory from classical statistics

    International Nuclear Information System (INIS)

    Wetterich, Christof

    2012-01-01

    An Ising-type classical statistical ensemble can describe the quantum physics of fermions if one chooses a particular law for the time evolution of the probability distribution. It accounts for the time evolution of a quantum field theory for Dirac particles in an external electromagnetic field. This yields in the non-relativistic one-particle limit the Schrödinger equation for a quantum particle in a potential. Interference or tunneling arise from classical probabilities.

  9. Antigravity and classical solutions of five-dimensional Kaluza-Klein theory

    International Nuclear Information System (INIS)

    Pollard, D.

    1983-01-01

    Classical solutions are exhibited of a graviton-graviphoton-graviscalar field theory which are antigravitating in the weak-field approximation. The theory itself is obtained by a Kaluza-Klein type reduction from five to four dimensions. The solutions are dyonic black holes with scalar charge. They share some similarities with the extreme Reissner-Nordstrom black holes of Einstein-Maxwell theory. (author)

  10. Relationships among Classical Test Theory and Item Response Theory Frameworks via Factor Analytic Models

    Science.gov (United States)

    Kohli, Nidhi; Koran, Jennifer; Henn, Lisa

    2015-01-01

    There are well-defined theoretical differences between the classical test theory (CTT) and item response theory (IRT) frameworks. It is understood that in the CTT framework, person and item statistics are test- and sample-dependent. This is not the perception with IRT. For this reason, the IRT framework is considered to be theoretically superior…

  11. Special relativity and classical field theory

    CERN Document Server

    Susskind, Leonard

    2017-01-01

    Physicist Leonard Susskind and data engineer Art Friedman are back. This time, they introduce readers to Einstein's special relativity and Maxwell's classical field theory. Using their typical brand of real math, enlightening drawings, and humor, Susskind and Friedman walk us through the complexities of waves, forces, and particles by exploring special relativity and electromagnetism. It's a must-read for both devotees of the series and any armchair physicist who wants to improve their knowledge of physics' deepest truths.

  12. Homogeneous nucleation in 4He: A corresponding-states analysis

    International Nuclear Information System (INIS)

    Sinha, D.N.; Semura, J.S.; Brodie, L.C.

    1982-01-01

    We report homogeneous-nucleation-temperature measurements in liquid 4 He over a bath-temperature range 2.31 4 He, in a region far from the critical point. A simple empirical form is presented for estimating the homogeneous nucleation temperatures for any liquid with a spherically symmetric interatomic potential. The 4 He data are compared with nucleation data for Ar, Kr, Xe, and H; theoretical predictions for 3 He are given in terms of reduced quantities. It is shown that the nucleation data for both quantum and classical liquids obey a quantum law of corresponding states (QCS). On the basis of this QCS analysis, predictions of homogeneous nucleation temperatures are made for hydrogen isotopes such as HD, DT, HT, and T 2

  13. Analysis of isothermal and cooling-rate-dependent immersion freezing by a unifying stochastic ice nucleation model

    Directory of Open Access Journals (Sweden)

    P. A. Alpert

    2016-02-01

    Full Text Available Immersion freezing is an important ice nucleation pathway involved in the formation of cirrus and mixed-phase clouds. Laboratory immersion freezing experiments are necessary to determine the range in temperature, T, and relative humidity, RH, at which ice nucleation occurs and to quantify the associated nucleation kinetics. Typically, isothermal (applying a constant temperature and cooling-rate-dependent immersion freezing experiments are conducted. In these experiments it is usually assumed that the droplets containing ice nucleating particles (INPs all have the same INP surface area (ISA; however, the validity of this assumption or the impact it may have on analysis and interpretation of the experimental data is rarely questioned. Descriptions of ice active sites and variability of contact angles have been successfully formulated to describe ice nucleation experimental data in previous research; however, we consider the ability of a stochastic freezing model founded on classical nucleation theory to reproduce previous results and to explain experimental uncertainties and data scatter. A stochastic immersion freezing model based on first principles of statistics is presented, which accounts for variable ISA per droplet and uses parameters including the total number of droplets, Ntot, and the heterogeneous ice nucleation rate coefficient, Jhet(T. This model is applied to address if (i a time and ISA-dependent stochastic immersion freezing process can explain laboratory immersion freezing data for different experimental methods and (ii the assumption that all droplets contain identical ISA is a valid conjecture with subsequent consequences for analysis and interpretation of immersion freezing. The simple stochastic model can reproduce the observed time and surface area dependence in immersion freezing experiments for a variety of methods such as: droplets on a cold-stage exposed to air or surrounded by an oil matrix, wind and

  14. Cavitation in a metallic liquid: Homogeneous nucleation and growth of nanovoids

    Energy Technology Data Exchange (ETDEWEB)

    Cai, Y. [Department of Modern Mechanics, CAS Key Laboratory of Materials Behavior and Design, University of Science and Technology of China, Hefei, Anhui 230027 (China); The Peac Institute of Multiscale Sciences, Chengdu, Sichuan 610207 (China); Wu, H. A., E-mail: wuha@ustc.edu.cn [Department of Modern Mechanics, CAS Key Laboratory of Materials Behavior and Design, University of Science and Technology of China, Hefei, Anhui 230027 (China); Luo, S. N., E-mail: sluo@pims.ac.cn [The Peac Institute of Multiscale Sciences, Chengdu, Sichuan 610207 (China)

    2014-06-07

    Large-scale molecular dynamics (MD) simulations are performed to investigate homogeneous nucleation and growth of nanovoids during cavitation in liquid Cu. We characterize in detail the atomistic cavitation processes by following the temporal evolution of cavities or voids, analyze the nucleation behavior with the mean first-passage time (MFPT) and survival probability (SP) methods, and discuss the results against classical nucleation theory (CNT), the Tolman equation for surface energy, independent calculation of surface tension via integrating the stress profiles, the Johnson-Mehl-Avrami (JMA) growth law, and the power law for nucleus size distributions. Cavitation in this representative metallic liquid is a high energy barrier Poisson processes, and the steady-state nucleation rates obtained from statistical runs with the MFPT and SP methods are in agreement. The MFPT method also yields the critical nucleus size and the Zeldovich factor. Fitting with the Tolman's equation to the MD simulations yields the surface energy of a planar interface (∼0.9 J m{sup −2}) and the Tolman length (0.4–0.5 Å), and those values are in accord with those from integrating the stress profiles of a planar interface. Independent CNT predictions of the nucleation rate (10{sup 33−34} s{sup −1} m{sup −3}) and critical size (3–4 Å in radius) are in agreement with the MFPT and SP results. The JMA law can reasonably describe the nucleation and growth process. The size distribution of subcritical nuclei appears to follow a power law with an exponent decreasing with increasing tension owing to coupled nucleation and growth, and that of the supercritical nuclei becomes flattened during further stress relaxation due to void coalescence.

  15. [Taxonomic theory for non-classical systematics].

    Science.gov (United States)

    Pavlinov, I Ia

    2012-01-01

    Outlined briefly are basic principles of construing general taxonomic theory for biological systematics considered in the context of non-classical scientific paradigm. The necessity of such kind of theory is substantiated, and some key points of its elaboration are exposed: its interpretation as a framework concept for the partial taxonomic theories in various schools of systematics; elaboration of idea of cognitive situation including three interrelated components, namely subject, object, and epistemic ones; its construing as a content-wisely interpreted quasi-axiomatics, with strong structuring of its conceptual space including demarcation between axioms and inferring rules; its construing as a "conceptual pyramid" of concepts of various levels of generality; inclusion of a basic model into definition of the taxonomic system (classification) regulating its content. Two problems are indicated as fundamental: definition of taxonomic diversity as a subject domain for the systematics as a whole; definition of onto-epistemological status of taxonomic system (classification) in general and of taxa in particular.

  16. The spin-statistics connection in classical field theory

    International Nuclear Information System (INIS)

    Morgan, J A

    2006-01-01

    The spin-statistics connection is obtained for a simple formulation of a classical field theory containing even and odd Grassmann variables. To that end, the construction of irreducible canonical realizations of the rotation group corresponding to general causal fields is reviewed. The connection is obtained by imposing local commutativity on the fields and exploiting the parity operation to exchange spatial coordinates in the scalar product of classical field evaluated at one spatial location with the same field evaluated at a distinct location. The spin-statistics connection for irreducible canonical realizations of the Poincare group of spin j is obtained in the form: classical fields and their conjugate momenta satisfy fundamental field-theoretic Poisson bracket relations for 2j even and fundamental Poisson antibracket relations for 2j odd

  17. All the mathematics in the world: logical validity and classical set theory

    Directory of Open Access Journals (Sweden)

    David Charles McCarty

    2017-12-01

    Full Text Available A recognizable topological model construction shows that any consistent principles of classical set theory, including the validity of the law of the excluded third, together with a standard class theory, do not suffice to demonstrate the general validity of the law of the excluded third. This result calls into question the classical mathematician's ability to offer solid justifications for the logical principles he or she favors.

  18. Classical trajectories and quantum field theory

    International Nuclear Information System (INIS)

    Vitiello, Giuseppe; Istituto Nazionale di Fisica Nucleare, Salerno

    2005-01-01

    The density matrix and the Wigner function formalism requires the doubling of the degrees of freedom in quantum mechanics (QM) and quantum field theory (QFT). The doubled degrees of freedom play the role of the thermal bath or environment degrees of freedom and are entangled with the system degrees of freedom. They also account for quantum noise in the fluctuating random forces in the system-environment coupling. The algebraic structure of QFT turns out to be the one of the deformed Hopf algebra. In such a frame, the trajectories in the space of the unitarily inequivalent representations of the canonical commutation relations turn out to be classical trajectories and, under convenient conditions, they may exhibit properties typical of classical chaotic trajectories in nonlinear dynamics. The quantum Brownian motion and the two-slit experiment in QM are discussed in connection with the doubling of the degrees of freedom. (author)

  19. Stochastic kinetics reveal imperative role of anisotropic interfacial tension to determine morphology and evolution of nucleated droplets in nematogenic films

    Science.gov (United States)

    Bhattacharjee, Amit Kumar

    2017-01-01

    For isotropic fluids, classical nucleation theory predicts the nucleation rate, barrier height and critical droplet size by ac- counting for the competition between bulk energy and interfacial tension. The nucleation process in liquid crystals is less understood. We numerically investigate nucleation in monolayered nematogenic films using a mesoscopic framework, in par- ticular, we study the morphology and kinetic pathway in spontaneous formation and growth of droplets of the stable phase in the metastable background. The parameter κ that quantifies the anisotropic elastic energy plays a central role in determining the geometric structure of the droplets. Noncircular nematic droplets with homogeneous director orientation are nucleated in a background of supercooled isotropic phase for small κ. For large κ, noncircular droplets with integer topological charge, accompanied by a biaxial ring at the outer surface, are nucleated. The isotropic droplet shape in a superheated nematic background is found to depend on κ in a similar way. Identical growth laws are found in the two cases, although an unusual two-stage mechanism is observed in the nucleation of isotropic droplets. Temporal distributions of successive events indi- cate the relevance of long-ranged elasticity-mediated interactions within the isotropic domains. Implications for a theoretical description of nucleation in anisotropic fluids are discussed.

  20. Relativistic classical limit of quantum theory

    International Nuclear Information System (INIS)

    Shin, G.R.; Rafelski, J.

    1993-01-01

    We study the classical limit of the equal-time relativistic quantum transport theory. We discuss in qualitative terms the need to fold first the Wigner function with a coarse-graining function. Only then does the singularity at ℎ→0 seem to be manageable. In the limit ℎ→0, we obtain the relativistic Vlasov equations for the particle and the antiparticle sector of the Fock space. Similarly, we address the evolution equations of the spin and the magnetic-moment density

  1. Towards establishing a combined rate law of nucleation and crystal growth - The case study of gypsum precipitation

    Science.gov (United States)

    Rendel, Pedro M.; Gavrieli, Ittai; Wolff-Boenisch, Domenik; Ganor, Jiwchar

    2018-03-01

    The main obstacle in the formulation of a quantitative rate-model for mineral precipitation is the absence of a rigorous method for coupling nucleation and growth processes. In order to link both processes, we conducted a series of batch experiments in which gypsum nucleation was followed by crystal growth. Experiments were carried out using various stirring methods in several batch vessels made of different materials. In the experiments, the initial degree of supersaturation of the solution with respect to gypsum (Ωgyp) was set between 1.58 and 1.82. Under these conditions, heterogeneous nucleation is the dominant nucleation mode. Based on changes in SO42- concentration with time, the induction time of gypsum nucleation and the following rate of crystal growth were calculated for each experiment. The induction time (6-104 h) was found to be a function of the vessel material, while the rates of crystal growth, which varied over three orders of magnitude, were strongly affected by the stirring speed and its mode (i.e. rocking, shaking, magnetic stirrer, and magnetic impeller). The SO42- concentration data were then used to formulate a forward model that couples the simple rate laws for nucleation and crystal growth of gypsum into a single kinetic model. Accordingly, the obtained rate law is based on classical nucleation theory and heterogeneous crystal growth.

  2. Classical and quantum contents of solvable game theory on Hilbert space

    International Nuclear Information System (INIS)

    Cheon, Taksu; Tsutsui, Izumi

    2006-01-01

    A simple and general formulation of the quantum game theory is presented, accommodating all possible strategies in the Hilbert space for the first time. The theory is solvable for the two strategy quantum game, which is shown to be equivalent to a family of classical games supplemented by quantum interference. Our formulation gives a clear perspective to understand why and how quantum strategies outmaneuver classical strategies. It also reveals novel aspects of quantum games such as the stone-scissor-paper phase sub-game and the fluctuation-induced moderation

  3. Simulations of a non-Markovian description of nucleation

    NARCIS (Netherlands)

    Kuipers, J.; Barkema, G.T.

    2010-01-01

    In most nucleation theories, the state of a nucleating system is described by a distribution of droplet masses and this distribution evolves as a memoryless stochastic process. This is incorrect for a large class of nucleating systems. In a recent paper [ J. Kuipers and G. T. Barkema, Phys. Rev. E

  4. Classical gauge theories on the coadjoint orbits of infinite dimensional groups

    International Nuclear Information System (INIS)

    Grabowski, M.P.; Virginia Polytechnic Inst. and State Univ., Blacksburg; Tze Chiahsiung

    1991-01-01

    We reformulate several classical gauge theories on the coadjoint orbits of the semidirect product of the gauge group and the Weyl group. The construction is given for the Yang-Mills theories in arbitrary spacetime dimension d, Chern-Simons topological theory (d=3) and higher dimensional topological models of Horowitz (d≥4). (orig.)

  5. Nanoscale Capillary Flows in Alumina: Testing the Limits of Classical Theory.

    Science.gov (United States)

    Lei, Wenwen; McKenzie, David R

    2016-07-21

    Anodic aluminum oxide (AAO) membranes have well-formed cylindrical channels, as small as 10 nm in diameter, in a close packed hexagonal array. The channels in AAO membranes simulate very small leaks that may be present for example in an aluminum oxide device encapsulation. The 10 nm alumina channel is the smallest that has been studied to date for its moisture flow properties and provides a stringent test of classical capillary theory. We measure the rate at which moisture penetrates channels with diameters in the range of 10 to 120 nm with moist air present at 1 atm on one side and dry air at the same total pressure on the other. We extend classical theory for water leak rates at high humidities by allowing for variable meniscus curvature at the entrance and show that the extended theory explains why the flow increases greatly when capillary filling occurs and enables the contact angle to be determined. At low humidities our measurements for air-filled channels agree well with theory for the interdiffusive flow of water vapor in air. The flow rate of water-filled channels is one order of magnitude less than expected from classical capillary filling theory and is coincidentally equal to the helium flow rate, validating the use of helium leak testing for evaluating moisture flows in aluminum oxide leaks.

  6. Small random perturbations of infinite dimensional dynamical systems and nucleation theory

    International Nuclear Information System (INIS)

    Cassandro, M.; Olivieri, E.; Picco, P.

    1985-06-01

    We consider a stochastic differential equation with a standard space-time white noise and a double well non symmetric potential. The equation without the white noise term exhibits several equilibria two of which are stable. We study, in the double limit zero noise and thermodynamic limit the large fluctuations and compute the transition probability between the two stable equilibria (tunnelling). The unique stationary measure associated to the stochastic process described by our equation is strictly related to the Gibbs measure for a ferromagnetic spin system subject to a Kac interaction. Our double limit corresponds to the one considered by Lobowitz and Penrose in their rigorous version of the mean field theory of the first order phase transitions. The tunnelling between the two (non equivalent) equilibrium configurations is interpreted as the decay from the metastable to the stable state. Our results are in qualitative agreement with the usual nucleation theory

  7. Introduction to classical and quantum field theory

    International Nuclear Information System (INIS)

    Ng, Tai-Kai

    2009-01-01

    This is the first introductory textbook on quantum field theory to be written from the point of view of condensed matter physics. As such, it presents the basic concepts and techniques of statistical field theory, clearly explaining how and why they are integrated into modern quantum (and classical) field theory, and includes the latest developments. Written by an expert in the field, with a broad experience in teaching and training, it manages to present such substantial topics as phases and phase transitions or solitons and instantons in an accessible and concise way. Divided into three parts, the first part covers fundamental physics and the mathematics background needed by students in order to enter the field, while the second part introduces more advanced concepts and techniques. Part III discusses applications of quantum field theory to a few basic problems. The emphasis here lies on how modern concepts of quantum field theory are embedded in these approaches, and also on the limitations of standard quantum field theory techniques in facing, 'real' physics problems. Throughout there are numerous end-of-chapter problems, and a free solutions manual is available for lecturers. (orig.)

  8. A post-classical theory of enamel biomineralization… and why we need one.

    Science.gov (United States)

    Simmer, James P; Richardson, Amelia S; Hu, Yuan-Yuan; Smith, Charles E; Ching-Chun Hu, Jan

    2012-09-01

    Enamel crystals are unique in shape, orientation and organization. They are hundreds of thousands times longer than they are wide, run parallel to each other, are oriented with respect to the ameloblast membrane at the mineralization front and are organized into rod or interrod enamel. The classical theory of amelogenesis postulates that extracellular matrix proteins shape crystallites by specifically inhibiting ion deposition on the crystal sides, orient them by binding multiple crystallites and establish higher levels of crystal organization. Elements of the classical theory are supported in principle by in vitro studies; however, the classical theory does not explain how enamel forms in vivo. In this review, we describe how amelogenesis is highly integrated with ameloblast cell activities and how the shape, orientation and organization of enamel mineral ribbons are established by a mineralization front apparatus along the secretory surface of the ameloblast cell membrane.

  9. Heterogeneous nucleation from a supercooled ionic liquid on a carbon surface.

    Science.gov (United States)

    He, Xiaoxia; Shen, Yan; Hung, Francisco R; Santiso, Erik E

    2016-12-07

    Classical molecular dynamics simulations were used to study the nucleation of the crystal phase of the ionic liquid [dmim + ][Cl - ] from its supercooled liquid phase, both in the bulk and in contact with a graphitic surface of D = 3 nm. By combining the string method in collective variables [Maragliano et al., J. Chem. Phys. 125, 024106 (2006)], with Markovian milestoning with Voronoi tessellations [Maragliano et al., J. Chem. Theory Comput. 5, 2589-2594 (2009)] and order parameters for molecular crystals [Santiso and Trout, J. Chem. Phys. 134, 064109 (2011)], we computed minimum free energy paths, the approximate size of the critical nucleus, the free energy barrier, and the rates involved in these nucleation processes. For homogeneous nucleation, the subcooled liquid phase has to overcome a free energy barrier of ∼85 kcal/mol to form a critical nucleus of size ∼3.6 nm, which then grows into the monoclinic crystal phase. This free energy barrier becomes about 42% smaller (∼49 kcal/mol) when the subcooled liquid phase is in contact with a graphitic disk, and the critical nucleus formed is about 17% smaller (∼3.0 nm) than the one observed for homogeneous nucleation. The crystal formed in the heterogeneous nucleation scenario has a structure that is similar to that of the bulk crystal, with the exception of the layers of ions next to the graphene surface, which have larger local density and the cations lie with their imidazolium rings parallel to the graphitic surface. The critical nucleus forms near the graphene surface separated only by these layers of ions. The heterogeneous nucleation rate (∼4.8 × 10 11 cm -3 s -1 ) is about one order of magnitude faster than the homogeneous rate (∼6.6 × 10 10 cm -3 s -1 ). The computed free energy barriers and nucleation rates are in reasonable agreement with experimental and simulation values obtained for the homogeneous and heterogeneous nucleation of other systems (ice, urea, Lennard-Jones spheres, and oxide

  10. Nucleation of voids and other irradiation-produced defect aggregates

    International Nuclear Information System (INIS)

    Wiedersich, H.; Katz, J.L.

    1976-01-01

    The nucleation of defect clusters in crystalline solids from radiation-produced defects is different from the usual nucleation processes in one important aspect: the condensing defects, interstitial atoms and vacancies, can mutually annihilate and are thus similar to matter and antimatter. The nucleation process is described as the simultaneous reaction of vacancies and interstitials (and gas atoms if present) with embryos of all sizes. The reaction rates for acquisition of point defects (and gas atoms) are calculated from their respective jump frequencies and concentrations in the supersaturated system. The reaction rates for emission of point defects are derived from the free energies of the defect clusters in the thermodynamic equilibrium system, i.e., the system without excess point defects. This procedure differs from that used in conventional nucleation theory and permits the inclusion of the ''antimatter'' defect into the set of reaction-rate equations in a straightforward manner. The method is applied to steady-state nucleation, during irradiation, of both dislocation loops and voids in the absence and in the presence of immobile and mobile gas. The predictions of the nucleation theory are shown to be in qualitative agreement with experimental observations, e.g., void densities increase with increasing displacement rates; gases such as helium enhance void nucleation; at low displacement rates and at high temperatures the presence of gas is essential to void formation. For quantitative predictions, the theory must be extended to include the termination of nucleation

  11. Dimers in nucleating vapors

    Science.gov (United States)

    Lushnikov, A. A.; Kulmala, M.

    1998-09-01

    The dimer stage of nucleation may affect considerably the rate of the nucleation process at high supersaturation of the nucleating vapor. Assuming that the dimer formation limits the nucleation rate, the kinetics of the particle formation-growth process is studied starting with the definition of dimers as bound states of two associating molecules. The partition function of dimer states is calculated by summing the Boltzmann factor over all classical bound states, and the equilibrium population of dimers is found for two types of intermolecular forces: the Lennard-Jones (LJ) and rectangular well+hard core (RW) potentials. The principle of detailed balance is used for calculating the evaporation rate of dimers. The kinetics of the particle formation-growth process is then investigated under the assumption that the trimers are stable with respect to evaporation and that the condensation rate is a power function of the particle mass. If the power exponent λ=n/(n+1) (n is a non-negative integer), the kinetics of the process is described by a finite set of moments of particle mass distribution. When the characteristic time of the particle formation by nucleation is much shorter than that of the condensational growth, n+2 universal functions of a nondimensional time define the kinetic process. These functions are calculated for λ=2/3 (gas-to-particle conversion in the free molecular regime) and λ=1/2 (formation of islands on surfaces).

  12. Mechanisms of nucleation in flashing flows

    International Nuclear Information System (INIS)

    Yan, F.; Giot, M.

    1989-01-01

    The mechanisms of nucleation have been analysed. Starting from the assumption that the activation of micro-cavities in the wall surfaces is the most probable nucleation mechanism in practical flashing system, the authors study in detail the nucleation in a micro-cavity. A three step nucleation criterion is proposed, namely: trapping cavity, activable cavity and active cavity. Then, a new nucleation model is presented. The output of the model is the prediction of the bubble departure frequency versus the thermodynamic state of the liquid and the geometry of the cavity. The model can also predict the nucleation site density if the nature of the wall and the surface roughness are know. The prediction have been successfully compared with some preliminary experimental results. By combining the present model with Jones'theory, the flashing inception is correctly predicted. The use of this nucleation model for the complete modelling of a flashing non-equilibrium flow is in progress

  13. On the classical origins of yangian symmetry in integrable field theory

    International Nuclear Information System (INIS)

    MacKay, N.J.

    1992-01-01

    We show that Drinfeld's yangian algebra, studied recently as the algebra of conserved charges in certain two-dimensional integrable quantum field theories, is also present in the classical theory as a Poisson-Hopf algebra, and exhibit explicitly the Serre relations, coproduct and antipode. (orig.)

  14. Representational Realism, Closed Theories and the Quantum to Classical Limit

    Science.gov (United States)

    de Ronde, Christian

    In this chapter, we discuss the representational realist stance as a pluralistontic approach to inter-theoretic relationships. Our stance stresses the fact that physical theories require the necessary consideration of a conceptual level of discourse which determines and configures the specific field of phenomena discussed by each particular theory. We will criticize the orthodox line of research which has grounded the analysis about QM in two (Bohrian) metaphysical presuppositions - accepted in the present as dogmas that all interpretations must follow. We will also examine how the orthodox project of "bridging the gap" between the quantum and the classical domains has constrained the possibilities of research, producing only a limited set of interpretational problems which only focus in the justification of "classical reality" and exclude the possibility of analyzing the possibilities of non-classical conceptual representations of QM. The representational realist stance introduces two new problems, namely, the superposition problem and the contextuality problem, which consider explicitly the conceptual representation of orthodox QM beyond the mere reference to mathematical structures and measurement outcomes. In the final part of the chapter, we revisit, from representational realist perspective, the quantum to classical limit and the orthodox claim that this inter-theoretic relation can be explained through the principle of decoherence.

  15. Minding one's P's and Q's: From the one loop effective action in quantum field theory to classical transport theory

    International Nuclear Information System (INIS)

    Jalilian-Marian, Jamal; Jeon, Sangyong; Venugopalan, Raju; Wirstam, Jens

    2000-01-01

    The one loop effective action in quantum field theory can be expressed as a quantum mechanical path integral over world lines, with internal symmetries represented by Grassmanian variables. In this paper, we develop a real time, many body, world line formalism for the one loop effective action. In particular, we study hot QCD and obtain the classical transport equations which, as Litim and Manuel have shown, reduce in the appropriate limit to the non-Abelian Boltzmann-Langevin equation first obtained by Boedeker. In the Vlasov limit, the classical kinetic equations are those that correspond to the hard thermal loop effective action. We also discuss the imaginary time world line formalism for a hot φ 4 theory, and elucidate its relation to classical transport theory. (c) 2000 The American Physical Society

  16. Heterogeneous nucleation of entrained eutectic Si in high purity melt spun Al-Si alloys investigated by entrained droplet technique and DSC

    International Nuclear Information System (INIS)

    Li, J H; Schumacher, P; Albu, M; Hofer, F; Ludwig, T H; Arnberg, L

    2016-01-01

    Entrained droplet technique and DSC analyses were employed to investigate the influence of trace elements of Sr, Eu and P on the heterogeneous nucleation of entrained eutectic Si in high purity melt spun Al-5wt.% Si alloys. Sr and Eu addition was found to exert negative effects on the nucleation process, while an increased undercooling was observed. This can be attributed to the formation of phosphide compounds having a lower free energy and hence may preferentially form compared to AlP. Only a trace P addition was found to have a profound effect on the nucleation process. The nucleation kinetics is discussed on the basis of the classical nucleation theory and the free growth model, respectively. The estimated AlP patch size was found to be sufficient for the free growth of Si to occur within the droplets, which strongly indicates that the nucleation of Si on an AlP patch or AlP particle is a limiting step for free growth. The maximum nucleation site density within one droplet is directly related to the size distribution of AlP particles or AlP patches for Si nucleation, but is independent of the cooling rates. Although the nucleation conditions were optimized in entrained droplet experiments, the observed mechanisms are also valid at moderate cooling conditions, such as in shape casting. (paper)

  17. Using Classical Test Theory and Item Response Theory to Evaluate the LSCI

    Science.gov (United States)

    Schlingman, Wayne M.; Prather, E. E.; Collaboration of Astronomy Teaching Scholars CATS

    2011-01-01

    Analyzing the data from the recent national study using the Light and Spectroscopy Concept Inventory (LSCI), this project uses both Classical Test Theory (CTT) and Item Response Theory (IRT) to investigate the LSCI itself in order to better understand what it is actually measuring. We use Classical Test Theory to form a framework of results that can be used to evaluate the effectiveness of individual questions at measuring differences in student understanding and provide further insight into the prior results presented from this data set. In the second phase of this research, we use Item Response Theory to form a theoretical model that generates parameters accounting for a student's ability, a question's difficulty, and estimate the level of guessing. The combined results from our investigations using both CTT and IRT are used to better understand the learning that is taking place in classrooms across the country. The analysis will also allow us to evaluate the effectiveness of individual questions and determine whether the item difficulties are appropriately matched to the abilities of the students in our data set. These results may require that some questions be revised, motivating the need for further development of the LSCI. This material is based upon work supported by the National Science Foundation under Grant No. 0715517, a CCLI Phase III Grant for the Collaboration of Astronomy Teaching Scholars (CATS). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

  18. What is so ‘classical’ about Classical Reception? Theories, Methodologies and Future Prospects

    OpenAIRE

    Anastasia Bakogianni

    2016-01-01

    This paper delivered at the University of Rio on 3rd June 2015 seeks to explore different approaches to the most fundamental questions in classical reception studies. What is classical reception? And more particularly what is so ‘classical’ about classical reception? It discusses current trends in theory and methodology via an analysis of two cinematic receptions of the ancient story of Electra; one that proclaims its debt to a classical text while the other masks its classical connections.

  19. Progress in the application of classical S-matrix theory to inelastic collision processes

    International Nuclear Information System (INIS)

    McCurdy, C.W.; Miller, W.H.

    1980-01-01

    Methods are described which effectively solve two of the technical difficulties associated with applying classical S-matrix theory to inelastic/reactive scattering. Specifically, it is shown that rather standard numerical methods can be used to solve the ''root search'' problem (i.e., the nonlinear boundary value problem necessary to impose semiclassical quantum conditions at the beginning and the end of the classical trajectories) and also how complex classical trajectories, which are necessary to describe classically forbidden (i.e., tunneling) processes, can be computed in a numerically stable way. Application is made to vibrational relaxation of H 2 by collision with He (within the helicity conserving approximation). The only remaining problem with regard to applying classical S-matrix theory to complex collision processes has to do with the availability of multidimensional uniform asymptotic formulas for interpolating the ''primitive'' semiclassical expressions between their various regions of validity

  20. Theories of Matter, Space and Time; Classical theories

    Science.gov (United States)

    Evans, N.; King, S. F.

    2017-12-01

    This book and its sequel ('Theories of Matter Space and Time: Quantum Theories') are taken from third and fourth year undergraduate Physics courses at Southampton University, UK. The aim of both books is to move beyond the initial courses in classical mechanics, special relativity, electromagnetism, and quantum theory to more sophisticated views of these subjects and their interdependence. The goal is to guide undergraduates through some of the trickier areas of theoretical physics with concise analysis while revealing the key elegance of each subject. The first chapter introduces the key areas of the principle of least action, an alternative treatment of Newtownian dynamics, that provides new understanding of conservation laws. In particular, it shows how the formalism evolved from Fermat's principle of least time in optics. The second introduces special relativity leading quickly to the need and form of four-vectors. It develops four-vectors for all kinematic variables and generalize Newton's second law to the relativistic environment; then returns to the principle of least action for a free relativistic particle. The third chapter presents a review of the integral and differential forms of Maxwell's equations before massaging them to four-vector form so that the Lorentz boost properties of electric and magnetic fields are transparent. Again, it then returns to the action principle to formulate minimal substitution for an electrically charged particle.

  1. Traffic breakdown at a signal: classical theory versus the three-phase theory of city traffic

    International Nuclear Information System (INIS)

    Kerner, Boris S; Schreckenberg, Michael; Klenov, Sergey L

    2014-01-01

    Physical reasons for a crucial difference between the results of a three-phase theory developed recently (Kerner 2011 Phys. Rev. E 84 045102(R); 2013 Europhys. Lett. 102 28010; 2014 Physica A 397 76) and the classical theory are explained. Microscopic characteristics of traffic passing a traffic signal during the green signal phase and their dependence on the duration of the green phase have been found. It turns out that a moving synchronized flow pattern (MSP), which occurs in under-saturated traffic at the signal, causes ‘compression’ of traffic flow: the rate of MSP discharge can be considerably larger than the saturation flow rate of the classical traffic theory of city traffic. This leads to a considerably larger rate of traffic passing the signal in comparison with the saturation flow rate. This effect together with traffic behavior at the upstream queue front explains the metastability of under-saturated traffic with respect to a random time-delayed traffic breakdown. (paper)

  2. Study on onset of nucleate boiling and net vapor generation point in subcooled flow boiling

    International Nuclear Information System (INIS)

    Ohtake, Hiroyasu; Wada, Noriyoshi; Koizumi, Yasuo

    2002-01-01

    The onset of nucleate boiling (ONB) and the point of net vapor generation on subcooled flow boiling, focusing on liquid subcooling and liquid velocity were investigated experimentally and analytically. Experiments were conducted using a copper thin-film (35μm) and subcooled water in a range of the liquid velocity from 0.27 to 4.6 m/s at 0.10MPa. The liquid subcoolings were 20, 30 and 40K, respectively. Temperatures at the onset of nucleate boiling obtained in the experiments increased with the liquid subcoolings and the liquid velocities. The increases in the temperature of ONB were represented with the classical stability theory of preexisting nuclei. The measured results of the net vapor generation agreed well with the results of correlation by Saha and Zuber in the range of the present experiments. (J.P.N.)

  3. On possibility of agreement of quantum mechanics with classical probability theory

    International Nuclear Information System (INIS)

    Slavnov, D.A.

    2006-01-01

    Paper describes a scheme to carry out a construction of the quantum mechanics where the quantum system is assumed to be a pattern of the open classical subsystems. It enables to make use both of the formal classical logic and the classical probability theory in the quantum mechanics. On the other hand, in terms of the mentioned approach one manages to ensure complete reconstruction of the quantum mechanics standard mathematical tool specifying its application limits. The problem dealing with the quantum state reduction is scrutinized [ru

  4. Experimental Investigation of the Role of Ions in Aerosol Nucleation

    Science.gov (United States)

    Pedersen, J. P.; Enghoff, M. B.; Bondo, T.; Johnson, M. S.; Paling, S.; Svensmark, H.

    2008-12-01

    The role of ions in producing aerosols in Earth's atmosphere is an area of very active research. Atmospheric (Clarke et al. 1998) and experimental (Berndt et al. 2005) observations have shown that the nucleation of aerosol particles can occur under conditions that cannot be explained by classical nucleation theory. Several ideas have been put forward to solve this nucleation problem, e.g. Ion-Induced Nucleation and Ternary Nucleation. Experimental investigations exploring the role of ions in particle production are scarce, and often at conditions far removed from those relevant for the lower part of the atmosphere (Bricard et al. 1968). Recent experimental work (Svensmark et al. 2007) demonstrated that ions, produced by cosmic rays in the atmosphere, are likely to play an important role in the production of new aerosol particles. The mechanism whereby energetic cosmic rays can promote the production of cloud condensation nuclei at low altitudes constitutes a link between cosmic rays and Earth's climate and there is thus a need to corroborate the results in a different experiment. The present results are obtained in the same laboratory, but using a new setup The experiments were conducted in a 50 L cylindrical reaction chamber made of electropolished stainless steel. Aerosols were grown using photochemically produced sulphuric acid and ionization levels were controlled with a Cs-137 gamma-source. An increase in nucleation was observed when the chamber was exposed to the radioactive source. The results were analyzed using a model based on the General Dynamic Equation and the analysis revealed that Ion Induced Nucleation is the most likely mechanism for the observed nucleation increases and thus confirm the previous results. Berndt, T, Böge, O., Stratmann, F., Heintzenberg, J. & Kulmala, M. (2005), Science, 307, 698--700 Bricard, J., Billard, F. & Madelaine, G. (1968), J. Geophys. Res. 73, 4487--4496 Clarke, A.D., Davis, D., Kapustin, V. N. Eisele, F. Chen, G. Paluch

  5. Nucleation of voids. Final report, October 1, 1971--January 31, 1977

    International Nuclear Information System (INIS)

    Katz, J.L.

    1977-10-01

    The successful prediction of the conditions under which nucleation occurs in metals, as a result of the high concentrations of vacancies and interstitial atoms (and gas atoms) present in reactor environments, has been accomplished by (1) generalizing homogeneous nucleation theory to account for nucleation of matter (i.e., vacancies) in the presence of its antimatter (i.e., interstitials), (2) further generalizing the theory to account for the effects of both trapped and soluble gas, and (3) modifying the theory to describe interstitial loop formation and including the effects of external stress

  6. What is so ‘classical’ about Classical Reception? Theories, Methodologies and Future Prospects

    Directory of Open Access Journals (Sweden)

    Anastasia Bakogianni

    2016-06-01

    Full Text Available This paper delivered at the University of Rio on 3rd June 2015 seeks to explore different approaches to the most fundamental questions in classical reception studies. What is classical reception? And more particularly what is so ‘classical’ about classical reception? It discusses current trends in theory and methodology via an analysis of two cinematic receptions of the ancient story of Electra; one that proclaims its debt to a classical text while the other masks its classical connections.

  7. Mathematical theories of classical particle channeling in perfect crystals

    International Nuclear Information System (INIS)

    Dumas, H. Scott

    2005-01-01

    We present an overview of our work on rigorous mathematical theories of channeling for highly energetic positive particles moving in classical perfect crystal potentials. Developed over the last two decades, these theories include: (i) a comprehensive, highly mathematical theory based on Nekhoroshev's theorem which embraces both axial and planar channeling as well as certain non-channeling particle motions (ii) a theory of axial channeling for relativistic particles based on a single-phase averaging method for ordinary differential equations and (iii) a theory of planar channeling for relativistic particles based on a two-phase averaging method for ordinary differential equations. Here we touch briefly on (i) and (ii), then focus on (iii). Together these theories place Lindhard's continuum model approximations on a firm mathematical foundation, and should serve as the starting point for more refined mathematical treatments of channeling

  8. Nucleation of superconductivity under rapid cycling of an electric field

    International Nuclear Information System (INIS)

    Bandyopadhyay, Malay

    2008-01-01

    The effect of an externally applied high-frequency oscillating electric field on the critical nucleation field of superconductivity in the bulk as well as at the surface of a superconductor is investigated in detail in this work. Starting from the linearized time-dependent Ginzburg-Landau (TDLG) theory, and using the variational principle, I have shown the analogy between a quantum harmonic oscillator with that of the nucleation of superconductivity in the bulk and a quantum double oscillator with that of the nucleation at the surface of a finite sample. The effective Hamiltonian approach of Cook et al (1985 Phys. Rev. A 31 564) is employed to incorporate the effect of an externally applied highly oscillating electric field. The critical nucleation field ratio is also calculated from the ground state energy method. The results obtained from these two approximate theories agree very well with the exact results for the case of an undriven system, which establishes the validity of these two approximate theories. It is observed that the highly oscillating electric field actually increases the bulk critical nucleation field (H c 2 ) as well as the surface critical nucleation field (H c 3 ) of superconductivity as compared to the case of absent electric field (ε 0 = 0). But the externally applied rapidly oscillating electric field accentuates the surface critical nucleation field more than the bulk critical nucleation field, i.e. the increase of H c 3 is 1.6592 times larger than that of H c 2

  9. Classical confining solutions of a tensor gauge theory incorporating colour

    International Nuclear Information System (INIS)

    Salam, A.; Strathdee, J.

    1977-04-01

    A mass-modified Einstein-Weyl gauge theory of colour carrying spin-two mesons is formulated. A classical solution is exhibited for the case of internal SU(2) symmetry which may confine quarks in colour singlets

  10. Geometric function theory: a modern view of a classical subject

    International Nuclear Information System (INIS)

    Crowdy, Darren

    2008-01-01

    Geometric function theory is a classical subject. Yet it continues to find new applications in an ever-growing variety of areas such as modern mathematical physics, more traditional fields of physics such as fluid dynamics, nonlinear integrable systems theory and the theory of partial differential equations. This paper surveys, with a view to modern applications, open problems and challenges in this subject. Here we advocate an approach based on the use of the Schottky–Klein prime function within a Schottky model of compact Riemann surfaces. (open problem)

  11. Interaction of the nucleation phenomena at adjacent sites in nucleate boiling

    International Nuclear Information System (INIS)

    Sultan, M.; Judd, R.L.

    1983-01-01

    The present investigation is an original study in nucleate pool boiling heat transfer combining theory and experiment in which water boiling at atmospheric pressure on a single copper surface at two different levels of heat and different levels of subcooling was studied. Cross spectral analysis of the signals generated by the emission of bubbles at adjacent nucleation sites was used to determine the relationship of the time elapsed between the start of bubble growth at the two neighbouring active sites with the distance separating them. The experimental results obtained indicated that for the lower level of heat flux at three different levels of subcooling, the elapsed time and distance were directly related. Theoretical predictions of a temperature disturbance propagating through the heating surface in the radial direction gave good agreement with the experimental findings, suggesting that this is the mechanism responsible for the activation of the surrounding nucleation sites

  12. Nucleation in an ultra low ionization environment

    DEFF Research Database (Denmark)

    Pedersen, Jens Olaf Pepke; Enghoff, Martin Andreas Bødker; Paling, Sean

    Atmospheric ions can enhance the nucleation of aerosols, as has been established by experiments, observation, and theory. In the clean marine atmosphere ionization is mainly caused by cosmic rays which in turn are controlled by the activity of the Sun, thus providing a potential link between solar...... activity and climate. In order to understand the effect ions may have on the production of cloud condensation nuclei the overall contribution of ion induced nucleation to the global production of secondary aerosols must be determined. One issue with determining this contribution is that several mechanisms...... for nucleation exist and it can be difficult to determine the relative importance of the various mechanisms in a given nucleation event when both ion induced and electrically neutral nucleation mechanisms are at work at the same time. We have carried out nucleation experiments in the Boulby Underground...

  13. Nucleation and creep of vortices in superfluids and clean superconductors

    International Nuclear Information System (INIS)

    Sonin, E.B.

    1995-01-01

    The paper is devoted to vortex nucleation in uniform and nonuniform superflows in superfluids, and to creep of vortices trapped by twin boundaries and columnar defects in isotropic and anisotropic superconductors. The shape of a nuclated loop which yields the maximal nucleation rate is defined from the balance of the Lorentz and the line-tension forces. If the trapping energy is small, the contact angle at which the vortex line meets the plane of the twin-boundary or the axis of the columnar defect is also small. This may strongly enhance the rate of thermal nucleation and especially of quantum nucleation. In the analysis of quantum tunnelling it was assumed that the vortex has no mass and its motion is governed by the Magnus force, as expected for superfluids and very pure superconductors. Quantum nucleation rate from the traditional quasiclassical theory of macroscopic tunnelling is compared with the nucleation rate derived from the Gross-Pitaevskii theory of a weakly nonideal Bose-gas. (orig.)

  14. Magnetization reversal in nucleation controlled magnets. I. Theory

    International Nuclear Information System (INIS)

    Ramesh, R.; Srikrishna, K.

    1988-01-01

    A statistical model, based upon earlier models of Brown [J. Appl. Phys. 33, 3022 (1962)] and McIntyre [J. Phys. D 3, 1430 (1970)] has been developed to examine the magnetization reversal of domain-wall nucleation controlled permanent magnets such as sintered Fe-Nd-B and SmCo 5 . Using a Poisson distribution of the defects on the surface of the grains, a ''weakest link statistics'' type model has been developed. The model has been used to calculate hysteresis loops for sintered Fe-Nd-B-type polycrystalline magnets. It is shown that the intrinsic coercivity measured for a bulk magnet should vary inversely as the logarithm of the surface area of the grain. The effect of demagnetizing field has been incorporated by a mean-field-type approximation, to calculate the overall nucleation field from the intrinsic coercivity. The hysteresis loops theoretically calculated are in excellent agreement with the overall form of those experimentally determined for similar nucleation controlled magnets. The model also predicts that for an inhomogeneous grain size distribution, such as a bimodal distribution, kinks will be observed in the second quadrant of the hysteresis loops

  15. Classical electromagnetic field theory in the presence of magnetic sources

    OpenAIRE

    Chen, Wen-Jun; Li, Kang; Naón, Carlos

    2001-01-01

    Using two new well defined 4-dimensional potential vectors, we formulate the classical Maxwell's field theory in a form which has manifest Lorentz covariance and SO(2) duality symmetry in the presence of magnetic sources. We set up a consistent Lagrangian for the theory. Then from the action principle we get both Maxwell's equation and the equation of motion of a dyon moving in the electro-magnetic field.

  16. Classical testing particles and (4 + N)-dimensional theories of space-time

    International Nuclear Information System (INIS)

    Nieto-Garcia, J.A.

    1986-01-01

    The Lagrangian theory of a classical relativistic spinning test particle (top) developed by Hanson and Regge and by Hojman is briefly reviewed. Special attention is devoted to the constraints imposed on the dynamical variables associated with the system of this theory. The equations for a relativistic top are formulated in a way suitable for use in the study of geometrical properties of the 4 + N-dimensional Kaluza-Klein background. It is shown that the equations of motion of a top in five dimensions reduce to the Hanson-Regge generalization of the Bargmann-Michel-Telegdi equations of motion in four dimensions when suitable conditions on the spin tensor are imposed. The classical bosonic relativistic string theory is discussed and the connection of this theory with the top theory is examined. It is found that the relation between the string and the top leads naturally to the consideration of a 3-dimensional extended system (called terron) which sweeps out a 4-dimensional surface as it evolves in a space-time. By using a square root procedure based on ideas by Teitelboim a theory of a supersymmetric top is developed. The quantization of the new supersymmetric system is discussed. Conclusions and suggestions for further research are given

  17. The classical electromagnetic theory which corresponds to the two dimensions quantum electrodynamics with massless fermions

    International Nuclear Information System (INIS)

    Galvao, C.A.P.; Mignaco, J.A.

    1994-01-01

    The classical electromagnetic theory is analysed which corresponds to the two-dimensional quantum electrodynamics with massless spinor fields (Schwinger model). The chiral anomaly is introduced as a currents property, which in the two-dimensional spinor fields are duality related. It is also shown that the resulting classical theory is consistent. (author). 5 refs

  18. The Gibbs free energy of homogeneous nucleation: From atomistic nuclei to the planar limit.

    Science.gov (United States)

    Cheng, Bingqing; Tribello, Gareth A; Ceriotti, Michele

    2017-09-14

    In this paper we discuss how the information contained in atomistic simulations of homogeneous nucleation should be used when fitting the parameters in macroscopic nucleation models. We show how the number of solid and liquid atoms in such simulations can be determined unambiguously by using a Gibbs dividing surface and how the free energy as a function of the number of solid atoms in the nucleus can thus be extracted. We then show that the parameters (the chemical potential, the interfacial free energy, and a Tolman correction) of a model based on classical nucleation theory can be fitted using the information contained in these free-energy profiles but that the parameters in such models are highly correlated. This correlation is unfortunate as it ensures that small errors in the computed free energy surface can give rise to large errors in the extrapolated properties of the fitted model. To resolve this problem we thus propose a method for fitting macroscopic nucleation models that uses simulations of planar interfaces and simulations of three-dimensional nuclei in tandem. We show that when the chemical potentials and the interface energy are pinned to their planar-interface values, more precise estimates for the Tolman length are obtained. Extrapolating the free energy profile obtained from small simulation boxes to larger nuclei is thus more reliable.

  19. Overview of classical test theory and item response theory for the quantitative assessment of items in developing patient-reported outcomes measures.

    Science.gov (United States)

    Cappelleri, Joseph C; Jason Lundy, J; Hays, Ron D

    2014-05-01

    The US Food and Drug Administration's guidance for industry document on patient-reported outcomes (PRO) defines content validity as "the extent to which the instrument measures the concept of interest" (FDA, 2009, p. 12). According to Strauss and Smith (2009), construct validity "is now generally viewed as a unifying form of validity for psychological measurements, subsuming both content and criterion validity" (p. 7). Hence, both qualitative and quantitative information are essential in evaluating the validity of measures. We review classical test theory and item response theory (IRT) approaches to evaluating PRO measures, including frequency of responses to each category of the items in a multi-item scale, the distribution of scale scores, floor and ceiling effects, the relationship between item response options and the total score, and the extent to which hypothesized "difficulty" (severity) order of items is represented by observed responses. If a researcher has few qualitative data and wants to get preliminary information about the content validity of the instrument, then descriptive assessments using classical test theory should be the first step. As the sample size grows during subsequent stages of instrument development, confidence in the numerical estimates from Rasch and other IRT models (as well as those of classical test theory) would also grow. Classical test theory and IRT can be useful in providing a quantitative assessment of items and scales during the content-validity phase of PRO-measure development. Depending on the particular type of measure and the specific circumstances, the classical test theory and/or the IRT should be considered to help maximize the content validity of PRO measures. Copyright © 2014 Elsevier HS Journals, Inc. All rights reserved.

  20. Generalized force in classical field theory. [Euler-Lagrange equations

    Energy Technology Data Exchange (ETDEWEB)

    Krause, J [Universidad Central de Venezuela, Caracas

    1976-02-01

    The source strengths of the Euler-Lagrange equations, for a system of interacting fields, are heuristically interpreted as generalized forces. The canonical form of the energy-momentum tensor thus consistently appears, without recourse to space-time symmetry arguments. A concept of 'conservative' generalized force in classical field theory is also briefly discussed.

  1. Gauge bridges in classical field theory

    International Nuclear Information System (INIS)

    Jakobs, S.

    2009-03-01

    In this thesis Poisson structures of two classical gauge field theories (Maxwell-Klein-Gordon- and Maxwell-Dirac-system) are constructed using the parametrix construction of Green's functions. Parametrices for the Maxwell-Klein-Gordon- and Maxwell-Dirac-system are constructed in Minkowski space and this construction is later generalized to curved space times for the Maxwell-Klein-Gordon-system. With these Green's functions Poisson brackets will be defined as Peierls brackets. Finally non-local, gauge invariant observables, the so-called ''gauge bridges''are constructed. Gauge bridges are the matrix elements of holonomy operators. It is shown, that these emerge from Poisson brackets of local, gauge invariant observables. (orig.)

  2. Classical Bianchi Type I Cosmology in K-Essence Theory

    International Nuclear Information System (INIS)

    Pimentel, Luis O.; Socorro, J.; Espinoza-García, Abraham

    2014-01-01

    We use one of the simplest forms of the K-essence theory and we apply it to the classical anisotropic Bianchi type I cosmological model, with a barotropic perfect fluid (p=γρ) modeling the usual matter content and with cosmological constant Λ. Classical exact solutions for any γ≠1 and Λ=0 are found in closed form, whereas solutions for Λ≠0 are found for particular values in the barotropic parameter. We present the possible isotropization of the cosmological model Bianchi I using the ratio between the anisotropic parameters and the volume of the universe. We also include a qualitative analysis of the analog of the Friedmann equation.

  3. Structural match of heterogeneously nucleated Mn(OH)_2(s) nanoparticles on quartz under various pH conditions

    International Nuclear Information System (INIS)

    Jung, Haesung; Lee, Byeongdu; Jun, Young-Shin

    2016-01-01

    The early nucleation stage of Mn (hydr)oxide on mineral surfaces is crucial to understand its occurrence and the cycling of nutrients in environmental systems. However, there are only limited studies on the heterogeneous nucleation of Mn(OH)_2(s) as the initial stage of Mn (hydr)oxide precipitation. Here, we investigated the effect of pH on the initial nucleation of Mn(OH)_2(s) on quartz. Under various pH conditions of 9.8, 9.9, and 10.1, we analyzed the structural matches between quartz and heterogeneously nucleated Mn(OH)_2(s). The structural matches were calculated by measuring lateral and vertical dimensions using grazing incidence small angle X-ray scattering (GISAXS) and atomic force microscopy (AFM), respectively. We found that a poorer structural match occurred at a higher pH than at a lower pH. The faster nucleation at a higher pH condition accounted for the observed poorer structural match. By fitting the structural match using classical nucleation theory, we also calculated the interfacial energy between Mn(OH)_2(s) and water (γ_n_f = 71 ± 7 mJ/m"2). The calculated m values and γ_n_f provided the variance of interfacial energy between quartz and Mn(OH)_2(s): γ_s_n = 262–272 mJ/m"2. As a result, this study provides new qualitative and quantitative information about heterogeneous nucleation on environmentally an abundant mineral surface, quartz, and it offers important underpinnings for understanding the fate and transport of trace ions in environmental systems.

  4. Theory on the Mechanism of DNA Renaturation: Stochastic Nucleation and Zipping.

    Directory of Open Access Journals (Sweden)

    Gnanapragasam Niranjani

    Full Text Available Renaturation of the complementary single strands of DNA is one of the important processes that requires better understanding in the view of molecular biology and biological physics. Here we develop a stochastic dynamical model on the DNA renaturation. According to our model there are at least three steps in the renaturation process viz. nonspecific-contact formation, correct-contact formation and nucleation, and zipping. Most of the earlier two-state models combined nucleation with nonspecific-contact formation step. In our model we suggest that it is considerably meaningful when we combine the nucleation with the zipping since nucleation is the initial step of zipping and nucleated and zipping molecules are indistinguishable. Nonspecific contact formation step is a pure three-dimensional diffusion controlled collision process. Whereas nucleation involves several rounds of one-dimensional slithering and internal displacement dynamics of one single strand of DNA on the other complementary strand in the process of searching for the correct-contact and then initiate nucleation. Upon nucleation, the stochastic zipping follows to generate a fully renatured double stranded DNA. It seems that the square-root dependency of the overall renaturation rate constant on the length of reacting single strands originates mainly from the geometric constraints in the diffusion controlled nonspecific-contact formation step. Further the inverse scaling of the renaturation rate on the viscosity of reaction medium also originates from nonspecific contact formation step. On the other hand the inverse scaling of the renaturation rate with the sequence complexity originates from the stochastic zipping which involves several rounds of crossing over the free-energy barrier at microscopic levels. When the sequence of renaturing single strands of DNA is repetitive with less complexity then the cooperative effects will not be noticeable since the parallel zipping will be a

  5. Rayleigh Scattering Density Measurements, Cluster Theory, and Nucleation Calculations at Mach 10

    Science.gov (United States)

    Balla, R. Jeffrey; Everhart, Joel L.

    2012-01-01

    In an exploratory investigation, quantitative unclustered laser Rayleigh scattering measurements of density were performed in the air in the NASA Langley Research Center's 31 in. Mach 10 wind tunnel. A review of 20 previous years of data in supersonic and Mach 6 hypersonic flows is presented where clustered signals typically overwhelmed molecular signals. A review of nucleation theory and accompanying nucleation calculations are also provided to interpret the current observed lack of clustering. Data were acquired at a fixed stagnation temperature near 990Kat five stagnation pressures spanning 2.41 to 10.0 MPa (350 to 1454 psi) using a pulsed argon fluoride excimer laser and double-intensified charge-coupled device camera. Data averaged over 371 images and 210 pixels along a 36.7mmline measured freestream densities that agree with computed isentropic-expansion densities to less than 2% and less than 6% at the highest and lowest densities, respectively. Cluster-free Mach 10 results are compared with previous clustered Mach 6 and condensation-free Mach 14 results. Evidence is presented indicating vibrationally excited oxygen and nitrogen molecules are absorbed as the clusters form, release their excess energy, and inhibit or possibly reverse the clustering process. Implications for delaying clustering and condensation onset in hypersonic and hypervelocity facilities are discussed.

  6. Lower Bound on the Energy Density in Classical and Quantum Field Theories.

    Science.gov (United States)

    Wall, Aron C

    2017-04-14

    A novel method for deriving energy conditions in stable field theories is described. In a local classical theory with one spatial dimension, a local energy condition always exists. For a relativistic field theory, one obtains the dominant energy condition. In a quantum field theory, there instead exists a quantum energy condition, i.e., a lower bound on the energy density that depends on information-theoretic quantities. Some extensions to higher dimensions are briefly discussed.

  7. Classical and quantum theories of the polarization bremsstrahlung in the local electron density model

    International Nuclear Information System (INIS)

    Astapenko, V.A.; Bureeva, L.A.; Lisitsa, V.S.

    2000-01-01

    Classical and quantum theories of polarization bremsstrahlung in a statistical (Thomas-Fermi) potential of complex atoms and ions are developed. The basic assumptions of the theories correspond to the approximations employed earlier in classical and quantum calculations of ordinary bremsstrahlung in a static potential. This makes it possible to study on a unified basis the contribution of both channels in the radiation taking account of their interference. The classical model makes it possible to obtain simple universal formulas for the spectral characteristics of the radiation. The theory is applied to electrons with moderate energies, which are characteristic for plasma applications, specifically, radiation from electrons on the argon-like ion KII at frequencies close to its ionization potential. The computational results show the importance of taking account of the polarization channel of the radiation for plasma with heavy ions

  8. Direct calculation of ice homogeneous nucleation rate for a molecular model of water

    Science.gov (United States)

    Haji-Akbari, Amir; Debenedetti, Pablo G.

    2015-01-01

    Ice formation is ubiquitous in nature, with important consequences in a variety of environments, including biological cells, soil, aircraft, transportation infrastructure, and atmospheric clouds. However, its intrinsic kinetics and microscopic mechanism are difficult to discern with current experiments. Molecular simulations of ice nucleation are also challenging, and direct rate calculations have only been performed for coarse-grained models of water. For molecular models, only indirect estimates have been obtained, e.g., by assuming the validity of classical nucleation theory. We use a path sampling approach to perform, to our knowledge, the first direct rate calculation of homogeneous nucleation of ice in a molecular model of water. We use TIP4P/Ice, the most accurate among existing molecular models for studying ice polymorphs. By using a novel topological approach to distinguish different polymorphs, we are able to identify a freezing mechanism that involves a competition between cubic and hexagonal ice in the early stages of nucleation. In this competition, the cubic polymorph takes over because the addition of new topological structural motifs consistent with cubic ice leads to the formation of more compact crystallites. This is not true for topological hexagonal motifs, which give rise to elongated crystallites that are not able to grow. This leads to transition states that are rich in cubic ice, and not the thermodynamically stable hexagonal polymorph. This mechanism provides a molecular explanation for the earlier experimental and computational observations of the preference for cubic ice in the literature. PMID:26240318

  9. Motion of small bodies in classical field theory

    International Nuclear Information System (INIS)

    Gralla, Samuel E.

    2010-01-01

    I show how prior work with R. Wald on geodesic motion in general relativity can be generalized to classical field theories of a metric and other tensor fields on four-dimensional spacetime that (1) are second-order and (2) follow from a diffeomorphism-covariant Lagrangian. The approach is to consider a one-parameter-family of solutions to the field equations satisfying certain assumptions designed to reflect the existence of a body whose size, mass, and various charges are simultaneously scaled to zero. (That such solutions exist places a further restriction on the class of theories to which our results apply.) Assumptions are made only on the spacetime region outside of the body, so that the results apply independent of the body's composition (and, e.g., black holes are allowed). The worldline 'left behind' by the shrinking, disappearing body is interpreted as its lowest-order motion. An equation for this worldline follows from the 'Bianchi identity' for the theory, without use of any properties of the field equations beyond their being second-order. The form of the force law for a theory therefore depends only on the ranks of its various tensor fields; the detailed properties of the field equations are relevant only for determining the charges for a particular body (which are the ''monopoles'' of its exterior fields in a suitable limiting sense). I explicitly derive the force law (and mass-evolution law) in the case of scalar and vector fields, and give the recipe in the higher-rank case. Note that the vector force law is quite complicated, simplifying to the Lorentz force law only in the presence of the Maxwell gauge symmetry. Example applications of the results are the motion of 'chameleon' bodies beyond the Newtonian limit, and the motion of bodies in (classical) non-Abelian gauge theory. I also make some comments on the role that scaling plays in the appearance of universality in the motion of bodies.

  10. Semi-classical approximation and the problem of boundary conditions in the theory of relativistic particle radiation

    International Nuclear Information System (INIS)

    Akhiezer, A.I.; Shul'ga, N.F.

    1991-01-01

    The process of relativistic particle radiation in an external field has been studied in the semi-classical approximation rather extensively. The main problem arising in the studies is in expressing the formula of the quantum theory of radiation in terms of classical quantities, for example of the classical trajectories. However, it still remains unclear how the particle trajectory is assigned, that is which particular initial or boundary conditions determine the trajectory in semi-classical approximation quantum theory of radiation. We shall try to solve this problem. Its importance comes from the fact that in some cases one and the same boundary conditions may give rise to two or more trajectories. We demonstrate that this fact must necessarily be taken into account on deriving the classical limit for the formulae of the quantum theory of radiation, since it leads to a specific interference effect in radiation. The method we used to deal with the problem is similar to the method employed by Fock to analyze the problem of a canonical transformation in classical and quantum mechanics. (author)

  11. Theoretical physics 3. Classical field theory. On electrodynamics, non-Abelian gauge theories, and gravitation. 4. ed.; Theoretische Physik 3. Klassische Feldtheorie. Von Elektrodynamik, nicht-Abelschen Eichtheorien und Gravitation

    Energy Technology Data Exchange (ETDEWEB)

    Scheck, Florian [Mainz Univ. (Germany). Inst. fuer Physik

    2017-09-01

    The following topics are dealt with: Maxwell's equations together with their symmetry and covariance, the Maxwell theory as classical field theory, simple applications of Maxwell's theory, local gauge theories, classical field theory of gravitation. (HSI)

  12. On the mathematical theory of classical fields and general relativity

    CERN Document Server

    Klainerman, S

    1993-01-01

    From the perspective of an analyst, like myself, the General Theory of Relativity provides an extrordinary rich and vastly virgin territory. It is the aim of my lecture to provide, first, an account of those aspects of the theory which attract me most and second a perspective of what has been accomplished so far in that respect. In trying to state our main objectives it helps to view General Relativity in the broader context of Classical Field Theory. EinsteiniVacuum equations, or shortly E—V, is already sufficiently complicated. I will thus restrict my attention to them.

  13. Methods of geometric function theory in classical and modern problems for polynomials

    International Nuclear Information System (INIS)

    Dubinin, Vladimir N

    2012-01-01

    This paper gives a survey of classical and modern theorems on polynomials, proved using methods of geometric function theory. Most of the paper is devoted to results of the author and his students, established by applying majorization principles for holomorphic functions, the theory of univalent functions, the theory of capacities, and symmetrization. Auxiliary results and the proofs of some of the theorems are presented. Bibliography: 124 titles.

  14. Noether symmetries, energy-momentum tensors, and conformal invariance in classical field theory

    International Nuclear Information System (INIS)

    Pons, Josep M.

    2011-01-01

    In the framework of classical field theory, we first review the Noether theory of symmetries, with simple rederivations of its essential results, with special emphasis given to the Noether identities for gauge theories. With this baggage on board, we next discuss in detail, for Poincare invariant theories in flat spacetime, the differences between the Belinfante energy-momentum tensor and a family of Hilbert energy-momentum tensors. All these tensors coincide on shell but they split their duties in the following sense: Belinfante's tensor is the one to use in order to obtain the generators of Poincare symmetries and it is a basic ingredient of the generators of other eventual spacetime symmetries which may happen to exist. Instead, Hilbert tensors are the means to test whether a theory contains other spacetime symmetries beyond Poincare. We discuss at length the case of scale and conformal symmetry, of which we give some examples. We show, for Poincare invariant Lagrangians, that the realization of scale invariance selects a unique Hilbert tensor which allows for an easy test as to whether conformal invariance is also realized. Finally we make some basic remarks on metric generally covariant theories and classical field theory in a fixed curved background.

  15. Lorentz invariance from classical particle paths in quantum field theory of electric and magnetic charge

    International Nuclear Information System (INIS)

    Brandt, R.A.; Neri, F.; Zwanziger, D.

    1979-01-01

    We establish the Lorentz invariance of the quantum field theory of electric and magnetic charge. This is a priori implausible because the theory is the second-quantized version of a classical field theory which is inconsistent if the minimally coupled charged fields are smooth functions. For our proof we express the generating functional for the gauge-invariant Green's functions of quantum electrodynamics: with or without magnetic charge: as a path integral over the trajectories of classical charged point particles. The electric-electric and electric-magnetic interactions contribute factors exp(JDJ) and exp(JD'K), where J and K are the electric and magnetic currents of classical point particles and D is the usual photon propagator. The propagator D' involves the Dirac string but exp(JD'K) depends on it only through a topological integer linking string and classical particle trajectories. The charge quantization condition e/sub i/g/sub j/ - g/sub i/e/sub j/ = integer then suffices to make the gauge-invariant Green's functions string independent. By implication our formulation shows that if the Green's functions of quantum electrodynamics are expressed as usual as functional integrals over classical charged fields, the smooth field configurations have measure zero and all the support of the Feynman measure lies on the trajectories of classical point particles

  16. Microscopic aspects of wetting using classical density functional theory

    Science.gov (United States)

    Yatsyshin, P.; Durán-Olivencia, M.-A.; Kalliadasis, S.

    2018-07-01

    Wetting is a rather efficient mechanism for nucleation of a phase (typically liquid) on the interface between two other phases (typically solid and gas). In many experimentally accessible cases of wetting, the interplay between the substrate structure, and the fluid–fluid and fluid–substrate intermolecular interactions brings about an entire ‘zoo’ of possible fluid configurations, such as liquid films with a thickness of a few nanometers, liquid nanodrops and liquid bridges. These fluid configurations are often associated with phase transitions occurring at the solid–gas interface and at lengths of just several molecular diameters away from the substrate. In this special issue article, we demonstrate how a fully microscopic classical density-functional framework can be applied to the efficient, rational and systematic exploration of the rich phase space of wetting phenomena. We consider a number of model prototype systems such as wetting on a planar wall, a chemically patterned wall and a wedge. Through density-functional computations we demonstrate that for these simply structured substrates the behaviour of the solid–gas interface is already highly complex and non-trivial.

  17. The classical limit of quantum theories: Particles in external metrics and with spin

    International Nuclear Information System (INIS)

    Hogreve, J.J.

    1983-01-01

    The intention of this work is to provide some further steps in this program, particullary the clarification of certain aspects of the classical limit of quantum theory. Here the classical limit is understood in the sense that we consider a family of quantum theories parametrized by (h/2π) > 0, and then take the limit (h/2π) -> 0. From a mathematical point of view we are thus in the area calles 'asymptotic perturbation theory'. In detail, we examine the canonical partition function Tr [esup(-x)] with x=tH((h/2π)) for Hamiltonians H ((h/2π)) involving the Laplace-Beltrami operator on manifolds, and show that after scaling it by (h/2π)sup(N) it converges to its corresponding classical counterpart. This is done in chapter I. In chapter II we prove the convergence to its classical limit of the partition function for Hamiltonians including spin degrees of freedom, i.e. Hamiltonians of Pauli type. In this case taking the classical limit includes also manipulation on the spin space in the sense that the weight of the representation of the spin operators has to tend to infinity simultanously as (h/2π) approaches zero. Under this procedure the spin space itself, that is the representation space of the spin operators, turn into certain coadjoint orbits of the respective Lie group. The main result of chapter III is a generalized Ehrenfest theorem; as (h/2π) -> 0 the quantum mechanical time evolution generated by Hamiltonians including external metrics and vector potentials becomes a solution of the corresponding classical canonical Hamiltonian equations. (orig./HSI) [de

  18. A classical density functional theory of ionic liquids.

    Science.gov (United States)

    Forsman, Jan; Woodward, Clifford E; Trulsson, Martin

    2011-04-28

    We present a simple, classical density functional approach to the study of simple models of room temperature ionic liquids. Dispersion attractions as well as ion correlation effects and excluded volume packing are taken into account. The oligomeric structure, common to many ionic liquid molecules, is handled by a polymer density functional treatment. The theory is evaluated by comparisons with simulations, with an emphasis on the differential capacitance, an experimentally measurable quantity of significant practical interest.

  19. Homogeneous nucleation rates of nitric acid dihydrate (NAD at simulated stratospheric conditions – Part II: Modelling

    Directory of Open Access Journals (Sweden)

    O. Möhler

    2006-01-01

    Full Text Available Activation energies ΔGact for the nucleation of nitric acid dihydrate (NAD in supercooled binary HNO3/H2O solution droplets were calculated from volume-based nucleation rate measurements using the AIDA (Aerosol, Interactions, and Dynamics in the Atmosphere aerosol chamber of Forschungszentrum Karlsruhe. The experimental conditions covered temperatures T between 192 and 197 K, NAD saturation ratios SNAD between 7 and 10, and nitric acid molar fractions of the nucleating sub-micron sized droplets between 0.26 and 0.28. Based on classical nucleation theory, a new parameterisation for ΔGact=A×(T ln SNAD−2+B is fitted to the experimental data with A=2.5×106 kcal K2 mol−1 and B=11.2−0.1(T−192 kcal mol−1. A and B were chosen to also achieve good agreement with literature data of ΔGact. The parameter A implies, for the temperature and composition range of our analysis, a mean interface tension σsl=51 cal mol−1 cm−2 between the growing NAD germ and the supercooled solution. A slight temperature dependence of the diffusion activation energy is represented by the parameter B. Investigations with a detailed microphysical process model showed that literature formulations of volume-based (Salcedo et al., 2001 and surface-based (Tabazadeh et al., 2002 nucleation rates significantly overestimate NAD formation rates when applied to the conditions of our experiments.

  20. Nucleation and growth of lead oxide particles in liquid lead-bismuth eutectic.

    Science.gov (United States)

    Gladinez, Kristof; Rosseel, Kris; Lim, Jun; Marino, Alessandro; Heynderickx, Geraldine; Aerts, Alexander

    2017-10-18

    Liquid lead-bismuth eutectic (LBE) is an important candidate to become the primary coolant of future, generation IV, nuclear fast reactors and Accelerator Driven System (ADS) concepts. One of the main challenges with the use of LBE as a coolant is to avoid its oxidation which results in solid lead oxide (PbO) precipitation. The chemical equilibria governing PbO formation are well understood. However, insufficient kinetic information is currently available for the development of LBE-based nuclear technology. Here, we report the results of experiments in which the nucleation, growth and dissolution of PbO in LBE during temperature cycling are measured by monitoring dissolved oxygen using potentiometric oxygen sensors. The metastable region, above which PbO nucleation can occur, has been determined under conditions relevant for the operation of LBE cooled nuclear systems and was found to be independent of setup geometry and thus thought to be widely applicable. A kinetic model to describe formation and dissolution of PbO particles in LBE is proposed, based on Classical Nucleation Theory (CNT) combined with mass transfer limited growth and dissolution. This model can accurately predict the experimentally observed changes in oxygen concentration due to nucleation, growth and dissolution of PbO, using the effective interfacial energy of a PbO nucleus in LBE as a fitting parameter. The results are invaluable to evaluate the consequences of oxygen ingress in LBE cooled nuclear systems under normal operating and accidental conditions and form the basis for the development of cold trap technology to avoid PbO formation in the primary reactor circuit.

  1. Classic theory for chromosome rearrangements with spatially restricted volume for broken ends interaction

    International Nuclear Information System (INIS)

    Omel'yanchuk, L.V.

    1997-01-01

    D. Lea classic theory for chromosomal rearrangements formation was modified to account for local interaction of broken chromosome ends. This assumption makes it possible to drastically improve coincidence of the theory and experiment in the case of complex rearrangements

  2. Quasiperiodical orbits in the scalar classical lambdaphi4 field theory

    International Nuclear Information System (INIS)

    Belova, T.I.; Kudryavtsev, A.E.

    1985-01-01

    New numerical and theoretical results of resonance kink-antikink (Kanti K) interactions in the classical one-dimentional space Higgs theory are presented. Earlier studies of these interactions revealed nine initial relative velocity-intervals with two-bounce Kanti K-collisions followed by the escape of kinks to infinite separations, the breathing solution was formed outside those intervals. Two-bounce Kanti K-interactions with the number of small oscillations between Kanti K-bounces up to 35 in the initial kink velocity interval 0.18 <= Vsub(infinite) <= 0.26 were found. Several examples for n-bounces Kanti K-interaction (n <= 6) are also found. The observed phenomenon can be explaned by the existence of quasi-two-periodical solutions of the nonlinear wave equation. The simple Hamiltonian with two degrees of freedom is studied. This model supplies quantitative descrtiptions of all numerical results for the field theory considered above. The considered phenomenon may be called ''autoquantization'' of a nonlinear classical scalar selfinteracting field

  3. Experimental Observation of Two Features Unexpected from the Classical Theories of Rubber Elasticity

    Science.gov (United States)

    Nishi, Kengo; Fujii, Kenta; Chung, Ung-il; Shibayama, Mitsuhiro; Sakai, Takamasa

    2017-12-01

    Although the elastic modulus of a Gaussian chain network is thought to be successfully described by classical theories of rubber elasticity, such as the affine and phantom models, verification experiments are largely lacking owing to difficulties in precisely controlling of the network structure. We prepared well-defined model polymer networks experimentally, and measured the elastic modulus G for a broad range of polymer concentrations and connectivity probabilities, p . In our experiment, we observed two features that were distinct from those predicted by classical theories. First, we observed the critical behavior G ˜|p -pc|1.95 near the sol-gel transition. This scaling law is different from the prediction of classical theories, but can be explained by analogy between the electric conductivity of resistor networks and the elasticity of polymer networks. Here, pc is the sol-gel transition point. Furthermore, we found that the experimental G -p relations in the region above C* did not follow the affine or phantom theories. Instead, all the G /G0-p curves fell onto a single master curve when G was normalized by the elastic modulus at p =1 , G0. We show that the effective medium approximation for Gaussian chain networks explains this master curve.

  4. Void nucleation at elevated temperatures under cascade-damage irradiation

    International Nuclear Information System (INIS)

    Semenov, A.A.; Woo, C.H.

    2002-01-01

    The effects on void nucleation of fluctuations respectively due to the randomness of point-defect migratory jumps, the random generation of free point defects in discrete packages, and the fluctuating rate of vacancy emission from voids are considered. It was found that effects of the cascade-induced fluctuations are significant only at sufficiently high total sink strength. At lower sink strengths and elevated temperatures, the fluctuation in the rate of vacancy emission is the dominant factor. Application of the present theory to the void nucleation in annealed pure copper neutron-irradiated at elevated temperatures with doses of 10 -4 -10 -2 NRT dpa showed reasonable agreement between theory and experiment. This application also predicts correctly the temporal development of large-scale spatial heterogeneous microstructure during the void nucleation stage. Comparison between calculated and experimental void nucleation rates in neutron-irradiated molybdenum at temperatures where vacancy emission from voids is negligible showed reasonable agreement as well. It was clearly demonstrated that the athermal shrinkage of relatively large voids experimentally observable in molybdenum at such temperatures may be easily explained in the framework of the present theory

  5. A review of phosphate mineral nucleation in biology and geobiology.

    Science.gov (United States)

    Omelon, Sidney; Ariganello, Marianne; Bonucci, Ermanno; Grynpas, Marc; Nanci, Antonio

    2013-10-01

    Relationships between geological phosphorite deposition and biological apatite nucleation have often been overlooked. However, similarities in biological apatite and phosphorite mineralogy suggest that their chemical formation mechanisms may be similar. This review serves to draw parallels between two newly described phosphorite mineralization processes, and proposes a similar novel mechanism for biologically controlled apatite mineral nucleation. This mechanism integrates polyphosphate biochemistry with crystal nucleation theory. Recently, the roles of polyphosphates in the nucleation of marine phosphorites were discovered. Marine bacteria and diatoms have been shown to store and concentrate inorganic phosphate (Pi) as amorphous, polyphosphate granules. Subsequent release of these P reserves into the local marine environment as Pi results in biologically induced phosphorite nucleation. Pi storage and release through an intracellular polyphosphate intermediate may also occur in mineralizing oral bacteria. Polyphosphates may be associated with biologically controlled apatite nucleation within vertebrates and invertebrates. Historically, biological apatite nucleation has been attributed to either a biochemical increase in local Pi concentration or matrix-mediated apatite nucleation control. This review proposes a mechanism that integrates both theories. Intracellular and extracellular amorphous granules, rich in both calcium and phosphorus, have been observed in apatite-biomineralizing vertebrates, protists, and atremate brachiopods. These granules may represent stores of calcium-polyphosphate. Not unlike phosphorite nucleation by bacteria and diatoms, polyphosphate depolymerization to Pi would be controlled by phosphatase activity. Enzymatic polyphosphate depolymerization would increase apatite saturation to the level required for mineral nucleation, while matrix proteins would simultaneously control the progression of new biological apatite formation.

  6. On some classical problems of descriptive set theory

    International Nuclear Information System (INIS)

    Kanovei, Vladimir G; Lyubetskii, Vasilii A

    2003-01-01

    The centenary of P.S. Novikov's birth provides an inspiring motivation to present, with full proofs and from a modern standpoint, the presumably definitive solutions of some classical problems in descriptive set theory which were formulated by Luzin [Lusin] and, to some extent, even earlier by Hadamard, Borel, and Lebesgue and relate to regularity properties of point sets. The solutions of these problems began in the pioneering works of Aleksandrov [Alexandroff], Suslin [Souslin], and Luzin (1916-17) and evolved in the fundamental studies of Goedel, Novikov, Cohen, and their successors. Main features of this branch of mathematics are that, on the one hand, it is an ordinary mathematical theory studying natural properties of point sets and functions and rather distant from general set theory or intrinsic problems of mathematical logic like consistency or Goedel's theorems, and on the other hand, it has become a subject of applications of the most subtle tools of modern mathematical logic

  7. On the consistency of classical and quantum supergravity theories

    Energy Technology Data Exchange (ETDEWEB)

    Hack, Thomas-Paul [II. Institute for Theoretical Physics, University of Hamburg (Germany); Makedonski, Mathias [Department of Mathematical Sciences, University of Copenhagen (Denmark); Schenkel, Alexander [Department of Stochastics, University of Wuppertal (Germany)

    2012-07-01

    It is known that pure N=1 supergravity in d=4 spacetime dimensions is consistent at a classical and quantum level, i.e. that in a particular gauge the field equations assume a hyperbolic form - ensuring causal propagation of the degrees of freedom - and that the associated canonical quantum field theory satisfies unitarity. It seems, however, that it is yet unclear whether these properties persist if one considers the more general and realistic case of N=1, d=4 supergravity theories including arbitrary matter fields. We partially clarify the issue by introducing novel hyperbolic gauges for the gravitino field and proving that they commute with the resulting equations of motion. Moreover, we review recent partial results on the unitarity of these general supergravity theories and suggest first steps towards a comprehensive unitarity proof.

  8. Remarks on the classical limit of quantum field theories

    International Nuclear Information System (INIS)

    Eckmann, J.P.

    1977-01-01

    Recently, there has been an increasing interest in computing quantum mechanical corrections to solutions of classical field equations. In this note, proceeding in the opposite way, theorems about the classical limit of relativistic quantum field models are summarized. These results are a byproduct of the so called 'constructive' approach to quantum field theory. Section 1 deals with generalities; in Section 2 the situation where no phase transitions occur is discussed in the limit h→0; and in Section 3 one result in the case where such a transition occurs is reformulated (Glimm et al). The validity of the loop expansion is discussed. It seems however that the tools to show the rigorous validity of soliton calculations are not yet prepared. (Auth.)

  9. An analogue of the Heisenberg uncertainty relation in prequantum classical field theory

    Energy Technology Data Exchange (ETDEWEB)

    Khrennikov, Andrei, E-mail: Andrei.Khrennikov@vxu.s [International Center for Mathematical Modelling in Physics and Cognitive Sciences, University of Vaexjoe, Vaexjoe (Sweden) and Institute of Information Security, Russian State University for Humanities, Moscow (Russian Federation)

    2010-02-01

    Prequantum classical statistical field theory (PCSFT) is a model that provides the possibility of representing averages of quantum observables, including correlations of observables on subsystems of a composite system, as averages with respect to fluctuations of classical random fields. PCSFT is a classical model of wave type. For example, 'electron' is described by electronic field. In contrast to quantum mechanics (QM), this field is a real physical field and not a field of probabilities. An important point is that the prequantum field of , for example, an electron contains the irreducible contribution of the background field vacuum fluctuations. In principle, the traditional QM-formalism can be considered as a special regularization procedure: subtraction of averages with respect to vacuum fluctuations. In this paper, we derive a classical analogue of the Heisenberg-Robertson inequality for dispersions of functionals of classical (prequantum) fields. The PCSFT Robertson-like inequality provides a restriction on the product of classical dispersions. However, this restriction is not so rigid as in QM.

  10. An analogue of the Heisenberg uncertainty relation in prequantum classical field theory

    International Nuclear Information System (INIS)

    Khrennikov, Andrei

    2010-01-01

    Prequantum classical statistical field theory (PCSFT) is a model that provides the possibility of representing averages of quantum observables, including correlations of observables on subsystems of a composite system, as averages with respect to fluctuations of classical random fields. PCSFT is a classical model of wave type. For example, 'electron' is described by electronic field. In contrast to quantum mechanics (QM), this field is a real physical field and not a field of probabilities. An important point is that the prequantum field of , for example, an electron contains the irreducible contribution of the background field vacuum fluctuations. In principle, the traditional QM-formalism can be considered as a special regularization procedure: subtraction of averages with respect to vacuum fluctuations. In this paper, we derive a classical analogue of the Heisenberg-Robertson inequality for dispersions of functionals of classical (prequantum) fields. The PCSFT Robertson-like inequality provides a restriction on the product of classical dispersions. However, this restriction is not so rigid as in QM.

  11. Foundations of quantum theory from classical concepts to operator algebras

    CERN Document Server

    Landsman, Klaas

    2017-01-01

    This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory. This book is Open Access under a CC BY licence.

  12. Aesthetic Creativity: Insights from Classical Literary Theory on Creative Learning

    Science.gov (United States)

    Hellstrom, Tomas Georg

    2011-01-01

    This paper addresses the subject of textual creativity by drawing on work done in classical literary theory and criticism, specifically new criticism, structuralism and early poststructuralism. The question of how readers and writers engage creatively with the text is closely related to educational concerns, though they are often thought of as…

  13. Imaging resolution signal-to-noise ratio in transverse phase amplification from classical information theory

    International Nuclear Information System (INIS)

    French, Doug; Huang Zun; Pao, H.-Y.; Jovanovic, Igor

    2009-01-01

    A quantum phase amplifier operated in the spatial domain can improve the signal-to-noise ratio in imaging beyond the classical limit. The scaling of the signal-to-noise ratio with the gain of the quantum phase amplifier is derived from classical information theory

  14. Classical Noether theory with application to the linearly damped particle

    International Nuclear Information System (INIS)

    Leone, Raphaël; Gourieux, Thierry

    2015-01-01

    This paper provides a modern presentation of Noether’s theory in the realm of classical dynamics, with application to the problem of a particle submitted to both a potential and a linear dissipation. After a review of the close relationships between Noether symmetries and first integrals, we investigate the variational point symmetries of the Lagrangian introduced by Bateman, Caldirola and Kanai. This analysis leads to the determination of all the time-independent potentials allowing such symmetries, in the one-dimensional and the radial cases. Then we develop a symmetry-based transformation of Lagrangians into autonomous others, and apply it to our problem. To be complete, we enlarge the study to Lie point symmetries which we associate logically to the Noether ones. Finally, we succinctly address the issue of a ‘weakened’ Noether’s theory, in connection with ‘on-flows’ symmetries and non-local constant of motions, because it has a direct physical interpretation in our specific problem. Since the Lagrangian we use gives rise to simple calculations, we hope that this work will be of didactic interest to graduate students, and give teaching material as well as food for thought for physicists regarding Noether’s theory and the recent developments around the idea of symmetry in classical mechanics. (paper)

  15. The classical field limit of scattering theory for non-relativistic many-boson systems. Pt. 1

    International Nuclear Information System (INIS)

    Ginibre, J.

    1979-01-01

    We study the classical field limit of non-relativistic many-boson theories in space dimension n >= 3. When h → 0, the correlation functions, which are the averages of products of bounded functions of field operators at different times taken in suitable states, converge to the corresponding functions of the appropriate solutions of the classical field equation, and the quantum fluctuations, are described by the equation obtained by linearizing the field equation around the classical solution. These properties were proved by Hepp for suitably regular potentials and in finite time intervals. Using a general theory of existence of global solutions and a general scattering theory for the clasical equation, we extend these results in two directions: (1) we consider more singular potentials, (2) more imortant, we prove that for dispersive classical solutions, the h → 0 limit is uniform in time in an appropriate representation of the field operators. As a consequence we obtain the convergence of suitable matrix elements of the wave operators and, if asymptotic completeness holds, of the S-matrix. (orig.) [de

  16. Classically integrable boundary conditions for affine Toda field theories

    International Nuclear Information System (INIS)

    Bowcock, P.; Corrigan, E.; Dorey, P.E.; Rietdijk, R.H.

    1995-01-01

    Boundary conditions compatible with classical integrability are studied both directly, using an approach based on the explicit construction of conserved quantities, and indirectly by first developing a generalisation of the Lax pair idea. The latter approach is closer to the spirit of earlier work by Sklyanin and yields a complete set of conjectures for permissible boundary conditions for any affine Toda field theory. (orig.)

  17. Bosonic Loop Diagrams as Perturbative Solutions of the Classical Field Equations in φ4-Theory

    International Nuclear Information System (INIS)

    Finster, Felix; Tolksdorf, Juergen

    2012-01-01

    Solutions of the classical φ 4 -theory in Minkowski space-time are analyzed in a perturbation expansion in the nonlinearity. Using the language of Feynman diagrams, the solution of the Cauchy problem is expressed in terms of tree diagrams which involve the retarded Green's function and have one outgoing leg. In order to obtain general tree diagrams, we set up a ''classical measurement process'' in which a virtual observer of a scattering experiment modifies the field and detects suitable energy differences. By adding a classical stochastic background field, we even obtain all loop diagrams. The expansions are compared with the standard Feynman diagrams of the corresponding quantum field theory.

  18. Bosonic Loop Diagrams as Perturbative Solutions of the Classical Field Equations in ϕ4-Theory

    Science.gov (United States)

    Finster, Felix; Tolksdorf, Jürgen

    2012-05-01

    Solutions of the classical ϕ4-theory in Minkowski space-time are analyzed in a perturbation expansion in the nonlinearity. Using the language of Feynman diagrams, the solution of the Cauchy problem is expressed in terms of tree diagrams which involve the retarded Green's function and have one outgoing leg. In order to obtain general tree diagrams, we set up a "classical measurement process" in which a virtual observer of a scattering experiment modifies the field and detects suitable energy differences. By adding a classical stochastic background field, we even obtain all loop diagrams. The expansions are compared with the standard Feynman diagrams of the corresponding quantum field theory.

  19. (Re)igniting a Sociological Imagination in Adult Education: The Continuing Relevance of Classical Theory

    Science.gov (United States)

    Lange, Elizabeth

    2015-01-01

    This article argues that sociology has been a foundational discipline for the field of adult education, but it has been largely implicit, until recently. This article contextualizes classical theories of sociology within contemporary critiques, reviews the historical roots of sociology and then briefly introduces the classical theories…

  20. Neo-classical theory of competition or Adam Smith's hand as mathematized ideology

    Science.gov (United States)

    McCauley, Joseph L.

    2001-10-01

    Orthodox economic theory (utility maximization, rational agents, efficient markets in equilibrium) is based on arbitrarily postulated, nonempiric notions. The disagreement between economic reality and a key feature of neo-classical economic theory was criticized empirically by Osborne. I show that the orthodox theory is internally self-inconsistent for the very reason suggested by Osborne: lack of invertibility of demand and supply as functions of price to obtain price as functions of supply and demand. The reason for the noninvertibililty arises from nonintegrable excess demand dynamics, a feature of their theory completely ignored by economists.

  1. A superfield generalization of the classical action-at-a-distance theory

    International Nuclear Information System (INIS)

    Tugai, V.V.; Zheltukhin, A.A.

    1994-07-01

    A generalization of the Fokker-Schwarzschild-Tetrode-Wheeler-Feynman electromagnetic theory onto the superspace is considered. The classical vector and spinor fields belonging to the Maxwell supermultiplet are built of the world-line coordinates of the charged particles in superspace. (author). 9 refs

  2. Applications of generalizability theory and their relations to classical test theory and structural equation modeling.

    Science.gov (United States)

    Vispoel, Walter P; Morris, Carrie A; Kilinc, Murat

    2018-03-01

    Although widely recognized as a comprehensive framework for representing score reliability, generalizability theory (G-theory), despite its potential benefits, has been used sparingly in reporting of results for measures of individual differences. In this article, we highlight many valuable ways that G-theory can be used to quantify, evaluate, and improve psychometric properties of scores. Our illustrations encompass assessment of overall reliability, percentages of score variation accounted for by individual sources of measurement error, dependability of cut-scores for decision making, estimation of reliability and dependability for changes made to measurement procedures, disattenuation of validity coefficients for measurement error, and linkages of G-theory with classical test theory and structural equation modeling. We also identify computer packages for performing G-theory analyses, most of which can be obtained free of charge, and describe how they compare with regard to data input requirements, ease of use, complexity of designs supported, and output produced. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

  3. Some connections between relativistic classical mechanics, statistical mechanics, and quantum field theory

    International Nuclear Information System (INIS)

    Remler, E.A.

    1977-01-01

    A gauge-invariant version of the Wigner representation is used to relate relativistic mechanics, statistical mechanics, and quantum field theory in the context of the electrodynamics of scalar particles. A unified formulation of quantum field theory and statistical mechanics is developed which clarifies the physics interpretation of the single-particle Wigner function. A covariant form of Ehrenfest's theorem is derived. Classical electrodynamics is derived from quantum field theory after making a random-phase approximation. The validity of this approximation is discussed

  4. On the construction of classical superstring field theories

    Energy Technology Data Exchange (ETDEWEB)

    Konopka, Sebastian Johann Hermann

    2016-07-01

    This thesis describes the construction of classical superstring field theories based on the small Hilbert space. First we describe the traditional construction of perturbative superstring theory as an integral over the supermoduli space of type II world sheets. The geometry of supermoduli space dictates many algebraic properties of the string field theory action. In particular it allows for an algebraisation of the construction problem for classical superstring field theories in terms of homotopy algebras. Next, we solve the construction problem for open superstrings based on Witten's star product. The construction is recursive and involves a choice of homotopy operator for the zero mode of the η-ghost. It turns out that the solution can be extended to the Neveu-Schwarz subsectors of all superstring field theories. The recursive construction involves a hierarchy of string products at various picture deficits. The construction is not entirely natural, but it is argued that different choices give rise to solutions related by a field redefinition. Due to the presence of odd gluing parameters for Ramond states the extension to full superstring field theory is non-trivial. Instead, we construct gauge-invariant equations of motion for all superstring field theories. The realisation of spacetime supersymmetry in the open string sector is highly non-trivial and is described explicitly for the solution based on Witten's star product. After a field redefinition the non-polynomial equations of motion and the small Hilbert space constraint become polynomial. This polynomial system is shown to be supersymmetric. Quite interestingly, the supersymmetry algebra closes only up to gauge transformations. This indicates that only the physical phase space realizes N=1 supersymmetry. Apart from the algebraic constraints dictated by the geometry of supermoduli space the equations of motion or action should reproduce the traditional string S-matrix. The S-matrix of a field

  5. Classical radiation zeros in gauge-theory amplitudes

    International Nuclear Information System (INIS)

    Brown, R.W.; Kowalski, K.L.; Brodsky, S.J.

    1983-01-01

    The electromagnetic radiation from classical convection currents in relativistic n-particle collisions is shown to vanish in certain kinematical zones, due to complete destructive interference of the classical radiation patterns of the incoming and outgoing charged lines. We prove that quantum tree photon amplitudes vanish in the same zones, at arbitrary photon momenta including spin, seagull, and internal-line currents, provided only that the electromagnetic couplings and any other derivative couplings are as prescribed by renormalizable local gauge theory (spins + #betta# is thus explained and examples with more particles are discussed. Conditions for the null zones to lie in physical regions are established. A new radiation representation, with the zeros manifest and of practical utility independently of whether the null zones are in physical regions is derived for the complete single-photon amplitude in tree approximation, using a gauge-invariant vertex expansion stemming from new internal-radiation decomposition identities. The question of whether amplitudes with closed loops can vanish in null zones is addressed. The null zone and these relations are discussed in terms of the Bargmann-Michel-Telegdi equation. The extension from photons to general massless gauge bosons is carried out

  6. Direct gauging of the Poincare group V. Group scaling, classical gauge theory, and gravitational corrections

    International Nuclear Information System (INIS)

    Edelen, D.G.B.

    1986-01-01

    Homogeneous scaling of the group space of the Poincare group, P 10 , is shown to induce scalings of all geometric quantities associated with the local action of P 10 . The field equations for both the translation and the Lorentz rotation compensating fields reduce to O(1) equations if the scaling parameter is set equal to the general relativistic gravitational coupling constant 8πGc -4 . Standard expansions of all field variables in power series in the scaling parameter give the following results. The zeroth-order field equations are exactly the classical field equations for matter fields on Minkowski space subject to local action of an internal symmetry group (classical gauge theory). The expansion process is shown to break P 10 -gauge covariance of the theory, and hence solving the zeroth-order field equations imposes an implicit system of P 10 -gauge conditions. Explicit systems of field equations are obtained for the first- and higher-order approximations. The first-order translation field equations are driven by the momentum-energy tensor of the matter and internal compensating fields in the zeroth order (classical gauge theory), while the first-order Lorentz rotation field equations are driven by the spin currents of the same classical gauge theory. Field equations for the first-order gravitational corrections to the matter fields and the gauge fields for the internal symmetry group are obtained. Direct Poincare gauge theory is thus shown to satisfy the first two of the three-part acid test of any unified field theory. Satisfaction of the third part of the test, at least for finite neighborhoods, seems probable

  7. Concurrent nucleation, formation and growth of two intermetallic compounds (Cu6Sn5 and Cu3Sn) during the early stages of lead-free soldering

    International Nuclear Information System (INIS)

    Park, M.S.; Arróyave, R.

    2012-01-01

    This study investigates the concurrent nucleation, formation and growth of two intermetallic compounds (IMCs), Cu 6 Sn 5 (η) and Cu 3 Sn (ε), during the early stages of soldering in the Cu–Sn system. The nucleation, formation and growth of the IMC layers is simulated through a multiphase-field model in which the concurrent nucleation of both IMC phases is considered to be a stochastic Poisson process with nucleation rates calculated from classical nucleation theory. CALPHAD thermodynamic models are used to calculate the local contributions to the free energy of the system and the driving forces for precipitation of the IMC phases. The nucleation parameters of the η phase are estimated from experimental results and those of the ε phase are assumed to be similar. A parametric investigation of the effects of model parameters (e.g. grain boundary (GB) diffusion rates, interfacial and GB energies) on morphological evolution and IMC layer growth rate is presented and compared with previous works in which nucleation was ignored . In addition, the resulting growth rates are compared with the available literature and it is found that, for a certain range in the model parameters, the agreement is quite satisfactory. This work provides valuable insight into the dominant mechanisms for mass transport as well as morphological evolution and growth of IMC layers during early stages of Pb-free soldering.

  8. A possibilistic uncertainty model in classical reliability theory

    International Nuclear Information System (INIS)

    De Cooman, G.; Capelle, B.

    1994-01-01

    The authors argue that a possibilistic uncertainty model can be used to represent linguistic uncertainty about the states of a system and of its components. Furthermore, the basic properties of the application of this model to classical reliability theory are studied. The notion of the possibilistic reliability of a system or a component is defined. Based on the concept of a binary structure function, the important notion of a possibilistic function is introduced. It allows to calculate the possibilistic reliability of a system in terms of the possibilistic reliabilities of its components

  9. Local gauge invariant Lagrangeans in classical field theories

    International Nuclear Information System (INIS)

    Grigore, D.R.

    1982-07-01

    We investigate the most general local gauge invariant Lagrangean in the framework of classical field theory. We rederive esentially Utiyama's result with a slight generalization. Our proof makes clear the importance of the so called current conditions, i.e. the requirement that the Noether currents are different from zero. This condition is of importance both in the general motivation for the introduction of the Yang-Mills fields and for the actual proof. Some comments are made about the basic mathematical structure of the problem - the gauge group. (author)

  10. Classical and quantum Liouville theory on the Riemann sphere with n>3 punctures (III)

    International Nuclear Information System (INIS)

    Shen Jianmin; Sheng Zhengmao; Wang Zhonghua

    1992-02-01

    We study the Classical and Quantum Liouville theory on the Riemann sphere with n>3 punctures. We get the quantum exchange algebra relations between the chiral components in the Liouville theory from our assumption on the principle of quantization. (author). 5 refs

  11. Aerosol nucleation induced by a high energy particle beam

    DEFF Research Database (Denmark)

    Enghoff, Martin Andreas Bødker; Pedersen, Jens Olaf Pepke; Uggerhøj, Ulrik I.

    The effect of ions in aerosol nucleation is a subject where much remains to be discovered. That ions can enhance nucleation has been shown by theory, observations, and experiments. However, the exact mechanism still remains to be determined. One question is if the nature of the ionization affects...... the nucleation. This is an essential question since many experiments have been performed using radioactive sources that ionize differently than the cosmic rays which are responsible for the majority of atmospheric ionization. Here we report on an experimental study of sulphuric acid aerosol nucleation under near...... atmospheric conditions using a 580 MeV electron beam to ionize the volume of the reaction chamber. We find a clear and significant contribution from ion induced nucleation and consider this to be an unambiguous observation of the ion-effect on aerosol nucleation using a particle beam under conditions not far...

  12. Effect of strain on surface diffusion and nucleation

    DEFF Research Database (Denmark)

    Brune, Harald; Bromann, Karsten; Röder, Holger

    1995-01-01

    The influence of strain on diffusion and nucleation has been studied by means of scanning tunneling microscopy and effective-medium theory for Ag self-diffusion on strained and unstrained (111) surfaces. Experimentally, the diffusion barrier is observed to be substantially lower on a pseudomorphic...... effect on surface diffusion and nucleation in heteroepitaxy and are thus of significance for the film morphology in the kinetic growth regime....

  13. Anthropology and social theory: renewing dialogue via the classics

    DEFF Research Database (Denmark)

    Thomassen, Bjørn

    2011-01-01

    Agnes Horvath, Bjørn Thomassen, & Dr Harald Wydra, editors of the Journal,International Political Anthropology “Anthropology and social theory: renewing dialogue via the classics” This paper argues that anthropology may represent a perspective from where social theory can renew itself. The presen......Agnes Horvath, Bjørn Thomassen, & Dr Harald Wydra, editors of the Journal,International Political Anthropology “Anthropology and social theory: renewing dialogue via the classics” This paper argues that anthropology may represent a perspective from where social theory can renew itself...... simply representing a view from "below", a politically correct appreciation of cultural diversity, or a taste for the exotic and marginal. It involves, we argue, attention towards key theoretical concepts developed within "classical" anthropology that uniquely facilitate a proper understanding...... in mechanical rationalisation on the one hand, and the mere stimulation of the senses on the other, guided by an exclusively materialistic and utilitarian vision of the human being and its social environment, it is possible to take inspiration from Antiquity in order to spark a renewal badly needed...

  14. Theory of pseudo-classical confinement and transmutation to L-mode

    International Nuclear Information System (INIS)

    Itoh, K.; Itoh, S.; Yagi, M.; Fukuyama, A.; Azumi, M.

    1993-05-01

    Theory of the self-sustained turbulence is developed for resistive plasma in toroidal devices. Pseudo-classical confinement is obtained in the low temperature limit. As temperature increases, the current-diffusivity prevails upon resistivity, and the turbulence nature changes so as to recover the L-mode transport. Comparison with experimental observation on this transition is made. Hartmann number is also given. (author)

  15. Wigner's dynamical transition state theory in phase space : classical and quantum

    NARCIS (Netherlands)

    Waalkens, Holger; Schubert, Roman; Wiggins, Stephen

    We develop Wigner's approach to a dynamical transition state theory in phase space in both the classical and quantum mechanical settings. The key to our development is the construction of a normal form for describing the dynamics in the neighbourhood of a specific type of saddle point that governs

  16. A plug flow model for chemical reactions and aerosol nucleation and growth in an alkali-containing flue gas

    DEFF Research Database (Denmark)

    Christensen, K. A.; Livbjerg, Hans

    2000-01-01

    multicomponent growth models are treated. The local gas phase composition is determined from a gas phase chemical equilibrium calculation combined with finite reaction rate kinetics for slower reactions. The model is useful in the analysis of boiler operation with respect to the formation of particles, HCl, SO2......The paper presents a numerical model for the simulation of gas to particle conversion and the chemical changes during cooling of a flue gas from the combustion of fuels rich in volatile alkali species. For the homogeneous nucleation of alkali species the model uses the classical theory modified...

  17. Nucleation theory with delayed interactions: an application to the early stages of the receptor-mediated adhesion/fusion kinetics of lipid vesicles.

    Science.gov (United States)

    Raudino, Antonio; Pannuzzo, Martina

    2010-01-28

    A semiquantitative theory aimed to describe the adhesion kinetics between soft objects, such as living cells or vesicles, has been developed. When rigid bodies are considered, the adhesion kinetics is successfully described by the classical Derjaguin, Landau, Verwey, and Overbeek (DLVO) picture, where the energy profile of two approaching bodies is given by a two asymmetrical potential wells separated by a barrier. The transition probability from the long-distance to the short-distance minimum defines the adhesion rate. Conversely, soft bodies might follow a different pathway to reach the short-distance minimum: thermally excited fluctuations give rise to local protrusions connecting the approaching bodies. These transient adhesion sites are stabilized by short-range adhesion forces (e.g., ligand-receptor interactions between membranes brought at contact distance), while they are destabilized both by repulsive forces and by the elastic deformation energy. Above a critical area of the contact site, the adhesion forces prevail: the contact site grows in size until the complete adhesion of the two bodies inside a short-distance minimum is attained. This nucleation mechanism has been developed in the framework of a nonequilibrium Fokker-Planck picture by considering both the adhesive patch growth and dissolution processes. In addition, we also investigated the effect of the ligand-receptor pairing kinetics at the adhesion site in the time course of the patch expansion. The ratio between the ligand-receptor pairing kinetics and the expansion rate of the adhesion site is of paramount relevance in determining the overall nucleation rate. The theory enables one to self-consistently include both thermodynamics (energy barrier height) and dynamic (viscosity) parameters, giving rise in some limiting cases to simple analytical formulas. The model could be employed to rationalize fusion kinetics between vesicles, provided the short-range adhesion transition is the rate

  18. Classical geometrical interpretation of ghost fields and anomalies in Yang-Mills theory and quantum gravity

    International Nuclear Information System (INIS)

    Thierry-Mieg, J.

    1985-01-01

    The reinterpretation of the BRS equations of Quantum Field Theory as the Maurer Cartan equation of a classical principal fiber bundle leads to a simple gauge invariant classification of the anomalies in Yang Mills theory and gravity

  19. Saturation and nucleation in hot nuclear systems

    International Nuclear Information System (INIS)

    Deangelis, A.R.

    1990-07-01

    We investigate nuclear fragmentation in a supersaturated system using classical nucleation theory. This allows us to go outside the normally applied constraint of chemical equilibrium. The system is governed by a virial equation of state, which we use to find an expression for the density as a function of pressure and temperature. The evolution of the system is discussed in terms of the phase diagram. Corrections are included to account for the droplet surface and all charges contained in the system. Using this model we investigate and discuss the effects of temperature and saturation, and compare the results to those of other models of fragmentation. We also discuss the limiting temperatures of the system for the cases with and without chemical equilibrium. We find that large nuclei will be formed in saturated systems, even above the limiting temperature as previously defined. We also find that saturation and temperature dominate surface and Coulomb effects. The effects are quite large, thus even a qualitative inspection of the yields may give an indication of the conditions during fragmentation

  20. Comparison of classical and modern theories of longitudinal wave propagation in elastic rods

    CSIR Research Space (South Africa)

    Shatalov, M

    2011-01-01

    Full Text Available Conference on Computational and Applied Mechanics SACAM10 Pretoria, 10?13 January 2010 ? SACAM COMPARISON OF CLASSICAL AND MODERN THEORIES OF LONGITUDINAL WAVE PROPAGATION IN ELASTIC RODS M. Shatalov*,?,?? , I. Fedotov? 1 , HM. Tenkam? 2, J. Marais..., Pretoria, 0001 FIN-40014, South Africa 1fedotovi@tut.ac.za, 2djouosseutenkamhm@tut.ac.za ?? Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa Keywords: Elastic rod, wave propagation, classical...

  1. Non-classical homogeneous precipitation mediated by compositional fluctuations in titanium alloys

    International Nuclear Information System (INIS)

    Nag, S.; Zheng, Y.; Williams, R.E.A.; Devaraj, A.; Boyne, A.; Wang, Y.; Collins, P.C.; Viswanathan, G.B.; Tiley, J.S.; Muddle, B.C.; Banerjee, R.

    2012-01-01

    This paper presents experimental evidence of homogeneous precipitation of the α-phase within the β matrix of a titanium alloy, and then accounts for this phase transformation by a new, non-classical mechanism involving compositional fluctuations, based on the pseudo-spinodal concept [1]. This mechanism involves local compositional fluctuations of small amplitude which, when of a certain magnitude, can favor thermodynamically certain regions of the β matrix to transform congruently to the α-phase but with compositions far from equilibrium. Subsequently, as measured experimentally using the tomographical atom probe, continuous diffusional partitioning between the parent β- and product α-phases during isothermal annealing drives their compositions towards equilibrium. For a given alloy composition, the decomposition mechanism is strongly temperature dependent, which would be expected for homogeneous precipitation via the compositional fluctuation-mediated mechanism but not necessarily for one based on classical nucleation theory. The applicability of this mechanism to phase transformations in general is noted.

  2. Fluctuations around classical solutions for gauge theories in Lagrangian and Hamiltonian approach

    International Nuclear Information System (INIS)

    Miskovic, Olivera; Pons, Josep M

    2006-01-01

    We analyse the dynamics of gauge theories and constrained systems in general under small perturbations around a classical solution in both Lagrangian and Hamiltonian formalisms. We prove that a fluctuations theory, described by a quadratic Lagrangian, has the same constraint structure and number of physical degrees of freedom as the original non-perturbed theory, assuming the non-degenerate solution has been chosen. We show that the number of Noether gauge symmetries is the same in both theories, but that the gauge algebra in the fluctuations theory becomes Abelianized. We also show that the fluctuations theory inherits all functionally independent rigid symmetries from the original theory and that these symmetries are generated by linear or quadratic generators according to whether the original symmetry is preserved by the background or is broken by it. We illustrate these results with examples

  3. The Effect of Spatial Heterogeneities on Nucleation Kinetics in Amorphous Aluminum Alloys

    Science.gov (United States)

    Shen, Ye

    The mechanical property of the Al based metallic glass could be enhanced significantly by introducing the high number density of Al-fcc nanocrystals (1021 ˜1023 m-3) to the amorphous matrix through annealing treatments, which motivates the study of the nucleation kinetics for the microstructure control. With the presence of a high number density (1025 m-3) of aluminum-like medium range order (MRO), the Al-Y-Fe metallic glass is considered to be spatially heterogeneous. Combining the classical nucleation theory with the structural configuration, a MRO seeded nucleation model has been proposed and yields theoretical steady state nucleation rates consistent with the experimental results. In addition, this model satisfies all the thermodynamic and kinetic constraints to be reasonable. Compared with the Al-Y-Fe system, the primary crystallization onset temperature decreases significantly and the transient delay time (tau) is shorter in the Al-Y-Fe-Pb(In) systems because the insoluble Pb and In nanoparticles in the amorphous matrix served as extrinsic spatial heterogeneity to provide the nucleation sites for Al-fcc precipitation and the high-resolution transmission electron microscopy (HRTEM) images of the Pb-Al interface revealed a good wetting behavior between the Al and Pb nanoparticles. The study of the transient delay time (tau) could provide insight on the transport behavior during the nucleation and a more convenient approach to evaluate the delay time has been developed by measuring the Al-Y-Fe amorphous alloy glass transition temperature (Tg) shift with the increasing annealing time (tannealing) in FlashDSC. The break point in the Tg vs. log(tannealing) plot has been identified to correspond to the delay time by the TEM characterization. FlashDSC tests with different heating rates and different compositions (Al-Y-Fe-Pb and Zn-Mg-Ca-Yb amorphous alloys) further confirmed the break point and delay time relationship. The amorphous matrix composition and the

  4. Classical geometrical interpretation of ghost fields and anomalies in Yang-Mills theory and quantum gravity

    International Nuclear Information System (INIS)

    Thierry-Mieg, J.

    1985-01-01

    This paper discusses the reinterpretation of the BRS equations of Quantum Field Theory as the Maurer Cartan equation of a classical principal fiber bundle leads to a simple gauge invariant classification of the anomalies in Yang Mills theory and gravity

  5. The laminar flow tube reactor as a quantitative tool for nucleation studies: Experimental results and theoretical analysis of homogeneous nucleation of dibutylphthalate

    International Nuclear Information System (INIS)

    Mikheev, Vladimir B.; Laulainen, Nels S.; Barlow, Stephan E.; Knott, Michael; Ford, Ian J.

    2000-01-01

    A laminar flow tube reactor was designed and constructed to provide an accurate, quantitative measurement of a nucleation rate as a function of supersaturation and temperature. Measurements of nucleation of a supersaturated vapor of dibutylphthalate have been made for the temperature range from -30.3 to +19.1 degree sign C. A thorough analysis of the possible sources of experimental uncertainties (such as defining the correct value of the initial vapor concentration, temperature boundary conditions on the reactor walls, accuracy of the calculations of the thermodynamic parameters of the nucleation zone, and particle concentration measurement) is given. Both isothermal and the isobaric nucleation rates were measured. The experimental data obtained were compared with the measurements of other experimental groups and with theoretical predictions made on the basis of the self-consistency correction nucleation theory. Theoretical analysis, based on the first and the second nucleation theorems, is also presented. The critical cluster size and the excess of internal energy of the critical cluster are obtained. (c) 2000 American Institute of Physics

  6. Classical tokamak transport theory

    International Nuclear Information System (INIS)

    Nocentini, Aldo

    1982-01-01

    A qualitative treatment of the classical transport theory of a magnetically confined, toroidal, axisymmetric, two-species plasma is presented. The 'weakly collisional' ('banana' and 'plateau') and 'collision dominated' ('Pfirsch-Schlueter' and 'highly collisional') regimes, as well as the Ware effect are discussed. The method used to evaluate the diffusion coffieicnts of particles and heat in the weakly collisional regime is based on stochastic argument, that requires an analysis of the characteristic collision frequencies and lengths for particles moving in a tokamak-like magnetic field. The same method is used to evaluate the Ware effect. In the collision dominated regime on the other hand, the particle and heat fluxes across the magnetic field lines are dominated by macroscopic effects so that, although it is possible to present them as diffusion (in fact, the fluxes turn out to be proportional to the density and temperature gradients), a macroscopic treatment is more appropriate. Hence, fluid equations are used to inveatigate the collision dominated regime, to which particular attention is devoted, having been shown relatively recently that it is more complicated than the usual Pfirsch-Schlueter regime. The whole analysis presented here is qualitative, aiming to point out the relevant physical mechanisms involved in the various regimes more than to develop a rigorous mathematical derivation of the diffusion coefficients, for which appropriate references are given. (author)

  7. Stochastic theory for classical and quantum mechanical systems

    International Nuclear Information System (INIS)

    Pena, L. de la; Cetto, A.M.

    1975-01-01

    From first principles a theory of stochastic processes in configuration space is formulated. The fundamental equations of the theory are an equation of motion which generalizes Newton's second law and an equation which expresses the condition of conservation of matter. Two types of stochastic motion are possible, both described by the same general equations, but leading in one case to classical Brownian motion behavior and in the other to quantum mechanical behavior. The Schroedinger equation, which is derived with no further assumption, is thus shown to describe a specific stochastic process. It is explicitly shown that only in the quantum mechanical process does the superposition of probability amplitudes give rise to interference phenomena; moreover, the presence of dissipative forces in the Brownian motion equations invalidates the superposition principle. At no point are any special assumptions made concerning the physical nature of the underlying stochastic medium, although some suggestions are discussed in the last section

  8. Classical, Semi-classical and Quantum Noise

    CERN Document Server

    Poor, H; Scully, Marlan

    2012-01-01

    David Middleton was a towering figure of 20th Century engineering and science and one of the founders of statistical communication theory. During the second World War, the young David Middleton, working with Van Fleck, devised the notion of the matched filter, which is the most basic method used for detecting signals in noise. Over the intervening six decades, the contributions of Middleton have become classics. This collection of essays by leading scientists, engineers and colleagues of David are in his honor and reflect the wide  influence that he has had on many fields. Also included is the introduction by Middleton to his forthcoming book, which gives a wonderful view of the field of communication, its history and his own views on the field that he developed over the past 60 years. Focusing on classical noise modeling and applications, Classical, Semi-Classical and Quantum Noise includes coverage of statistical communication theory, non-stationary noise, molecular footprints, noise suppression, Quantum e...

  9. The void nucleation mechanism within lead phase during spallation of leaded brass

    Science.gov (United States)

    Yang, Yang; Wang, Can; Chen, Xingzhi; Chen, Kaiguo; Hu, Haibo; Fu, Yanan

    2018-07-01

    The incipient spall behaviours of Cu-34%Zn-3%Pb leaded brass samples with annealed and cryogenic-treated conditions were loaded using one-stage light gas gun experiments. The effect of Pb-phase on dynamic damage nucleation in leaded brass specimens was investigated by means of optical microscopy, scanning electron microscopy and x-ray computer tomography. It was found that the voids of incipient spall were mainly nucleated in the interior of the lead (no tensile stress would be produced within lead according to the impact theory) instead of nucleated at the phase interface as expected by quasi-static damage fracture theory. A nucleation model is proposed in the present work that is the asymmetry high compression zones in the centre of the lead-phase were formed by the rarefaction wave convergence effects of matrix/quasi-spherical lead interface, which caused adiabatic temperature rise that exceeded melting point of lead due to severe plastic deformation, finally led to local melting and void nucleation. In addition, the spall strength and damage rate increased with the increase in the Pb-phase number.

  10. Marshaling Resources: A Classic Grounded Theory Study of Online Learners

    Directory of Open Access Journals (Sweden)

    Barbara Yalof

    2014-06-01

    Full Text Available Classic grounded theory (CGT was used to identify a main concern of online students in higher education. One of the main impediments to studying online is a sense of isolation and lack of access to support systems as students navigate through complex requirements of their online programs. Hypothetical probability statements illustrate the imbalance between heightened needs of virtual learners and perceived inadequate support provided by educational institutions. The core variable, marshaling resources, explains how peer supports sustain motivation toward successful program completion. Understanding the critical contribution virtual interpersonal networks make towards maximizing resources by group problem solving is a significant aspect of this theory. Keywords: Online learning, e-learning, personal learning networks, peer networks

  11. Nucleation of strange matter in dense stellar cores

    International Nuclear Information System (INIS)

    Horvath, J.E.; Benvenuto, O.G.; Vucetich, H.

    1992-01-01

    We investigate the nucleation of strange quark matter inside hot, dense nuclear matter. Applying Zel'dovich's kinetic theory of nucleation we find a lower limit of the temperature T for strange-matter bubbles to appear, which happens to be satisfied inside the Kelvin-Helmholtz cooling era of a compact star life but not much after it. Our bounds thus suggest that a prompt conversion could be achieved, giving support to earlier expectations for nonstandard type-II supernova scenarios

  12. Weak values in a classical theory with an epistemic restriction

    International Nuclear Information System (INIS)

    Karanjai, Angela; Cavalcanti, Eric G; Bartlett, Stephen D; Rudolph, Terry

    2015-01-01

    Weak measurement of a quantum system followed by postselection based on a subsequent strong measurement gives rise to a quantity called the weak value: a complex number for which the interpretation has long been debated. We analyse the procedure of weak measurement and postselection, and the interpretation of the associated weak value, using a theory of classical mechanics supplemented by an epistemic restriction that is known to be operationally equivalent to a subtheory of quantum mechanics. Both the real and imaginary components of the weak value appear as phase space displacements in the postselected expectation values of the measurement device's position and momentum distributions, and we recover the same displacements as in the quantum case by studying the corresponding evolution in our theory of classical mechanics with an epistemic restriction. By using this epistemically restricted theory, we gain insight into the appearance of the weak value as a result of the statistical effects of post selection, and this provides us with an operational interpretation of the weak value, both its real and imaginary parts. We find that the imaginary part of the weak value is a measure of how much postselection biases the mean phase space distribution for a given amount of measurement disturbance. All such biases proportional to the imaginary part of the weak value vanish in the limit where disturbance due to measurement goes to zero. Our analysis also offers intuitive insight into how measurement disturbance can be minimized and the limits of weak measurement. (paper)

  13. Classical and Quantum Nonlinear Integrable Systems: Theory and Application

    International Nuclear Information System (INIS)

    Brzezinski, Tomasz

    2003-01-01

    This is a very interesting collection of introductory and review articles on the theory and applications of classical and quantum integrable systems. The book reviews several integrable systems such as the KdV equation, vertex models, RSOS and IRF models, spin chains, integrable differential equations, discrete systems, Ising, Potts and other lattice models and reaction--diffusion processes, as well as outlining major methods of solving integrable systems. These include Lax pairs, Baecklund and Miura transformations, the inverse scattering method, various types of the Bethe Ansatz, Painleve methods, the dbar method and fusion methods to mention just a few. The book is divided into two parts, each containing five chapters. The first part is devoted to classical integrable systems and introduces the subject through the KdV equation, and then proceeds through Painleve analysis, discrete systems and two-dimensional integrable partial differential equations, to culminate in the review of solvable lattice models in statistical physics, solved through the coordinate and algebraic Bethe Ansatz methods. The second part deals with quantum integrable systems, and begins with an outline of unifying approaches to quantum, statistical, ultralocal and non-ultralocal systems. The theory and methods of solving quantum integrable spin chains are then described. Recent developments in applying Bethe Ansatz methods in condensed matter physics, including superconductivity and nanoscale physics, are reviewed. The book concludes with an introduction to diffusion-reaction processes. Every chapter is devoted to a different subject and is self-contained, and thus can be read separately. A reader interesting in classical methods of solitons, such as the methods of solving the KdV equation, can start from Chapter 1, while a reader interested in the Bethe Ansatz method can immediately proceed to Chapter 5, and so on. Thus the book should appeal and be useful to a wide range of theoretical

  14. Comparison of classical and modern theories of longitudinal wave propagation in elastic rods

    CSIR Research Space (South Africa)

    Shatalov, M

    2009-07-01

    Full Text Available are constructed for the classical, Rayleigh, Bishop, and Mindlin-Herrmann models in which the general solutions of the problem are obtained. The principles of construction of the multimode theories, corresponding equations and orthogonality conditions...

  15. Information flow, causality, and the classical theory of tachyons

    International Nuclear Information System (INIS)

    Basano, L.

    1977-01-01

    Causal paradoxes arising in the tachyon theory have been systematically solved by using the reinterpretation principle as a consequence of which cause and effect no longer retain an absolute meaning. However, even in the tachyon theory, a cause is always seen to chronologically precede its effect, but this is obtained at the price of allowing cause and effect to be interchanged when required. A recent result has shown that this interchange-ability of cause and effect must not be unlimited if heavy paradoxes are to be avoided. This partial recovery of the classical concept of causality has been expressed by the conjecture that transcendent tachyons cannot be absorbed by a tachyon detector. In this paper the directional properties of the flow of information between two observers in relative motion and its consequences on the logical self-consistency of the theory of superluminal particles are analyzed. It is shown that the above conjecture does not provide a satisfactory solution to the problem because it implies that tachyons of any speed cannot be intercepted by the same detector. (author)

  16. Kinetics of transformations nucleated on random parallel planes: analytical modelling and computer simulation

    International Nuclear Information System (INIS)

    Rios, Paulo R; Assis, Weslley L S; Ribeiro, Tatiana C S; Villa, Elena

    2012-01-01

    In a classical paper, Cahn derived expressions for the kinetics of transformations nucleated on random planes and lines. He used those as a model for nucleation on the boundaries, edges and vertices of a polycrystal consisting of equiaxed grains. In this paper it is demonstrated that Cahn's expression for random planes may be used in situations beyond the scope envisaged in Cahn's original paper. For instance, we derived an expression for the kinetics of transformations nucleated on random parallel planes that is identical to that formerly obtained by Cahn considering random planes. Computer simulation of transformations nucleated on random parallel planes is carried out. It is shown that there is excellent agreement between simulated results and analytical solutions. Such an agreement is to be expected if both the simulation and the analytical solution are correct. (paper)

  17. Second quantization of classical nonlinear relativistic field theory. Pt. 2

    International Nuclear Information System (INIS)

    Balaban, T.

    1976-01-01

    The construction of a relativistic interacting local quantum field is given in two steps: first the classical nonlinear relativistic field theory is written down in terms of Poisson brackets, with initial conditions as canonical variables: next a representation of Poisson bracket Lie algebra by means of linear operators in the topological vector space is given and an explicit form of a local interacting relativistic quantum field PHI is obtained. (orig./BJ) [de

  18. Optimal control theory for quantum-classical systems: Ehrenfest molecular dynamics based on time-dependent density-functional theory

    International Nuclear Information System (INIS)

    Castro, A; Gross, E K U

    2014-01-01

    We derive the fundamental equations of an optimal control theory for systems containing both quantum electrons and classical ions. The system is modeled with Ehrenfest dynamics, a non-adiabatic variant of molecular dynamics. The general formulation, that needs the fully correlated many-electron wavefunction, can be simplified by making use of time-dependent density-functional theory. In this case, the optimal control equations require some modifications that we will provide. The abstract general formulation is complemented with the simple example of the H 2 + molecule in the presence of a laser field. (paper)

  19. Uniting the Spheres: Modern Feminist Theory and Classic Texts in AP English

    Science.gov (United States)

    Drew, Simao J. A.; Bosnic, Brenda G.

    2008-01-01

    High school teachers Simao J. A. Drew and Brenda G. Bosnic help familiarize students with gender role analysis and feminist theory. Students examine classic literature and contemporary texts, considering characters' historical, literary, and social contexts while expanding their understanding of how patterns of identity and gender norms exist and…

  20. The energy–momentum tensor(s in classical gauge theories

    Directory of Open Access Journals (Sweden)

    Daniel N. Blaschke

    2016-11-01

    Full Text Available We give an introduction to, and review of, the energy–momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space–time. For the canonical energy–momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy–momentum tensor. The relationship with the Einstein–Hilbert tensor following from the coupling to a gravitational field is also discussed.

  1. Geometrical phases from global gauge invariance of nonlinear classical field theories

    International Nuclear Information System (INIS)

    Garrison, J.C.; Chiao, R.Y.

    1988-01-01

    We show that the geometrical phases recently discovered in quantum mechanics also occur naturally in the theory of any classical complex multicomponent field satisfying nonlinear equations derived from a Lagrangean with is invariant under gauge transformations of the first kind. Some examples are the paraxial wave equation for nonlinear optics, and Ginzburg-Landau equations for complex order parameters in condensed-matter physics

  2. A Comparative Study of Nucleation Parameterizations: 2. Three-Dimensional Model Application and Evaluation

    Science.gov (United States)

    Following the examination and evaluation of 12 nucleation parameterizations presented in part 1, 11 of them representing binary, ternary, kinetic, and cluster‐activated nucleation theories are evaluated in the U.S. Environmental Protection Agency Community Multiscale Air Quality ...

  3. Relativistic and nonrelativistic classical field theory on fivedimensional space-time

    International Nuclear Information System (INIS)

    Kunzle, H.P.; Duval, C.

    1985-07-01

    This paper is a sequel to earlier ones in which, on the one hand, classical field theories were described on a curved Newtonian space-time, and on the other hand, the Newtonian gravitation theory was formulated on a fivedimensional space-time with a metric of signature and a covariantly constant vector field. Here we show that Lagrangians for matter fields are easily formulated on this extended space-time from simple invariance arguments and that stress-energy tensors can be derived from them in the usual manner so that four-dimensional space-time expressions are obtained that are consistent in the relativistic as well as in the Newtonian case. In the former the theory is equivalent to General Relativity. When the magnitude of the distinguished vector field vanishes equations for the (covariant) Newtonian limit follow. We demonstrate this here explicity in the case of the Klein-Gordon/Schroedinger and the Dirac field and its covariant nonrelativistic analogue, the Levy-Leblond field. Especially in the latter example the covariant Newtonian theory simplifies dramatically in this fivedimensional form

  4. Coherent states with classical motion: from an analytic method complementary to group theory

    International Nuclear Information System (INIS)

    Nieto, M.M.

    1982-01-01

    From the motivation of Schroedinger, that of finding states which follow the motion which a classical particle would have in a given potential, we discuss generalizations of the coherent states of the harmonic oscillator. We focus on a method which is the analytic complement to the group theory point of view. It uses a minimum uncertainty formalism as its basis. We discuss the properties and time evolution of these states, always keeping in mind the desire to find quantum states which follow the classical motion

  5. Force-Field Functor Theory: Classical Force-Fields which Reproduce Equilibrium Quantum Distributions

    Directory of Open Access Journals (Sweden)

    Ryan eBabbush

    2013-10-01

    Full Text Available Feynman and Hibbs were the first to variationally determine an effective potential whose associated classical canonical ensemble approximates the exact quantum partition function. We examine the existence of a map between the local potential and an effective classical potential which matches the exact quantum equilibrium density and partition function. The usefulness of such a mapping rests in its ability to readily improve Born-Oppenheimer potentials for use with classical sampling. We show that such a map is unique and must exist. To explore the feasibility of using this result to improve classical molecular mechanics, we numerically produce a map from a library of randomly generated one-dimensional potential/effective potential pairs then evaluate its performance on independent test problems. We also apply the map to simulate liquid para-hydrogen, finding that the resulting radial pair distribution functions agree well with path integral Monte Carlo simulations. The surprising accessibility and transferability of the technique suggest a quantitative route to adapting Born-Oppenheimer potentials, with a motivation similar in spirit to the powerful ideas and approximations of density functional theory.

  6. Three dimensional classical theory of rainbow scattering of atoms from surfaces

    International Nuclear Information System (INIS)

    Pollak, Eli; Miret-Artes, Salvador

    2010-01-01

    Graphical abstract: In this work, we extend to three dimensions our previous stochastic classical theory on surface rainbow scattering. The stochastic phonon bath is modeled in terms of linear coupling of the phonon modes to the motion of the scattered particle. We take into account the three polarizations of the phonons. Closed formulae are derived for the angular and energy loss distributions. They are readily implemented when assuming that the vertical interaction with the surface is described by a Morse potential. The hard wall limit of the theory is derived and applied to some model corrugated potentials. We find that rainbow structure of the scattered angular distribution reflects the underlying symmetries of the surface. We also distinguish between 'normal rainbows' and 'super rainbows'. The latter occur when the two eigenvalues of the Hessian of the corrugation function vanish simultaneously. - Abstract: In this work, we extend to three dimensions our previous stochastic classical theory on surface rainbow scattering. The stochastic phonon bath is modeled in terms of linear coupling of the phonon modes to the motion of the scattered particle. We take into account the three polarizations of the phonons. Closed formulae are derived for the angular and energy loss distributions. They are readily implemented when assuming that the vertical interaction with the surface is described by a Morse potential. The hard wall limit of the theory is derived and applied to some model corrugated potentials. We find that rainbow structure of the scattered angular distribution reflects the underlying symmetries of the surface. We also distinguish between 'normal rainbows' and 'super rainbows'. The latter occur when the two eigenvalues of the Hessian of the corrugation function vanish simultaneously.

  7. Outline of a classical theory of quantum physics and gravitation

    International Nuclear Information System (INIS)

    Gallop, J.W.

    1975-01-01

    It is argued that in the manner in which the Galilean-Newtonian physics may be said to have explained the Ptolemaic-Copernican theories in terms which have since been called classical, so also Milner's theories of the structure of matter may be said to explain present day quantum and relativistic theory. In both cases the former employ the concept of force and the latter, by contrast, are geometrical theories. Milner envisaged space as being stressed, whereas Einstein thought of it as strained. Development of Milner's theory from criticisms and suggestions made by Kilmister has taken it further into the realms of quantum and gravitational physics, where it is found to give a more physically comprehensible explanation of the phenomena. Further, it shows why present day quantum theory is cast in a statistical form. The theory is supported by many predictions such as the ratio of Planck's constant to the mass of the electron, the value of the fine structure constant and reason for apparent variations in past measurements, the magnetic moment of the electron and proton of the stable particles such as the neutron Λ and Σ together with the kaon, and a relation between the universal gravitational constant and Hubble's constant - all within published experimental accuracy. The latest results to be accounted for by the theory are the masses of the newly discovered psi particles and confirmation of the value of the decay of Newton's gravitational constant obtained from lunar measurements. (author)

  8. Nucleation of Recrystallization studied by EBSP and 3DXRD

    DEFF Research Database (Denmark)

    West, Stine

    2009-01-01

    When a deformed crystalline material is annealed, recrystallization will typically take place. In this process new perfect crystals nucleate and grow, consuming the deformation structure. Traditionally, nucleation theories state that the crystal orientations of these new grains were already present...... in the deformed state, but several experiments have shown the emergence of what appears to be new orientations. The purpose of the present project was to observe nucleation of recrystallization both on surfaces and in the bulk. Special focus was on the possible formation of nuclei with orientations not present...... in the deformed matrix before annealing. To facilitate the nucleation studies, a well-annealed starting material was prepared from high-purity aluminum with a large average grain size and almost straight grain boundaries mostly forming triple junctions with angles close to 120°. The large grain size was necessary...

  9. First passage times in homogeneous nucleation: Dependence on the total number of particles

    International Nuclear Information System (INIS)

    Yvinec, Romain; Bernard, Samuel; Pujo-Menjouet, Laurent; Hingant, Erwan

    2016-01-01

    Motivated by nucleation and molecular aggregation in physical, chemical, and biological settings, we present an extension to a thorough analysis of the stochastic self-assembly of a fixed number of identical particles in a finite volume. We study the statistics of times required for maximal clusters to be completed, starting from a pure-monomeric particle configuration. For finite volumes, we extend previous analytical approaches to the case of arbitrary size-dependent aggregation and fragmentation kinetic rates. For larger volumes, we develop a scaling framework to study the first assembly time behavior as a function of the total quantity of particles. We find that the mean time to first completion of a maximum-sized cluster may have a surprisingly weak dependence on the total number of particles. We highlight how higher statistics (variance, distribution) of the first passage time may nevertheless help to infer key parameters, such as the size of the maximum cluster. Finally, we present a framework to quantify formation of macroscopic sized clusters, which are (asymptotically) very unlikely and occur as a large deviation phenomenon from the mean-field limit. We argue that this framework is suitable to describe phase transition phenomena, as inherent infrequent stochastic processes, in contrast to classical nucleation theory

  10. The nucleation of vorticity by ions in superfluid 4He

    International Nuclear Information System (INIS)

    Muirhead, C.M.; Vinen, W.F.; Donnelly, R.J.

    1985-01-01

    The theory developed in Part I is extended to include a discussion of nucleation by negative ions in the presence of dissolved 3 He at a concentration such that at a low temperature the negative ion bubble is likely to have adsorbed on its surface either one or two 3 He atoms. It is argued that the adsorbed 3 He atom can change the nucleation rate for two reasons: the atom can modify the perturbation applied to the helium at the surface of the ions; and it can act as a source of energy. The second of these effects is explored in some detail. It is shown that the 3 He atom is probably less strongly bound to the ion than it would be to the core of a vortex line; furthermore the atom adsorbed onto the surface of the ion can exist in a number of excited states (Shikin states), which are thermally populated even at quite low temperatures. Therefore, when nucleation of a vortex takes place, the 3 He atom might move from the ion surface to the core of the vortex or simply from one Shikin state to another of lower energy; in either case there is a release of energy. The existence of this energy release means, first, that nucleation becomes energetically possible at a reduced ionic velocity and secondly, that the energy barrier opposing nucleation is reduced in size. Therefore the critical velocity for vortex nucleation is reduced, and, for a given supercritical velocity, the rate of nucleation is increased. Addition of a second 3 He atom would have a similar effect. Further experiments are required to check the detailed predictions of the theory. (author)

  11. The Relation between Classical and Quantum Electrodynamics

    Directory of Open Access Journals (Sweden)

    Mario Bacelar Valente

    2011-01-01

    Full Text Available Quantum electrodynamics presents intrinsic limitations in the description of physical processes that make it impossible to recover from it the type of description we have in classical electrodynamics. Hence one cannot consider classical electrodynamics as reducing to quantum electrodynamics and being recovered from it by some sort of limiting procedure. Quantum electrodynamics has to be seen not as an more fundamental theory, but as an upgrade of classical electrodynamics, which permits an extension of classical theory to the description of phenomena that, while being related to the conceptual framework of the classical theory, cannot be addressed from the classical theory.

  12. Relative Role of Gas Generation and Displacement Rates in Cavity Nucleation and Growth

    DEFF Research Database (Denmark)

    Singh, Bachu Narain; Foreman, A. J E.

    1984-01-01

    Problems of helium diffusion and clustering during irradiation are analysed. Using the “homogeneous” nucleation theory , the effect of damage rate on cavity density is calculated for different gas generation to damage rate ratios. The influence of gas mobility on cavity nucleation has been...

  13. Theory of linear physical systems theory of physical systems from the viewpoint of classical dynamics, including Fourier methods

    CERN Document Server

    Guillemin, Ernst A

    2013-01-01

    An eminent electrical engineer and authority on linear system theory presents this advanced treatise, which approaches the subject from the viewpoint of classical dynamics and covers Fourier methods. This volume will assist upper-level undergraduates and graduate students in moving from introductory courses toward an understanding of advanced network synthesis. 1963 edition.

  14. Evolution of a magnetic bubble after quantum nucleation

    Science.gov (United States)

    Defranzo, A.; Gunther, L.

    1989-06-01

    Chudnovsky and Gunther recently presented a theory of quantum nucleation in a ferromagnet [Phys. Rev. B 37, 9455 (1989)]. As a sequel, this paper is concerned with the evolution of the magnetic bubble after its materialization.

  15. Dynamics of unitarization by classicalization

    International Nuclear Information System (INIS)

    Dvali, Gia; Pirtskhalava, David

    2011-01-01

    We study dynamics of the classicalization phenomenon suggested in G. Dvali et al. , according to which a class of non-renormalizable theories self-unitarizes at very high-energies via creation of classical configurations (classicalons). We study this phenomenon in an explicit model of derivatively-self-coupled scalar that serves as a prototype for a Nambu-Goldstone-Stueckelberg field. We prepare the initial state in form of a collapsing wave-packet of a small occupation number but of very high energy, and observe that the classical configuration indeed develops. Our results confirm the previous estimates, showing that because of self-sourcing the wave-packet forms a classicalon configuration with radius that increases with center of mass energy. Thus, classicalization takes place before the waves get any chance of probing short-distances. The self-sourcing by energy is the crucial point, which makes classicalization phenomenon different from the ordinary dispersion of the wave-packets in other interacting theories. Thanks to this, unlike solitons or other non-perturbative objects, the production of classicalons is not only unsuppressed, but in fact dominates the high-energy scattering. In order to make the difference between classicalizing and non-classicalizing theories clear, we use a language in which the scattering cross section in a generic theory can be universally understood as a geometric cross section set by a classical radius down to which waves can propagate freely, before being scattered. We then show, that in non-classicalizing examples this radius shrinks with increasing energy and becomes microscopic, whereas in classicalizing theories expands and becomes macroscopic. We study analogous scattering in a Galileon system and discover that classicalization also takes place there, although somewhat differently. We thus observe, that classicalization is source-sensitive and that Goldstones pass the first test.

  16. Three dimensional classical theory of rainbow scattering of atoms from surfaces

    Energy Technology Data Exchange (ETDEWEB)

    Pollak, Eli, E-mail: eli.pollak@weizmann.ac.il [Chemical Physics Department, Weizmann Institute of Science, 76100 Rehovoth (Israel); Miret-Artes, Salvador [Instituto de Fisica Fundamental, Consejo Superior de Investigaciones Cientificas, Serrano 123, 28006 Madrid (Spain)

    2010-10-05

    Graphical abstract: In this work, we extend to three dimensions our previous stochastic classical theory on surface rainbow scattering. The stochastic phonon bath is modeled in terms of linear coupling of the phonon modes to the motion of the scattered particle. We take into account the three polarizations of the phonons. Closed formulae are derived for the angular and energy loss distributions. They are readily implemented when assuming that the vertical interaction with the surface is described by a Morse potential. The hard wall limit of the theory is derived and applied to some model corrugated potentials. We find that rainbow structure of the scattered angular distribution reflects the underlying symmetries of the surface. We also distinguish between 'normal rainbows' and 'super rainbows'. The latter occur when the two eigenvalues of the Hessian of the corrugation function vanish simultaneously. - Abstract: In this work, we extend to three dimensions our previous stochastic classical theory on surface rainbow scattering. The stochastic phonon bath is modeled in terms of linear coupling of the phonon modes to the motion of the scattered particle. We take into account the three polarizations of the phonons. Closed formulae are derived for the angular and energy loss distributions. They are readily implemented when assuming that the vertical interaction with the surface is described by a Morse potential. The hard wall limit of the theory is derived and applied to some model corrugated potentials. We find that rainbow structure of the scattered angular distribution reflects the underlying symmetries of the surface. We also distinguish between 'normal rainbows' and 'super rainbows'. The latter occur when the two eigenvalues of the Hessian of the corrugation function vanish simultaneously.

  17. Classical theory of rotational rainbow scattering from uncorrugated surfaces

    International Nuclear Information System (INIS)

    Khodorkovsky, Yuri; Averbukh, Ilya Sh; Pollak, Eli

    2010-01-01

    A classical perturbation theory is developed to study rotational rainbow scattering of molecules from uncorrugated frozen surfaces. Considering the interaction of the rigid rotor with the translational motion towards the surface to be weak allows for a perturbative treatment, in which the known zeroth order motion is that of a freely rotating molecule hitting a surface. Using perturbation theory leads to explicit expressions for the angular momentum deflection function with respect to the initial orientational angle of the rotor that are valid for any magnitude of the initial angular momentum. The rotational rainbows appear as peaks both in the final angular momentum and rotational energy distributions, as well as peaks in the angular distribution, although the surface is assumed to be uncorrugated. The derived analytic expressions are compared with numerical simulation data. Even when the rotational motion is significantly coupled to the translational motion, the predictions of the perturbative treatment remain qualitatively correct.

  18. A course in mathematical physics 2 classical field theory

    CERN Document Server

    Thirring, Walter

    1978-01-01

    In the past decade the language and methods ofmodern differential geometry have been increasingly used in theoretical physics. What seemed extravagant when this book first appeared 12 years ago, as lecture notes, is now a commonplace. This fact has strengthened my belief that today students of theoretical physics have to learn that language-and the sooner the better. Afterall, they willbe the professors ofthe twenty-first century and it would be absurd if they were to teach then the mathematics of the nineteenth century. Thus for this new edition I did not change the mathematical language. Apart from correcting some mistakes I have only added a section on gauge theories. In the last decade it has become evident that these theories describe fundamental interactions, and on the classical level their structure is suffi­ cientlyclear to qualify them for the minimum amount ofknowledge required by a theoretician. It is with much regret that I had to refrain from in­ corporating the interesting developments in Kal...

  19. Clustering of amines and hydrazines in atmospheric nucleation

    Science.gov (United States)

    Li, Siyang; Qu, Kun; Zhao, Hailiang; Ding, Lei; Du, Lin

    2016-06-01

    It has been proved that the presence of amines in the atmosphere can enhance aerosol formation. Hydrazine (HD) and its substituted derivatives, monomethylhydrazine (MMH) and unsymmetrical dimethylhydrazine (UDMH), which are organic derivatives of amine and ammonia, are common trace atmospheric species that may contribute to the growth of nucleation clusters. The structures of the hydrazine and amine clusters containing one or two common nucleation molecules (ammonia, water, methanol and sulfuric acid) have been optimized using density functional theory (DFT) methods. The clusters growth mechanism has been explored from the thermochemistry by calculating the Gibbs free energies of adding an ammonia, water, methanol or sulfuric acid molecule step by step at room temperature, respectively. The results show that hydrazine and its derivatives could enhance heteromolecular homogeneous nucleation in the earth's atmosphere.

  20. Overview of Classical Test Theory and Item Response Theory for Quantitative Assessment of Items in Developing Patient-Reported Outcome Measures

    Science.gov (United States)

    Cappelleri, Joseph C.; Lundy, J. Jason; Hays, Ron D.

    2014-01-01

    Introduction The U.S. Food and Drug Administration’s patient-reported outcome (PRO) guidance document defines content validity as “the extent to which the instrument measures the concept of interest” (FDA, 2009, p. 12). “Construct validity is now generally viewed as a unifying form of validity for psychological measurements, subsuming both content and criterion validity” (Strauss & Smith, 2009, p. 7). Hence both qualitative and quantitative information are essential in evaluating the validity of measures. Methods We review classical test theory and item response theory approaches to evaluating PRO measures including frequency of responses to each category of the items in a multi-item scale, the distribution of scale scores, floor and ceiling effects, the relationship between item response options and the total score, and the extent to which hypothesized “difficulty” (severity) order of items is represented by observed responses. Conclusion Classical test theory and item response theory can be useful in providing a quantitative assessment of items and scales during the content validity phase of patient-reported outcome measures. Depending on the particular type of measure and the specific circumstances, either one or both approaches should be considered to help maximize the content validity of PRO measures. PMID:24811753

  1. Laboratory measurements and model sensitivity studies of dust deposition ice nucleation

    Directory of Open Access Journals (Sweden)

    G. Kulkarni

    2012-08-01

    Full Text Available We investigated the ice nucleating properties of mineral dust particles to understand the sensitivity of simulated cloud properties to two different representations of contact angle in the Classical Nucleation Theory (CNT. These contact angle representations are based on two sets of laboratory deposition ice nucleation measurements: Arizona Test Dust (ATD particles of 100, 300 and 500 nm sizes were tested at three different temperatures (−25, −30 and −35 °C, and 400 nm ATD and kaolinite dust species were tested at two different temperatures (−30 and −35 °C. These measurements were used to derive the onset relative humidity with respect to ice (RHice required to activate 1% of dust particles as ice nuclei, from which the onset single contact angles were then calculated based on CNT. For the probability density function (PDF representation, parameters of the log-normal contact angle distribution were determined by fitting CNT-predicted activated fraction to the measurements at different RHice. Results show that onset single contact angles vary from ~18 to 24 degrees, while the PDF parameters are sensitive to the measurement conditions (i.e. temperature and dust size. Cloud modeling simulations were performed to understand the sensitivity of cloud properties (i.e. ice number concentration, ice water content, and cloud initiation times to the representation of contact angle and PDF distribution parameters. The model simulations show that cloud properties are sensitive to onset single contact angles and PDF distribution parameters. The comparison of our experimental results with other studies shows that under similar measurement conditions the onset single contact angles are consistent within ±2.0 degrees, while our derived PDF parameters have larger discrepancies.

  2. The KAM story a friendly introduction to the content, history, and significance of classical Kolmogorov-Arnold-Moser theory

    CERN Document Server

    Dumas, H Scott

    2014-01-01

    This is a semi-popular mathematics book aimed at a broad readership of mathematically literate scientists, especially mathematicians and physicists who are not experts in classical mechanics or KAM theory, and scientific-minded readers. Parts of the book should also appeal to less mathematically trained readers with an interest in the history or philosophy of science. The scope of the book is broad: it not only describes KAM theory in some detail, but also presents its historical context (thus showing why it was a 'breakthrough'). Also discussed are applications of KAM theory (especially to celestial mechanics and statistical mechanics) and the parts of mathematics and physics in which KAM theory resides (dynamical systems, classical mechanics, and Hamiltonian perturbation theory). Although a number of sources on KAM theory are now available for experts, this book attempts to fill a long-standing gap at a more descriptive level. It stands out very clearly from existing publications on KAM theory because it ...

  3. Geometry of Lagrangian first-order classical field theories

    International Nuclear Information System (INIS)

    Echeverria-Enriquez, A.; Munoz-Lecanda, M.C.; Roman-Roy, N.

    1996-01-01

    We construct a lagrangian geometric formulation for first-order field theories using the canonical structures of first-order jet bundles, which are taken as the phase spaces of the systems in consideration. First of all, we construct all the geometric structures associated with a first-order jet bundle and, using them, we develop the lagrangian formalism, defining the canonical forms associated with a lagrangian density and the density of lagrangian energy, obtaining the Euler-Lagrange equations in two equivalent ways: as the result of a variational problem and developing the jet field formalism (which is a formulation more similar to the case of mechanical systems). A statement and proof of Noether's theorem is also given, using the latter formalism. Finally, some classical examples are briefly studied. (orig.)

  4. On the validity of the classical hydrodynamic lubrication theory applied to squeeze film dampers

    International Nuclear Information System (INIS)

    Danaila, S; Moraru, L

    2010-01-01

    Squeeze film dampers (SFD) are devices utilized to control vibrations of the shafts of high-speed rotating machinery. The SFD - squirrel cage combination is probably the most used system for tuning the stiffness and damping of the supports for rotors installed on ball bearings. Squeeze film dampers are essentially hydrodynamic bearings which contain the ball bearings housings of ball-bearings supported shafts. Consequently, the oil film within the SFD are influenced only by the precession and nutation of the shaft, that is the flow of the oil within the damper is not directly influenced by the spin of the rotor. However, in the classical theory, the flow in the thin film is also governed by the Reynolds equation. In this paper, some of the limits of the classical theory of the SFD are discussed and theoretical and experimental studies, which illustrate the ideas presented herein, are presented as well. The orbits of an unbalanced rotor that is supported by a ball-bearings-SFD-squirrel-cage assembly at one end and by rigidly mounted ball bearings at the other end are computed using the bearing forces provided by the classical short bearing theory. The numerical model also includes the properties of the squirrel cage. The parameters of the squirrel cage were measured, together with the effect of the friction within the assembly. Experimental unbalance responses were also collected for various rotation speeds and unbalances to validate the numerical simulations.

  5. The scales of brane nucleation processes

    International Nuclear Information System (INIS)

    Alwis, S.P. de

    2007-01-01

    The scales associated with Brown-Teitelboim-Bousso-Polchinski processes of brane nucleation, which result in changes of the flux parameters and the number of D-branes, are discussed in the context of type IIB models with all moduli stabilized. It is argued that such processes are unlikely to be described by effective field theory

  6. Generalization of the Activated Complex Theory of Reaction Rates. II. Classical Mechanical Treatment

    Science.gov (United States)

    Marcus, R. A.

    1964-01-01

    In its usual classical form activated complex theory assumes a particular expression for the kinetic energy of the reacting system -- one associated with a rectilinear motion along the reaction coordinate. The derivation of the rate expression given in the present paper is based on the general kinetic energy expression.

  7. Nucleation and condensation in the primitive solar nebula

    International Nuclear Information System (INIS)

    Cameron, A.G.W.; Fegley, M.B.

    1982-01-01

    It is pointed out that the primitive solar nebula may be modeled using the frictionally induced transport theory of Lynden-Bell and Pringle (1974) if the principal frictional mechanism within the nebula is turbulent viscosity. The present investigation is concerned with the construction of a model of a section of the primitive solar nebula as a basis for the study of nucleation and condensation processes within this section. The construction involves a relatively simple application of the Lynden-Bell and Pringle theory subject to steady mass flow conditions. The calculations which are conducted in connection with the investigation indicate that by the time the gas in the primitive solar nebula has become sufficiently supercooled to nucleate condensation centers, several different compounds, including the magnesium silicates forsterite and enstatite (MgSiO 3 ), will probably be able to condense on the growing condensation center

  8. COMPETITION: CLASSICAL VERSUS NEOCLASSICAL VIEW

    OpenAIRE

    Mihaela Cornelia Sandu

    2013-01-01

    Competition is an important element from economical theory. Over time it has experienced several definitions and classifications much of them being contradictory. In this paper I will make a parallel between classical and neoclassical point of view according to competition. Keywords. Competition; neoclassical theory; classical theory; monopolistic; perfect competition.

  9. An application of information theory to stochastic classical gravitational fields

    Science.gov (United States)

    Angulo, J.; Angulo, J. C.; Angulo, J. M.

    2018-06-01

    The objective of this study lies on the incorporation of the concepts developed in the Information Theory (entropy, complexity, etc.) with the aim of quantifying the variation of the uncertainty associated with a stochastic physical system resident in a spatiotemporal region. As an example of application, a relativistic classical gravitational field has been considered, with a stochastic behavior resulting from the effect induced by one or several external perturbation sources. One of the key concepts of the study is the covariance kernel between two points within the chosen region. Using this concept and the appropriate criteria, a methodology is proposed to evaluate the change of uncertainty at a given spatiotemporal point, based on available information and efficiently applying the diverse methods that Information Theory provides. For illustration, a stochastic version of the Einstein equation with an added Gaussian Langevin term is analyzed.

  10. Application of nonequilibrium quantum statistical mechanics to homogeneous nucleation

    International Nuclear Information System (INIS)

    Larson, A.R.; Cantrell, C.D.

    1978-01-01

    The master equation for cluster growth and evaporation is derived from many-body quantum mechanics and from a modified version of quantum damping theory used in laser physics. For application to nucleation theory, the quantum damping theory has been generalized to include system and reservoir states that are not separate entities. Formulae for rate constants are obtained. Solutions of the master equation yield equations of state and system-averaged quantities recognized as thermodynamic variables. Formulae for Helmholtz free energies of clusters in a Debye approximation are derived. Coexistence-line equations for pressure volume, and number of clusters are obtained from equations-of-state analysis. Coexistence-line and surface-tension data are used to obtain values of parameters for the Debye approximation. These data are employed in calculating both the nucleation current in diffusion cloud chamber experiments and the onset of condensation in expansion nozzle experiments. Theoretical and experimental results are similar for both cloud-chamber and nozzle experiments, which measure water

  11. Heterogeneous ice nucleation in aqueous solutions: the role of water activity.

    Science.gov (United States)

    Zobrist, B; Marcolli, C; Peter, T; Koop, T

    2008-05-01

    Heterogeneous ice nucleation experiments have been performed with four different ice nuclei (IN), namely nonadecanol, silica, silver iodide and Arizona test dust. All IN are either immersed in the droplets or located at the droplets surface. The IN were exposed to various aqueous solutions, which consist of (NH4)2SO4, H2SO4, MgCl2, NaCl, LiCl, Ca(NO3)2, K2CO3, CH3COONa, ethylene glycol, glycerol, malonic acid, PEG300 or a NaCl/malonic acid mixture. Freezing was studied using a differential scanning calorimeter and a cold finger cell. The results show that the heterogeneous ice freezing temperatures decrease with increasing solute concentration; however, the magnitude of this effect is solute dependent. In contrast, when the results are analyzed in terms of the solution water activity a very consistent behavior emerges: heterogeneous ice nucleation temperatures for all four IN converge each onto a single line, irrespective of the nature of the solute. We find that a constant offset with respect to the ice melting point curve, Deltaaw,het, can describe the observed freezing temperatures for each IN. Such a behavior is well-known for homogeneous ice nucleation from supercooled liquid droplets and has led to the development of water-activity-based ice nucleation theory. The large variety of investigated solutes together with different general types of ice nuclei studied (monolayers, ionic crystals, covalently bound network-forming compounds, and a mixture of chemically different crystallites) underlines the general applicability of water-activity-based ice nucleation theory also for heterogeneous ice nucleation in the immersion mode. Finally, the ice nucleation efficiencies of the various IN, as well as the atmospheric implication of the developed parametrization are discussed.

  12. Molecular sizes of lichen ice nucleation sites determined by gamma radiation inactivation analysis

    International Nuclear Information System (INIS)

    Kieft, T.L.; Ruscetti, T.

    1992-01-01

    It has previously been shown that some species of lichen fungi contain proteinaceous ice nuclei which are active at temperatures as warm as −2 °C. This experiment was undertaken to determine the molecular sizes of ice nuclei in the lichen fungus Rhizoplaca chrysoleuca and to compare them to bacterial ice nuclei from Pseudomonas syringae. Gamma radiation inactivation analysis was used to determine molecular weights. Radiation inactivation analysis is based on target theory, which states that the likelihood of a molecule being inactivated by gamma rays increases as its size increases. Three different sources of ice nuclei from the lichen R. chrysoleuca were tested: field-collected lichens, extract of lichen fungus, and a pure culture of the fungus R. chrysoleuca. P. syringae strain Cit7 was used as a source of bacterial ice nuclei. Samples were lyophilized, irradiated with gamma doses ranging from 0 to 10.4 Mrads, and then tested for ice nucleation activity using a droplet-freezing assay. Data for all four types of samples were in rough agreement; sizes of nucleation sites increased logarithmically with increasing temperatures of ice nucleation activity. Molecular weights of nucleation sites active between −3 and −4 °C from the bacteria and from the field-collected lichens were approximately 1.0 × 10 6 Da. Nuclei from the lichen fungus and in the lichen extract appeared to be slightly smaller but followed the same log-normal pattern with temperature of ice nucleation activity. The data for both the bacterial and lichen ice nuclei are in agreement with ice nucleation theory which states that the size of ice nucleation sites increases logarithmically as the temperature of nucleation increases linearly. This suggests that although some differences exist between bacterial and lichen ice nucleation sites, their molecular sizes are quite similar

  13. A note on the nucleation with multiple steps: Parallel and series nucleation

    OpenAIRE

    Iwamatsu, Masao

    2012-01-01

    Parallel and series nucleation are the basic elements of the complex nucleation process when two saddle points exist on the free-energy landscape. It is pointed out that the nucleation rates follow formulas similar to those of parallel and series connection of resistors or conductors in an electric circuit. Necessary formulas to calculate individual nucleation rates at the saddle points and the total nucleation rate are summarized and the extension to the more complex nucleation process is su...

  14. Microstructure development in Kolmogorov, Johnson-Mehl, and Avrami nucleation and growth kinetics

    Science.gov (United States)

    Pineda, Eloi; Crespo, Daniel

    1999-08-01

    A statistical model with the ability to evaluate the microstructure developed in nucleation and growth kinetics is built in the framework of the Kolmogorov, Johnson-Mehl, and Avrami theory. A populational approach is used to compute the observed grain-size distribution. The impingement process which delays grain growth is analyzed, and the effective growth rate of each population is estimated considering the previous grain history. The proposed model is integrated for a wide range of nucleation and growth protocols, including constant nucleation, pre-existing nuclei, and intermittent nucleation with interface or diffusion-controlled grain growth. The results are compared with Monte Carlo simulations, giving quantitative agreement even in cases where previous models fail.

  15. Quantum and classical behavior in interacting bosonic systems

    Energy Technology Data Exchange (ETDEWEB)

    Hertzberg, Mark P. [Institute of Cosmology & Department of Physics and Astronomy, Tufts University,Medford, MA 02155 (United States)

    2016-11-21

    It is understood that in free bosonic theories, the classical field theory accurately describes the full quantum theory when the occupancy numbers of systems are very large. However, the situation is less understood in interacting theories, especially on time scales longer than the dynamical relaxation time. Recently there have been claims that the quantum theory deviates spectacularly from the classical theory on this time scale, even if the occupancy numbers are extremely large. Furthermore, it is claimed that the quantum theory quickly thermalizes while the classical theory does not. The evidence for these claims comes from noticing a spectacular difference in the time evolution of expectation values of quantum operators compared to the classical micro-state evolution. If true, this would have dramatic consequences for many important phenomena, including laboratory studies of interacting BECs, dark matter axions, preheating after inflation, etc. In this work we critically examine these claims. We show that in fact the classical theory can describe the quantum behavior in the high occupancy regime, even when interactions are large. The connection is that the expectation values of quantum operators in a single quantum micro-state are approximated by a corresponding classical ensemble average over many classical micro-states. Furthermore, by the ergodic theorem, a classical ensemble average of local fields with statistical translation invariance is the spatial average of a single micro-state. So the correlation functions of the quantum and classical field theories of a single micro-state approximately agree at high occupancy, even in interacting systems. Furthermore, both quantum and classical field theories can thermalize, when appropriate coarse graining is introduced, with the classical case requiring a cutoff on low occupancy UV modes. We discuss applications of our results.

  16. Hilbert space theory of classical electrodynamics

    Indian Academy of Sciences (India)

    Furthermore, following Bondar et al, {\\it Phys. Rev.} A 88, 052108 (2013), it is pointed out that quantum processes that preserve the positivity or nonpositivity of theWigner function can be implemented by classical optics. This may be useful in interpreting quantum information processing in terms of classical optics.

  17. Monte-Carlo simulation of defect-cluster nucleation in metals during irradiation

    International Nuclear Information System (INIS)

    Nakasuji, Toshiki; Morishita, Kazunori; Ruan, Xiaoyong

    2017-01-01

    Highlights: • Monte-Carlo simulations were performed to investigate the nucleation process of copper-vacancy clusters in Fe. • Nucleation paths were obtained as a function of temperature and the damage rate. - Abstract: A multiscale modeling approach was applied to investigate the nucleation process of CRPs (copper rich precipitates, i.e., copper-vacancy clusters) in α-Fe containing 1 at.% Cu during irradiation. Monte-Carlo simulations were performed to investigate the nucleation process, with the rate theory equation analysis to evaluate the concentration of displacement defects, along with the molecular dynamics technique to know CRP thermal stabilities in advance. Our MC simulations showed that there is long incubation period at first, followed by a rapid growth of CRPs. The incubation period depends on irradiation conditions such as the damage rate and temperature. CRP’s composition during nucleation varies with time. The copper content of CRPs shows relatively rich at first, and then becomes poorer as the precipitate size increases. A widely-accepted model of CRP nucleation process is finally proposed.

  18. Monte-Carlo simulation of defect-cluster nucleation in metals during irradiation

    Energy Technology Data Exchange (ETDEWEB)

    Nakasuji, Toshiki, E-mail: t-nakasuji@iae.kyoto-u.ac.jp [Graduate School of Energy Science, Kyoto University, Uji, Kyoto 611-0011 (Japan); Morishita, Kazunori [Institute of Advanced Energy, Kyoto University, Uji, Kyoto 611-0011 (Japan); Ruan, Xiaoyong [Graduate School of Energy Science, Kyoto University, Uji, Kyoto 611-0011 (Japan)

    2017-02-15

    Highlights: • Monte-Carlo simulations were performed to investigate the nucleation process of copper-vacancy clusters in Fe. • Nucleation paths were obtained as a function of temperature and the damage rate. - Abstract: A multiscale modeling approach was applied to investigate the nucleation process of CRPs (copper rich precipitates, i.e., copper-vacancy clusters) in α-Fe containing 1 at.% Cu during irradiation. Monte-Carlo simulations were performed to investigate the nucleation process, with the rate theory equation analysis to evaluate the concentration of displacement defects, along with the molecular dynamics technique to know CRP thermal stabilities in advance. Our MC simulations showed that there is long incubation period at first, followed by a rapid growth of CRPs. The incubation period depends on irradiation conditions such as the damage rate and temperature. CRP’s composition during nucleation varies with time. The copper content of CRPs shows relatively rich at first, and then becomes poorer as the precipitate size increases. A widely-accepted model of CRP nucleation process is finally proposed.

  19. Revision of nucleated boiling mechanisms

    International Nuclear Information System (INIS)

    Converti, J.; Balino, J.L.

    1987-01-01

    The boiling occurrence plays an important role in the power reactors energy transfer. But still, there is not a final theory on the boiling mechanisms. This paper presents a critical analysis of the most important nucleated boiling models that appear in literature. The conflicting points are identified and experiments are proposed to clear them up. Some of these experiments have been performed at the Thermohydraulics laboratory (Bariloche Atomic Center). (Author)

  20. Geometry of Lagrangian first-order classical field theories

    Energy Technology Data Exchange (ETDEWEB)

    Echeverria-Enriquez, A. [Univ. Politecnica de Cataluna, Barcelona (Spain). Departamento de Matematica Aplicada y Telematica; Munoz-Lecanda, M.C. [Univ. Politecnica de Cataluna, Barcelona (Spain). Departamento de Matematica Aplicada y Telematica; Roman-Roy, N. [Univ. Politecnica de Cataluna, Barcelona (Spain). Departamento de Matematica Aplicada y Telematica

    1996-10-01

    We construct a lagrangian geometric formulation for first-order field theories using the canonical structures of first-order jet bundles, which are taken as the phase spaces of the systems in consideration. First of all, we construct all the geometric structures associated with a first-order jet bundle and, using them, we develop the lagrangian formalism, defining the canonical forms associated with a lagrangian density and the density of lagrangian energy, obtaining the Euler-Lagrange equations in two equivalent ways: as the result of a variational problem and developing the jet field formalism (which is a formulation more similar to the case of mechanical systems). A statement and proof of Noether`s theorem is also given, using the latter formalism. Finally, some classical examples are briefly studied. (orig.)

  1. Arsenic flux dependence of island nucleation on InAs(001)

    International Nuclear Information System (INIS)

    Grosse, Frank; Barvosa-Carter, William; Zinck, Jenna; Wheeler, Matthew; Gyure, Mark F.

    2002-01-01

    The initial stages of InAs(001) homoepitaxial growth are investigated using a combination of kinetic Monte Carlo simulations based on ab initio density functional theory and scanning tunneling microscopy. In the two dimensional island nucleation mode investigated, the island number density is found to decrease with increasing As. This behavior is explained by a suppression of the effective In-adatom density leading to a reduction in island nucleation. The relevant microscopic processes responsible for this reduction are identified

  2. A note on the nucleation with multiple steps: parallel and series nucleation.

    Science.gov (United States)

    Iwamatsu, Masao

    2012-01-28

    Parallel and series nucleation are the basic elements of the complex nucleation process when two saddle points exist on the free-energy landscape. It is pointed out that the nucleation rates follow formulas similar to those of parallel and series connection of resistors or conductors in an electric circuit. Necessary formulas to calculate individual nucleation rates at the saddle points and the total nucleation rate are summarized, and the extension to the more complex nucleation process is suggested. © 2012 American Institute of Physics

  3. Ice nucleation and cloud microphysical properties in tropical tropopause layer cirrus

    Directory of Open Access Journals (Sweden)

    E. J. Jensen

    2010-02-01

    Full Text Available In past modeling studies, it has generally been assumed that the predominant mechanism for nucleation of ice in the uppermost troposphere is homogeneous freezing of aqueous aerosols. However, recent in situ and remote-sensing measurements of the properties of cirrus clouds at very low temperatures in the tropical tropopause layer (TTL are broadly inconsistent with theoretial predictions based on the homogeneous freezing assumption. The nearly ubiquitous occurence of gravity waves in the TTL makes the predictions from homogeneous nucleation theory particularly difficult to reconcile with measurements. These measured properties include ice number concentrations, which are much lower than theory predicts; ice crystal size distributions, which are much broader than theory predicts; and cloud extinctions, which are much lower than theory predicts. Although other explanations are possible, one way to limit ice concentrations is to have on the order of 50 L−1 effective ice nuclei (IN that could nucleate ice at relatively low supersaturations. We suggest that ammonium sulfate particles, which would be dry much of the time in the cold TTL, are a potential IN candidate for TTL cirrus. However, this mechanism remains to be fully quantified for the size distribution of ammonium sulfate (possibly internally mixed with organics actually present in the upper troposphere. Possible implications of the observed cloud microphysical properties for ice sedimentation, dehydration, and cloud persistence are also discussed.

  4. Classical correlations, Bell inequalities, and communication complexity

    Energy Technology Data Exchange (ETDEWEB)

    Wilms, Johannes; Alber, Gernot [Institut fuer Angewandte Physik, Technische Universitaet Darmstadt, D-64289 Darmstadt (Germany); Percival, Ian C. [Department of Physics, Univ. of London (United Kingdom)

    2007-07-01

    A computer program is presented which is capable of exploring generalizations of Bell-type inequalities for arbitrary numbers of classical inputs and outputs. Thereby, polytopes can be described which represent classical local realistic theories, classical theories without signaling, or classical theories with explicit signaling. These latter polytopes may also be of interest for exploring basic problems of communication complexity. As a first application the influence of non-perfect detectors is discussed in simple Bell experiments.

  5. Suppression of saturated nucleate boiling by forced convective flow

    International Nuclear Information System (INIS)

    Bennett, D.L.; Davis, M.W.; Hertzler, B.L.

    1980-01-01

    Tube-side forced convective boiling nitrogen and oxygen and thin film shell-side forced convective boiling R-11 data demonstrate a reduction in the heat transfer coefficient associated with nucleate boiling as the two-phase friction pressure drop increases. Techniques proposed in the literature to account for nucleate boiling during forced convective boiling are discussed. The observed suppression of nucleate boiling for the tube-side data is compared against the Chen correlation. Although general agreement is exhibited, supporting the interactive heat transfer mechanism theory, better agreement is obtained by defining a bubble growth region within the thermal boundary layer. The data suggests that the size of the bubble growth region is independent of the friction drop, but is only a function of the physical properties of the boiling liquid. 15 refs

  6. Nucleation of microcrystalline silicon: on the effect of the substrate surface nature and nano-imprint topography

    International Nuclear Information System (INIS)

    Palmans, J; Faraz, T; Verheijen, M A; Kessels, W M M; Creatore, M

    2016-01-01

    The nucleation of microcrystalline silicon thin-films has been investigated for various substrate natures and topographies. An earlier nucleation onset on aluminium-doped zinc oxide compared to glass substrates has been revealed, associated with a microstructure enhancement and reduced surface energy. Both aspects resulted in a larger crystallite density, following classical nucleation theory. Additionally, the nucleation onset was (plasma deposition) condition-dependent. Therefore, surface chemistry and its interplay with the plasma have been proposed as key factors affecting nucleation and growth. As such, preliminary proof of the substrate nature’s role in microcrystalline silicon growth has been provided. Subsequently, the impact of nano-imprint lithography prepared surfaces on the initial microcrystalline silicon growth has been explored. Strong topographies, with a 5-fold surface area enhancement, led to a reduction in crystalline volume fraction of ∼20%. However, no correlation between topography and microstructure has been found. Instead, the suppressed crystallization has been partially ascribed to a reduced growth flux, limited surface diffusion and increased incubation layer thickness, originating from the surface area enhancement when transiting from flat to nanostructured surfaces. Furthermore, fundamental plasma parameters have been reviewed in relation with surface topography. Strong topographies are not expected to affect the ion-to-growth flux ratio. However, the reduced ion flux (due to increasing surface area) further limited the already weak ion energy transfer to surface processes. Additionally, the atomic hydrogen flux, i.e. the driving force for microcrystalline growth, has been found to decrease by a factor of 10 when transiting from flat to nanostructured topography. This resulted in an almost 6-fold reduction of the hydrogen-to-growth flux ratio, a much stronger effect than the ion-to-growth flux ratio. Since previous studies regarding

  7. Chaos, scaling and existence of a continuum limit in classical non-Abelian lattice gauge theory

    International Nuclear Information System (INIS)

    Nielsen, H.B.; Rugh, H.H.; Rugh, S.E.

    1996-01-01

    We discuss space-time chaos and scaling properties for classical non-Abelian gauge fields discretized on a spatial lattice. We emphasize that there is a open-quote no goclose quotes for simulating the original continuum classical gauge fields over a long time span since there is a never ending dynamical cascading towards the ultraviolet. We note that the temporal chaotic properties of the original continuum gauge fields and the lattice gauge system have entirely different scaling properties thereby emphasizing that they are entirely different dynamical systems which have only very little in common. Considered as a statistical system in its own right the lattice gauge system in a situation where it has reached equilibrium comes closest to what could be termed a open-quotes continuum limitclose quotes in the limit of very small energies (weak non-linearities). We discuss the lattice system both in the limit for small energies and in the limit of high energies where we show that there is a saturation of the temporal chaos as a pure lattice artifact. Our discussion focuses not only on the temporal correlations but to a large extent also on the spatial correlations in the lattice system. We argue that various conclusions of physics have been based on monitoring the non-Abelian lattice system in regimes where the fields are correlated over few lattice units only. This is further evidenced by comparison with results for Abelian lattice gauge theory. How the real time simulations of the classical lattice gauge theory may reach contact with the real time evolution of (semi-classical aspects of) the quantum gauge theory (e.g. Q.C.D.) is left an important question to be further examined

  8. [A non-classical approach to medical practices: Michel Foucault and Actor-Network Theory].

    Science.gov (United States)

    Bińczyk, E

    2001-01-01

    The text presents an analysis of medical practices stemming from two sources: Michel Foucault's conception and the research of Annemarie Mol and John Law, representatives of a trend known as Actor-Network Theory. Both approaches reveal significant theoretical kinship: they can be successfully consigned to the framework of non-classical sociology of science. I initially refer to the cited conceptions as a version of non-classical sociology of medicine. The identity of non-classical sociology of medicine hinges on the fact that it undermines the possibility of objective definitions of disease, health and body. These are rather approached as variable social and historical phenomena, co-constituted by medical practices. To both Foucault and Mol the main object of interest was not medicine as such, but rather the network of medical practices. Mol and Law sketch a new theoretical perspective for the analysis of medical practices. They attempt to go beyond the dichotomous scheme of thinking about the human body as an object of medical research and the subject of private experience. Research on patients suffering blood-sugar deficiency provide the empirical background for the thesis of Actor-Network Theory representatives. Michel Foucault's conceptions are extremely critical of medical practices. The French researcher describes the processes of 'medicalising' Western society as the emergence of a new type of power. He attempts to sensitise the reader to the ethical dimension of the processes of medicalising society.

  9. Vapour–to–liquid nucleation: Nucleation theorems for nonisothermal–nonideal case

    Energy Technology Data Exchange (ETDEWEB)

    Malila, J.; McGraw, R.; Napari, I.; Laaksonen, A.

    2010-08-29

    Homogeneous vapour-to-liquid nucleation, a basic process of aerosol formation, is often considered as a type example of nucleation phenomena, while most treatment of the subject introduce several simplifying assumptions (ideal gas phase, incompressible nucleus, isothermal kinetics, size-independent surface free energy...). During last decades, nucleation theorems have provided new insights into properties of critical nuclei facilitating direct comparison between laboratory experiments and molecular simulations. These theorems are, despite of their generality, often applied in forms where the aforementioned assumptions are made. Here we present forms of nucleation theorems that explicitly take into account these effects and allow direct estimation of their importance. Only assumptions are Arrhenius-type kinetics of nucleation process and exclusion carrier gas molecules from the critical nucleus.

  10. An empirical comparison of Item Response Theory and Classical Test Theory

    Directory of Open Access Journals (Sweden)

    Špela Progar

    2008-11-01

    Full Text Available Based on nonlinear models between the measured latent variable and the item response, item response theory (IRT enables independent estimation of item and person parameters and local estimation of measurement error. These properties of IRT are also the main theoretical advantages of IRT over classical test theory (CTT. Empirical evidence, however, often failed to discover consistent differences between IRT and CTT parameters and between invariance measures of CTT and IRT parameter estimates. In this empirical study a real data set from the Third International Mathematics and Science Study (TIMSS 1995 was used to address the following questions: (1 How comparable are CTT and IRT based item and person parameters? (2 How invariant are CTT and IRT based item parameters across different participant groups? (3 How invariant are CTT and IRT based item and person parameters across different item sets? The findings indicate that the CTT and the IRT item/person parameters are very comparable, that the CTT and the IRT item parameters show similar invariance property when estimated across different groups of participants, that the IRT person parameters are more invariant across different item sets, and that the CTT item parameters are at least as much invariant in different item sets as the IRT item parameters. The results furthermore demonstrate that, with regards to the invariance property, IRT item/person parameters are in general empirically superior to CTT parameters, but only if the appropriate IRT model is used for modelling the data.

  11. Autocatalytic microtubule nucleation determines the size and mass of Xenopus laevis egg extract spindles.

    Science.gov (United States)

    Decker, Franziska; Oriola, David; Dalton, Benjamin; Brugués, Jan

    2018-01-11

    Regulation of size and growth is a fundamental problem in biology. A prominent example is the formation of the mitotic spindle, where protein concentration gradients around chromosomes are thought to regulate spindle growth by controlling microtubule nucleation. Previous evidence suggests that microtubules nucleate throughout the spindle structure. However, the mechanisms underlying microtubule nucleation and its spatial regulation are still unclear. Here, we developed an assay based on laser ablation to directly probe microtubule nucleation events in Xenopus laevis egg extracts. Combining this method with theory and quantitative microscopy, we show that the size of a spindle is controlled by autocatalytic growth of microtubules, driven by microtubule-stimulated microtubule nucleation. The autocatalytic activity of this nucleation system is spatially regulated by the limiting amounts of active microtubule nucleators, which decrease with distance from the chromosomes. This mechanism provides an upper limit to spindle size even when resources are not limiting. © 2018, Decker et al.

  12. Quantum flesh on classical bones: Semiclassical bridges across the quantum-classical divide

    Energy Technology Data Exchange (ETDEWEB)

    Bokulich, Alisa [Center for Philosophy and History of Science, Boston University, Boston, MA (United States)

    2014-07-01

    Traditionally quantum mechanics is viewed as having made a sharp break from classical mechanics, and the concepts and methods of these two theories are viewed as incommensurable with one another. A closer examination of the history of quantum mechanics, however, reveals that there is a strong sense in which quantum mechanics was built on the backbone of classical mechanics. As a result, there is a considerable structural continuity between these two theories, despite their important differences. These structural continuities provide a ground for semiclassical methods in which classical structures, such as trajectories, are used to investigate and model quantum phenomena. After briefly tracing the history of semiclassical approaches, I show how current research in semiclassical mechanics is revealing new bridges across the quantum-classical divide.

  13. Prequantum classical statistical field theory: background field as a source of everything?

    International Nuclear Information System (INIS)

    Khrennikov, Andrei

    2011-01-01

    Prequantum classical statistical field theory (PCSFT) is a new attempt to consider quantum mechanics (QM) as an emergent phenomenon, cf. with De Broglie's 'double solution' approach, Bohmian mechanics, stochastic electrodynamics (SED), Nelson's stochastic QM and its generalization by Davidson, 't Hooft's models and their development by Elze. PCSFT is a comeback to a purely wave viewpoint on QM, cf. with early Schrodinger. There is no quantum particles at all, only waves. In particular, photons are simply wave-pulses of the classical electromagnetic field, cf. SED. Moreover, even massive particles are special 'prequantum fields': the electron field, the neutron field, and so on. PCSFT claims that (sooner or later) people will be able to measure components of these fields: components of the 'photonic field' (the classical electromagnetic field of low intensity), electronic field, neutronic field, and so on. At the moment we are able to produce quantum correlations as correlations of classical Gaussian random fields. In this paper we are interested in mathematical and physical reasons of usage of Gaussian fields. We consider prequantum signals (corresponding to quantum systems) as composed of a huge number of wave-pulses (on very fine prequantum time scale). We speculate that the prequantum background field (the field of 'vacuum fluctuations') might play the role of a source of such pulses, i.e., the source of everything.

  14. Thermally activated vapor bubble nucleation: The Landau-Lifshitz-Van der Waals approach

    Science.gov (United States)

    Gallo, Mirko; Magaletti, Francesco; Casciola, Carlo Massimo

    2018-05-01

    Vapor bubbles are formed in liquids by two mechanisms: evaporation (temperature above the boiling threshold) and cavitation (pressure below the vapor pressure). The liquid resists in these metastable (overheating and tensile, respectively) states for a long time since bubble nucleation is an activated process that needs to surmount the free energy barrier separating the liquid and the vapor states. The bubble nucleation rate is difficult to assess and, typically, only for extremely small systems treated at an atomistic level of detail. In this work a powerful approach, based on a continuum diffuse interface modeling of the two-phase fluid embedded with thermal fluctuations (fluctuating hydrodynamics), is exploited to study the nucleation process in homogeneous conditions, evaluating the bubble nucleation rates and following the long-term dynamics of the metastable system, up to the bubble coalescence and expansion stages. In comparison with more classical approaches, this methodology allows us on the one hand to deal with much larger systems observed for a much longer time than possible with even the most advanced atomistic models. On the other, it extends continuum formulations to thermally activated processes, impossible to deal with in a purely determinist setting.

  15. Mechanism of nucleation and growth of hydrogen porosity in solidifying A356 aluminum alloy: an analytical solution

    International Nuclear Information System (INIS)

    Li, K.-D.; Chang, Edward

    2004-01-01

    This study derives an analytical solution for the mechanism of nucleation and growth of hydrogen pore in the solidifying A356 aluminum alloy. A model of initial transient hydrogen redistribution in the growing dendritic grain is used to modify the lever rule for the mechanism of nucleation of pore. The model predicts the fraction of solid at nucleation, the temperature range of nucleation, the radius of hydrogen diffusion cell, and the supersaturation of hydrogen needed for nucleation. The role of solidus velocity in nucleation is explained. The parameters calculated from the model of nucleation are used for analyzing the mechanism of kinetic diffusion-controlled growth of pore, in which the mathematical transformations of variables are introduced. With the transformations, it is argued that the diffusion problem involving the liquid and solid phases during solidification could be treated as a classic problem of precipitation in the single-phase medium treated by Ham or Avrami. The analytical solution for the nucleation of pore is compared with the mechanism of macrosegregation. The predicted volume percent of porosity and radius of pore based on the mechanism of growth of pore is discussed with respect to the thermodynamic solution, the published experimental data, the numerical solutions, and the role of interdendritic fluid flow governed by Darcy's law

  16. The Manifestations of Positive Leader Roles in Classical Theories of Leadership

    Directory of Open Access Journals (Sweden)

    Joanna Wegner

    2017-06-01

    Full Text Available The aim of the paper is to identify the key functions performed by leaders in organisations, and to study how positive leaders affect their teams and the results achieved by subordinates. The paper analyses, through the lens of positive leadership, the importance of motivation, communication between organisational members, as well as delegation and transfer of responsibility manifested in classical theories of leader­ship. The literature survey is the main data collection technique applied to achieve the aim of the paper.

  17. Classical logic and logicism in human thought

    OpenAIRE

    Elqayam, Shira

    2012-01-01

    This chapter explores the role of classical logic as a theory of human reasoning. I distinguish between classical logic as a normative, computational and algorithmic system, and review its role is theories of human reasoning since the 1960s. The thesis I defend is that psychological theories have been moving further and further away from classical logic on all three levels. I examine some prominent example of logicist theories, which incorporate logic in their psychological account, includin...

  18. Calculation of the spin-isospin response functions in an extended semi-classical theory

    International Nuclear Information System (INIS)

    Chanfray, G.

    1987-01-01

    We present a semi-classical calculation of the spin isospin response-functions beyond Thomas-Fermi theory. We show that surface-peaked ℎ 2 corrections reduce the collective effects predicted by Thomas-Fermi calculations. These effects, small for a volume response, become important for surface responses probed by hadrons. This yields a considerable improvement of the agreement with the (p, p') Los Alamos data

  19. Quantum classical correspondence in nonrelativistic electrodynamics

    International Nuclear Information System (INIS)

    Ritchie, B.; Weatherford, C.A.

    1999-01-01

    A form of classical electrodynamic field exists which gives exact agreement with the operator field of quantum electrodynamics (QED) for the Lamb shift of a harmonically bound point electron. Here it is pointed out that this form of classical theory, with its physically acceptable interpretation, is the result of an unconventional resolution of a mathematically ambiguous term in classical field theory. Finally, a quantum classical correspondence principle is shown to exist in the sense that the classical field and expectation value of the QED operator field are identical, if retardation is neglected in the latter

  20. PREFACE: Classical density functional theory methods in soft and hard matter Classical density functional theory methods in soft and hard matter

    Science.gov (United States)

    Haataja, Mikko; Gránásy, László; Löwen, Hartmut

    2010-08-01

    , about a half of which are related to the theoretical materials science community and the other half came from the soft-matter community. We begin by discussing papers related to PFC. Diverse subjects related to the phase-field crystal model include exciting topics such as predicting/controlling the equilibrium phase behavior [19, 18, 17] and kinetics of epitaxial island formation on nano-membranes [20]. Moreover, phase-field crystal modeling has proved to be very successful in simulating homogeneous and heterogeneous crystal nucleation and growth, and several aspects of these phenomena are discussed in this issue [18, 21]. Finally, it is shown how to incorporate additional orientational degrees of freedom within the PFC approach to model liquid crystals [22]. On the DFT side, the other papers in this special issue deal with problems associated with advanced DFT techniques and applications. The existence of a structural instability in sub-critical crystalline fluctuations in a supercooled liquid within a square-gradient theory is discussed in [23]. Fundamental measure theory for hard-body systems is improved by discussing a correction term in detail, as discussed in [24]. A mean-field-like density functional for charges is applied to the effective interaction between charged colloids obtained within a cell model [25]. The remaining articles provide fundamental insight into how to supplement DDFT-type methods with hydrodynamics [26, 27], highlight the role of the projection operator technique in deriving dynamical density functional theories [28], and demonstrate how perturbation methods can be employed to compute the properties of solid-liquid interfaces [29]. This particular collection of papers demonstrates rather convincingly the significant potential that classical density functional techniques possess in modeling complex systems built of either soft or hard matter (or combinations thereof). While the PFC approach offers a simple and appealing means to simulate

  1. Thermodynamics and kinetics of binary nucleation in ideal-gas mixtures.

    Science.gov (United States)

    Alekseechkin, Nikolay V

    2015-08-07

    The nonisothermal single-component theory of droplet nucleation [N. V. Alekseechkin, Physica A 412, 186 (2014)] is extended to binary case; the droplet volume V, composition x, and temperature T are the variables of the theory. An approach based on macroscopic kinetics (in contrast to the standard microscopic model of nucleation operating with the probabilities of monomer attachment and detachment) is developed for the droplet evolution and results in the derived droplet motion equations in the space (V, x, T)—equations for V̇≡dV/dt, ẋ, and Ṫ. The work W(V, x, T) of the droplet formation is obtained in the vicinity of the saddle point as a quadratic form with diagonal matrix. Also, the problem of generalizing the single-component Kelvin equation for the equilibrium vapor pressure to binary case is solved; it is presented here as a problem of integrability of a Pfaffian equation. The equation for Ṫ is shown to be the first law of thermodynamics for the droplet, which is a consequence of Onsager's reciprocal relations and the linked-fluxes concept. As an example of ideal solution for demonstrative numerical calculations, the o-xylene-m-xylene system is employed. Both nonisothermal and enrichment effects are shown to exist; the mean steady-state overheat of droplets and their mean steady-state enrichment are calculated with the help of the 3D distribution function. Some qualitative peculiarities of the nucleation thermodynamics and kinetics in the water-sulfuric acid system are considered in the model of regular solution. It is shown that there is a small kinetic parameter in the theory due to the small amount of the acid in the vapor and, as a consequence, the nucleation process is isothermal.

  2. Generalizability Theory and Classical Test Theory

    Science.gov (United States)

    Brennan, Robert L.

    2011-01-01

    Broadly conceived, reliability involves quantifying the consistencies and inconsistencies in observed scores. Generalizability theory, or G theory, is particularly well suited to addressing such matters in that it enables an investigator to quantify and distinguish the sources of inconsistencies in observed scores that arise, or could arise, over…

  3. On void nucleation

    International Nuclear Information System (INIS)

    Subbotin, A.V.

    1978-01-01

    Nucleation of viable voids in irradiated materials is considered. The mechanism of evaporation and absorption of interstitials and vacancies disregarding the possibility of void merging is laid down into the basis of the discussion. The effect of irradiated material structure on void nucleation is separated from the effect of the properties of supersaturated solutions of vacancies and interstitials. An analytical expression for the nucleation rate is obtained and analyzed in different cases. The interstitials are concluded to effect severely the nucleation rate of viable voids

  4. Accurate Calculations of Rotationally Inelastic Scattering Cross Sections Using Mixed Quantum/Classical Theory.

    Science.gov (United States)

    Semenov, Alexander; Babikov, Dmitri

    2014-01-16

    For computational treatment of rotationally inelastic scattering of molecules, we propose to use the mixed quantum/classical theory, MQCT. The old idea of treating translational motion classically, while quantum mechanics is used for rotational degrees of freedom, is developed to the new level and is applied to Na + N2 collisions in a broad range of energies. Comparison with full-quantum calculations shows that MQCT accurately reproduces all, even minor, features of energy dependence of cross sections, except scattering resonances at very low energies. The remarkable success of MQCT opens up wide opportunities for computational predictions of inelastic scattering cross sections at higher temperatures and/or for polyatomic molecules and heavier quenchers, which is computationally close to impossible within the full-quantum framework.

  5. Mathematical physics classical mechanics

    CERN Document Server

    Knauf, Andreas

    2018-01-01

    As a limit theory of quantum mechanics, classical dynamics comprises a large variety of phenomena, from computable (integrable) to chaotic (mixing) behavior. This book presents the KAM (Kolmogorov-Arnold-Moser) theory and asymptotic completeness in classical scattering. Including a wealth of fascinating examples in physics, it offers not only an excellent selection of basic topics, but also an introduction to a number of current areas of research in the field of classical mechanics. Thanks to the didactic structure and concise appendices, the presentation is self-contained and requires only knowledge of the basic courses in mathematics. The book addresses the needs of graduate and senior undergraduate students in mathematics and physics, and of researchers interested in approaching classical mechanics from a modern point of view.

  6. Crystal nucleation and dendrite growth of metastable phases in undercooled melts

    International Nuclear Information System (INIS)

    Herlach, Dieter

    2011-01-01

    Research highlights: → Homogenous nucleation. → Effects of convection on dendrite growth kinetics. → Description of disorder trapping validated by experiment. - Abstract: An undercooled melt possesses an enhanced free enthalpy that opens up the possibility to crystallize metastable crystalline solids in competition with their stable counterparts. Crystal nucleation selects the crystallographic phase whereas the growth dynamics controls microstructure evolution. We apply containerless processing techniques such as electromagnetic and electrostatic levitation to containerlesss undercool and solidify metallic melts. Owing to the complete avoidance of heterogeneous nucleation on container-walls a large undercooling range becomes accessible with the extra benefit that the freely suspended drop is direct accessible for in situ observation of crystallization far away from equilibrium. Results of investigations of maximum undercoolability on pure zirconium are presented showing the limit of maximum undercoolability set by the onset of homogeneous nucleation. Rapid dendrite growth is measured as a function of undercooling by a high-speed camera and analysed within extended theories of non-equilibrium solidification. In such both supersaturated solid solutions and disordered superlattice structure of intermetallics are formed at high growth velocities. A sharp interface theory of dendrite growth is capable to describe the non-equilibrium solidification phenomena during rapid crystallization of deeply undercooled melts. Eventually, anomalous growth behaviour of Al-rich Al-Ni alloys is presented, which may be caused by forced convection.

  7. Sectors of solutions and minimal energies in classical Liouville theories for strings

    International Nuclear Information System (INIS)

    Johansson, L.; Kihlberg, A.; Marnelius, R.

    1984-01-01

    All classical solutions of the Liouville theory for strings having finite stable minimum energies are calculated explicitly together with their minimal energies. Our treatment automatically includes the set of natural solitonlike singularities described by Jorjadze, Pogrebkov, and Polivanov. Since the number of such singularities is preserved in time, a sector of solutions is not only characterized by its boundary conditions but also by its number of singularities. Thus, e.g., the Liouville theory with periodic boundary conditions has three different sectors of solutions with stable minimal energies containing zero, one, and two singularities. (Solutions with more singularities have no stable minimum energy.) It is argued that singular solutions do not make the string singular and therefore may be included in the string quantization

  8. Responses of Mixed-Phase Cloud Condensates and Cloud Radiative Effects to Ice Nucleating Particle Concentrations in NCAR CAM5 and DOE ACME Climate Models

    Science.gov (United States)

    Liu, X.; Shi, Y.; Wu, M.; Zhang, K.

    2017-12-01

    Mixed-phase clouds frequently observed in the Arctic and mid-latitude storm tracks have the substantial impacts on the surface energy budget, precipitation and climate. In this study, we first implement the two empirical parameterizations (Niemand et al. 2012 and DeMott et al. 2015) of heterogeneous ice nucleation for mixed-phase clouds in the NCAR Community Atmosphere Model Version 5 (CAM5) and DOE Accelerated Climate Model for Energy Version 1 (ACME1). Model simulated ice nucleating particle (INP) concentrations based on Niemand et al. and DeMott et al. are compared with those from the default ice nucleation parameterization based on the classical nucleation theory (CNT) in CAM5 and ACME, and with in situ observations. Significantly higher INP concentrations (by up to a factor of 5) are simulated from Niemand et al. than DeMott et al. and CNT especially over the dust source regions in both CAM5 and ACME. Interestingly the ACME model simulates higher INP concentrations than CAM5, especially in the Polar regions. This is also the case when we nudge the two models' winds and temperature towards the same reanalysis, indicating more efficient transport of aerosols (dust) to the Polar regions in ACME. Next, we examine the responses of model simulated cloud liquid water and ice water contents to different INP concentrations from three ice nucleation parameterizations (Niemand et al., DeMott et al., and CNT) in CAM5 and ACME. Changes in liquid water path (LWP) reach as much as 20% in the Arctic regions in ACME between the three parameterizations while the LWP changes are smaller and limited in the Northern Hemispheric mid-latitudes in CAM5. Finally, the impacts on cloud radiative forcing and dust indirect effects on mixed-phase clouds are quantified with the three ice nucleation parameterizations in CAM5 and ACME.

  9. Reversible island nucleation and growth with anomalous diffusion

    Science.gov (United States)

    Sabbar, Ehsan H.; Amar, Jacques G.

    2017-10-01

    Motivated by recent experiments on submonolayer organic film growth with anomalous diffusion, a general rate-equation (RE) theory of submonolayer island nucleation and growth was developed (Amar and Semaan, 2016) [23], which takes into account the critical island-size i, island fractal dimension df, substrate dimension d, and diffusion exponent μ, and good agreement with simulations was found for the case of irreversible growth corresponding to a critical island-size i = 1 with d = 2 . However, since many experiments correspond to a critical island-size larger than 1, it is of interest to determine if the RE predictions also hold in the case of reversible island nucleation with anomalous diffusion. Here we present the results of simulations of submonolayer growth with i = 2 (d = 2) which were carried out for both the case of superdiffusion (μ > 1) and subdiffusion (μ deposited monomers, excellent agreement is obtained with the predictions of the generalized RE theory for the exponents χ(μ) and χ1(μ) which describe the dependence of the island and monomer densities at fixed coverage on deposition rate F. In addition, the exponents do not depend on whether or not monomers remain superdiffusive or are thermalized (e.g. undergo regular diffusion) after detaching from a dimer. However, we also find that, as was previously found in the case of irreversible growth, the exponent χ only approaches its asymptotic value logarithmically with increasing 1/F. This result has important implications for the interpretation of experiments. Good agreement with the RE theory is also found in the case of subdiffusion for point-islands. However, in the case of ramified islands with subdiffusion and i = 2 , the exponents are significantly higher than predicted due to the fact that monomer capture dominates in the nucleation regime. A modified RE theory which takes this into account is presented, and excellent agreement is found with our simulations.

  10. Fundamental Elements and Interactions of Nature: A Classical Unification Theory

    Directory of Open Access Journals (Sweden)

    Tianxi Zhang

    2010-04-01

    Full Text Available A classical unification theory that completely unifies all the fundamental interactions of nature is developed. First, the nature is suggested to be composed of the following four fundamental elements: mass, radiation, electric charge, and color charge. All known types of matter or particles are a combination of one or more of the four fundamental elements. Photons are radiation; neutrons have only mass; protons have both mass and electric charge; and quarks contain mass, electric charge, and color charge. The nature fundamental interactions are interactions among these nature fundamental elements. Mass and radiation are two forms of real energy. Electric and color charges are considered as two forms of imaginary energy. All the fundamental interactions of nature are therefore unified as a single interaction between complex energies. The interaction between real energies is the gravitational force, which has three types: mass-mass, mass-radiation, and radiation-radiation interactions. Calculating the work done by the mass-radiation interaction on a photon derives the Einsteinian gravitational redshift. Calculating the work done on a photon by the radiation-radiation interaction derives a radiation redshift, which is much smaller than the gravitational redshift. The interaction between imaginary energies is the electromagnetic (between electric charges, weak (between electric and color charges, and strong (between color charges interactions. In addition, we have four imaginary forces between real and imaginary energies, which are mass-electric charge, radiation-electric charge, mass-color charge, and radiation-color charge interactions. Among the four fundamental elements, there are ten (six real and four imaginary fundamental interactions. This classical unification theory deepens our understanding of the nature fundamental elements and interactions, develops a new concept of imaginary energy for electric and color charges, and provides a

  11. Fundamental Elements and Interactions of Nature: A Classical Unification Theory

    Directory of Open Access Journals (Sweden)

    Zhang T. X.

    2010-04-01

    Full Text Available A classical unification theory that completely unifies all the fundamental interactions of nature is developed. First, the nature is suggested to be composed of the following four fundamental elements: mass, radiation, electric charge, and color charge. All known types of matter or particles are a combination of one or more of the four fundamental elements. Photons are radiation; neutrons have only mass; protons have both mass and electric charge; and quarks contain mass, electric charge, and color charge. The nature fundamental interactions are interactions among these nature fundamental elements. Mass and radiation are two forms of real energy. Electric and color charges are con- sidered as two forms of imaginary energy. All the fundamental interactions of nature are therefore unified as a single interaction between complex energies. The interac- tion between real energies is the gravitational force, which has three types: mass-mass, mass-radiation, and radiation-radiation interactions. Calculating the work done by the mass-radiation interaction on a photon derives the Einsteinian gravitational redshift. Calculating the work done on a photon by the radiation-radiation interaction derives a radiation redshift, which is much smaller than the gravitational redshift. The interaction between imaginary energies is the electromagnetic (between electric charges, weak (between electric and color charges, and strong (between color charges interactions. In addition, we have four imaginary forces between real and imaginary energies, which are mass-electric charge, radiation-electric charge, mass-color charge, and radiation- color charge interactions. Among the four fundamental elements, there are ten (six real and four imaginary fundamental interactions. This classical unification theory deep- ens our understanding of the nature fundamental elements and interactions, develops a new concept of imaginary energy for electric and color charges, and provides a

  12. Equation of Motion of a Mass Point in Gravitational Field and Classical Tests of Gauge Theory of Gravity

    International Nuclear Information System (INIS)

    Wu Ning; Zhang Dahua

    2007-01-01

    A systematic method is developed to study the classical motion of a mass point in gravitational gauge field. First, by using Mathematica, a spherical symmetric solution of the field equation of gravitational gauge field is obtained, which is just the traditional Schwarzschild solution. Combining the principle of gauge covariance and Newton's second law of motion, the equation of motion of a mass point in gravitational field is deduced. Based on the spherical symmetric solution of the field equation and the equation of motion of a mass point in gravitational field, we can discuss classical tests of gauge theory of gravity, including the deflection of light by the sun, the precession of the perihelia of the orbits of the inner planets and the time delay of radar echoes passing the sun. It is found that the theoretical predictions of these classical tests given by gauge theory of gravity are completely the same as those given by general relativity.

  13. Classical field theory in the space of reference frames. [Space-time manifold, action principle

    Energy Technology Data Exchange (ETDEWEB)

    Toller, M [Dipartimento di Matematica e Fisica, Libera Universita, Trento (Italy)

    1978-03-11

    The formalism of classical field theory is generalized by replacing the space-time manifold M by the ten-dimensional manifold S of all the local reference frames. The geometry of the manifold S is determined by ten vector fields corresponding to ten operationally defined infinitesimal transformations of the reference frames. The action principle is written in terms of a differential 4-form in the space S (the Lagrangian form). Densities and currents are represented by differential 3-forms in S. The field equations and the connection between symmetries and conservation laws (Noether's theorem) are derived from the action principle. Einstein's theory of gravitation and Maxwell's theory of electromagnetism are reformulated in this language. The general formalism can also be used to formulate theories in which charge, energy and momentum cannot be localized in space-time and even theories in which a space-time manifold cannot be defined exactly in any useful way.

  14. Binary Homogeneous Nucleation in Selected Aqueous

    Czech Academy of Sciences Publication Activity Database

    Maršík, František; Němec, Tomáš; Hrubý, Jan; Demo, Pavel; Kožíšek, Zdeněk; Petr, V.; Kolovratník, M.

    2008-01-01

    Roč. 37, č. 12 (2008), s. 1671-1708 ISSN 0095-9782 R&D Projects: GA ČR(CZ) GA101/05/2524; GA AV ČR KJB400760701; GA MŠk(CZ) 1M06031; GA AV ČR IBS2076003 Institutional research plan: CEZ:AV0Z20760514; CEZ:AV0Z10100520 Keywords : nucleation * steam * theory Subject RIV: BJ - Thermodynamics Impact factor: 1.241, year: 2008 http://www.springerlink.com/content/104381/

  15. Nucleation in Synoptically Forced Cirrostratus

    Science.gov (United States)

    Lin, R.-F.; Starr, D. OC.; Reichardt, J.; DeMott, P. J.

    2004-01-01

    Formation and evolution of cirrostratus in response to weak, uniform and constant synoptic forcing is simulated using a one-dimensional numerical model with explicit microphysics, in which the particle size distribution in each grid box is fully resolved. A series of tests of the model response to nucleation modes (homogeneous-freezing-only/heterogeneous nucleation) and heterogeneous nucleation parameters are performed. In the case studied here, nucleation is first activated in the prescribed moist layer. A continuous cloud-top nucleation zone with a depth depending on the vertical humidity gradient and one of the nucleation parameters is developed afterward. For the heterogeneous nucleation cases, intermittent nucleation zones in the mid-upper portion of the cloud form where the relative humidity is on the rise, because existent ice crystals do not uptake excess water vapor efficiently, and ice nuclei (IN) are available. Vertical resolution as fine as 1 m is required for realistic simulation of the homogeneous-freezing-only scenario, while the model resolution requirement is more relaxed in the cases where heterogeneous nucleation dominates. Bulk microphysical and optical properties are evaluated and compared. Ice particle number flux divergence, which is due to the vertical gradient of the gravity-induced particle sedimentation, is constantly and rapidly changing the local ice number concentration, even in the nucleation zone. When the depth of the nucleation zone is shallow, particle number concentration decreases rapidly as ice particles grow and sediment away from the nucleation zone. When the depth of the nucleation zone is large, a region of high ice number concentration can be sustained. The depth of nucleation zone is an important parameter to be considered in parametric treatments of ice cloud generation.

  16. Vapor nucleation paths in lyophobic nanopores.

    Science.gov (United States)

    Tinti, Antonio; Giacomello, Alberto; Casciola, Carlo Massimo

    2018-04-19

    liquids in mesoporous materials of characteristic size of ca. 4nm, the nanoscale effects reported for smaller pores have a minor role. The atomistic estimates for the nucleation free-energy barrier are in qualitative accord with those that can be obtained using a macroscopic, capillary-based nucleation theory.

  17. Matricial theory in classical photoelasticity

    International Nuclear Information System (INIS)

    Apostol, D.

    1980-01-01

    The matrix calculus in classical photoelasticity is used. Transfer functions for different polariscope arrangements are calculated. Linear polariscopes, circular polariscopes, double-exposure method to obtain isochromatics and Tardy and Senarmont method of measuring fractional relative retardations are analysed using coherency matrix formalism. (author)

  18. Supersaturated calcium carbonate solutions are classical

    Energy Technology Data Exchange (ETDEWEB)

    Henzler, Katja; Fetisov, Evgenii O.; Galib, Mirza; Baer, Marcel D.; Legg, Benjamin A.; Borca, Camelia; Xto, Jacinta M.; Pin, Sonia; Fulton, John L.; Schenter, Gregory K.; Govind, Niranjan; Siepmann, J. Ilja; Mundy, Christopher J.; Huthwelker, Thomas; De Yoreo, James J.

    2018-01-01

    We will present a description of nucleation phenomena in the condensed phase that takes into account non-ideal solution effects associated with cluster-cluster interaction. To do this we employ aggregation-volume bias Monte Carlo simulation, making the estimation of free-energy of large pre-critical clusters of sizes 10-20 tractable. We will compare and contrast empirical potential and electronic structure (e.g. Density functional theory) based descriptions of molecular interaction associated with the nucleation of CaCO3, highlighting free-energy trends and qualitative differences in populations of pre-critical clusters as a function of supersaturation. The influence of how the precise local interaction influences the non-ideal solution behavior on the nucleation and growth processes will be highlighted. This research was supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences.

  19. Pure classical SU(2) Yang-Mills theory with potentials invariant under a U(1) gauge subgroup

    International Nuclear Information System (INIS)

    Bacry, H.

    1978-07-01

    The present article is devoted to pure SU(2) classical Yang-Mills theories whose potentials are invariant under a U(1) gauge subgroup. Such potentials are shown to be associated with classical Maxwell-like fields with magnetic sources as 't Hooft's monopole is associated with the Dirac magnetic monopole. Conversely, the authors give Yang-Mills potentials corresponding to some Maxwell-like fields, in particular static magnetic fields with emphasis on those with cylindrical symmetry (including the dipole and other multipoles) and the ephemerons corresponding to an instantaneous magnetic multipole

  20. Classical- and quantum mechanical Coulomb scattering

    International Nuclear Information System (INIS)

    Gratzl, W.

    1987-01-01

    Because in textbooks the quantum mechanical Coulomb scattering is either ignored or treated unsatisfactory, the present work attempts to present a physically plausible, mathematically correct but elementary treatment in a way that it can be used in textbooks and lectures on quantum mechanics. Coulomb scattering is derived as a limiting case of a screened Coulomb potential (finite range) within a time dependent quantum scattering theory. The difference in the asymptotic conditions for potentials of finite versus infinite range leads back to the classical Coulomb scattering. In the classical framework many concepts of the quantum theory can be introduced and are useful in an intuitive understanding of the quantum theory. The differences between classical and quantum scattering theory are likewise useful for didactic purposes. (qui)

  1. Analysis of isothermal and cooling rate dependent immersion freezing by a unifying stochastic ice nucleation model

    Science.gov (United States)

    Alpert, P. A.; Knopf, D. A.

    2015-05-01

    apparent cooling rate dependence ofJhet is explained by assuming identical ISA in each droplet. When accounting for ISA variability, the cooling rate dependence of ice nucleation kinetics vanishes as expected from classical nucleation theory. The model simulations allow for a quantitative experimental uncertainty analysis for parameters Ntot, T, RH, and the ISA variability. In an idealized cloud parcel model applying variability in ISAs for each droplet, the model predicts enhanced immersion freezing temperatures and greater ice crystal production compared to a case when ISAs are uniform in each droplet. The implications of our results for experimental analysis and interpretation of the immersion freezing process are discussed.

  2. Second order classical perturbation theory for atom surface scattering: Analysis of asymmetry in the angular distribution

    Energy Technology Data Exchange (ETDEWEB)

    Zhou, Yun, E-mail: zhou.yun.x@gmail.com; Pollak, Eli, E-mail: eli.pollak@weizmann.ac.il [Chemical Physics Department, Weizmann Institute of Science, 76100 Rehovot (Israel); Miret-Artés, Salvador, E-mail: s.miret@iff.csic.es [Instituto de Fisica Fundamental, Consejo Superior de Investigaciones Cientificas, Serrano 123, 28006 Madrid (Spain)

    2014-01-14

    A second order classical perturbation theory is developed and applied to elastic atom corrugated surface scattering. The resulting theory accounts for experimentally observed asymmetry in the final angular distributions. These include qualitative features, such as reduction of the asymmetry in the intensity of the rainbow peaks with increased incidence energy as well as the asymmetry in the location of the rainbow peaks with respect to the specular scattering angle. The theory is especially applicable to “soft” corrugated potentials. Expressions for the angular distribution are derived for the exponential repulsive and Morse potential models. The theory is implemented numerically to a simplified model of the scattering of an Ar atom from a LiF(100) surface.

  3. Classical evolution and quantum generation in generalized gravity theories including string corrections and tachyons: Unified analyses

    International Nuclear Information System (INIS)

    Hwang, Jai-chan; Noh, Hyerim

    2005-01-01

    We present cosmological perturbation theory based on generalized gravity theories including string theory correction terms and a tachyonic complication. The classical evolution as well as the quantum generation processes in these varieties of gravity theories are presented in unified forms. These apply both to the scalar- and tensor-type perturbations. Analyses are made based on the curvature variable in two different gauge conditions often used in the literature in Einstein's gravity; these are the curvature variables in the comoving (or uniform-field) gauge and the zero-shear gauge. Applications to generalized slow-roll inflation and its consequent power spectra are derived in unified forms which include a wide range of inflationary scenarios based on Einstein's gravity and others

  4. Second order classical perturbation theory for atom surface scattering: analysis of asymmetry in the angular distribution.

    Science.gov (United States)

    Zhou, Yun; Pollak, Eli; Miret-Artés, Salvador

    2014-01-14

    A second order classical perturbation theory is developed and applied to elastic atom corrugated surface scattering. The resulting theory accounts for experimentally observed asymmetry in the final angular distributions. These include qualitative features, such as reduction of the asymmetry in the intensity of the rainbow peaks with increased incidence energy as well as the asymmetry in the location of the rainbow peaks with respect to the specular scattering angle. The theory is especially applicable to "soft" corrugated potentials. Expressions for the angular distribution are derived for the exponential repulsive and Morse potential models. The theory is implemented numerically to a simplified model of the scattering of an Ar atom from a LiF(100) surface.

  5. Classical dynamics and its quantum analogues

    International Nuclear Information System (INIS)

    Park, D.

    1979-01-01

    In this book the author establishes mathematical connections between classical and quantum mechanics, between ray optics and wave optics. The approach is to consider classical mechanics as a limiting case of quantum mechanics, and ray optics as a limiting case of wave optics. The conceptual background is discussed where necessary, so the reader should be already fairly familiar with it. The main goal of this approach is the revelation that classical and quantum theory are not so different conceptually as one thinks at first exposure. The first chapters recall the basic facts about light waves and light rays and demonstrate the construction of Newtonian orbits from Schroedinger waves. In the following the Lagrangian and Hamiltonian formulation of few-body system is developed showing as often as possible the relations to the corresponding quantum systems. To illustrate the theory planetary motion using perturbation theory is treated in some detail and several calculations in general relativity such as the deflection and retardation of light by the sun and the precession of planetary perikelia are included. The final parts deal with the motions of systems of many particles. The quantum mechanics of rigid bodies is presented in analogy with the classical theory and contrasts are noted. There is also a discussion of the roles of spinors in the two theories. The book is intended as a text in classical mechanics for readers which have already some knowledge in classical and quantum mechanics. It may help to deepen their understanding of the relation between the old and new theory and show something of the ways in which new discoveries are made. (orig.) 891 HJ/orig. 892 BRE

  6. Wigner's dynamical transition state theory in phase space: classical and quantum

    International Nuclear Information System (INIS)

    Waalkens, Holger; Schubert, Roman; Wiggins, Stephen

    2008-01-01

    We develop Wigner's approach to a dynamical transition state theory in phase space in both the classical and quantum mechanical settings. The key to our development is the construction of a normal form for describing the dynamics in the neighbourhood of a specific type of saddle point that governs the evolution from reactants to products in high dimensional systems. In the classical case this is the standard Poincaré–Birkhoff normal form. In the quantum case we develop a normal form based on the Weyl calculus and an explicit algorithm for computing this quantum normal form. The classical normal form allows us to discover and compute the phase space structures that govern classical reaction dynamics. From this knowledge we are able to provide a direct construction of an energy dependent dividing surface in phase space having the properties that trajectories do not locally 're-cross' the surface and the directional flux across the surface is minimal. Using this, we are able to give a formula for the directional flux through the dividing surface that goes beyond the harmonic approximation. We relate this construction to the flux–flux autocorrelation function which is a standard ingredient in the expression for the reaction rate in the chemistry community. We also give a classical mechanical interpretation of the activated complex as a normally hyperbolic invariant manifold (NHIM), and further describe the structure of the NHIM. The quantum normal form provides us with an efficient algorithm to compute quantum reaction rates and we relate this algorithm to the quantum version of the flux–flux autocorrelation function formalism. The significance of the classical phase space structures for the quantum mechanics of reactions is elucidated by studying the phase space distribution of scattering states. The quantum normal form also provides an efficient way of computing Gamov–Siegert resonances. We relate these resonances to the lifetimes of the quantum activated

  7. Cytoplasmic Nucleation and Atypical Branching Nucleation Generate Endoplasmic Microtubules in Physcomitrella patens[OPEN

    Science.gov (United States)

    Nakaoka, Yuki; Kimura, Akatsuki; Tani, Tomomi; Goshima, Gohta

    2015-01-01

    The mechanism underlying microtubule (MT) generation in plants has been primarily studied using the cortical MT array, in which fixed-angled branching nucleation and katanin-dependent MT severing predominate. However, little is known about MT generation in the endoplasm. Here, we explored the mechanism of endoplasmic MT generation in protonemal cells of Physcomitrella patens. We developed an assay that utilizes flow cell and oblique illumination fluorescence microscopy, which allowed visualization and quantification of individual MT dynamics. MT severing was infrequently observed, and disruption of katanin did not severely affect MT generation. Branching nucleation was observed, but it showed markedly variable branch angles and was occasionally accompanied by the transport of nucleated MTs. Cytoplasmic nucleation at seemingly random locations was most frequently observed and predominated when depolymerized MTs were regrown. The MT nucleator γ-tubulin was detected at the majority of the nucleation sites, at which a single MT was generated in random directions. When γ-tubulin was knocked down, MT generation was significantly delayed in the regrowth assay. However, nucleation occurred at a normal frequency in steady state, suggesting the presence of a γ-tubulin-independent backup mechanism. Thus, endoplasmic MTs in this cell type are generated in a less ordered manner, showing a broader spectrum of nucleation mechanisms in plants. PMID:25616870

  8. On the Ice Nucleation Spectrum

    Science.gov (United States)

    Barahona, D.

    2012-01-01

    This work presents a novel formulation of the ice nucleation spectrum, i.e. the function relating the ice crystal concentration to cloud formation conditions and aerosol properties. The new formulation is physically-based and explicitly accounts for the dependency of the ice crystal concentration on temperature, supersaturation, cooling rate, and particle size, surface area and composition. This is achieved by introducing the concepts of ice nucleation coefficient (the number of ice germs present in a particle) and nucleation probability dispersion function (the distribution of ice nucleation coefficients within the aerosol population). The new formulation is used to generate ice nucleation parameterizations for the homogeneous freezing of cloud droplets and the heterogeneous deposition ice nucleation on dust and soot ice nuclei. For homogeneous freezing, it was found that by increasing the dispersion in the droplet volume distribution the fraction of supercooled droplets in the population increases. For heterogeneous ice nucleation the new formulation consistently describes singular and stochastic behavior within a single framework. Using a fundamentally stochastic approach, both cooling rate independence and constancy of the ice nucleation fraction over time, features typically associated with singular behavior, were reproduced. Analysis of the temporal dependency of the ice nucleation spectrum suggested that experimental methods that measure the ice nucleation fraction over few seconds would tend to underestimate the ice nuclei concentration. It is shown that inferring the aerosol heterogeneous ice nucleation properties from measurements of the onset supersaturation and temperature may carry significant error as the variability in ice nucleation properties within the aerosol population is not accounted for. This work provides a simple and rigorous ice nucleation framework where theoretical predictions, laboratory measurements and field campaign data can be

  9. Answer to 'Information flow, causality, and the classical theory of tachyons'

    International Nuclear Information System (INIS)

    Recami, E.; Pavsic, M.

    1978-01-01

    Recently Basano (Int. J. Theor. Phys.; 16:715 (1977)) in a paper entitled 'Information Flow, Causality and the Classical Theory of Tachyons' commented on earlier work by the present authors. In answer to those comments it is pointed out that although 'Extended Relativity' seems to allow one to solve any causal paradoxes with both usual particles and tachyons nevertheless a number of paradoxes are continuously proposed. It has already been shown by the authors that tachyons possibly do not imply any causality violations even in macro-physics but Basano claimed that the procedure lead to new, different paradoxes. It is here demonstrated that such presumed difficulties do not exist. (U.K.)

  10. Solution to the hierarchy problem from an almost decoupled hidden sector within a classically scale invariant theory

    International Nuclear Information System (INIS)

    Foot, Robert; Kobakhidze, Archil; Volkas, Raymond R.; McDonald, Kristian L.

    2008-01-01

    If scale invariance is a classical symmetry then both the Planck scale and the weak scale should emerge as quantum effects. We show that this can be realized in simple scale invariant theories with a hidden sector. The weak/Planck scale hierarchy emerges in the (technically natural) limit in which the hidden sector decouples from the ordinary sector. In this limit, finite corrections to the weak scale are consequently small, while quadratic divergences are absent by virtue of classical scale invariance, so there is no hierarchy problem

  11. Planar nucleation and crystallization in the annealing process of ion implanted silicon

    International Nuclear Information System (INIS)

    Luo Yimin; Chen Zhenhua; Chen Ding

    2010-01-01

    According to thermodynamic and kinetic theory, considering the variation of bulk free energy and superficial energy after nucleation as well as the migration of atoms, we study systematically the planar nucleation and crystallization that relate to two possible transition mechanisms in the annealing process of ion implanted Si: (1) liquid/solid transition: the critical nucleation work is equal to half the increased superficial energy and inversely proportional to the supercooling ΔT. Compared with bulk nucleation, the radius of the critical nucleus decreases by half, and the nucleation rate attains its maximum at T = T m /2. (2) amorphous/crystalline transition: the atoms contained in the critical nucleus and situated on its surface, as well as critical nucleation work, are all directly proportional to the height of the nucleus, and the nucleation barrier is equal to half the superficial energy too. In addition, we take SiGe semiconductor as a specific example for calculation; a value of 0.03 eV/atom is obtained for the elastic strain energy, and a more reasonable result can be gotten after taking into account its effect on transition Finally, we reach the following conclusion as a result of the calculation: for the annealing of ion implanted Si, no matter what the transition method is-liquid or solid planar nucleation-the recrystallization process is actually carried out layer by layer on the crystal substrate, and the probability of forming a 'rod-like' nucleus is much larger than that of a 'plate-like' nucleus. (semiconductor materials)

  12. Understanding twinning nucleation and dislocation core structure through interscale hybrid method

    DEFF Research Database (Denmark)

    Xu, Ben; Zhang, Xiaodan

    2014-01-01

    The variety of emerging simulation methods and improved computational power advance the understanding in nanometals as a good compensation of the experiments. In this paper, the first principle methods are discussed, especially as a useful combination of the classical molecular dynamics, to overc......, to overcome the disadvantages of the latter method. Two examples are given as: the nucleation of the {10-12} deformation twinning in magnesium, and the screw dislocation core structure with/without hydrogen in tungsten....

  13. On covariant Poisson brackets in classical field theory

    International Nuclear Information System (INIS)

    Forger, Michael; Salles, Mário O.

    2015-01-01

    How to give a natural geometric definition of a covariant Poisson bracket in classical field theory has for a long time been an open problem—as testified by the extensive literature on “multisymplectic Poisson brackets,” together with the fact that all these proposals suffer from serious defects. On the other hand, the functional approach does provide a good candidate which has come to be known as the Peierls–De Witt bracket and whose construction in a geometrical setting is now well understood. Here, we show how the basic “multisymplectic Poisson bracket” already proposed in the 1970s can be derived from the Peierls–De Witt bracket, applied to a special class of functionals. This relation allows to trace back most (if not all) of the problems encountered in the past to ambiguities (the relation between differential forms on multiphase space and the functionals they define is not one-to-one) and also to the fact that this class of functionals does not form a Poisson subalgebra

  14. On covariant Poisson brackets in classical field theory

    Energy Technology Data Exchange (ETDEWEB)

    Forger, Michael [Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, BR–05315-970 São Paulo, SP (Brazil); Salles, Mário O. [Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, BR–05315-970 São Paulo, SP (Brazil); Centro de Ciências Exatas e da Terra, Universidade Federal do Rio Grande do Norte, Campus Universitário – Lagoa Nova, BR–59078-970 Natal, RN (Brazil)

    2015-10-15

    How to give a natural geometric definition of a covariant Poisson bracket in classical field theory has for a long time been an open problem—as testified by the extensive literature on “multisymplectic Poisson brackets,” together with the fact that all these proposals suffer from serious defects. On the other hand, the functional approach does provide a good candidate which has come to be known as the Peierls–De Witt bracket and whose construction in a geometrical setting is now well understood. Here, we show how the basic “multisymplectic Poisson bracket” already proposed in the 1970s can be derived from the Peierls–De Witt bracket, applied to a special class of functionals. This relation allows to trace back most (if not all) of the problems encountered in the past to ambiguities (the relation between differential forms on multiphase space and the functionals they define is not one-to-one) and also to the fact that this class of functionals does not form a Poisson subalgebra.

  15. Unified field theory from the classical wave equation: Preliminary application to atomic and nuclear structure

    Energy Technology Data Exchange (ETDEWEB)

    Múnera, Héctor A., E-mail: hmunera@hotmail.com [Centro Internacional de Física (CIF), Apartado Aéreo 4948, Bogotá, Colombia, South America (Colombia); Retired professor, Department of Physics, Universidad Nacional de Colombia, Bogotá, Colombia, South America (Colombia)

    2016-07-07

    It is postulated that there exists a fundamental energy-like fluid, which occupies the flat three-dimensional Euclidean space that contains our universe, and obeys the two basic laws of classical physics: conservation of linear momentum, and conservation of total energy; the fluid is described by the classical wave equation (CWE), which was Schrödinger’s first candidate to develop his quantum theory. Novel solutions for the CWE discovered twenty years ago are nonharmonic, inherently quantized, and universal in the sense of scale invariance, thus leading to quantization at all scales of the universe, from galactic clusters to the sub-quark world, and yielding a unified Lorentz-invariant quantum theory ab initio. Quingal solutions are isomorphic under both neo-Galilean and Lorentz transformations, and exhibit nother remarkable property: intrinsic unstability for large values of ℓ (a quantum number), thus limiting the size of each system at a given scale. Unstability and scale-invariance together lead to nested structures observed in our solar system; unstability may explain the small number of rows in the chemical periodic table, and nuclear unstability of nuclides beyond lead and bismuth. Quingal functions lend mathematical basis for Boscovich’s unified force (which is compatible with many pieces of evidence collected over the past century), and also yield a simple geometrical solution for the classical three-body problem, which is a useful model for electronic orbits in simple diatomic molecules. A testable prediction for the helicoidal-type force is suggested.

  16. Adsorption of dysprosium on the graphite (0001) surface: Nucleation and growth at 300 K

    International Nuclear Information System (INIS)

    Kwolek, Emma J.; Lii-Rosales, Ann; Lei, Huaping; Wang, Cai-Zhuang; Tringides, Michael C.; Evans, James W.; Wallingford, Mark; Zhou, Yinghui; Thiel, Patricia A.

    2016-01-01

    We have studied nucleation and growth of Dy islands on the basal plane of graphite at 300 K using scanning tunneling microscopy, density functional theory (DFT) in a form that includes van der Waals interactions, and analytic theory. The interaction of atomic Dy with graphite is strong, while the diffusion barrier is small. Experiment shows that at 300 K, the density of nucleated islands is close to the value predicted for homogeneous nucleation, using critical nucleus size of 1 and the DFT-derived diffusion barrier. Homogeneous nucleation is also supported by the monomodal shape of the island size distributions. Comparison with the published island density of Dy on graphene shows that the value is about two orders of magnitude smaller on graphite, which can be attributed to more effective charge screening in graphite. The base of each island is 3 atomic layers high and atomically ordered, forming a coincidence lattice with the graphite. Islands resist coalescence, probably due to multiple rotational orientations associated with the coincidence lattice. Upper levels grow as discernible single-atom layers. Analysis of the level populations reveals significant downward interlayer transport, which facilitates growth of the base. This island shape is metastable, since more compact three-dimensional islands form at elevated growth temperature.

  17. Adsorption of dysprosium on the graphite (0001) surface: Nucleation and growth at 300 K

    Energy Technology Data Exchange (ETDEWEB)

    Kwolek, Emma J.; Lii-Rosales, Ann [The Ames Laboratory, Ames, Iowa 50011 (United States); Department of Chemistry, Iowa State University, Ames, Iowa 50011 (United States); Lei, Huaping; Wang, Cai-Zhuang; Tringides, Michael C.; Evans, James W. [The Ames Laboratory, Ames, Iowa 50011 (United States); Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011 (United States); Wallingford, Mark; Zhou, Yinghui [The Ames Laboratory, Ames, Iowa 50011 (United States); Thiel, Patricia A., E-mail: pthiel@iastate.edu [The Ames Laboratory, Ames, Iowa 50011 (United States); Department of Chemistry, Iowa State University, Ames, Iowa 50011 (United States); Department of Materials Science and Engineering, Iowa State University, Ames, Iowa 50011 (United States)

    2016-12-07

    We have studied nucleation and growth of Dy islands on the basal plane of graphite at 300 K using scanning tunneling microscopy, density functional theory (DFT) in a form that includes van der Waals interactions, and analytic theory. The interaction of atomic Dy with graphite is strong, while the diffusion barrier is small. Experiment shows that at 300 K, the density of nucleated islands is close to the value predicted for homogeneous nucleation, using critical nucleus size of 1 and the DFT-derived diffusion barrier. Homogeneous nucleation is also supported by the monomodal shape of the island size distributions. Comparison with the published island density of Dy on graphene shows that the value is about two orders of magnitude smaller on graphite, which can be attributed to more effective charge screening in graphite. The base of each island is 3 atomic layers high and atomically ordered, forming a coincidence lattice with the graphite. Islands resist coalescence, probably due to multiple rotational orientations associated with the coincidence lattice. Upper levels grow as discernible single-atom layers. Analysis of the level populations reveals significant downward interlayer transport, which facilitates growth of the base. This island shape is metastable, since more compact three-dimensional islands form at elevated growth temperature.

  18. Size Fluctuations of Near Critical Nuclei and Gibbs Free Energy for Nucleation of BDA on Cu(001)

    Science.gov (United States)

    Schwarz, Daniel; van Gastel, Raoul; Zandvliet, Harold J. W.; Poelsema, Bene

    2012-07-01

    We present a low-energy electron microscopy study of nucleation and growth of BDA on Cu(001) at low supersaturation. At sufficiently high coverage, a dilute BDA phase coexists with c(8×8) crystallites. The real-time microscopic information allows a direct visualization of near-critical nuclei, determination of the supersaturation and the line tension of the crystallites, and, thus, derivation of the Gibbs free energy for nucleation. The resulting critical nucleus size nicely agrees with the measured value. Nuclei up to 4-6 times larger still decay with finite probability, urging reconsideration of the classic perception of a critical nucleus.

  19. Macroscopic models for vehicular flows and crowd dynamics theory and applications classical and non–classical advanced mathematics for real life applications

    CERN Document Server

    Rosini, Massimiliano Daniele

    2013-01-01

    This monograph  presents a systematic treatment of the theory for hyperbolic conservation laws and their applications to vehicular traffics and crowd dynamics. In the first part of the book, the author presents very basic considerations and gradually introduces the mathematical tools necessary to describe and understand the mathematical models developed in the following parts focusing on vehicular and pedestrian traffic. The book is a self-contained valuable resource for advanced courses in mathematical modeling, physics and civil engineering. A number of examples and figures facilitate a better understanding of the underlying concepts and motivations for the students. Important new techniques are presented, in particular the wave front tracking algorithm, the operator splitting approach, the non-classical theory of conservation laws and the constrained problems. This book is the first to present a comprehensive account of these fundamental new mathematical advances.  

  20. Classical higher-order processes

    DEFF Research Database (Denmark)

    Montesi, Fabrizio

    2017-01-01

    Classical Processes (CP) is a calculus where the proof theory of classical linear logic types processes à la Π-calculus, building on a Curry-Howard correspondence between session types and linear propositions. We contribute to this research line by extending CP with process mobility, inspired by ...

  1. Theoretical equation of state for classical fluids. I. Test by perturbation theory

    International Nuclear Information System (INIS)

    Gil-Villegas, A.; Chavez, M.; Del Rio, F.

    1993-01-01

    This paper shows how to construct the theoretical equation of state (TEOS) of a classical simple fluid. The theory relies on the mean collisional diameter and range, and maps the thermodynamical properties of the fluid into those of an equivalent square-well (ESW) fluid of appropriate depth ε , diameter σ and range R. It is shown that the ESW has the same pressure as the fluid of interest. Hence the THEOS of any simple fluid takes the form of a SW EOS of the given ε , σ and R. The theory is applied to a Lennard-Jones (LJ) system in a first-order perturbation. The mapping equation have a physical solution for densities where the SW EOS is accurate; the resulting LJ TEOS agrees very well with the results of computer simulations, and compares favorably with the recent TEOS developed by Song and Mason. (Author). 17 refs, 7 figs, 1 tab

  2. Theory of the interface between a classical plasma and a hard wall

    International Nuclear Information System (INIS)

    Ballone, P.; Pastore, G.; Tosi, M.P.; Trieste Univ.

    1983-09-01

    The interfacial density profile of a classical one-component plasma confined by a hard wall is studied in planar and spherical geometries. The approach adapts to interfacial problems a modified hypernetted-chain approximation developed by Lado and by Rosenfeld and Ashcroft for the bulk structure of simple liquids. The specific new aim is to embody self-consistently into the theory a 'contact theorem', fixing the plasma density at the wall through an equilibrium condition which involves the electrical potential drop across the interface and the bulk pressure. The theory is brought into fully quantitative contact with computer simulation data for a plasma confined in a spherical cavity of large but finite radius. It is also shown that the interfacial potential at the point of zero charge is accurately reproduced by suitably combining the contact theorem with relevant bulk properties in a simple, approximate representation of the interfacial charge density profile. (author)

  3. Psychosocial Intervention Use in Long-Stay Dementia Care: A Classic Grounded Theory.

    Science.gov (United States)

    Hunter, Andrew; Keady, John; Casey, Dympna; Grealish, Annmarie; Murphy, Kathy

    2016-12-01

    The objective of this study was to develop a substantive grounded theory of staff psychosocial intervention use with residents with dementia in long-stay care. "Becoming a person again" emerged as the core category accounting for staffs' psychosocial intervention use within long-stay care. Interview data were collected from participants in nine Irish long-stay settings: 14 residents with dementia, 19 staff nurses, one clinical facilitator, seven nurse managers, 21 nursing assistants, and five relatives. Constant comparative method guided the data collection and analysis. The researcher's theoretical memos, based on unstructured observation, and applicable extant literature were also included as data. By identifying the mutuality of the participants' experiences, this classic grounded theory explains staff motivation toward psychosocial intervention use within long-stay care. It also explains how institutional factors interact with those personal factors that incline individuals toward psychosocial intervention use. © The Author(s) 2016.

  4. Escaping the crunch: Gravitational effects in classical transitions

    International Nuclear Information System (INIS)

    Johnson, Matthew C.; Yang, I-Sheng

    2010-01-01

    During eternal inflation, a landscape of vacua can be populated by the nucleation of bubbles. These bubbles inevitably collide, and collisions sometimes displace the field into a new minimum in a process known as a classical transition. In this paper, we examine some new features of classical transitions that arise when gravitational effects are included. Using the junction condition formalism, we study the conditions for energy conservation in detail, and solve explicitly for the types of allowed classical transition geometries. We show that the repulsive nature of domain walls, and the de Sitter expansion associated with a positive energy minimum, can allow for classical transitions to vacua of higher energy than that of the colliding bubbles. Transitions can be made out of negative or zero energy (terminal) vacua to a de Sitter phase, restarting eternal inflation, and populating new vacua. However, the classical transition cannot produce vacua with energy higher than the original parent vacuum, which agrees with previous results on the construction of pockets of false vacuum. We briefly comment on the possible implications of these results for various measure proposals in eternal inflation.

  5. Classicality in quantum mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Dreyer, Olaf [Theoretical Physics, Blackett Laboratory, Imperial College London, London, SW7 2AZ (United Kingdom)

    2007-05-15

    In this article we propose a solution to the measurement problem in quantum mechanics. We point out that the measurement problem can be traced to an a priori notion of classicality in the formulation of quantum mechanics. If this notion of classicality is dropped and instead classicality is defined in purely quantum mechanical terms the measurement problem can be avoided. We give such a definition of classicality. It identifies classicality as a property of large quantum system. We show how the probabilistic nature of quantum mechanics is a result of this notion of classicality. We also comment on what the implications of this view are for the search of a quantum theory of gravity.

  6. Classicality in quantum mechanics

    International Nuclear Information System (INIS)

    Dreyer, Olaf

    2007-01-01

    In this article we propose a solution to the measurement problem in quantum mechanics. We point out that the measurement problem can be traced to an a priori notion of classicality in the formulation of quantum mechanics. If this notion of classicality is dropped and instead classicality is defined in purely quantum mechanical terms the measurement problem can be avoided. We give such a definition of classicality. It identifies classicality as a property of large quantum system. We show how the probabilistic nature of quantum mechanics is a result of this notion of classicality. We also comment on what the implications of this view are for the search of a quantum theory of gravity

  7. Mixed Quantum/Classical Theory for Molecule-Molecule Inelastic Scattering: Derivations of Equations and Application to N2 + H2 System.

    Science.gov (United States)

    Semenov, Alexander; Babikov, Dmitri

    2015-12-17

    The mixed quantum classical theory, MQCT, for inelastic scattering of two molecules is developed, in which the internal (rotational, vibrational) motion of both collision partners is treated with quantum mechanics, and the molecule-molecule scattering (translational motion) is described by classical trajectories. The resultant MQCT formalism includes a system of coupled differential equations for quantum probability amplitudes, and the classical equations of motion in the mean-field potential. Numerical tests of this theory are carried out for several most important rotational state-to-state transitions in the N2 + H2 system, in a broad range of collision energies. Besides scattering resonances (at low collision energies) excellent agreement with full-quantum results is obtained, including the excitation thresholds, the maxima of cross sections, and even some smaller features, such as slight oscillations of energy dependencies. Most importantly, at higher energies the results of MQCT are nearly identical to the full quantum results, which makes this approach a good alternative to the full-quantum calculations that become computationally expensive at higher collision energies and for heavier collision partners. Extensions of this theory to include vibrational transitions or general asymmetric-top rotor (polyatomic) molecules are relatively straightforward.

  8. Classical dynamics a modern perspective

    CERN Document Server

    Sudarshan, Ennackal Chandy George

    2016-01-01

    Classical dynamics is traditionally treated as an early stage in the development of physics, a stage that has long been superseded by more ambitious theories. Here, in this book, classical dynamics is treated as a subject on its own as well as a research frontier. Incorporating insights gained over the past several decades, the essential principles of classical dynamics are presented, while demonstrating that a number of key results originally considered only in the context of quantum theory and particle physics, have their foundations in classical dynamics.Graduate students in physics and practicing physicists will welcome the present approach to classical dynamics that encompasses systems of particles, free and interacting fields, and coupled systems. Lie groups and Lie algebras are incorporated at a basic level and are used in describing space-time symmetry groups. There is an extensive discussion on constrained systems, Dirac brackets and their geometrical interpretation. The Lie-algebraic description of ...

  9. Classical density functional theory & simulations on a coarse-grained model of aromatic ionic liquids.

    Science.gov (United States)

    Turesson, Martin; Szparaga, Ryan; Ma, Ke; Woodward, Clifford E; Forsman, Jan

    2014-05-14

    A new classical density functional approach is developed to accurately treat a coarse-grained model of room temperature aromatic ionic liquids. Our major innovation is the introduction of charge-charge correlations, which are treated in a simple phenomenological way. We test this theory on a generic coarse-grained model for aromatic RTILs with oligomeric forms for both cations and anions, approximating 1-alkyl-3-methyl imidazoliums and BF₄⁻, respectively. We find that predictions by the new density functional theory for fluid structures at charged surfaces are very accurate, as compared with molecular dynamics simulations, across a range of surface charge densities and lengths of the alkyl chain. Predictions of interactions between charged surfaces are also presented.

  10. The relation between classical and quantum mechanics

    International Nuclear Information System (INIS)

    Taylor, Peter.

    1984-01-01

    The thesis examines the relationship between classical and quantum mechanics from philosophical, mathematical and physical standpoints. Arguments are presented in favour of 'conjectural realism' in scientific theories, distinguished by explicit contextual structure and empirical testability. The formulations of classical and quantum mechanics, based on a general theory of mechanics is investigated, as well as the mathematical treatments of these subjects. Finally the thesis questions the validity of 'classical limits' and 'quantisations' in intertheoretic reduction. (UK)

  11. A non-classical view of the modulation of mineral precipitation by organic additives

    Science.gov (United States)

    Ruiz-Agudo, Encarnacion; Ruiz-Agudo, Cristina; Burgos-Cara, Alejandro; Putnis, Christine; Rodriguez-Navarro, Carlos; Putnis, Andrew

    2016-04-01

    Questions persist on the mechanisms of crystallization of sparingly soluble minerals such as calcium carbonate, calcium oxalate or barium sulphate. Compared to CaCO3, the mechanisms of nucleation and growth in the CaC2O4-H2O or BaSO4-H2O systems have received less attention. These phases are important due to their relevance as biominerals and/or unwanted mineral deposits in technological applications. Growing evidence suggests that sparingly soluble salts form by non-classical nucleation and growth pathways, where pre-nucleation ion associates and amorphous (solid or liquid) precursor phase(s) play a critical role (e.g. Rodríguez-Navarro et al. (2015), Ruiz-Agudo et al. (2015)). Indeed the identification of pre-nucleation species in these systems and their strong interactions with organic compounds (Verch et al. 2011) raises the possibility that the control of organics on biomineralization may begin even earlier than previously thought. A sound knowledge of the physical mechanisms by which acidic macromolecules affect nucleation and early growth may offer general insights concerning the molecular control of biomineralization, as well as being critical for improving strategies to control unwanted mineral deposition or for the synthesis of biomimetic materials. Here we present investigations on the initial stages of the precipitation of these relevant minerals in organic-free solutions to identify the precipitation pathway and to look for any potential precursor phase(s) to the final, crystalline polymorph. As well, we explore the effects that several acidic organic compounds have on the different precipitation stages identified. We find that organic additives such as citric acid, polyacrilic acid or a commercial copolymer of maleic acid/allyl sulfonic acid with phosphonate groups can be active at modifying pre-nucleation stages (destabilizing of pre-nucleation species or hampering the aggregation and growth of pre-nucleation associates) and subsequently strongly

  12. Protein crystal nucleation in pores.

    Science.gov (United States)

    Nanev, Christo N; Saridakis, Emmanuel; Chayen, Naomi E

    2017-01-16

    The most powerful method for protein structure determination is X-ray crystallography which relies on the availability of high quality crystals. Obtaining protein crystals is a major bottleneck, and inducing their nucleation is of crucial importance in this field. An effective method to form crystals is to introduce nucleation-inducing heterologous materials into the crystallization solution. Porous materials are exceptionally effective at inducing nucleation. It is shown here that a combined diffusion-adsorption effect can increase protein concentration inside pores, which enables crystal nucleation even under conditions where heterogeneous nucleation on flat surfaces is absent. Provided the pore is sufficiently narrow, protein molecules approach its walls and adsorb more frequently than they can escape. The decrease in the nucleation energy barrier is calculated, exhibiting its quantitative dependence on the confinement space and the energy of interaction with the pore walls. These results provide a detailed explanation of the effectiveness of porous materials for nucleation of protein crystals, and will be useful for optimal design of such materials.

  13. From c-number to q-numbers the classical analogy in the history of quantum theory

    CERN Document Server

    Darrigol, Olivier

    1992-01-01

    The history of quantum theory is a maze of conceptual problems, through which Olivier Darrigol provides a lucid and learned guide, tracking the role of formal analogies between classical and quantum theory. From Planck's first introduction of the quantum of action to Dirac's formulation of quantum mechanics, Darrigol illuminates not only the history of quantum theory but also the role of analogies in scientific thinking and theory change. Unlike previous works, which have tended to focus on qualitative, global arguments, Darrigol's study follows the lines of mathematical reasoning and symbolizing and so is able to show the motivations of early quantum theorists more precisely—and provocatively—than ever before. Erudite and original, From c-Numbers to q-Numbers sets a new standard as a philosophically perceptive and mathematically precise history of quantum mechanics. For years to come it will influence historical and philosophical discussions of twentieth-century physics.

  14. Gas–liquid nucleation at large metastability: unusual features and a new formalism

    International Nuclear Information System (INIS)

    Santra, Mantu; Singh, Rakesh S; Bagchi, Biman

    2011-01-01

    Nucleation at large metastability is still largely an unsolved problem, even though it is a problem of tremendous current interest, with wide-ranging practical value, from atmospheric research to materials science. It is now well accepted that the classical nucleation theory (CNT) fails to provide a qualitative picture and gives incorrect quantitative values for such quantities as activation-free energy barrier and supersaturation dependence of nucleation rate, especially at large metastability. In this paper, we present an alternative formalism to treat nucleation at large supersaturation by introducing an extended set of order parameters in terms of the kth largest liquid-like clusters, where k = 1 is the largest cluster in the system, k = 2 is the second largest cluster and so on. At low supersaturation, the size of the largest liquid-like cluster acts as a suitable order parameter. At large supersaturation, the free energy barrier for the largest liquid-like cluster disappears. We identify this supersaturation as the one at the onset of kinetic spinodal. The kinetic spinodal is system-size-dependent. Beyond kinetic spinodal many clusters grow simultaneously and competitively and hence the nucleation and growth become collective. In order to describe collective growth, we need to consider the full set of order parameters. We derive an analytic expression for the free energy of formation of the kth largest cluster. The expression predicts that, at large metastability (beyond kinetic spinodal), the barrier of growth for several largest liquid-like clusters disappears, and all these clusters grow simultaneously. The approach to the critical size occurs by barrierless diffusion in the cluster size space. The expression for the rate of barrier crossing predicts weaker supersaturation dependence than what is predicted by CNT at large metastability. Such a crossover behavior has indeed been observed in recent experiments (but eluded an explanation till now). In order

  15. Gas-liquid nucleation at large metastability: unusual features and a new formalism

    Science.gov (United States)

    Santra, Mantu; Singh, Rakesh S.; Bagchi, Biman

    2011-03-01

    Nucleation at large metastability is still largely an unsolved problem, even though it is a problem of tremendous current interest, with wide-ranging practical value, from atmospheric research to materials science. It is now well accepted that the classical nucleation theory (CNT) fails to provide a qualitative picture and gives incorrect quantitative values for such quantities as activation-free energy barrier and supersaturation dependence of nucleation rate, especially at large metastability. In this paper, we present an alternative formalism to treat nucleation at large supersaturation by introducing an extended set of order parameters in terms of the kth largest liquid-like clusters, where k = 1 is the largest cluster in the system, k = 2 is the second largest cluster and so on. At low supersaturation, the size of the largest liquid-like cluster acts as a suitable order parameter. At large supersaturation, the free energy barrier for the largest liquid-like cluster disappears. We identify this supersaturation as the one at the onset of kinetic spinodal. The kinetic spinodal is system-size-dependent. Beyond kinetic spinodal many clusters grow simultaneously and competitively and hence the nucleation and growth become collective. In order to describe collective growth, we need to consider the full set of order parameters. We derive an analytic expression for the free energy of formation of the kth largest cluster. The expression predicts that, at large metastability (beyond kinetic spinodal), the barrier of growth for several largest liquid-like clusters disappears, and all these clusters grow simultaneously. The approach to the critical size occurs by barrierless diffusion in the cluster size space. The expression for the rate of barrier crossing predicts weaker supersaturation dependence than what is predicted by CNT at large metastability. Such a crossover behavior has indeed been observed in recent experiments (but eluded an explanation till now). In order

  16. Gauge bridges in classical field theory; Eichbruecken in der klassischen Feldtheorie

    Energy Technology Data Exchange (ETDEWEB)

    Jakobs, S.

    2009-03-15

    In this thesis Poisson structures of two classical gauge field theories (Maxwell-Klein-Gordon- and Maxwell-Dirac-system) are constructed using the parametrix construction of Green's functions. Parametrices for the Maxwell-Klein-Gordon- and Maxwell-Dirac-system are constructed in Minkowski space and this construction is later generalized to curved space times for the Maxwell-Klein-Gordon-system. With these Green's functions Poisson brackets will be defined as Peierls brackets. Finally non-local, gauge invariant observables, the so-called 'gauge bridges'are constructed. Gauge bridges are the matrix elements of holonomy operators. It is shown, that these emerge from Poisson brackets of local, gauge invariant observables. (orig.)

  17. Laws of alloyed cementite particles nucleation during heat-resistant steels carburizing

    Directory of Open Access Journals (Sweden)

    M. Yu. Semenov

    2014-01-01

    Full Text Available The article considers a problem analyzing a nucleation of cementite type carbides in carburized heat-resistant steels for the turbofan engines gear wheels.The verification of previously hypothesized mechanism of dislocation nucleation particles chromium-alloyed cementite during process of carburizing was accepted as an objective of the work.As a methodological basis of this paper were accepted the numerical experiments based on the kinetic theory of nucleation, as well as on the known results of experimental studies.According to the kinetic theory of nucleation, a new phase in the solid solutions take place in the defects of the crystal structure of the metal such as inter-grain boundaries and dislocations clusters. A principle feature of the inter-grain boundary mechanism of nucleation is formation of carbide lattice. It is of great practical interest because the cementite lattice drops mechanical properties of hardened parts.According to the experimental studies, the average chromium concentration in the alloyed cementite twice exceeds its Cr content in the heat-resistant steels. Furthermore, the areas of abnormally high (more than ten times in comparison with the average content chromium concentration in cementite have been experimentally revealed.Numerical experiments have revealed that the nucleation of cementite particles alloyed with chromium (chromium concentration of 3% or more occurs, mainly, by the dislocation mechanism on the concentration fluctuations of the alloying element. According to calculations, an obligatory prerequisite to start an active nucleation process of new phase in the solid solution is a local increase of the chromium concentration up to 40%.Despite the lack of physical prerequisites for the formation of chromium precipitates, this phenomenon is explained by a strong chemical affinity of chromium and carbon, causing diffusion of chromium atoms in the region of the carbon atoms clusters. The formation of carbon

  18. Complex analysis fundamentals of the classical theory of functions

    CERN Document Server

    Stalker, John

    1998-01-01

    This clear, concise introduction to the classical theory of one complex variable is based on the premise that "anything worth doing is worth doing with interesting examples." The content is driven by techniques and examples rather than definitions and theorems. This self-contained monograph is an excellent resource for a self-study guide and should appeal to a broad audience. The only prerequisite is a standard calculus course. The first chapter deals with a beautiful presentation of special functions. . . . The third chapter covers elliptic and modular functions. . . in much more detail, and from a different point of view, than one can find in standard introductory books. . . . For [the] subjects that are omitted, the author has suggested some excellent references for the reader who wants to go through these topics. The book is read easily and with great interest. It can be recommended to both students as a textbook and to mathematicians and physicists as a useful reference. ---Mathematical Reviews Mainly or...

  19. A New Semi-Symmetric Unified Field Theory of the Classical Fields of Gravity and Electromagnetism

    Directory of Open Access Journals (Sweden)

    Suhendro I.

    2007-10-01

    Full Text Available We attempt to present a classical theoretical framework in which the gravitational and electromagnetic fields are unified as intrinsic geometric objects in the space-time manifold. For this purpose, we first present the preliminary geometric considerations dealing with the metric differential geometry of Cartan connections. The unified field theory is then developed as an extension of the general theory of relativity based on a semi- symmetric Cartan connection which is meant to be as close as possible structurally to the symmetric connection of the Einstein-Riemann space-time.

  20. FOREWORD: Heterogenous nucleation and microstructure formation—a scale- and system-bridging approach Heterogenous nucleation and microstructure formation—a scale- and system-bridging approach

    Science.gov (United States)

    Emmerich, H.

    2009-11-01

    be obtained. The research on colloidal systems is now at a point, at which it promises, in a symbiotic approach with metal physics, to make significant contributions to the identification of the above key parameters. So it has e.g. become possible to tune the interaction potential in colloids and thus to adjust it to display generic mechanisms of heterogeneous nucleation and microstructure-formation [17]. This offers several advantages compared to experimental investigations in metals: the crystallization of fluidic colloidal systems is much slower than the crystallization of metals. Moreover colloids are transparent in the field of optical light, so it is possible to study nucleation in situ by using novel optical research methods (confocal light microscopy)—thus, determining the above key parameters. For this reason the DFG Research Priority Program 1296 employs a system- and scale-bridging interdisciplinary scientific approach intended to thereby contribute to a comprehensive multiscale understanding of the basic mechanisms determining heterogenous nucleation and initial microstructure formation, which might successively be an applicable material system-independently. Initially its focus—and thus the focus of this issue—will be on the simplest types of model systems for heterogenous crystalline orders, on pure metals, binary metal alloys, and colloids. Theoretically and simulation based these systems are jointly studied based on density functional theory (DFT), molecular simulation methods (MC/MD) and the phase-field method at the same time aiming at a rigorous connection of these methods. The joint approach comprising theory and experiment is depicted in figure 1. More specifically the following questions are addressed and the first advances on these can be found in this issue: Heterogeneous nucleation: what does a critical nucleation grain look like? Does the classical concept of a contact angle make sense for heterogeneous nucleation? Can claims made

  1. Theoretical prediction of crystallization kinetics of a supercooled Lennard-Jones fluid

    Science.gov (United States)

    Gunawardana, K. G. S. H.; Song, Xueyu

    2018-05-01

    The first order curvature correction to the crystal-liquid interfacial free energy is calculated using a theoretical model based on the interfacial excess thermodynamic properties. The correction parameter (δ), which is analogous to the Tolman length at a liquid-vapor interface, is found to be 0.48 ± 0.05 for a Lennard-Jones (LJ) fluid. We show that this curvature correction is crucial in predicting the nucleation barrier when the size of the crystal nucleus is small. The thermodynamic driving force (Δμ) corresponding to available simulated nucleation conditions is also calculated by combining the simulated data with a classical density functional theory. In this paper, we show that the classical nucleation theory is capable of predicting the nucleation barrier with excellent agreement to the simulated results when the curvature correction to the interfacial free energy is accounted for.

  2. Classical Dimensional Transmutation and Confinement

    CERN Document Server

    Dvali, Gia; Mukhanov, Slava

    2011-01-01

    We observe that probing certain classical field theories by external sources uncovers the underlying renormalization group structure, including the phenomenon of dimensional transmutation, at purely-classical level. We perform this study on an example of $\\lambda\\phi^{4}$ theory and unravel asymptotic freedom and triviality for negative and positives signs of $\\lambda$ respectively. We derive exact classical $\\beta$ function equation. Solving this equation we find that an isolated source has an infinite energy and therefore cannot exist as an asymptotic state. On the other hand a dipole, built out of two opposite charges, has finite positive energy. At large separation the interaction potential between these two charges grows indefinitely as a distance in power one third.

  3. Non-equilibrium phase stabilization versus bubble nucleation at a nanoscale-curved Interface

    Science.gov (United States)

    Schiffbauer, Jarrod; Luo, Tengfei

    Using continuum dynamic van der Waals theory in a radial 1D geometry with a Lennard-Jones fluid model, we investigate the nature of vapor bubble nucleation near a heated, nanoscale-curved convex interface. Vapor bubble nucleation and growth are observed for interfaces with sufficiently large radius of curvature while phase stabilization of a superheated fluid layer occurs at interfaces with smaller radius. The hypothesis that the high Laplace pressure required for stable equilibrium of very small bubbles is responsible for phase stability is tested by effectively varying the parameter which controls liquid-vapor surface tension. In doing so, the liquid-vapor surface tension- hence Laplace pressure-is shown to have limited effect on phase stabilization vs. bubble nucleation. However, the strong dependence of nucleation on leading-order momentum transport, i.e. viscous dissipation, near the heated inner surface is demonstrated. We gratefully acknowledge ND Energy for support through the ND Energy Postdoctoral Fellowship program and the Army Research Office, Grant No. W911NF-16-1-0267, managed by Dr. Chakrapani Venanasi.

  4. Nanostructure control: Nucleation and diffusion studies for predictable ultra thin film morphologies

    Energy Technology Data Exchange (ETDEWEB)

    Hershberger, Matthew [Iowa State Univ., Ames, IA (United States)

    2017-05-06

    This thesis covers PhD research on two systems with unique and interesting physics. The first system is lead (Pb) deposited on the silicon (111) surface with the 7x7 reconstruction. Pb and Si are mutually bulk insoluble resulting in this system being an ideal case for studying metal and semiconductor interactions. Initial Pb deposition causes an amorphous wetting layer to form across to surface. Continued deposition results in Pb(111) island growth. Classic literature has classified this system as the Stranski-Krastanov growth mode although the system is not near equilibrium conditions. Our research shows a growth mode distinctly different than classical expectations and begins a discussion of reclassifying diffusion and nucleation for systems far away from the well-studied equilibrium cases.

  5. The Nucleation Potency of In Situ-Formed Oxides in Liquid Iron

    Science.gov (United States)

    Xu, Mingqin; Wang, Lu; Lu, Wenquan; Zeng, Long; Nadendla, Hari-Babu; Wang, Yun; Li, Jun; Hu, Qiaodan; Xia, Mingxu; Li, Jianguo

    2018-03-01

    The nucleation potency of iron oxides was verified experimentally through nucleation undercooling of liquid iron using aerodynamic levitation technology for minimized container contaminations. Steady undercooling values were subsequently obtained from multiple melting and freezing thermal cycles, with the average undercooling values of 223 K ± 3 K and 75 K ± 6 K (223 °C ± 3 °C and 75 °C ± 6 °C) for FeO-contained liquid and Fe3O4-contained liquid, respectively. The statistical results showed a negligible difference in the sizes and numbers of particles between FeO and Fe3O4 particles, indicating that the nucleation potency difference is attributed to the nature of nucleants rather than particle size or numbers. Furthermore, high-resolution transmission electron microscopy analysis showed that the potential nucleation interfaces can be assumed as { 1 1 0}_{{δ {{-Fe}}}} //( 0 0\\bar{2})_{FeO} and { 1 1 2}_{{δ {{-Fe}}}} //(\\bar{2} 0 2 )_{{{Fe}3 {O}4 }} , based on the detected exposed crystal planes of the oxide particles. Both the interfaces have relatively large values of lattice misfit, consistent with the experimentally measured undercooling based on Turnbull's lattice matching theory.

  6. Understanding the breakdown of classic two-phase theory and spray atomization at engine-relevant conditions

    Science.gov (United States)

    Dahms, Rainer N.

    2016-04-01

    A generalized framework for multi-component liquid injections is presented to understand and predict the breakdown of classic two-phase theory and spray atomization at engine-relevant conditions. The analysis focuses on the thermodynamic structure and the immiscibility state of representative gas-liquid interfaces. The most modern form of Helmholtz energy mixture state equation is utilized which exhibits a unique and physically consistent behavior over the entire two-phase regime of fluid densities. It is combined with generalized models for non-linear gradient theory and for liquid injections to quantify multi-component two-phase interface structures in global thermal equilibrium. Then, the Helmholtz free energy is minimized which determines the interfacial species distribution as a consequence. This minimal free energy state is demonstrated to validate the underlying assumptions of classic two-phase theory and spray atomization. However, under certain engine-relevant conditions for which corroborating experimental data are presented, this requirement for interfacial thermal equilibrium becomes unsustainable. A rigorously derived probability density function quantifies the ability of the interface to develop internal spatial temperature gradients in the presence of significant temperature differences between injected liquid and ambient gas. Then, the interface can no longer be viewed as an isolated system at minimal free energy. Instead, the interfacial dynamics become intimately connected to those of the separated homogeneous phases. Hence, the interface transitions toward a state in local equilibrium whereupon it becomes a dense-fluid mixing layer. A new conceptual view of a transitional liquid injection process emerges from a transition time scale analysis. Close to the nozzle exit, the two-phase interface still remains largely intact and more classic two-phase processes prevail as a consequence. Further downstream, however, the transition to dense-fluid mixing

  7. Understanding the breakdown of classic two-phase theory and spray atomization at engine-relevant conditions

    Energy Technology Data Exchange (ETDEWEB)

    Dahms, Rainer N., E-mail: Rndahms@sandia.gov [Combustion Research Facility, Sandia National Laboratories, Livermore, California 94551 (United States)

    2016-04-15

    A generalized framework for multi-component liquid injections is presented to understand and predict the breakdown of classic two-phase theory and spray atomization at engine-relevant conditions. The analysis focuses on the thermodynamic structure and the immiscibility state of representative gas-liquid interfaces. The most modern form of Helmholtz energy mixture state equation is utilized which exhibits a unique and physically consistent behavior over the entire two-phase regime of fluid densities. It is combined with generalized models for non-linear gradient theory and for liquid injections to quantify multi-component two-phase interface structures in global thermal equilibrium. Then, the Helmholtz free energy is minimized which determines the interfacial species distribution as a consequence. This minimal free energy state is demonstrated to validate the underlying assumptions of classic two-phase theory and spray atomization. However, under certain engine-relevant conditions for which corroborating experimental data are presented, this requirement for interfacial thermal equilibrium becomes unsustainable. A rigorously derived probability density function quantifies the ability of the interface to develop internal spatial temperature gradients in the presence of significant temperature differences between injected liquid and ambient gas. Then, the interface can no longer be viewed as an isolated system at minimal free energy. Instead, the interfacial dynamics become intimately connected to those of the separated homogeneous phases. Hence, the interface transitions toward a state in local equilibrium whereupon it becomes a dense-fluid mixing layer. A new conceptual view of a transitional liquid injection process emerges from a transition time scale analysis. Close to the nozzle exit, the two-phase interface still remains largely intact and more classic two-phase processes prevail as a consequence. Further downstream, however, the transition to dense-fluid mixing

  8. Causality and superluminal behavior in classical field theories: Applications to k-essence theories and modified-Newtonian-dynamics-like theories of gravity

    International Nuclear Information System (INIS)

    Bruneton, Jean-Philippe

    2007-01-01

    Field theories with Lorentz (or diffeomorphism invariant) action can exhibit superluminal behavior through the breaking of local Lorentz invariance. Quantum induced superluminal velocities are well-known examples of this effect. The issue of the causal behavior of such propagation is somewhat controversial in the literature and we intend to clarify it. We provide a careful analysis of the meaning of causality in classical relativistic field theories and stress the role played by the Cauchy problem and the notion of chronology. We show that, in general, superluminal behavior threatens causality only if one assumes that a prior chronology in spacetime exists. In the case where superluminal propagation occurs, however, there are at least two nonconformally related metrics in spacetime and thus two available notions of chronology. These two chronologies are on equal footing, and it would thus be misleading to choose ab initio one of them to define causality. Rather, we provide a formulation of causality in which no prior chronology is assumed. We argue that this is the only way to deal with the issue of causality in the case where some degrees of freedom propagate faster than others. In that framework, then, it is shown that superluminal propagation is not necessarily noncausal, the final answer depending on the existence of an initial data formulation. This also depends on global properties of spacetime that we discuss in detail. As an illustration of these conceptual issues, we consider two field theories, namely, k-essence scalar fields and bimetric theories of gravity, and we derive the conditions imposed by causality. We discuss various applications such as the dark energy problem, modified-Newtonian-dynamics-like theories of gravity, and varying speed of light theories

  9. Classical mechanics including an introduction to the theory of elasticity

    CERN Document Server

    Hentschke, Reinhard

    2017-01-01

    This textbook teaches classical mechanics as one of the foundations of physics. It describes the mechanical stability and motion in physical systems ranging from the molecular to the galactic scale. Aside from the standard topics of mechanics in the physics curriculum, this book includes an introduction to the theory of elasticity and its use in selected modern engineering applications, e.g. dynamic mechanical analysis of viscoelastic materials. The text also covers many aspects of numerical mechanics, ranging from the solution of ordinary differential equations, including molecular dynamics simulation of many particle systems, to the finite element method. Attendant Mathematica programs or parts thereof are provided in conjunction with selected examples. Numerous links allow the reader to connect to related subjects and research topics. Among others this includes statistical mechanics (separate chapter), quantum mechanics, space flight, galactic dynamics, friction, and vibration spectroscopy. An introductory...

  10. Classical generalized transition-state theory. Application to a collinear reaction with two saddle points

    International Nuclear Information System (INIS)

    Garrett, B.C.; Truhlar, D.G.; Grev, R.S.

    1981-01-01

    Accurate classical dynamical fixed-energy reaction probabilities and fixed-temperature rate constants are calculated for the collinear reaction H + FH on a low-barrier model potential energy surface. The calculations cover energies from 0.1 to 100 kcal/mol above threshold and temperatures of 100 to 10,000 K. The accurate results are used to test five approximate theories: conventional transition-state theory (TST), canonical variational theory (CVT), improved canonical variational theory (ICVT), microcanonical variational theory (μVT), and the unified statistical model (US). The first four of these theories involve a single dividing surface in phase space, and the US theory involves three dividing surfaces. The tests are particularly interesting because the potential energy surface has two identical saddle points. At temperatures from 100 to 2000 K, the μVt is the most accurate theory, with errors in the range 11 to 14%; for temperatures from 2000 to 10,000 K, the US theory is the most successful, with errors in the range 3 to 14%. Over the whole range, a factor of 100 in temperature, both theories have errors of 35% or less. Even TST has errors of 47% or less over the whole factor-of-100 temperature range. Although the US model should become exact at threshold for this system, it already underestimates the reaction probability by a factor of 0.64 at 0.1 kcal/mol above threshold. TST and μVT agree with each other within 12% up to an energy 13 kcal/mol above the saddle point energy. 3 figures, 2 tables

  11. Understanding the Planck blackbody spectrum and Landau diamagnetism within classical electromagnetism

    International Nuclear Information System (INIS)

    Boyer, Timothy H

    2016-01-01

    Electromagnetism is a relativistic theory, and one must exercise care in coupling this theory with nonrelativistic classical mechanics and with nonrelativistic classical statistical mechanics. Indeed historically, both the blackbody radiation spectrum and diamagnetism within classical theory have been misunderstood because of two crucial failures: (1) the neglect of classical electromagnetic zero-point radiation, and (2) the use of erroneous combinations of nonrelativistic mechanics with relativistic electrodynamics. Here we review the treatment of classical blackbody radiation, and show that the presence of Lorentz-invariant classical electromagnetic zero-point radiation can explain both the Planck blackbody spectrum and Landau diamagnetism at thermal equilibrium within classical electromagnetic theory. The analysis requires that relativistic electromagnetism is joined appropriately with simple nonrelativistic mechanical systems which can be regarded as the zero-velocity limits of relativistic systems, and that nonrelativistic classical statistical mechanics is applied only in the low-frequency limit when zero-point energy makes no contribution. (paper)

  12. Climate Impacts of Ice Nucleation

    Science.gov (United States)

    Gettelman, Andrew; Liu, Xiaohong; Barahona, Donifan; Lohmann, Ulrike; Chen, Celia

    2012-01-01

    Several different ice nucleation parameterizations in two different General Circulation Models (GCMs) are used to understand the effects of ice nucleation on the mean climate state, and the Aerosol Indirect Effects (AIE) of cirrus clouds on climate. Simulations have a range of ice microphysical states that are consistent with the spread of observations, but many simulations have higher present-day ice crystal number concentrations than in-situ observations. These different states result from different parameterizations of ice cloud nucleation processes, and feature different balances of homogeneous and heterogeneous nucleation. Black carbon aerosols have a small (0.06 Wm(exp-2) and not statistically significant AIE when included as ice nuclei, for nucleation efficiencies within the range of laboratory measurements. Indirect effects of anthropogenic aerosols on cirrus clouds occur as a consequence of increasing anthropogenic sulfur emissions with different mechanisms important in different models. In one model this is due to increases in homogeneous nucleation fraction, and in the other due to increases in heterogeneous nucleation with coated dust. The magnitude of the effect is the same however. The resulting ice AIE does not seem strongly dependent on the balance between homogeneous and heterogeneous ice nucleation. Regional effects can reach several Wm2. Indirect effects are slightly larger for those states with less homogeneous nucleation and lower ice number concentration in the base state. The total ice AIE is estimated at 0.27 +/- 0.10 Wm(exp-2) (1 sigma uncertainty). This represents a 20% offset of the simulated total shortwave AIE for ice and liquid clouds of 1.6 Wm(sup-2).

  13. Thermal Stress Analysis of a Continuous and Pulsed End-Pumped Nd:YAG Rod Crystal Using Non-Classic Conduction Heat Transfer Theory

    Science.gov (United States)

    Mojahedi, Mahdi; Shekoohinejad, Hamidreza

    2018-02-01

    In this paper, temperature distribution in the continuous and pulsed end-pumped Nd:YAG rod crystal is determined using nonclassical and classical heat conduction theories. In order to find the temperature distribution in crystal, heat transfer differential equations of crystal with consideration of boundary conditions are derived based on non-Fourier's model and temperature distribution of the crystal is achieved by an analytical method. Then, by transferring non-Fourier differential equations to matrix equations, using finite element method, temperature and stress of every point of crystal are calculated in the time domain. According to the results, a comparison between classical and nonclassical theories is represented to investigate rupture power values. In continuous end pumping with equal input powers, non-Fourier theory predicts greater temperature and stress compared to Fourier theory. It also shows that with an increase in relaxation time, crystal rupture power decreases. Despite of these results, in single rectangular pulsed end-pumping condition, with an equal input power, Fourier theory indicates higher temperature and stress rather than non-Fourier theory. It is also observed that, when the relaxation time increases, maximum amounts of temperature and stress decrease.

  14. Homogeneous bubble nucleation in binary systems of liquid solvent and dissolved gas

    Czech Academy of Sciences Publication Activity Database

    Němec, Tomáš

    2016-01-01

    Roč. 467, March (2016), s. 26-37 ISSN 0301-0104 R&D Projects: GA ČR GAP101/10/1819; GA ČR GA13-23550S Institutional support: RVO:61388998 Keywords : bubble nucleation * binary nucleation theory * dissolved gas Subject RIV: BJ - Thermodynamics Impact factor: 1.767, year: 2016 http://ac.els-cdn.com/S0301010416000124/1-s2.0-S0301010416000124-main.pdf?_tid=7797c8a0-fb13-11e5-ba55-00000aab0f6c&acdnat=1459849853_b9a5413fefc3e9199e844a9ccc97f514

  15. Classical probabilities for Majorana and Weyl spinors

    International Nuclear Information System (INIS)

    Wetterich, C.

    2011-01-01

    Highlights: → Map of classical statistical Ising model to fermionic quantum field theory. → Lattice-regularized real Grassmann functional integral for single Weyl spinor. → Emerging complex structure characteristic for quantum physics. → A classical statistical ensemble describes a quantum theory. - Abstract: We construct a map between the quantum field theory of free Weyl or Majorana fermions and the probability distribution of a classical statistical ensemble for Ising spins or discrete bits. More precisely, a Grassmann functional integral based on a real Grassmann algebra specifies the time evolution of the real wave function q τ (t) for the Ising states τ. The time dependent probability distribution of a generalized Ising model obtains as p τ (t)=q τ 2 (t). The functional integral employs a lattice regularization for single Weyl or Majorana spinors. We further introduce the complex structure characteristic for quantum mechanics. Probability distributions of the Ising model which correspond to one or many propagating fermions are discussed explicitly. Expectation values of observables can be computed equivalently in the classical statistical Ising model or in the quantum field theory for fermions.

  16. The Segal chronogeometric redshift - a classical analysis

    International Nuclear Information System (INIS)

    Fairchild, E.E. Jr.; Washington Univ., St. Louis, Mo.

    1977-01-01

    An error is shown to exist in the Segal chronogeometric redshift theory. The redshift distance relation of z=tan 2 (d/2R) derived by Segal using quantum theory violates the classical correspondence limit. The corrected result derived using simple classical arguments is z=tan 2 (d/R). This result gives the same predictions for small redshift objects but differs for large redshift objects such as quasars. The difference is shown to be caused by inconsistencies in the quantum derivation. Correcting these makes the quantum result equal to the classical result as one would expect from the correspondence principle. The impact of the correction on the predictions of the theory is discussed. (orig.) [de

  17. Modular forms a classical approach

    CERN Document Server

    Cohen, Henri

    2017-01-01

    The theory of modular forms is a fundamental tool used in many areas of mathematics and physics. It is also a very concrete and "fun" subject in itself and abounds with an amazing number of surprising identities. This comprehensive textbook, which includes numerous exercises, aims to give a complete picture of the classical aspects of the subject, with an emphasis on explicit formulas. After a number of motivating examples such as elliptic functions and theta functions, the modular group, its subgroups, and general aspects of holomorphic and nonholomorphic modular forms are explained, with an emphasis on explicit examples. The heart of the book is the classical theory developed by Hecke and continued up to the Atkin-Lehner-Li theory of newforms and including the theory of Eisenstein series, Rankin-Selberg theory, and a more general theory of theta series including the Weil representation. The final chapter explores in some detail more general types of modular forms such as half-integral weight, Hilbert, Jacob...

  18. Ice nucleation triggered by negative pressure.

    Science.gov (United States)

    Marcolli, Claudia

    2017-11-30

    Homogeneous ice nucleation needs supercooling of more than 35 K to become effective. When pressure is applied to water, the melting and the freezing points both decrease. Conversely, melting and freezing temperatures increase under negative pressure, i.e. when water is stretched. This study presents an extrapolation of homogeneous ice nucleation temperatures from positive to negative pressures as a basis for further exploration of ice nucleation under negative pressure. It predicts that increasing negative pressure at temperatures below about 262 K eventually results in homogeneous ice nucleation while at warmer temperature homogeneous cavitation, i. e. bubble nucleation, dominates. Negative pressure occurs locally and briefly when water is stretched due to mechanical shock, sonic waves, or fragmentation. The occurrence of such transient negative pressure should suffice to trigger homogeneous ice nucleation at large supercooling in the absence of ice-nucleating surfaces. In addition, negative pressure can act together with ice-inducing surfaces to enhance their intrinsic ice nucleation efficiency. Dynamic ice nucleation can be used to improve properties and uniformity of frozen products by applying ultrasonic fields and might also be relevant for the freezing of large drops in rainclouds.

  19. Quantum models of classical systems

    International Nuclear Information System (INIS)

    Hájíček, P

    2015-01-01

    Quantum statistical methods that are commonly used for the derivation of classical thermodynamic properties are extended to classical mechanical properties. The usual assumption that every real motion of a classical mechanical system is represented by a sharp trajectory is not testable and is replaced by a class of fuzzy models, the so-called maximum entropy (ME) packets. The fuzzier are the compared classical and quantum ME packets, the better seems to be the match between their dynamical trajectories. Classical and quantum models of a stiff rod will be constructed to illustrate the resulting unified quantum theory of thermodynamic and mechanical properties. (paper)

  20. Field transformations and the classical equation of motion in chiral perturbation theory

    International Nuclear Information System (INIS)

    Scherer, S.; Fearing, H.W.

    1995-01-01

    The construction of effective Lagrangians commonly involves the application of the ''classical equation of motion'' to eliminate redundant structures and thus generate the minimal number of independent terms. We investigate this procedure in the framework of chiral perturbation theory with particular emphasis on the new features which appear at O(p 6 ). The use of the ''classical equation of motion'' is interpreted in terms of field transformations. Such an interpretation is crucial if one wants to bring a given Lagrangian into a canonical form with a minimal number of terms. We emphasize that the application of field transformations leads to a modification of the coefficients of higher-order terms as well as eliminating structures, or what is equivalent, expressing certain structures in terms of already known different structures. This will become relevant once one considers the problem of expressing in canonical form a model effective interaction containing terms beyond next-to-leading order, i.e., beyond O(p 4 ). In such circumstances the naive application of the clasical equation of motion to simply drop terms, as is commonly done at lowest order, leads to subtle errors, which we discuss

  1. Semi-classical quantization of chaotic billiards

    International Nuclear Information System (INIS)

    Smilansky, U.

    1992-02-01

    The semi-classical quantization of chaotic billiards will be developed using scattering theory approach. This will be used to introduce and explain the inherent difficulties in the semi-classical quantization of chaos, and to show some of the modern tools which were developed recently to overcome these difficulties. To this end, we shall first obtain a semi-classical secular equation which is based on a finite number of classical periodic orbits. We shall use it to derive some spectral properties, and in particular to investigate the relationship between spectral statistics of quantum chaotic systems and the predictions of random-matrix theory. We shall finally discuss an important family of chaotic billiard, whose statistics does not follow any of the canonical ensembles, (GOE,GUE,...) but rather, corresponds to a new universality class. (author)

  2. Fermions from classical statistics

    International Nuclear Information System (INIS)

    Wetterich, C.

    2010-01-01

    We describe fermions in terms of a classical statistical ensemble. The states τ of this ensemble are characterized by a sequence of values one or zero or a corresponding set of two-level observables. Every classical probability distribution can be associated to a quantum state for fermions. If the time evolution of the classical probabilities p τ amounts to a rotation of the wave function q τ (t)=±√(p τ (t)), we infer the unitary time evolution of a quantum system of fermions according to a Schroedinger equation. We establish how such classical statistical ensembles can be mapped to Grassmann functional integrals. Quantum field theories for fermions arise for a suitable time evolution of classical probabilities for generalized Ising models.

  3. Comparison of classical reaction paths and tunneling paths studied with the semiclassical instanton theory.

    Science.gov (United States)

    Meisner, Jan; Markmeyer, Max N; Bohner, Matthias U; Kästner, Johannes

    2017-08-30

    Atom tunneling in the hydrogen atom transfer reaction of the 2,4,6-tri-tert-butylphenyl radical to 3,5-di-tert-butylneophyl, which has a short but strongly curved reaction path, was investigated using instanton theory. We found the tunneling path to deviate qualitatively from the classical intrinsic reaction coordinate, the steepest-descent path in mass-weighted Cartesian coordinates. To perform that comparison, we implemented a new variant of the predictor-corrector algorithm for the calculation of the intrinsic reaction coordinate. We used the reaction force analysis method as a means to decompose the reaction barrier into structural and electronic components. Due to the narrow energy barrier, atom tunneling is important in the abovementioned reaction, even above room temperature. Our calculated rate constants between 350 K and 100 K agree well with experimental values. We found a H/D kinetic isotope effect of almost 10 6 at 100 K. Tunneling dominates the protium transfer below 400 K and the deuterium transfer below 300 K. We compared the lengths of the tunneling path and the classical path for the hydrogen atom transfer in the reaction HCl + Cl and quantified the corner cutting in this reaction. At low temperature, the tunneling path is about 40% shorter than the classical path.

  4. Physics of aerosols - Second part: nucleation-condensation-ions-electrification-optical properties

    International Nuclear Information System (INIS)

    Bricard, Jean

    1977-01-01

    This report is made of two volumes. Volume 1 includes the general properties of aerosols, the fundamentals of the theory of gases and mechanics are related to particle suspensions, ant the theories of diffusion and coagulation with their applications to atmospheric aerosols. Volume 2 begins with a chapter on nucleation (gas-particle conversion) in the case of one vapor, then two vapors, followed by the theory of aerosol evaporation. The following two chapters are devoted to the study of ions and their attachment to aerosol particles. Finally their optical properties are stated in the last chapter

  5. Amines in the Earth’s Atmosphere: A Density Functional Theory Study of the Thermochemistry of Pre-Nucleation Clusters

    Directory of Open Access Journals (Sweden)

    Jason Herb

    2011-02-01

    Full Text Available The impact of organic species which are present in the Earth’s atmosphere on the burst of new particles is critically important for the understanding of the molecular nature of atmospheric nucleation phenomena. Amines have recently been proposed as possible stabilizers of binary pre-nucleation clusters. In order to advance the understanding of atmospheric nucleation phenomena, a quantum-chemical study of hydrogen-bonded complexes of binary sulfuric acid-water clusters with methyl-, dimethyl- and trimethylamines representing common atmospheric organic species, vegetation products and laboratory impurities has been carried out. The thermochemical stability of the sulfuric acid-amines-water complexes was found to be higher than that of the sulfuric acid-ammonia-water complexes, in qualitative agreement with the previous studies. However, the enhancement in stability due to amines appears to not be large enough to overcome the difference in typical atmospheric concentrations of ammonia and amines. Further research is needed in order to address the existing uncertainties and to reach a final conclusion about the importance of amines for the atmospheric nucleation.

  6. Consistent classical supergravity theories

    International Nuclear Information System (INIS)

    Muller, M.

    1989-01-01

    This book offers a presentation of both conformal and Poincare supergravity. The consistent four-dimensional supergravity theories are classified. The formulae needed for further modelling are included

  7. Crystallization of aqueous ammonium sulfate particles internally mixed with soot and kaolinite: crystallization relative humidities and nucleation rates.

    Science.gov (United States)

    Pant, Atul; Parsons, Matthew T; Bertram, Allan K

    2006-07-20

    Using optical microscopy, we investigated the crystallization of aqueous ammonium sulfate droplets containing soot and kaolinite, as well as the crystallization of aqueous ammonium sulfate droplets free of solid material. Our results show that soot did not influence the crystallization RH of aqueous ammonium sulfate particles under our experimental conditions. In contrast, kaolinite increased the crystallization RH of the aqueous ammonium sulfate droplets by approximately 10%. In addition, our results show that the crystallization RH of aqueous ammonium sulfate droplets free of solid material does not depend strongly on particle size. This is consistent with conclusions made previously in the literature, based on comparisons of results from different laboratories. From the crystallization results we determined the homogeneous nucleation rates of crystalline ammonium sulfate in aqueous ammonium sulfate droplets and the heterogeneous nucleation rates of crystalline ammonium sulfate in aqueous ammonium sulfate particles containing kaolinite. Using classical nucleation theory and our experimental data, we determined that the interfacial tension between an ammonium sulfate critical nucleus and an aqueous ammonium sulfate solution is 0.064 +/- 0.003 J m(-2) (in agreement with our previous measurements), and the contact angle between an ammonium sulfate critical nucleus and a kaolinite surface is 59 +/- 2 degrees. On the basis of our results, we argue that soot will not influence the crystallization RH of aqueous ammonium sulfate droplets in the atmosphere, but kaolinite can significantly modify the crystallization RH of atmospheric ammonium sulfate droplets. As an example, the CRH50 (the relative humidity at which 50% of the droplets crystallize) ranges from about 41 to 51% RH when the diameter of the kaolinite inclusion ranges from 0.1 to 5 microm. For comparison, the CRH50 of aqueous ammonium sulfate droplets (0.5 microm diameter) free of solid material is

  8. Heat transfer enhancement on nucleate boiling

    International Nuclear Information System (INIS)

    Zhuang, M.; Guibai, L.

    1990-01-01

    This paper reports on enhancement of nucleate boiling heat transfer with additives that was investigated experimentally. More than fifteen kinds of additives were chosen and tested. Eight kinds of effective additives which can enhance nucleate boiling heat transfer were selected. Experimental results showed that boiling heat transfer coefficient of water was increased by 1 to 5 times and that of R-113 was increased by 1 to 4 times when trace amount additives were put in the two boiling liquids. There exist optimum concentrations for the additives, respectively, which can enhance nucleate boiling heat transfer rate best. In order to analyze the mechanism of the enhancement of boiling heat transfer with additives, the surface tension and the bubble departure diameter were measured. The nucleation sites were investigated by use of high-speed photograph. Experimental results showed that nucleation sites increase with additive amount increasing and get maximum. Increasing nucleation sites is one of the most important reason why nucleate boiling heat transfer can be enhanced with additives

  9. Role of nucleation in nanodiamond film growth

    International Nuclear Information System (INIS)

    Lifshitz, Y.; Lee, C.H.; Wu, Y.; Zhang, W.J.; Bello, I.; Lee, S.T.

    2006-01-01

    Nanodiamond films were deposited using different microwave plasma chemical vapor deposition schemes following several nucleation pretreatment methods. The nucleation efficiency and the films structure were investigated using scanning and transmission electron microscopy and Raman spectroscopy. C 2 dimer growth (CH 4 and H 2 in 90% Ar) cannot nucleate diamond and works only on existing diamond surfaces. The methyl radical process (up to 20% CH 4 in H 2 ) allows some nucleation probability on appropriate substrates. Prolonged bias enhanced nucleation initiates both diamond nucleation and growth. C 2 dimer growth results in pure nanodiamond free of amorphous carbon, while prolonged bias enhanced nucleation forms an amorphous carbon/nanodiamond composite

  10. Bukhvostov–Lipatov model and quantum-classical duality

    Directory of Open Access Journals (Sweden)

    Vladimir V. Bazhanov

    2018-02-01

    Full Text Available The Bukhvostov–Lipatov model is an exactly soluble model of two interacting Dirac fermions in 1+1 dimensions. The model describes weakly interacting instantons and anti-instantons in the O(3 non-linear sigma model. In our previous work [arXiv:1607.04839] we have proposed an exact formula for the vacuum energy of the Bukhvostov–Lipatov model in terms of special solutions of the classical sinh-Gordon equation, which can be viewed as an example of a remarkable duality between integrable quantum field theories and integrable classical field theories in two dimensions. Here we present a complete derivation of this duality based on the classical inverse scattering transform method, traditional Bethe ansatz techniques and analytic theory of ordinary differential equations. In particular, we show that the Bethe ansatz equations defining the vacuum state of the quantum theory also define connection coefficients of an auxiliary linear problem for the classical sinh-Gordon equation. Moreover, we also present details of the derivation of the non-linear integral equations determining the vacuum energy and other spectral characteristics of the model in the case when the vacuum state is filled by 2-string solutions of the Bethe ansatz equations.

  11. Bukhvostov-Lipatov model and quantum-classical duality

    Science.gov (United States)

    Bazhanov, Vladimir V.; Lukyanov, Sergei L.; Runov, Boris A.

    2018-02-01

    The Bukhvostov-Lipatov model is an exactly soluble model of two interacting Dirac fermions in 1 + 1 dimensions. The model describes weakly interacting instantons and anti-instantons in the O (3) non-linear sigma model. In our previous work [arxiv:arXiv:1607.04839] we have proposed an exact formula for the vacuum energy of the Bukhvostov-Lipatov model in terms of special solutions of the classical sinh-Gordon equation, which can be viewed as an example of a remarkable duality between integrable quantum field theories and integrable classical field theories in two dimensions. Here we present a complete derivation of this duality based on the classical inverse scattering transform method, traditional Bethe ansatz techniques and analytic theory of ordinary differential equations. In particular, we show that the Bethe ansatz equations defining the vacuum state of the quantum theory also define connection coefficients of an auxiliary linear problem for the classical sinh-Gordon equation. Moreover, we also present details of the derivation of the non-linear integral equations determining the vacuum energy and other spectral characteristics of the model in the case when the vacuum state is filled by 2-string solutions of the Bethe ansatz equations.

  12. Chandrasekhar limit: an elementary approach based on classical physics and quantum theory

    Science.gov (United States)

    Pinochet, Jorge; Van Sint Jan, Michael

    2016-05-01

    In a brief article published in 1931, Subrahmanyan Chandrasekhar made public an important astronomical discovery. In his article, the then young Indian astrophysicist introduced what is now known as the Chandrasekhar limit. This limit establishes the maximum mass of a stellar remnant beyond which the repulsion force between electrons due to the exclusion principle can no longer stop the gravitational collapse. In the present article, we create an elemental approximation to the Chandrasekhar limit, accessible to non-graduate science and engineering students. The article focuses especially on clarifying the origins of Chandrasekhar’s discovery and the underlying physical concepts. Throughout the article, only basic algebra is used as well as some general notions of classical physics and quantum theory.

  13. Inelastic Scattering of Identical Molecules within Framework of the Mixed Quantum/Classical Theory: Application to Rotational Excitations in H2 + H2.

    Science.gov (United States)

    Semenov, Alexander; Babikov, Dmitri

    2016-06-09

    Theoretical foundation is laid out for description of permutation symmetry in the inelastic scattering processes that involve collisions of two identical molecules, within the framework of the mixed quantum/classical theory (MQCT). In this approach, the rotational (and vibrational) states of two molecules are treated quantum-mechanically, whereas their translational motion (responsible for scattering) is treated classically. This theory is applied to H2 + H2 system, and the state-to-state transition cross sections are compared versus those obtained from the full-quantum calculations and experimental results from the literature. Good agreement is found in all cases. It is also found that results of MQCT, where the Coriolis coupling is included classically, are somewhat closer to exact full-quantum results than results of the other approximate quantum methods, where those coupling terms are neglected. These new developments allow applications of MQCT to a broad variety of molecular systems and processes.

  14. An Analysis of Cross Racial Identity Scale Scores Using Classical Test Theory and Rasch Item Response Models

    Science.gov (United States)

    Sussman, Joshua; Beaujean, A. Alexander; Worrell, Frank C.; Watson, Stevie

    2013-01-01

    Item response models (IRMs) were used to analyze Cross Racial Identity Scale (CRIS) scores. Rasch analysis scores were compared with classical test theory (CTT) scores. The partial credit model demonstrated a high goodness of fit and correlations between Rasch and CTT scores ranged from 0.91 to 0.99. CRIS scores are supported by both methods.…

  15. Modalities of gene action predicted by the classical evolutionary biological theory of aging.

    Science.gov (United States)

    Martin, George M

    2007-04-01

    What might now be referred to as the "classical" evolutionary biological theory of why we age has had a number of serious challenges in recent years. While the theory might therefore have to be modified under certain circumstances, in the author's opinion, it still provides the soundest theoretical basis for thinking about how we age. Nine modalities of gene action that have the potential to modulate processes of aging are reviewed, including the two most widely reviewed and accepted concepts ("antagonistic pleiotropy" and "mutation accumulation"). While several of these nine mechanisms can be regarded as derivatives of the antagonistic pleiotropic concept, they frame more specific questions for future research. Such research should pursue what appears to be the dominant factor in the determination of intraspecific variations in longevity-stochastic mechanisms, most likely based upon epigenetics. This contrasts with the dominant factor in the determination of interspecific variations in longevity-the constitutional genome, most likely based upon variations in regulatory loci.

  16. Diamond Nucleation Using Polyethene

    Science.gov (United States)

    Morell, Gerardo (Inventor); Makarov, Vladimir (Inventor); Varshney, Deepak (Inventor); Weiner, Brad (Inventor)

    2013-01-01

    The invention presents a simple, non-destructive and non-abrasive method of diamond nucleation using polyethene. It particularly describes the nucleation of diamond on an electrically viable substrate surface using polyethene via chemical vapor deposition (CVD) technique in a gaseous environment.

  17. Contributions of Heterogeneous Ice Nucleation, Large-Scale Circulation, and Shallow Cumulus Detrainment to Cloud Phase Transition in Mixed-Phase Clouds with NCAR CAM5

    Science.gov (United States)

    Liu, X.; Wang, Y.; Zhang, D.; Wang, Z.

    2016-12-01

    Mixed-phase clouds consisting of both liquid and ice water occur frequently at high-latitudes and in mid-latitude storm track regions. This type of clouds has been shown to play a critical role in the surface energy balance, surface air temperature, and sea ice melting in the Arctic. Cloud phase partitioning between liquid and ice water determines the cloud optical depth of mixed-phase clouds because of distinct optical properties of liquid and ice hydrometeors. The representation and simulation of cloud phase partitioning in state-of-the-art global climate models (GCMs) are associated with large biases. In this study, the cloud phase partition in mixed-phase clouds simulated from the NCAR Community Atmosphere Model version 5 (CAM5) is evaluated against satellite observations. Observation-based supercooled liquid fraction (SLF) is calculated from CloudSat, MODIS and CPR radar detected liquid and ice water paths for clouds with cloud-top temperatures between -40 and 0°C. Sensitivity tests with CAM5 are conducted for different heterogeneous ice nucleation parameterizations with respect to aerosol influence (Wang et al., 2014), different phase transition temperatures for detrained cloud water from shallow convection (Kay et al., 2016), and different CAM5 model configurations (free-run versus nudged winds and temperature, Zhang et al., 2015). A classical nucleation theory-based ice nucleation parameterization in mixed-phase clouds increases the SLF especially at temperatures colder than -20°C, and significantly improves the model agreement with observations in the Arctic. The change of transition temperature for detrained cloud water increases the SLF at higher temperatures and improves the SLF mostly over the Southern Ocean. Even with the improved SLF from the ice nucleation and shallow cumulus detrainment, the low SLF biases in some regions can only be improved through the improved circulation with the nudging technique. Our study highlights the challenges of

  18. The limitations on applying classical thin plate theory to thin annular plates clamped on the inner boundary

    Directory of Open Access Journals (Sweden)

    Daniel W. Zietlow

    2012-12-01

    Full Text Available The experimentally measured resonance frequencies of a thin annular plate with a small ratio of inner to outer radii and clamped on the inner boundary are compared to the predictions of classical thin-plate (CTP theory and a finite-element (FE model. The results indicate that, contrary to the conclusions presented in a number of publications, CTP theory does not accurately predict the frequencies of a relatively small number of resonant modes at lower frequencies. It is shown that these inaccuracies are attributable to shear deformations, which are thought to be negligible in thin plates and are neglected in CTP theory. Of particular interest is the failure of CTP theory to accurately predict the resonance frequency of the lowest vibrational mode, which was shifted approximately 30% by shear motion at the inner boundary.

  19. Principles of physics from quantum field theory to classical mechanics

    CERN Document Server

    Jun, Ni

    2014-01-01

    This book starts from a set of common basic principles to establish the formalisms in all areas of fundamental physics, including quantum field theory, quantum mechanics, statistical mechanics, thermodynamics, general relativity, electromagnetic field, and classical mechanics. Instead of the traditional pedagogic way, the author arranges the subjects and formalisms in a logical-sequential way, i.e. all the formulas are derived from the formulas before them. The formalisms are also kept self-contained. Most of the required mathematical tools are also given in the appendices. Although this book covers all the disciplines of fundamental physics, the book is concise and can be treated as an integrated entity. This is consistent with the aphorism that simplicity is beauty, unification is beauty, and thus physics is beauty. The book may be used as an advanced textbook by graduate students. It is also suitable for physicists who wish to have an overview of fundamental physics. Readership: This is an advanced gradua...

  20. On the paramagnetism of spin in the classical limit

    International Nuclear Information System (INIS)

    Hogreve, H.

    1985-12-01

    We consider particles with spin 1/2 in external electromagnetic fields. Although in many quantum mechanical situations they show a paramagnetic behaviour, within non-relativistic quantum theory a universal paramagnetic influence of spin fails to be true in general. Here we investigate the paramagnetism of spin in the framework of a classical theory. Applying previous results for the classical limit slash-h→O we obtain a classical expression corresponding to the quantum partition function of Hamiltonians with spin variables. For this classical partition function simple estimates lead to a paramagnetic inequality which demonstrates that indeed in the classical limit the spin shows a general paramagnetic behaviour. (author)