Subchannel measurements of the equilibrium quality and mass flux distribution in a rod bundle

International Nuclear Information System (INIS)

Lahey, R.T. Jr.

1986-01-01

An experiment was performed to measure the equilibrium subchannel void and mass flux distribution in a simulated BWR rod bundle. These new equilibrium subchannel data are unique and represent an excellent basis for subchannel ''void drift'' model development and assessment. Equilibrium subchannel void and mass flux distributions have been determined from the data presented herein. While the form of these correlations agree with the results of previous theoretical investigations, they should be generalized with caution since the current data base has been taken at only one (low) system pressure. Clearly there is a need for equilibrium subchannel data at higher system pressures if mechanistic subchannel models are to be developed

Statistical approach to partial equilibrium analysis

Science.gov (United States)

Wang, Yougui; Stanley, H. E.

2009-04-01

A statistical approach to market equilibrium and efficiency analysis is proposed in this paper. One factor that governs the exchange decisions of traders in a market, named willingness price, is highlighted and constitutes the whole theory. The supply and demand functions are formulated as the distributions of corresponding willing exchange over the willingness price. The laws of supply and demand can be derived directly from these distributions. The characteristics of excess demand function are analyzed and the necessary conditions for the existence and uniqueness of equilibrium point of the market are specified. The rationing rates of buyers and sellers are introduced to describe the ratio of realized exchange to willing exchange, and their dependence on the market price is studied in the cases of shortage and surplus. The realized market surplus, which is the criterion of market efficiency, can be written as a function of the distributions of willing exchange and the rationing rates. With this approach we can strictly prove that a market is efficient in the state of equilibrium.

About the functions of the Wigner distribution for the q-deformed harmonic oscillator model

International Nuclear Information System (INIS)

Atakishiev, N.M.; Nagiev, S.M.; Djafarov, E.I.; Imanov, R.M.

2005-01-01

Full text : A q-deformed model of the linear harmonic oscillator in the Wigner phase-space is studied. It was derived an explicit expression for the Wigner probability distribution function, as well as the Wigner distribution function of a thermodynamic equilibrium for this model

The stress distribution in shell bodies and wings as an equilibrium problem

Science.gov (United States)

Wagner, H

1937-01-01

This report treats the stress distribution in shell-shaped airplane components (fuselage, wings) as an equilibrium problem; it includes both cylindrical and non-cylindrical shells. In particular, it treats the stress distribution at the point of stress application and at cut-out points.

Fluctuation-dissipation relation and stationary distribution of an exactly solvable many-particle model for active biomatter far from equilibrium.

Science.gov (United States)

Netz, Roland R

2018-05-14

An exactly solvable, Hamiltonian-based model of many massive particles that are coupled by harmonic potentials and driven by stochastic non-equilibrium forces is introduced. The stationary distribution and the fluctuation-dissipation relation are derived in closed form for the general non-equilibrium case. Deviations from equilibrium are on one hand characterized by the difference of the obtained stationary distribution from the Boltzmann distribution; this is possible because the model derives from a particle Hamiltonian. On the other hand, the difference between the obtained non-equilibrium fluctuation-dissipation relation and the standard equilibrium fluctuation-dissipation theorem allows us to quantify non-equilibrium in an alternative fashion. Both indicators of non-equilibrium behavior, i.e., deviations from the Boltzmann distribution and deviations from the equilibrium fluctuation-dissipation theorem, can be expressed in terms of a single non-equilibrium parameter α that involves the ratio of friction coefficients and random force strengths. The concept of a non-equilibrium effective temperature, which can be defined by the relation between fluctuations and the dissipation, is by comparison with the exactly derived stationary distribution shown not to hold, even if the effective temperature is made frequency dependent. The analysis is not confined to close-to-equilibrium situations but rather is exact and thus holds for arbitrarily large deviations from equilibrium. Also, the suggested harmonic model can be obtained from non-linear mechanical network systems by an expansion in terms of suitably chosen deviatory coordinates; the obtained results should thus be quite general. This is demonstrated by comparison of the derived non-equilibrium fluctuation dissipation relation with experimental data on actin networks that are driven out of equilibrium by energy-consuming protein motors. The comparison is excellent and allows us to extract the non-equilibrium

Fluctuation-dissipation relation and stationary distribution of an exactly solvable many-particle model for active biomatter far from equilibrium

Science.gov (United States)

Netz, Roland R.

2018-05-01

An exactly solvable, Hamiltonian-based model of many massive particles that are coupled by harmonic potentials and driven by stochastic non-equilibrium forces is introduced. The stationary distribution and the fluctuation-dissipation relation are derived in closed form for the general non-equilibrium case. Deviations from equilibrium are on one hand characterized by the difference of the obtained stationary distribution from the Boltzmann distribution; this is possible because the model derives from a particle Hamiltonian. On the other hand, the difference between the obtained non-equilibrium fluctuation-dissipation relation and the standard equilibrium fluctuation-dissipation theorem allows us to quantify non-equilibrium in an alternative fashion. Both indicators of non-equilibrium behavior, i.e., deviations from the Boltzmann distribution and deviations from the equilibrium fluctuation-dissipation theorem, can be expressed in terms of a single non-equilibrium parameter α that involves the ratio of friction coefficients and random force strengths. The concept of a non-equilibrium effective temperature, which can be defined by the relation between fluctuations and the dissipation, is by comparison with the exactly derived stationary distribution shown not to hold, even if the effective temperature is made frequency dependent. The analysis is not confined to close-to-equilibrium situations but rather is exact and thus holds for arbitrarily large deviations from equilibrium. Also, the suggested harmonic model can be obtained from non-linear mechanical network systems by an expansion in terms of suitably chosen deviatory coordinates; the obtained results should thus be quite general. This is demonstrated by comparison of the derived non-equilibrium fluctuation dissipation relation with experimental data on actin networks that are driven out of equilibrium by energy-consuming protein motors. The comparison is excellent and allows us to extract the non-equilibrium

Optimal Dispatching of Active Distribution Networks Based on Load Equilibrium

Directory of Open Access Journals (Sweden)

Xiao Han

2017-12-01

Full Text Available This paper focuses on the optimal intraday scheduling of a distribution system that includes renewable energy (RE generation, energy storage systems (ESSs, and thermostatically controlled loads (TCLs. This system also provides time-of-use pricing to customers. Unlike previous studies, this study attempts to examine how to optimize the allocation of electric energy and to improve the equilibrium of the load curve. Accordingly, we propose a concept of load equilibrium entropy to quantify the overall equilibrium of the load curve and reflect the allocation optimization of electric energy. Based on this entropy, we built a novel multi-objective optimal dispatching model to minimize the operational cost and maximize the load curve equilibrium. To aggregate TCLs into the optimization objective, we introduced the concept of a virtual power plant (VPP and proposed a calculation method for VPP operating characteristics based on the equivalent thermal parameter model and the state-queue control method. The Particle Swarm Optimization algorithm was employed to solve the optimization problems. The simulation results illustrated that the proposed dispatching model can achieve cost reductions of system operations, peak load curtailment, and efficiency improvements, and also verified that the load equilibrium entropy can be used as a novel index of load characteristics.

Equilibrium distribution of hard-sphere systems and revised Enskog theory

NARCIS (Netherlands)

Beijeren, H. van

1983-01-01

A revised Enskog theory (RET) is shown to lead to a correct equilibrium distribution in hard-sphere systems in a stationary external potential, while the standard Enskog theory (SET) does not. Attention is given to the s-component hard-sphere mixture with constant external potential acting on

Evolution of longitudinal equilibrium distribution in the adiabatic regime

International Nuclear Information System (INIS)

Wei, J.; Lee, S.Y.; Ruggiero, A.G.

1990-01-01

Evolution of longitudinal equilibrium distribution of a hadron bunch under the beam-environment interaction is investigated based on a self-consistent solution of the Vlasov equation. The effect of this interaction on the distribution can be characterized by a dimensionless quantity in analogy to the one describing the microwave-instability criterion. In the case that the coupling impedance (Z/n) is reactive and frequency independent, the change in the distribution results in a stabilization that keeps the bunch below the instability threshold; microwave instability is thus eliminated. Monte Carlo simulation for the microwave instability agrees with analytic solution of the Vlasov equation provided that bunch shape distortion due to the coupling is taken into account

Unique supply function equilibrium with capacity constraints

International Nuclear Information System (INIS)

Holmberg, Paer

2008-01-01

Consider a market where producers submit supply functions to a procurement auction with uncertain demand, e.g. an electricity auction. In the Supply Function Equilibrium (SFE), every firm commits to the supply function that maximises expected profit in the one-shot game given the supply functions of competitors. A basic weakness of the SFE is the presence of multiple equilibria. This paper shows that with (i) symmetric producers, (ii) perfectly inelastic demand, (iii) a price cap, and (iv) capacity constraints that bind with a positive probability, there exists a unique, symmetric SFE. (author)

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.

A study of chemical equilibrium of tri-component mixtures of hydrogen isotopes

International Nuclear Information System (INIS)

Cristescu, Ioana; Cristescu, I.; Peculea, M.

1998-01-01

In this paper we present a model for computing the equilibrium constants for chemical reactions between hydrogen's isotopes as function of temperature. The equilibrium constants were expressed with the aid of Gibbs potential and the partition function of the mixture. We assessed the partition function for hydrogen's isotopes having in view that some nuclei are fermions and other bosons. As results we plotted the values of equilibrium constants as function of temperature. Knowing these values we determined the deuterium distribution on species (for mixture H 2 -HD-D 2 ) as function of total deuterium concentration and the tritium distribution on species (for mixtures D 2 -DT-T 2 and H 2 -HT-T 2 ) as function of total tritium concentration. (authors)

NHPP-Based Software Reliability Models Using Equilibrium Distribution

Science.gov (United States)

Xiao, Xiao; Okamura, Hiroyuki; Dohi, Tadashi

Non-homogeneous Poisson processes (NHPPs) have gained much popularity in actual software testing phases to estimate the software reliability, the number of remaining faults in software and the software release timing. In this paper, we propose a new modeling approach for the NHPP-based software reliability models (SRMs) to describe the stochastic behavior of software fault-detection processes. The fundamental idea is to apply the equilibrium distribution to the fault-detection time distribution in NHPP-based modeling. We also develop efficient parameter estimation procedures for the proposed NHPP-based SRMs. Through numerical experiments, it can be concluded that the proposed NHPP-based SRMs outperform the existing ones in many data sets from the perspective of goodness-of-fit and prediction performance.

Equilibrium and nonequilibrium solvation and solute electronic structure

International Nuclear Information System (INIS)

Kim, H.J.; Hynes, J.T.

1990-01-01

When a molecular solute is immersed in a polar and polarizable solvent, the electronic wave function of the solute system is altered compared to its vacuum value; the solute electronic structure is thus solvent-dependent. Further, the wave function will be altered depending upon whether the polarization of the solvent is or is not in equilibrium with the solute charge distribution. More precisely, while the solvent electronic polarization should be in equilibrium with the solute electronic wave function, the much more sluggish solvent orientational polarization need not be. We call this last situation non-equilibrium solvation. We outline a nonlinear Schroedinger equation approach to these issues

Equilibrium charge distribution on a finite straight one-dimensional wire

Science.gov (United States)

Batle, Josep; Ciftja, Orion; Abdalla, Soliman; Elhoseny, Mohamed; Alkhambashi, Majid; Farouk, Ahmed

2017-09-01

The electrostatic properties of uniformly charged regular bodies are prominently discussed on college-level electromagnetism courses. However, one of the most basic problems of electrostatics that deals with how a continuous charge distribution reaches equilibrium is rarely mentioned at this level. In this work we revisit the problem of equilibrium charge distribution on a straight one-dimensional (1D) wire with finite length. The majority of existing treatments in the literature deal with the 1D wire as a limiting case of a higher-dimensional structure that can be treated analytically for a Coulomb interaction potential between point charges. Surprisingly, different models (for instance, an ellipsoid or a cylinder model) may lead to different results, thus there is even some ambiguity on whether the problem is well-posed. In this work we adopt a different approach where we do not start with any higher-dimensional body that reduces to a 1D wire in the appropriate limit. Instead, our starting point is the obvious one, a finite straight 1D wire that contains charge. However, the new tweak in the model is the assumption that point charges interact with each other via a non-Coulomb power-law interaction potential. This potential is well-behaved, allows exact analytical results and approaches the standard Coulomb interaction potential as a limit. The results originating from this approach suggest that the equilibrium charge distribution for a finite straight 1D wire is a uniform charge density when the power-law interaction potential approaches the Coulomb interaction potential as a suitable limit. We contrast such a finding to results obtained using a different regularised logarithmic interaction potential which allows exact treatment in 1D. The present self-contained material may be of interest to instructors teaching electromagnetism as well as students who will discover that simple-looking problems may sometimes pose important scientific challenges.

Equilibrium charge distribution on a finite straight one-dimensional wire

International Nuclear Information System (INIS)

Batle, Josep; Ciftja, Orion; Abdalla, Soliman; Elhoseny, Mohamed; Farouk, Ahmed; Alkhambashi, Majid

2017-01-01

The electrostatic properties of uniformly charged regular bodies are prominently discussed on college-level electromagnetism courses. However, one of the most basic problems of electrostatics that deals with how a continuous charge distribution reaches equilibrium is rarely mentioned at this level. In this work we revisit the problem of equilibrium charge distribution on a straight one-dimensional (1D) wire with finite length. The majority of existing treatments in the literature deal with the 1D wire as a limiting case of a higher-dimensional structure that can be treated analytically for a Coulomb interaction potential between point charges. Surprisingly, different models (for instance, an ellipsoid or a cylinder model) may lead to different results, thus there is even some ambiguity on whether the problem is well-posed. In this work we adopt a different approach where we do not start with any higher-dimensional body that reduces to a 1D wire in the appropriate limit. Instead, our starting point is the obvious one, a finite straight 1D wire that contains charge. However, the new tweak in the model is the assumption that point charges interact with each other via a non-Coulomb power-law interaction potential. This potential is well-behaved, allows exact analytical results and approaches the standard Coulomb interaction potential as a limit. The results originating from this approach suggest that the equilibrium charge distribution for a finite straight 1D wire is a uniform charge density when the power-law interaction potential approaches the Coulomb interaction potential as a suitable limit. We contrast such a finding to results obtained using a different regularised logarithmic interaction potential which allows exact treatment in 1D. The present self-contained material may be of interest to instructors teaching electromagnetism as well as students who will discover that simple-looking problems may sometimes pose important scientific challenges. (paper)

Allowance for effects of thermodynamic nonideality in sedimentation equilibrium distributions reflecting protein dimerization.

Science.gov (United States)

Wills, Peter R; Scott, David J; Winzor, Donald J

2012-03-01

This reexamination of a high-speed sedimentation equilibrium distribution for α-chymotrypsin under slightly acidic conditions (pH 4.1, I(M) 0.05) has provided experimental support for the adequacy of nearest-neighbor considerations in the allowance for effects of thermodynamic nonideality in the characterization of protein self-association over a moderate concentration range (up to 8 mg/mL). A widely held but previously untested notion about allowance for thermodynamic nonideality effects is thereby verified experimentally. However, it has also been shown that a greater obstacle to better characterization of protein self-association is likely to be the lack of a reliable estimate of monomer net charge, a parameter that has a far more profound effect on the magnitude of the measured equilibrium constant than any deficiency in current procedures for incorporating the effects of thermodynamic nonideality into the analysis of sedimentation equilibrium distributions reflecting reversible protein self-association. Copyright © 2011 Elsevier Inc. All rights reserved.

MEASURING NEBULAR TEMPERATURES: THE EFFECT OF NEW COLLISION STRENGTHS WITH EQUILIBRIUM AND {kappa}-DISTRIBUTED ELECTRON ENERGIES

Energy Technology Data Exchange (ETDEWEB)

Nicholls, David C.; Dopita, Michael A.; Sutherland, Ralph S.; Kewley, Lisa J. [Research School of Astronomy and Astrophysics, Australian National University, Cotter Rd., Weston ACT 2611 (Australia); Palay, Ethan, E-mail: david@mso.anu.edu.au [Department of Astronomy, Ohio State University, Columbus, OH 43210 (United States)

2013-08-15

In this paper we develop tools for observers to use when analyzing nebular spectra for temperatures and metallicities, with two goals: to present a new, simple method to calculate equilibrium electron temperatures for collisionally excited line flux ratios, using the latest atomic data; and to adapt current methods to include the effects of possible non-equilibrium ''{kappa}'' electron energy distributions. Adopting recent collision strength data for [O III], [S III], [O II], [S II], and [N II], we find that existing methods based on older atomic data seriously overestimate the electron temperatures, even when considering purely Maxwellian statistics. If {kappa} distributions exist in H II regions and planetary nebulae as they do in solar system plasmas, it is important to investigate the observational consequences. This paper continues our previous work on the {kappa} distribution. We present simple formulaic methods that allow observers to (1) measure equilibrium electron temperatures and atomic abundances using the latest atomic data, and (2) to apply simple corrections to existing equilibrium analysis techniques to allow for possible non-equilibrium effects. These tools should lead to better consistency in temperature and abundance measurements, and a clearer understanding of the physics of H II regions and planetary nebulae.

Replacing leads by self-energies using non-equilibrium Green's functions

International Nuclear Information System (INIS)

Michael, Fredrick; Johnson, M.D.

2003-01-01

Open quantum systems consist of semi-infinite leads which transport electrons to and from the device of interest. We show here that within the non-equilibrium Green's function technique for continuum systems, the leads can be replaced by simple c-number self-energies. Our starting point is an approach for continuum systems developed by Feuchtwang. The reformulation developed here is simpler to understand and carry out than the somewhat unwieldly manipulations typical in the Feuchtwang method. The self-energies turn out to have a limited variability: the retarded self-energy Σ r depends on the arbitrary choice of internal boundary conditions, but the non-equilibrium self-energy or scattering function Σ which determines transport is invariant for a broad class of boundary conditions. Expressed in terms of these self-energies, continuum non-equilibrium transport calculations take a particularly simple form similar to that developed for discrete systems

Thermal equilibrium in Einstein's elevator.

Science.gov (United States)

Sánchez-Rey, Bernardo; Chacón-Acosta, Guillermo; Dagdug, Leonardo; Cubero, David

2013-05-01

We report fully relativistic molecular-dynamics simulations that verify the appearance of thermal equilibrium of a classical gas inside a uniformly accelerated container. The numerical experiments confirm that the local momentum distribution in this system is very well approximated by the Jüttner function-originally derived for a flat spacetime-via the Tolman-Ehrenfest effect. Moreover, it is shown that when the acceleration or the container size is large enough, the global momentum distribution can be described by the so-called modified Jüttner function, which was initially proposed as an alternative to the Jüttner function.

Derivation of the chemical-equilibrium rate coefficient using scattering theory

Science.gov (United States)

Mickens, R. E.

1977-01-01

Scattering theory is applied to derive the equilibrium rate coefficient for a general homogeneous chemical reaction involving ideal gases. The reaction rate is expressed in terms of the product of a number of normalized momentum distribution functions, the product of the number of molecules with a given internal energy state, and the spin-averaged T-matrix elements. An expression for momentum distribution at equilibrium for an arbitrary molecule is presented, and the number of molecules with a given internal-energy state is represented by an expression which includes the partition function.

Calculation of the equilibrium distribution for a deleterious gene by the finite Fourier transform.

Science.gov (United States)

Lange, K

1982-03-01

In a population of constant size every deleterious gene eventually attains a stochastic equilibrium between mutation and selection. The individual probabilities of this equilibrium distribution can be computed by an application of the finite Fourier transform to an appropriate branching process formula. Specific numerical examples are discussed for the autosomal dominants, Huntington's chorea and chondrodystrophy, and for the X-linked recessive, Becker's muscular dystrophy.

Coupled double-distribution-function lattice Boltzmann method for the compressible Navier-Stokes equations.

Science.gov (United States)

Li, Q; He, Y L; Wang, Y; Tao, W Q

2007-11-01

A coupled double-distribution-function lattice Boltzmann method is developed for the compressible Navier-Stokes equations. Different from existing thermal lattice Boltzmann methods, this method can recover the compressible Navier-Stokes equations with a flexible specific-heat ratio and Prandtl number. In the method, a density distribution function based on a multispeed lattice is used to recover the compressible continuity and momentum equations, while the compressible energy equation is recovered by an energy distribution function. The energy distribution function is then coupled to the density distribution function via the thermal equation of state. In order to obtain an adjustable specific-heat ratio, a constant related to the specific-heat ratio is introduced into the equilibrium energy distribution function. Two different coupled double-distribution-function lattice Boltzmann models are also proposed in the paper. Numerical simulations are performed for the Riemann problem, the double-Mach-reflection problem, and the Couette flow with a range of specific-heat ratios and Prandtl numbers. The numerical results are found to be in excellent agreement with analytical and/or other solutions.

Non-equilibrium flow and sediment transport distribution over mobile river dunes

Science.gov (United States)

Hoitink, T.; Naqshband, S.; McElroy, B. J.

2017-12-01

Flow and sediment transport are key processes in the morphodynamics of river dunes. During floods in several rivers (e.g., the Elkhorn, Missouri, Niobrara, and Rio Grande), dunes are observed to grow rapidly as flow strength increases, undergoing an unstable transition regime, after which they are washed out in what is called upper stage plane bed. This morphological evolution of dunes to upper stage plane bed is the strongest bed-form adjustment during non-equilibrium flows and is associated with a significant change in hydraulic roughness and water levels. Detailed experimental investigations, however, have mostly focused on fixed dunes limited to equilibrium flow and bed conditions that are rare in natural channels. Our understanding of the underlying sedimentary processes that result into the washing out of dunes is therefore very limited. In the present study, using the Acoustic Concentration and Velocity Profiler (ACVP), we were able to quantify flow structure and sediment transport distribution over mobile non-equilibrium dunes. Under these non-equilibrium flow conditions average dune heights were decreasing while dune lengths were increasing. Preliminary results suggest that this morphological behaviour is due to a positive phase lag between sediment transport maximum and topographic maximum leading to a larger erosion on the dune stoss side compared to deposition on dune lee side.

Metastable Equilibrium Solubility Distribution of Carbonated Apatite as a Function of Solution Composition.

Science.gov (United States)

Chhettry; Wang; Hsu; Fox; Baig; Barry; Zhuang; Otsuka; Higuchi

1999-10-01

Previous studies have shown that carbonated apatites (CAPs) exhibit the phenomenon of metastable equilibrium solubility (MES) in weak acid media. The purpose of the present investigation was to examine two questions: first, whether the MES concept is applicable to a broader range of solution conditions and, second, whether a driving force function associated with a surface complex having a constant stoichiometry governs the dissolution of CAP and, if so, what is this stoichiometry. CAP preparations with carbonate contents of 1.8-5.7 wt% (synthesized by hydrolysis of dicalcium phosphate anhydrate in solutions of varying bicarbonate levels or by direct precipitation from supersaturated calcium/phosphate/carbonate solutions) were studied as follows. MES distributions for each of the CAP preparations were determined by equilibrating the CAP under stirred conditions in a series of acetate buffers (0.10 M) containing various levels of calcium and phosphate in the pH range 4.5-6.5 and a solution calcium/phosphate ratio in the range 0.1-10. The amount dissolved in each instance was regarded as the fraction of the CAP possessing an MES value greater than that corresponding to the ion activity product (IAP) of the equilibrating solution. The solution IAPs were calculated from the solution compositions using plausible calcium phosphate stoichiometries, viz., dicalcium phosphate dihydrate, octacalcium phosphate, tricalcium phosphate, hydroxyapatite, carbonated apatite (based on the bulk composition of the particular CAP involved in the experiment), and tetracalcium phosphate. The fraction of CAP dissolved was plotted against the solution IAPs for each experimental set using each of the six assumed stoichiometries for the surface complex. The results demonstrated that the MES concept was applicable to all of the CAP preparations in media of various solution compositions and different pH levels. The most important new outcome of this study was that MES profiles for each of the

Fundamental functions in equilibrium thermodynamics

NARCIS (Netherlands)

Horst, H.J. ter

In the standard presentations of the principles of Gibbsian equilibrium thermodynamics one can find several gaps in the logic. For a subject that is as widely used as equilibrium thermodynamics, it is of interest to clear up such questions of mathematical rigor. In this paper it is shown that using

Models of supply function equilibrium with applications to the electricity industry

Science.gov (United States)

Aromi, J. Daniel

Electricity market design requires tools that result in a better understanding of incentives of generators and consumers. Chapter 1 and 2 provide tools and applications of these tools to analyze incentive problems in electricity markets. In chapter 1, models of supply function equilibrium (SFE) with asymmetric bidders are studied. I prove the existence and uniqueness of equilibrium in an asymmetric SFE model. In addition, I propose a simple algorithm to calculate numerically the unique equilibrium. As an application, a model of investment decisions is considered that uses the asymmetric SFE as an input. In this model, firms can invest in different technologies, each characterized by distinct variable and fixed costs. In chapter 2, option contracts are introduced to a supply function equilibrium (SFE) model. The uniqueness of the equilibrium in the spot market is established. Comparative statics results on the effect of option contracts on the equilibrium price are presented. A multi-stage game where option contracts are traded before the spot market stage is considered. When contracts are optimally procured by a central authority, the selected profile of option contracts is such that the spot market price equals marginal cost for any load level resulting in a significant reduction in cost. If load serving entities (LSEs) are price takers, in equilibrium, there is no trade of option contracts. Even when LSEs have market power, the central authority's solution cannot be implemented in equilibrium. In chapter 3, we consider a game in which a buyer must repeatedly procure an input from a set of firms. In our model, the buyer is able to sign long term contracts that establish the likelihood with which the next period contract is awarded to an entrant or the incumbent. We find that the buyer finds it optimal to favor the incumbent, this generates more intense competition between suppliers. In a two period model we are able to completely characterize the optimal mechanism.

Hidden symmetries and equilibrium properties of multiplicative white-noise stochastic processes

International Nuclear Information System (INIS)

Arenas, Zochil González; Barci, Daniel G

2012-01-01

Multiplicative white-noise stochastic processes continue to attract attention in a wide area of scientific research. The variety of prescriptions available for defining them makes the development of general tools for their characterization difficult. In this work, we study equilibrium properties of Markovian multiplicative white-noise processes. For this, we define the time reversal transformation for such processes, taking into account that the asymptotic stationary probability distribution depends on the prescription. Representing the stochastic process in a functional Grassmann formalism, we avoid the necessity of fixing a particular prescription. In this framework, we analyze equilibrium properties and study hidden symmetries of the process. We show that, using a careful definition of the equilibrium distribution and taking into account the appropriate time reversal transformation, usual equilibrium properties are satisfied for any prescription. Finally, we present a detailed deduction of a covariant supersymmetric formulation of a multiplicative Markovian white-noise process and study some of the constraints that it imposes on correlation functions using Ward–Takahashi identities. (paper)

Hidden symmetries and equilibrium properties of multiplicative white-noise stochastic processes

Science.gov (United States)

González Arenas, Zochil; Barci, Daniel G.

2012-12-01

Multiplicative white-noise stochastic processes continue to attract attention in a wide area of scientific research. The variety of prescriptions available for defining them makes the development of general tools for their characterization difficult. In this work, we study equilibrium properties of Markovian multiplicative white-noise processes. For this, we define the time reversal transformation for such processes, taking into account that the asymptotic stationary probability distribution depends on the prescription. Representing the stochastic process in a functional Grassmann formalism, we avoid the necessity of fixing a particular prescription. In this framework, we analyze equilibrium properties and study hidden symmetries of the process. We show that, using a careful definition of the equilibrium distribution and taking into account the appropriate time reversal transformation, usual equilibrium properties are satisfied for any prescription. Finally, we present a detailed deduction of a covariant supersymmetric formulation of a multiplicative Markovian white-noise process and study some of the constraints that it imposes on correlation functions using Ward-Takahashi identities.

Non-equilibrium work distribution for interacting colloidal particles under friction

International Nuclear Information System (INIS)

Gomez-Solano, Juan Ruben; July, Christoph; Mehl, Jakob; Bechinger, Clemens

2015-01-01

We experimentally investigate the non-equilibrium steady-state distribution of the work done by an external force on a mesoscopic system with many coupled degrees of freedom: a colloidal crystal mechanically driven across a commensurate periodic light field. Since this system mimics the spatiotemporal dynamics of a crystalline surface moving on a corrugated substrate, our results show general properties of the work distribution for atomically flat surfaces undergoing friction. We address the role of several parameters which can influence the shape of the work distribution, e.g. the number of particles used to locally probe the properties of the system and the time interval to measure the work. We find that, when tuning the control parameters to induce particle depinning from the substrate, there is an abrupt change of the shape of the work distribution. While in the completely static and sliding friction regimes the work distribution is Gaussian, non-Gaussian tails show up due to the spatiotemporal heterogeneity of the particle dynamics during the transition between these two regimes. (paper)

Transition in the equilibrium distribution function of relativistic particles.

Science.gov (United States)

Mendoza, M; Araújo, N A M; Succi, S; Herrmann, H J

2012-01-01

We analyze a transition from single peaked to bimodal velocity distribution in a relativistic fluid under increasing temperature, in contrast with a non-relativistic gas, where only a monotonic broadening of the bell-shaped distribution is observed. Such transition results from the interplay between the raise in thermal energy and the constraint of maximum velocity imposed by the speed of light. We study the Bose-Einstein, the Fermi-Dirac, and the Maxwell-Jüttner distributions, and show that they all exhibit the same qualitative behavior. We characterize the nature of the transition in the framework of critical phenomena and show that it is either continuous or discontinuous, depending on the group velocity. We analyze the transition in one, two, and three dimensions, with special emphasis on twodimensions, for which a possible experiment in graphene, based on the measurement of the Johnson-Nyquist noise, is proposed.

Exciton distribution function and secondary radiation in polar semiconductors

International Nuclear Information System (INIS)

Trallero Giner, C.; Sotolongo Costa, O.

1985-07-01

An explicit non-equilibrium distribution function for excitons in the ground state n=1 in the case when the fundamental interaction is with acoustical phonons is calculated for polar semiconductors. Using it, a general expression for the secondary radiation cross-section (valid for Raman, hot and thermalized luminescence processes), is obtained. The results are applied to explain the temperature dependence of the 1LO and 2LO luminescence lines half-width in CdS single crystals. The relative contributions of 3LO Raman and luminescence intensities and the variation of the secondary emission spectrum as function of exciton life-time are studied. Comparison with experimental results yields quantitative agreement. (author)

Recurrence Relations for the Equilibrium Means of Distributions Arising in Chemical Reactions

Directory of Open Access Journals (Sweden)

E.K. Elsheikh

1997-12-01

Full Text Available In this paper we derive recurrence relations that describe how the equilibrium mean of the number molecules of a reactant varies with each of the parameters defining the initial state for four basic reversible chemical reactions. In essence, the relations provide a rationale for updating the equilibrium mean following the addition (or removal of a molecule of one of the types involved in the reaction, there being a relation for each type. With a new parameterization introduced for each reaction, the relations provide a convenient means of evaluating the means, variances and other important moments without any need to work out the underlying distributions. As an application, the relations are used to numerically assess-approximate expressions for the means and variances.

Classical and Quantum Models in Non-Equilibrium Statistical Mechanics: Moment Methods and Long-Time Approximations

Directory of Open Access Journals (Sweden)

Ramon F. Alvarez-Estrada

2012-02-01

Full Text Available We consider non-equilibrium open statistical systems, subject to potentials and to external “heat baths” (hb at thermal equilibrium at temperature T (either with ab initio dissipation or without it. Boltzmann’s classical equilibrium distributions generate, as Gaussian weight functions in momenta, orthogonal polynomials in momenta (the position-independent Hermite polynomialsHn’s. The moments of non-equilibrium classical distributions, implied by the Hn’s, fulfill a hierarchy: for long times, the lowest moment dominates the evolution towards thermal equilibrium, either with dissipation or without it (but under certain approximation. We revisit that hierarchy, whose solution depends on operator continued fractions. We review our generalization of that moment method to classical closed many-particle interacting systems with neither a hb nor ab initio dissipation: with initial states describing thermal equilibrium at T at large distances but non-equilibrium at finite distances, the moment method yields, approximately, irreversible thermalization of the whole system at T, for long times. Generalizations to non-equilibrium quantum interacting systems meet additional difficulties. Three of them are: (i equilibrium distributions (represented through Wigner functions are neither Gaussian in momenta nor known in closed form; (ii they may depend on dissipation; and (iii the orthogonal polynomials in momenta generated by them depend also on positions. We generalize the moment method, dealing with (i, (ii and (iii, to some non-equilibrium one-particle quantum interacting systems. Open problems are discussed briefly.

Modelling non-equilibrium thermodynamic systems from the speed-gradient principle.

Science.gov (United States)

Khantuleva, Tatiana A; Shalymov, Dmitry S

2017-03-06

The application of the speed-gradient (SG) principle to the non-equilibrium distribution systems far away from thermodynamic equilibrium is investigated. The options for applying the SG principle to describe the non-equilibrium transport processes in real-world environments are discussed. Investigation of a non-equilibrium system's evolution at different scale levels via the SG principle allows for a fresh look at the thermodynamics problems associated with the behaviour of the system entropy. Generalized dynamic equations for finite and infinite number of constraints are proposed. It is shown that the stationary solution to the equations, resulting from the SG principle, entirely coincides with the locally equilibrium distribution function obtained by Zubarev. A new approach to describe time evolution of systems far from equilibrium is proposed based on application of the SG principle at the intermediate scale level of the system's internal structure. The problem of the high-rate shear flow of viscous fluid near the rigid plane plate is discussed. It is shown that the SG principle allows closed mathematical models of non-equilibrium processes to be constructed.This article is part of the themed issue 'Horizons of cybernetical physics'. © 2017 The Author(s).

Equilibrium sampling by reweighting nonequilibrium simulation trajectories.

Science.gov (United States)

Yang, Cheng; Wan, Biao; Xu, Shun; Wang, Yanting; Zhou, Xin

2016-03-01

Based on equilibrium molecular simulations, it is usually difficult to efficiently visit the whole conformational space of complex systems, which are separated into some metastable regions by high free energy barriers. Nonequilibrium simulations could enhance transitions among these metastable regions and then be applied to sample equilibrium distributions in complex systems, since the associated nonequilibrium effects can be removed by employing the Jarzynski equality (JE). Here we present such a systematical method, named reweighted nonequilibrium ensemble dynamics (RNED), to efficiently sample equilibrium conformations. The RNED is a combination of the JE and our previous reweighted ensemble dynamics (RED) method. The original JE reproduces equilibrium from lots of nonequilibrium trajectories but requires that the initial distribution of these trajectories is equilibrium. The RED reweights many equilibrium trajectories from an arbitrary initial distribution to get the equilibrium distribution, whereas the RNED has both advantages of the two methods, reproducing equilibrium from lots of nonequilibrium simulation trajectories with an arbitrary initial conformational distribution. We illustrated the application of the RNED in a toy model and in a Lennard-Jones fluid to detect its liquid-solid phase coexistence. The results indicate that the RNED sufficiently extends the application of both the original JE and the RED in equilibrium sampling of complex systems.

Behavior of Triple Langmuir Probes in Non-Equilibrium Plasmas

Science.gov (United States)

Polzin, Kurt A.; Ratcliffe, Alicia C.

2018-01-01

The triple Langmuir probe is an electrostatic probe in which three probe tips collect current when inserted into a plasma. The triple probe differs from a simple single Langmuir probe in the nature of the voltage applied to the probe tips. In the single probe, a swept voltage is applied to the probe tip to acquire a waveform showing the collected current as a function of applied voltage (I-V curve). In a triple probe three probe tips are electrically coupled to each other with constant voltages applied between each of the tips. The voltages are selected such that they would represent three points on the single Langmuir probe I-V curve. Elimination of the voltage sweep makes it possible to measure time-varying plasma properties in transient plasmas. Under the assumption of a Maxwellian plasma, one can determine the time-varying plasma temperature T(sub e)(t) and number density n(sub e)(t) from the applied voltage levels and the time-histories of the collected currents. In the present paper we examine the theory of triple probe operation, specifically focusing on the assumption of a Maxwellian plasma. Triple probe measurements have been widely employed for a number of pulsed and timevarying plasmas, including pulsed plasma thrusters (PPTs), dense plasma focus devices, plasma flows, and fusion experiments. While the equilibrium assumption may be justified for some applications, it is unlikely that it is fully justifiable for all pulsed and time-varying plasmas or for all times during the pulse of a plasma device. To examine a simple non-equilibrium plasma case, we return to basic governing equations of probe current collection and compute the current to the probes for a distribution function consisting of two Maxwellian distributions with different temperatures (the two-temperature Maxwellian). A variation of this method is also employed, where one of the Maxwellians is offset from zero (in velocity space) to add a suprathermal beam of electrons to the tail of the

Modeling of Eddy current distribution and equilibrium reconstruction in the SST-1 Tokamak

International Nuclear Information System (INIS)

Banerjee, Santanu; Sharma, Deepti; Radhakrishnana, Srinivasan; Daniel, Raju; Shankara Joisa, Y.; Atrey, Parveen Kumar; Pathak, Surya Kumar; Singh, Amit Kumar

2015-01-01

Toroidal continuity of the vacuum vessel and the cryostat leads to the generation of large eddy currents in these passive structures during the Ohmic phase of the steady state superconducting tokamak SST-1. This reduces the magnitude of the loop voltage seen by the plasma as also delays its buildup. During the ramping down of the Ohmic transformer current (OT), the resultant eddy currents flowing in the passive conductors play a crucial role in governing the plasma equilibrium. Amount of this eddy current and its distribution has to be accurately determined such that this can be fed to the equilibrium reconstruction code as an input. For the accurate inclusion of the effect of eddy currents in the reconstruction, the toroidally continuous conducting structures like the vacuum vessel and the cryostat with large poloidal cross-section and any other poloidal field (PF) coil sitting idle on the machine are broken up into a large number of co-axial toroidal current carrying filaments. The inductance matrix for this large set of toroidal current carrying conductors is calculated using the standard Green's function and the induced currents are evaluated for the OT waveform of each plasma discharge. Consistency of this filament model is cross-checked with the 11 in-vessel and 12 out-vessel toroidal flux loop signals in SST-1. Resistances of the filaments are adjusted to reproduce the experimental measurements of these flux loops in pure OT shots and shots with OT and vertical field (BV). Such shots are taken routinely in SST-1 without the fill gas to cross-check the consistency of the filament model. A Grad-Shafranov (GS) equation solver, named as IPREQ, has been developed in IPR to reconstruct the plasma equilibrium through searching for the best-fit current density profile. Ohmic transformer current (OT), vertical field coil current (BV), currents in the passive filaments along with the plasma pressure (p) and current (I p ) profiles are used as inputs to the IPREQ

Equilibrium distributions of free charged particles and molecules in systems with non-plane boundaries

International Nuclear Information System (INIS)

Usenko, A.S.

1995-01-01

The equilibrium space-inhomogeneous distributions of free and pair bound charged particles are calculated in the dipole approximation for the plasma-molecular cylinder and sphere. It is shown that the space and orientational distributions of charged particles and molecules in these systems are similar to those in the cases of plasma-molecular system restricted by one or two parallel planes. The influence of the parameters of outer medium and a plasma-molecular system on the space and orientational distributions of charged particles and molecules is studied in detail

The influence of the deviation from the equilibrium deuteron distribution on the neutron spectra in linear pinch geometries

International Nuclear Information System (INIS)

Deutsch, R.; Herold, H.; Kaeppeler, H.J.; Schmidt, H.

1982-07-01

In order to analyse the influence of the deviation from the equilibrium distribution of the fast deuterons on the neutron spectrum, the limiting case, corresponding to a two-dimensional mono-energetic deuteron distribution, was studied. An essential difference in comparison to the equilibrium case is the appearance of a pronounced peak in the side-on spectra at Esub(n)approx.=2.5 MeV. A comparison of the theoretical and experimental data was made. If we take into account the relaxation processes, there results a good agreement between theory and experiment. (orig.)

Non-Equilibrium Liouville and Wigner Equations: Moment Methods and Long-Time Approximations

Directory of Open Access Journals (Sweden)

Ramon F. Álvarez-Estrada

2014-03-01

Full Text Available We treat the non-equilibrium evolution of an open one-particle statistical system, subject to a potential and to an external “heat bath” (hb with negligible dissipation. For the classical equilibrium Boltzmann distribution, Wc,eq, a non-equilibrium three-term hierarchy for moments fulfills Hermiticity, which allows one to justify an approximate long-time thermalization. That gives partial dynamical support to Boltzmann’s Wc,eq, out of the set of classical stationary distributions, Wc;st, also investigated here, for which neither Hermiticity nor that thermalization hold, in general. For closed classical many-particle systems without hb (by using Wc,eq, the long-time approximate thermalization for three-term hierarchies is justified and yields an approximate Lyapunov function and an arrow of time. The largest part of the work treats an open quantum one-particle system through the non-equilibrium Wigner function, W. Weq for a repulsive finite square well is reported. W’s (< 0 in various cases are assumed to be quasi-definite functionals regarding their dependences on momentum (q. That yields orthogonal polynomials, HQ,n(q, for Weq (and for stationary Wst, non-equilibrium moments, Wn, of W and hierarchies. For the first excited state of the harmonic oscillator, its stationary Wst is a quasi-definite functional, and the orthogonal polynomials and three-term hierarchy are studied. In general, the non-equilibrium quantum hierarchies (associated with Weq for the Wn’s are not three-term ones. As an illustration, we outline a non-equilibrium four-term hierarchy and its solution in terms of generalized operator continued fractions. Such structures also allow one to formulate long-time approximations, but make it more difficult to justify thermalization. For large thermal and de Broglie wavelengths, the dominant Weq and a non-equilibrium equation for W are reported: the non-equilibrium hierarchy could plausibly be a three-term one and possibly not

MHD equilibrium with toroidal rotation

International Nuclear Information System (INIS)

Li, J.

1987-03-01

The present work attempts to formulate the equilibrium of axisymmetric plasma with purely toroidal flow within ideal MHD theory. In general, the inertial term Rho(v.Del)v caused by plasma flow is so complicated that the equilibrium equation is completely different from the Grad-Shafranov equation. However, in the case of purely toroidal flow the equilibrium equation can be simplified so that it resembles the Grad-Shafranov equation. Generally one arbitrary two-variable functions and two arbitrary single variable functions, instead of only four single-variable functions, are allowed in the new equilibrium equations. Also, the boundary conditions of the rotating (with purely toroidal fluid flow, static - without any fluid flow) equilibrium are the same as those of the static equilibrium. So numerically one can calculate the rotating equilibrium as a static equilibrium. (author)

Determination of Hot-Carrier Distribution Functions in Uniaxially Stressed p-Type Germanium

DEFF Research Database (Denmark)

Christensen, Ove

1973-01-01

This paper gives a description of an experimental determination of distribution functions in k→ space of hot holes in uniaxially compressed germanium. The hot-carrier studies were made at 85°K at fields up to 1000 V/cm and uniaxial stresses up to 11 800 kg/cm2. The field and stress were always in...... probabilities with stress. A model based on the nonparabolicity of the upper p3 / 2 level is proposed for the negative differential conductivity in stressed p-type Ge....... function has been assumed. The parameters of the distribution function are then fitted to the experimental modulation. The calculation of absorption was performed numerically, using a four-band k→·p→ model. This model was checked for consistency by comparing with piezoabsorption measurements performed...... in thermal equilibrium. The average carrier energy calculated from the distribution function shows a fast increase with stress and almost saturates when the strain splitting of the two p3 / 2 levels reaches the optical-phonon energy. This saturation is interpreted in terms of the change in scattering...

Thermal equilibrium properties of an intense relativistic electron beam

International Nuclear Information System (INIS)

Davidson, R.C.; Uhm, H.S.

1979-01-01

The thermal equilibrium properties of an intense relativistic electron beam with distribution function f 0 /sub b/=Z -1 /sub b/exp[-(H-β/sub b/cP/sub z/-ω/sub b/P/sub theta/) /T] are investigated. This choice of f 0 /sub b/ allows for a mean azimuthal rotation of the beam electrons (when ω/sub b/not =0), and corresponds to an important generalization of the distribution function first analyzed by Bennett. Beam equilibrium properties, including axial velocity profile V 0 /sub z/b(r), azimuthal velocity profile V 0 /sub thetab/(r), beam temperature profile T 0 /sub b/(r), beam density profile n 0 /sub b/(r), and equilibrium self-field profiles, are calculated for a broad range of system parameters. For appropriate choice of beam rotation velocity ω/sub b/, it is found that radially confined equilibrium solutions [with n 0 /sub b/(r→infinity) =0] exist even in the absence of a partially neutralizing ion background that weakens the repulsive space-charge force. The necessary and sufficient conditions for radially confined equilibria are ω - /sub b/ + /sub b/ for 0 2 /sub b/p /ω 2 /sub b/c) (1-f-β 2 /sub b/) 2 /sub b/p/ω 2 /sub b/c) (1-f-β 2 /sub b/) <0

Module description of TOKAMAK equilibrium code MEUDAS

International Nuclear Information System (INIS)

Suzuki, Masaei; Hayashi, Nobuhiko; Matsumoto, Taro; Ozeki, Takahisa

2002-01-01

The analysis of an axisymmetric MHD equilibrium serves as a foundation of TOKAMAK researches, such as a design of devices and theoretical research, the analysis of experiment result. For this reason, also in JAERI, an efficient MHD analysis code has been developed from start of TOKAMAK research. The free boundary equilibrium code ''MEUDAS'' which uses both the DCR method (Double-Cyclic-Reduction Method) and a Green's function can specify the pressure and the current distribution arbitrarily, and has been applied to the analysis of a broad physical subject as a code having rapidity and high precision. Also the MHD convergence calculation technique in ''MEUDAS'' has been built into various newly developed codes. This report explains in detail each module in ''MEUDAS'' for performing convergence calculation in solving the MHD equilibrium. (author)

Dynamical equations for time-ordered Green’s functions: from the Keldysh time-loop contour to equilibrium at finite and zero temperature

International Nuclear Information System (INIS)

Ness, H; Dash, L K

2012-01-01

We study the dynamical equation of the time-ordered Green’s function at finite temperature. We show that the time-ordered Green’s function obeys a conventional Dyson equation only at equilibrium and in the limit of zero temperature. In all other cases, i.e. finite temperature at equilibrium or non-equilibrium, the time-ordered Green’s function obeys instead a modified Dyson equation. The derivation of this result is obtained from the general formalism of the non-equilibrium Green’s functions on the Keldysh time-loop contour. At equilibrium, our result is fully consistent with the Matsubara temperature Green’s function formalism and also justifies rigorously the correction terms introduced in an ad hoc way with Hedin and Lundqvist. Our results show that one should use the appropriate dynamical equation for the time-ordered Green’s function when working beyond the equilibrium zero-temperature limit.

The negotiated equilibrium model of spinal cord function.

Science.gov (United States)

Wolpaw, Jonathan R

2018-04-16

The belief that the spinal cord is hardwired is no longer tenable. Like the rest of the CNS, the spinal cord changes during growth and aging, when new motor behaviours are acquired, and in response to trauma and disease. This paper describes a new model of spinal cord function that reconciles its recently appreciated plasticity with its long recognized reliability as the final common pathway for behaviour. According to this model, the substrate of each motor behaviour comprises brain and spinal plasticity: the plasticity in the brain induces and maintains the plasticity in the spinal cord. Each time a behaviour occurs, the spinal cord provides the brain with performance information that guides changes in the substrate of the behaviour. All the behaviours in the repertoire undergo this process concurrently; each repeatedly induces plasticity to preserve its key features despite the plasticity induced by other behaviours. The aggregate process is a negotiation among the behaviours: they negotiate the properties of the spinal neurons and synapses that they all use. The ongoing negotiation maintains the spinal cord in an equilibrium - a negotiated equilibrium - that serves all the behaviours. This new model of spinal cord function is supported by laboratory and clinical data, makes predictions borne out by experiment, and underlies a new approach to restoring function to people with neuromuscular disorders. Further studies are needed to test its generality, to determine whether it may apply to other CNS areas such as the cerebral cortex, and to develop its therapeutic implications. This article is protected by copyright. All rights reserved. This article is protected by copyright. All rights reserved.

The effect of additional equilibrium stress functions on the three-node hybrid-mixed curved beam element

International Nuclear Information System (INIS)

Kim, Jin Gon; Park, Yong Kuk

2008-01-01

To develop an effective hybrid-mixed element, it is extremely critical as to how to assume the stress field. This research article demonstrates the effect of additional equilibrium stress functions to enhance the numerical performance of the locking-free three-node hybrid-mixed curved beam element, proposed in Saleeb and Chang's previous work. It is exceedingly complicated or even infeasible to determine the stress functions to satisfy fully both the equilibrium conditions and suppression of kinematic deformation modes in the three-node hybrid-mixed formulation. Accordingly, the additional stress functions to satisfy partially or fully equilibrium conditions are incorporated in this study. Several numerical examples for static and dynamic problems confirm that the newly proposed element with these additional stress functions is highly effective regardless of the slenderness ratio and curvature of arches in static and dynamic analyses

Equilibrium state of colliding electron beams

Directory of Open Access Journals (Sweden)

R. L. Warnock

2003-10-01

Full Text Available We study a nonlinear integral equation that is a necessary condition on the equilibrium phase-space distribution function of stored, colliding electron beams. It is analogous to the Haïssinski equation, being derived from Vlasov-Fokker-Planck theory, but is quite different in form. The equation is analyzed for the case of the Chao-Ruth model of the beam-beam interaction in 1 degree of freedom, a so-called strong-strong model with nonlinear beam-beam force. We prove the existence of a unique solution, for sufficiently small beam current, by an application of the implicit function theorem. We have not yet proved that this solution is positive, as would be required to establish existence of an equilibrium. There is, however, numerical evidence of a positive solution. We expect that our analysis can be extended to more realistic models.

Potential and flux field landscape theory. I. Global stability and dynamics of spatially dependent non-equilibrium systems.

Science.gov (United States)

Wu, Wei; Wang, Jin

2013-09-28

We established a potential and flux field landscape theory to quantify the global stability and dynamics of general spatially dependent non-equilibrium deterministic and stochastic systems. We extended our potential and flux landscape theory for spatially independent non-equilibrium stochastic systems described by Fokker-Planck equations to spatially dependent stochastic systems governed by general functional Fokker-Planck equations as well as functional Kramers-Moyal equations derived from master equations. Our general theory is applied to reaction-diffusion systems. For equilibrium spatially dependent systems with detailed balance, the potential field landscape alone, defined in terms of the steady state probability distribution functional, determines the global stability and dynamics of the system. The global stability of the system is closely related to the topography of the potential field landscape in terms of the basins of attraction and barrier heights in the field configuration state space. The effective driving force of the system is generated by the functional gradient of the potential field alone. For non-equilibrium spatially dependent systems, the curl probability flux field is indispensable in breaking detailed balance and creating non-equilibrium condition for the system. A complete characterization of the non-equilibrium dynamics of the spatially dependent system requires both the potential field and the curl probability flux field. While the non-equilibrium potential field landscape attracts the system down along the functional gradient similar to an electron moving in an electric field, the non-equilibrium flux field drives the system in a curly way similar to an electron moving in a magnetic field. In the small fluctuation limit, the intrinsic potential field as the small fluctuation limit of the potential field for spatially dependent non-equilibrium systems, which is closely related to the steady state probability distribution functional, is

Non-equilibrium thermionic electron emission for metals at high temperatures

Science.gov (United States)

Domenech-Garret, J. L.; Tierno, S. P.; Conde, L.

2015-08-01

Stationary thermionic electron emission currents from heated metals are compared against an analytical expression derived using a non-equilibrium quantum kappa energy distribution for the electrons. The latter depends on the temperature decreasing parameter κ ( T ) , which decreases with increasing temperature and can be estimated from raw experimental data and characterizes the departure of the electron energy spectrum from equilibrium Fermi-Dirac statistics. The calculations accurately predict the measured thermionic emission currents for both high and moderate temperature ranges. The Richardson-Dushman law governs electron emission for large values of kappa or equivalently, moderate metal temperatures. The high energy tail in the electron energy distribution function that develops at higher temperatures or lower kappa values increases the emission currents well over the predictions of the classical expression. This also permits the quantitative estimation of the departure of the metal electrons from the equilibrium Fermi-Dirac statistics.

Distribution functions for fluids in random media

International Nuclear Information System (INIS)

Madden, W.G.; Glandt, E.D.

1988-01-01

A random medium is considered, composed of identifiable interactive sites or obstacles equilibrated at a high temperature and then quenched rapidly to form a rigid structure, statistically homogeneous on all but molecular length scales. The equilibrium statistical mechanics of a fluid contained inside this quenched medium is discussed. Various particle-particle and particle-obstacle correlation functions, which differ form the corresponding functions for a fully equilibrated binary mixture, are defined through an averaging process over the static ensemble of obstacle configurations and applications of topological reduction techniques. The Ornstein-Zernike equations also differ from their equilibrium counterparts

Radial Distribution Functions of Strongly Coupled Two-Temperature Plasmas

Science.gov (United States)

Shaffer, Nathaniel R.; Tiwari, Sanat Kumar; Baalrud, Scott D.

2017-10-01

We present tests of three theoretical models for the radial distribution functions (RDFs) in two-temperature strongly coupled plasmas. RDFs are useful in extending plasma thermodynamics and kinetic theory to strong coupling, but they are usually known only for thermal equilibrium or for approximate one-component model plasmas. Accurate two-component modeling is necessary to understand the impact of strong coupling on inter-species transport, e.g., ambipolar diffusion and electron-ion temperature relaxation. We demonstrate that the Seuferling-Vogel-Toeppfer (SVT) extension of the hypernetted chain equations not only gives accurate RDFs (as compared with classical molecular dynamics simulations), but also has a simple connection with the Yukawa OCP model. This connection gives a practical means to recover the structure of the electron background from knowledge of the ion-ion RDF alone. Using the model RDFs in Effective Potential Theory, we report the first predictions of inter-species transport coefficients of strongly coupled plasmas far from equilibrium. This work is supported by NSF Grant No. PHY-1453736, AFSOR Award No. FA9550-16-1-0221, and used XSEDE computational resources.

Self-consistent particle distribution of a bunched beam in RF field

CERN Document Server

Batygin, Y K

2002-01-01

An analytical solution for the self-consistent particle equilibrium distribution in an RF field with transverse focusing is found. The solution is attained in the approximation of a high brightness beam. The distribution function in phase space is determined as a stationary function of the energy integral. Equipartitioning of the beam distribution between degrees of freedom follows directly from the choice of the stationary distribution function. Analytical expressions for r-z equilibrium beam profile and maximum beam current in RF field are obtained.

A simple approximation of moments of the quasi-equilibrium distribution of an extended stochastic theta-logistic model with non-integer powers.

Science.gov (United States)

Bhowmick, Amiya Ranjan; Bandyopadhyay, Subhadip; Rana, Sourav; Bhattacharya, Sabyasachi

2016-01-01

The stochastic versions of the logistic and extended logistic growth models are applied successfully to explain many real-life population dynamics and share a central body of literature in stochastic modeling of ecological systems. To understand the randomness in the population dynamics of the underlying processes completely, it is important to have a clear idea about the quasi-equilibrium distribution and its moments. Bartlett et al. (1960) took a pioneering attempt for estimating the moments of the quasi-equilibrium distribution of the stochastic logistic model. Matis and Kiffe (1996) obtain a set of more accurate and elegant approximations for the mean, variance and skewness of the quasi-equilibrium distribution of the same model using cumulant truncation method. The method is extended for stochastic power law logistic family by the same and several other authors (Nasell, 2003; Singh and Hespanha, 2007). Cumulant truncation and some alternative methods e.g. saddle point approximation, derivative matching approach can be applied if the powers involved in the extended logistic set up are integers, although plenty of evidence is available for non-integer powers in many practical situations (Sibly et al., 2005). In this paper, we develop a set of new approximations for mean, variance and skewness of the quasi-equilibrium distribution under more general family of growth curves, which is applicable for both integer and non-integer powers. The deterministic counterpart of this family of models captures both monotonic and non-monotonic behavior of the per capita growth rate, of which theta-logistic is a special case. The approximations accurately estimate the first three order moments of the quasi-equilibrium distribution. The proposed method is illustrated with simulated data and real data from global population dynamics database. Copyright © 2015 Elsevier Inc. All rights reserved.

Equilibrium Structures and Absorption Spectra for SixOy Molecular Clusters using Density Functional Theory

Science.gov (United States)

2017-05-05

Naval Research Laboratory Washington, DC 20375-5320 NRL/MR/6390--17-9724 Equilibrium Structures and Absorption Spectra for SixOy Molecular Clusters...TELEPHONE NUMBER (include area code) b. ABSTRACT c. THIS PAGE 18. NUMBER OF PAGES 17. LIMITATION OF ABSTRACT Equilibrium Structures and Absorption...and electronic excited-state absorption spectra for eqilibrium structures of SixOy molecular clusters using density function theory (DFT) and time

Sheet beam model for intense space charge: Application to Debye screening and the distribution of particle oscillation frequencies in a thermal equilibrium beam

Directory of Open Access Journals (Sweden)

Steven M. Lund

2011-05-01

Full Text Available A one-dimensional Vlasov-Poisson model for sheet beams is reviewed and extended to provide a simple framework for analysis of space-charge effects. Centroid and rms envelope equations including image-charge effects are derived and reasonable parameter equivalences with commonly employed 2D transverse models of unbunched beams are established. This sheet-beam model is then applied to analyze several problems of fundamental interest. A sheet-beam thermal equilibrium distribution in a continuous focusing channel is constructed and shown to have analogous properties to two- and three-dimensional thermal equilibrium models in terms of the equilibrium structure and Debye screening properties. The simpler formulation for sheet beams is exploited to explicitly calculate the distribution of particle oscillation frequencies within a thermal equilibrium beam. It is shown that as space-charge intensity increases, the frequency distribution becomes broad, suggesting that beams with strong space-charge can have improved stability relative to beams with weak space-charge.

Multiple spatial scaling and the weak-coupling approximation. I. General formulation and equilibrium theory

Energy Technology Data Exchange (ETDEWEB)

Kleinsmith, P E [Carnegie-Mellon Univ., Pittsburgh, Pa. (USA)

1976-04-01

Multiple spatial scaling is incorporated in a modified form of the Bogoliubov plasma cluster expansion; then this proposed reformulation of the plasma weak-coupling approximation is used to derive, from the BBGKY Hierarchy, a decoupled set of equations for the one-and two-particle distribution functions in the limit as the plasma parameter goes to zero. Because the reformulated cluster expansion permits retention of essential two-particle collisional information in the limiting equations, while simultaneously retaining the well-established Debye-scale relative ordering of the correlation functions, decoupling of the Hierarchy is accomplished without introduction of the divergence problems encountered in the Bogoliubov theory, as is indicated by an exact solution of the limiting equations for the equilibrium case. To establish additional links with existing plasma equilibrium theories, the two-particle equilibrium correlation function is used to calculate the interaction energy and the equation of state. The limiting equation for the equilibrium three-particle correlation function is then developed, and a formal solution is obtained.

Calculation of momentum distribution function of a non-thermal fermionic dark matter

Energy Technology Data Exchange (ETDEWEB)

Biswas, Anirban; Gupta, Aritra, E-mail: anirbanbiswas@hri.res.in, E-mail: aritra@hri.res.in [Harish-Chandra Research Institute, Chhatnag Road, Jhunsi, Allahabad 211 019 (India)

2017-03-01

The most widely studied scenario in dark matter phenomenology is the thermal WIMP scenario. Inspite of numerous efforts to detect WIMP, till now we have no direct evidence for it. A possible explanation for this non-observation of dark matter could be because of its very feeble interaction strength and hence, failing to thermalise with the rest of the cosmic soup. In other words, the dark matter might be of non-thermal origin where the relic density is obtained by the so-called freeze-in mechanism. Furthermore, if this non-thermal dark matter is itself produced substantially from the decay of another non-thermal mother particle, then their distribution functions may differ in both size and shape from the usual equilibrium distribution function. In this work, we have studied such a non-thermal (fermionic) dark matter scenario in the light of a new type of U(1){sub B−L} model. The U(1){sub B−L} model is interesting, since, besides being anomaly free, it can give rise to neutrino mass by Type II see-saw mechanism. Moreover, as we will show, it can accommodate a non-thermal fermionic dark matter as well. Starting from the collision terms, we have calculated the momentum distribution function for the dark matter by solving a coupled system of Boltzmann equations. We then used it to calculate the final relic abundance, as well as other relevant physical quantities. We have also compared our result with that obtained from solving the usual Boltzmann (or rate) equations directly in terms of comoving number density, Y . Our findings suggest that the latter approximation is valid only in cases where the system under study is close to equilibrium, and hence should be used with caution.

Identifying apparent local stable isotope equilibrium in a complex non-equilibrium system.

Science.gov (United States)

He, Yuyang; Cao, Xiaobin; Wang, Jianwei; Bao, Huiming

2018-02-28

Although being out of equilibrium, biomolecules in organisms have the potential to approach isotope equilibrium locally because enzymatic reactions are intrinsically reversible. A rigorous approach that can describe isotope distribution among biomolecules and their apparent deviation from equilibrium state is lacking, however. Applying the concept of distance matrix in graph theory, we propose that apparent local isotope equilibrium among a subset of biomolecules can be assessed using an apparent fractionation difference (|Δα|) matrix, in which the differences between the observed isotope composition (δ') and the calculated equilibrium fractionation factor (1000lnβ) can be more rigorously evaluated than by using a previous approach for multiple biomolecules. We tested our |Δα| matrix approach by re-analyzing published data of different amino acids (AAs) in potato and in green alga. Our re-analysis shows that biosynthesis pathways could be the reason for an apparently close-to-equilibrium relationship inside AA families in potato leaves. Different biosynthesis/degradation pathways in tubers may have led to the observed isotope distribution difference between potato leaves and tubers. The analysis of data from green algae does not support the conclusion that AAs are further from equilibrium in glucose-cultured green algae than in the autotrophic ones. Application of the |Δα| matrix can help us to locate potential reversible reactions or reaction networks in a complex system such as a metabolic system. The same approach can be broadly applied to all complex systems that have multiple components, e.g. geochemical or atmospheric systems of early Earth or other planets. Copyright © 2017 John Wiley & Sons, Ltd.

Module description of TOKAMAK equilibrium code MEUDAS

Energy Technology Data Exchange (ETDEWEB)

Suzuki, Masaei; Hayashi, Nobuhiko; Matsumoto, Taro; Ozeki, Takahisa [Japan Atomic Energy Research Inst., Naka, Ibaraki (Japan). Naka Fusion Research Establishment

2002-01-01

The analysis of an axisymmetric MHD equilibrium serves as a foundation of TOKAMAK researches, such as a design of devices and theoretical research, the analysis of experiment result. For this reason, also in JAERI, an efficient MHD analysis code has been developed from start of TOKAMAK research. The free boundary equilibrium code ''MEUDAS'' which uses both the DCR method (Double-Cyclic-Reduction Method) and a Green's function can specify the pressure and the current distribution arbitrarily, and has been applied to the analysis of a broad physical subject as a code having rapidity and high precision. Also the MHD convergence calculation technique in ''MEUDAS'' has been built into various newly developed codes. This report explains in detail each module in ''MEUDAS'' for performing convergence calculation in solving the MHD equilibrium. (author)

Equilibrium and stochastic resonance in finite chains of noisy bistable elements

International Nuclear Information System (INIS)

Morillo, Manuel; Gomez-Ordonez, Jose; Casado, Jose Manuel

2010-01-01

Graphical abstract: We analyze the dependence of the equilibrium distribution of a collective variable of a chain on relevant parameters including the chain size and its connectivity. We also analyze the stochastic resonance effect of the same variable. - Abstract: Using numerical simulations, we analyze equilibrium properties of finite chains of coupled noisy bistable units and their response to weak time periodic forces. Finite chains with global as well as local (nearest neighbors) coupling are considered. We focus on the study of a collective variable defined as the arithmetic mean of the variables characterizing each element of the chain. By contrast with the case of infinite size chains, where the coexistence of several equilibrium distributions for the same values of parameters is possible, for finite chains just a single equilibrium distribution exists for given values of the parameters. We demonstrate that, regardless of the chain connectivity, there exist transition lines separating regions in parameter space where the equilibrium distribution function is either monomodal or multimodal. The location of the transition line depends on the chain connectivity and the size of the system. For driven chains, the response of the system shows stochastic resonant effects. For the two types of chains considered, both the power spectral amplification and the signal-to-noise ratio of the collective variable are analyzed as the noise strength, the coupling parameter and the number of bistable units in the system are varied. Compared with the effects observed in single unit systems, the collective variable shows a strong enhancement of the stochastic resonance effects.

Non-equilibrium coupling of protein structure and function to translation-elongation kinetics.

Science.gov (United States)

Sharma, Ajeet K; O'Brien, Edward P

2018-04-01

Protein folding research has been dominated by the assumption that thermodynamics determines protein structure and function. And that when the folding process is compromised in vivo the proteostasis machinery-chaperones, deaggregases, the proteasome-work to restore proteins to their soluble, functional form or degrade them to maintain the cellular pool of proteins in a quasi-equilibrium state. During the past decade, however, more and more proteins have been identified for which altering only their speed of synthesis alters their structure and function, the efficiency of the down-stream processes they take part in, and cellular phenotype. Indeed, evidence has emerged that evolutionary selection pressures have encoded translation-rate information into mRNA molecules to coordinate diverse co-translational processes. Thus, non-equilibrium physics can play a fundamental role in influencing nascent protein behavior, mRNA sequence evolution, and disease. Here, we discuss how our understanding of this phenomenon is being advanced by the application of theoretical tools from the physical sciences. Copyright © 2018 Elsevier Ltd. All rights reserved.

Non-equilibrium thermodynamics and energy distribution function of neutron gas in constant power reactor under coupling of neutrons and medium

International Nuclear Information System (INIS)

Hayasaka, Hideo

1983-01-01

The thermodynamics and the energy distribution function of the neutron gas in a constant power reactor are considered, taking into account the burn-up of fuel. To separate the secular motion of neutrons owing to fuel burn-up and the microscopic fluctuations of neutrons around this motion, a long time of the order of several months is divided into m equal intervals, and the respective states corresponding to m small time intervals are treated as quasi-stationary states. The local energy distribution function of the neutron gas in the quasi-stationary state is given by a generalized Boltzmann distribution specified by the respective generalized activity coefficient for each subsystem. The effects of fuel burn-up on the respective distribution functions for successive small time intervals are taken into account through various quantities relating to reactor physics, depending upon the fuel burn-up, by successive approximation. (author)

Thermodynamic chemical energy transfer mechanisms of non-equilibrium, quasi-equilibrium, and equilibrium chemical reactions

International Nuclear Information System (INIS)

Roh, Heui-Seol

2015-01-01

Chemical energy transfer mechanisms at finite temperature are explored by a chemical energy transfer theory which is capable of investigating various chemical mechanisms of non-equilibrium, quasi-equilibrium, and equilibrium. Gibbs energy fluxes are obtained as a function of chemical potential, time, and displacement. Diffusion, convection, internal convection, and internal equilibrium chemical energy fluxes are demonstrated. The theory reveals that there are chemical energy flux gaps and broken discrete symmetries at the activation chemical potential, time, and displacement. The statistical, thermodynamic theory is the unification of diffusion and internal convection chemical reactions which reduces to the non-equilibrium generalization beyond the quasi-equilibrium theories of migration and diffusion processes. The relationship between kinetic theories of chemical and electrochemical reactions is also explored. The theory is applied to explore non-equilibrium chemical reactions as an illustration. Three variable separation constants indicate particle number constants and play key roles in describing the distinct chemical reaction mechanisms. The kinetics of chemical energy transfer accounts for the four control mechanisms of chemical reactions such as activation, concentration, transition, and film chemical reactions. - Highlights: • Chemical energy transfer theory is proposed for non-, quasi-, and equilibrium. • Gibbs energy fluxes are expressed by chemical potential, time, and displacement. • Relationship between chemical and electrochemical reactions is discussed. • Theory is applied to explore nonequilibrium energy transfer in chemical reactions. • Kinetics of non-equilibrium chemical reactions shows the four control mechanisms

The geometry of finite equilibrium sets

DEFF Research Database (Denmark)

Balasko, Yves; Tvede, Mich

2009-01-01

We investigate the geometry of finite datasets defined by equilibrium prices, income distributions, and total resources. We show that the equilibrium condition imposes no restrictions if total resources are collinear, a property that is robust to small perturbations. We also show that the set...... of equilibrium datasets is pathconnected when the equilibrium condition does impose restrictions on datasets, as for example when total resources are widely noncollinear....

Distributional impacts of carbon pricing: A general equilibrium approach with micro-data for households

International Nuclear Information System (INIS)

Rausch, Sebastian; Metcalf, Gilbert E.; Reilly, John M.

2011-01-01

Many policies to limit greenhouse gas emissions have at their core efforts to put a price on carbon emissions. Carbon pricing impacts households both by raising the cost of carbon intensive products and by changing factor prices. A complete analysis requires taking both effects into account. The impact of carbon pricing is determined by heterogeneity in household spending patterns across income groups as well as heterogeneity in factor income patterns across income groups. It is also affected by precise formulation of the policy (how is the revenue from carbon pricing distributed) as well as the treatment of other government policies (e.g. the treatment of transfer payments). What is often neglected in analyses of policy is the heterogeneity of impacts across households even within income or regional groups. In this paper, we incorporate 15,588 households from the U.S. Consumer and Expenditure Survey data as individual agents in a comparative-static general equilibrium framework. These households are represented within the MIT USREP model, a detailed general equilibrium model of the U.S. economy. In particular, we categorize households by full household income (factor income as well as transfer income) and apply various measures of lifetime income to distinguish households that are temporarily low-income (e.g., retired households drawing down their financial assets) from permanently low-income households. We also provide detailed within-group distributional measures of burden impacts from various policy scenarios. - Highlights: → We develop a simulation model with 15,588 households to study the distributional impacts of carbon pricing in the US. → Sources side impacts have typically been ignored in the literature biasing studies towards finding carbon pricing to be regressive. → Our general equilibrium framework allows us to capture uses and sources side impacts from carbon pricing. → We find that variation in impacts within broad socioeconomic groups may

Nanoscale Correlated Disorder in Out-of-Equilibrium Myelin Ultrastructure.

Science.gov (United States)

Campi, Gaetano; Di Gioacchino, Michael; Poccia, Nicola; Ricci, Alessandro; Burghammer, Manfred; Ciasca, Gabriele; Bianconi, Antonio

2018-01-23

Ultrastructural fluctuations at nanoscale are fundamental to assess properties and functionalities of advanced out-of-equilibrium materials. We have taken myelin as a model of supramolecular assembly in out-of-equilibrium living matter. Myelin sheath is a simple stable multilamellar structure of high relevance and impact in biomedicine. Although it is known that myelin has a quasi-crystalline ultrastructure, there is no information on its fluctuations at nanoscale in different states due to limitations of the available standard techniques. To overcome these limitations, we have used scanning micro X-ray diffraction, which is a unique non-invasive probe of both reciprocal and real space to visualize statistical fluctuations of myelin order of the sciatic nerve of Xenopus laevis. The results show that the ultrastructure period of the myelin is stabilized by large anticorrelated fluctuations at nanoscale, between hydrophobic and hydrophilic layers. The ratio between the total thickness of hydrophilic and hydrophobic layers defines the conformational parameter, which describes the different states of myelin. Our key result is that myelin in its out-of-equilibrium functional state fluctuates point-to-point between different conformations showing a correlated disorder described by a Levy distribution. As the system approaches the thermodynamic equilibrium in an aged state, the disorder loses its correlation degree and the structural fluctuation distribution changes to Gaussian. In a denatured state at low pH, it changes to a completely disordered stage. Our results aim to clarify the degradation mechanism in biological systems by associating these states with ultrastructural dynamic fluctuations at nanoscale.

Random walk to a nonergodic equilibrium concept

Science.gov (United States)

Bel, G.; Barkai, E.

2006-01-01

Random walk models, such as the trap model, continuous time random walks, and comb models, exhibit weak ergodicity breaking, when the average waiting time is infinite. The open question is, what statistical mechanical theory replaces the canonical Boltzmann-Gibbs theory for such systems? In this paper a nonergodic equilibrium concept is investigated, for a continuous time random walk model in a potential field. In particular we show that in the nonergodic phase the distribution of the occupation time of the particle in a finite region of space approaches U- or W-shaped distributions related to the arcsine law. We show that when conditions of detailed balance are applied, these distributions depend on the partition function of the problem, thus establishing a relation between the nonergodic dynamics and canonical statistical mechanics. In the ergodic phase the distribution function of the occupation times approaches a δ function centered on the value predicted based on standard Boltzmann-Gibbs statistics. The relation of our work to single-molecule experiments is briefly discussed.

Decay of non-equilibrium polariton condensate in semiconductors

International Nuclear Information System (INIS)

Beloussov, I.V.; Shvera, Y.M.

1993-08-01

Excitation dynamics of polariton quantum fluctuations arising in direct-gap semi-conductor as a result of parametric decay of non-equilibrium polariton condensate with non-zero wave vector is studied. The predominant mechanism of polariton scattering is supposed to be exciton-exciton interaction. Steady state which corresponds to the case of dynamic equilibrium between the polariton condensate and quantum fluctuations is obtained. Distribution functions of non-condensate polaritons are localized in the resonant regions, corresponding to two-particle excitation of polaritons from the condensate. The spectrum of elementary excitations in steady state coincides with usual polariton energy with the shift proportional to initial density of polariton condensate. (author). 25 refs

Thermal equilibrium and statistical thermometers in special relativity.

Science.gov (United States)

Cubero, David; Casado-Pascual, Jesús; Dunkel, Jörn; Talkner, Peter; Hänggi, Peter

2007-10-26

There is an intense debate in the recent literature about the correct generalization of Maxwell's velocity distribution in special relativity. The most frequently discussed candidate distributions include the Jüttner function as well as modifications thereof. Here we report results from fully relativistic one-dimensional molecular dynamics simulations that resolve the ambiguity. The numerical evidence unequivocally favors the Jüttner distribution. Moreover, our simulations illustrate that the concept of "thermal equilibrium" extends naturally to special relativity only if a many-particle system is spatially confined. They make evident that "temperature" can be statistically defined and measured in an observer frame independent way.

The Geometry of Finite Equilibrium Datasets

DEFF Research Database (Denmark)

Balasko, Yves; Tvede, Mich

We investigate the geometry of finite datasets defined by equilibrium prices, income distributions, and total resources. We show that the equilibrium condition imposes no restrictions if total resources are collinear, a property that is robust to small perturbations. We also show that the set...... of equilibrium datasets is pathconnected when the equilibrium condition does impose restrictions on datasets, as for example when total resources are widely non collinear....

Unifying distribution functions: some lesser known distributions.

Science.gov (United States)

Moya-Cessa, J R; Moya-Cessa, H; Berriel-Valdos, L R; Aguilar-Loreto, O; Barberis-Blostein, P

2008-08-01

We show that there is a way to unify distribution functions that describe simultaneously a classical signal in space and (spatial) frequency and position and momentum for a quantum system. Probably the most well known of them is the Wigner distribution function. We show how to unify functions of the Cohen class, Rihaczek's complex energy function, and Husimi and Glauber-Sudarshan distribution functions. We do this by showing how they may be obtained from ordered forms of creation and annihilation operators and by obtaining them in terms of expectation values in different eigenbases.

A Strategic-Equilibrium Based

Directory of Open Access Journals (Sweden)

Gabriel J. Turbay

2011-03-01

Full Text Available The strategic equilibrium of an N-person cooperative game with transferable utility is a system composed of a cover collection of subsets of N and a set of extended imputations attainable through such equilibrium cover. The system describes a state of coalitional bargaining stability where every player has a bargaining alternative against any other player to support his corresponding equilibrium claim. Any coalition in the sable system may form and divide the characteristic value function of the coalition as prescribed by the equilibrium payoffs. If syndicates are allowed to form, a formed coalition may become a syndicate using the equilibrium payoffs as disagreement values in bargaining for a part of the complementary coalition incremental value to the grand coalition when formed. The emergent well known-constant sum derived game in partition function is described in terms of parameters that result from incumbent binding agreements. The strategic-equilibrium corresponding to the derived game gives an equal value claim to all players.  This surprising result is alternatively explained in terms of strategic-equilibrium based possible outcomes by a sequence of bargaining stages that when the binding agreements are in the right sequential order, von Neumann and Morgenstern (vN-M non-discriminatory solutions emerge. In these solutions a preferred branch by a sufficient number of players is identified: the weaker players syndicate against the stronger player. This condition is referred to as the stronger player paradox.  A strategic alternative available to the stronger players to overcome the anticipated not desirable results is to voluntarily lower his bargaining equilibrium claim. In doing the original strategic equilibrium is modified and vN-M discriminatory solutions may occur, but also a different stronger player may emerge that has eventually will have to lower his equilibrium claim. A sequence of such measures converges to the equal

Equilibrium theory of island biogeography: A review

Science.gov (United States)

Angela D. Yu; Simon A. Lei

2001-01-01

The topography, climatic pattern, location, and origin of islands generate unique patterns of species distribution. The equilibrium theory of island biogeography creates a general framework in which the study of taxon distribution and broad island trends may be conducted. Critical components of the equilibrium theory include the species-area relationship, island-...

Equilibrium beam distribution in an electron storage ring near linear synchrobetatron coupling resonances

Directory of Open Access Journals (Sweden)

Boaz Nash

2006-03-01

Full Text Available Linear dynamics in a storage ring can be described by the one-turn map matrix. In the case of a resonance where two of the eigenvalues of this matrix are degenerate, a coupling perturbation causes a mixing of the uncoupled eigenvectors. A perturbation formalism is developed to find eigenvalues and eigenvectors of the one-turn map near such a linear resonance. Damping and diffusion due to synchrotron radiation can be obtained by integrating their effects over one turn, and the coupled eigenvectors can be used to find the coupled damping and diffusion coefficients. Expressions for the coupled equilibrium emittances and beam distribution moments are then derived. In addition to the conventional instabilities at the sum, integer, and half-integer resonances, it is found that the coupling can cause an instability through antidamping near a sum resonance even when the symplectic dynamics are stable. As one application of this formalism, the case of linear synchrobetatron coupling is analyzed where the coupling is caused by dispersion in the rf cavity, or by a crab cavity. Explicit closed-form expressions for the sum/difference resonances are given along with the integer/half-integer resonances. The integer and half-integer resonances caused by coupling require particular care. We find an example of this with the case of a crab cavity for the integer resonance of the synchrotron tune. Whether or not there is an instability is determined by the value of the horizontal betatron tune, a unique feature of these coupling-caused integer or half-integer resonances. Finally, the coupled damping and diffusion coefficients along with the equilibrium invariants and projected emittances are plotted as a function of the betatron and synchrotron tunes for an example storage ring based on PEP-II.

Non-canonical distribution and non-equilibrium transport beyond weak system-bath coupling regime: A polaron transformation approach

Science.gov (United States)

Xu, Dazhi; Cao, Jianshu

2016-08-01

The concept of polaron, emerged from condense matter physics, describes the dynamical interaction of moving particle with its surrounding bosonic modes. This concept has been developed into a useful method to treat open quantum systems with a complete range of system-bath coupling strength. Especially, the polaron transformation approach shows its validity in the intermediate coupling regime, in which the Redfield equation or Fermi's golden rule will fail. In the polaron frame, the equilibrium distribution carried out by perturbative expansion presents a deviation from the canonical distribution, which is beyond the usual weak coupling assumption in thermodynamics. A polaron transformed Redfield equation (PTRE) not only reproduces the dissipative quantum dynamics but also provides an accurate and efficient way to calculate the non-equilibrium steady states. Applications of the PTRE approach to problems such as exciton diffusion, heat transport and light-harvesting energy transfer are presented.

Equilibrium and stability properties of relativistic electron rings and E-layers

International Nuclear Information System (INIS)

Uhm, H.

1976-01-01

Equilibrium and stability properties of magnetically confined partially-neutralized thin electron ring and E-layer are investigated using the Vlasov-Maxwell equations. The analysis is carried out within the context of the assumption that the minor dimensions (a,b) of the system are much less than the collisionless skin depth (c/antiω/sub p/). The equilibrium configuration of the E-layer is assumed to be an infinitely long, azimuthally symmetric hollow electron beam which is aligned parallel to a uniform axial magnetic field. On the other hand, the electron ring is located at the midplane of an externally imposed mirror field which acts to confine the ring both axially and radially. The equilibrium properties of the E-layer and electron ring are obtained self-consistently for several choices of equilibrium electron distribution function. The negative-mass instability analysis is carried out for the relativistic E-layer equilibrium in which all of the electrons have the same transverse energy and a spread in canonical angular momentum, assuming a fixed ion background. The ion resonance instability properties are investigated for a relativistic nonneutral E-layer aligned parallel to a uniform magnetic field and located between two ground coaxial cylindrical conductors. The stability properties of a nonrelativistic electron ring is investigated within the framework of the linearized Vlasov-Poisson equations. The dispersion relation is obtained for the self-consistent electron distribution function in which all electrons have the same value of energy an the same value of canonical angular momentum. The positive ions in the electron ring are assumed to form an immobile partially neutralizing background. The stability criteria as well as the instability growth rates are derived and discussed including the effect of geometrical configuration of the system. Equilibrium space-charge effects play a significant role in stability behavior

Lattice Boltzmann method with the cell-population equilibrium

International Nuclear Information System (INIS)

Zhou Xiaoyang; Cheng Bing; Shi Baochang

2008-01-01

The central problem of the lattice Boltzmann method (LBM) is to construct a discrete equilibrium. In this paper, a multi-speed 1D cell-model of Boltzmann equation is proposed, in which the cell-population equilibrium, a direct non-negative approximation to the continuous Maxwellian distribution, plays an important part. By applying the explicit one-order Chapman–Enskog distribution, the model reduces the transportation and collision, two basic evolution steps in LBM, to the transportation of the non-equilibrium distribution. Furthermore, 1D dam-break problem is performed and the numerical results agree well with the analytic solutions

The non-equilibrium Green's function method for nanoscale device simulation

CERN Document Server

Pourfath, Mahdi

2014-01-01

For modeling the transport of carriers in nanoscale devices, a Green-function formalism is the most accurate approach. Due to the complexity of the formalism, one should have a deep understanding of the underlying principles and use smart approximations and numerical methods for solving the kinetic equations at a reasonable computational time. In this book the required concepts from quantum and statistical mechanics and numerical methods for calculating Green functions are presented. The Green function is studied in detail for systems both under equilibrium and under nonequilibrium conditions. Because the formalism enables rigorous modeling of different scattering mechanisms in terms of self-energies, but an exact evaluation of self-energies for realistic systems is not possible, their approximation and inclusion in the quantum kinetic equations of the Green functions are elaborated. All the elements of the kinetic equations, which are the device Hamiltonian, contact self-energies, and scattering self-energie...

H TO Zn IONIZATION EQUILIBRIUM FOR THE NON-MAXWELLIAN ELECTRON κ-DISTRIBUTIONS: UPDATED CALCULATIONS

International Nuclear Information System (INIS)

Dzifčáková, E.; Dudík, J.

2013-01-01

New data for the calculation of ionization and recombination rates have been published in the past few years, most of which are included in the CHIANTI database. We used these data to calculate collisional ionization and recombination rates for the non-Maxwellian κ-distributions with an enhanced number of particles in the high-energy tail, which have been detected in the solar transition region and the solar wind. Ionization equilibria for elements H to Zn are derived. The κ-distributions significantly influence both the ionization and recombination rates and widen the ion abundance peaks. In comparison with the Maxwellian distribution, the ion abundance peaks can also be shifted to lower or higher temperatures. The updated ionization equilibrium calculations result in large changes for several ions, notably Fe VIII-Fe XIV. The results are supplied in electronic form compatible with the CHIANTI database.

A new algorithm to compute conjectured supply function equilibrium in electricity markets

International Nuclear Information System (INIS)

Diaz, Cristian A.; Villar, Jose; Campos, Fco Alberto; Rodriguez, M. Angel

2011-01-01

Several types of market equilibria approaches, such as Cournot, Conjectural Variation (CVE), Supply Function (SFE) or Conjectured Supply Function (CSFE) have been used to model electricity markets for the medium and long term. Among them, CSFE has been proposed as a generalization of the classic Cournot. It computes the equilibrium considering the reaction of the competitors against changes in their strategy, combining several characteristics of both CVE and SFE. Unlike linear SFE approaches, strategies are linearized only at the equilibrium point, using their first-order Taylor approximation. But to solve CSFE, the slope or the intercept of the linear approximations must be given, which has been proved to be very restrictive. This paper proposes a new algorithm to compute CSFE. Unlike previous approaches, the main contribution is that the competitors' strategies for each generator are initially unknown (both slope and intercept) and endogenously computed by this new iterative algorithm. To show the applicability of the proposed approach, it has been applied to several case examples where its qualitative behavior has been analyzed in detail. (author)

Equilibrium and non-equilibrium controls on the abundances of clumped isotopologues of methane during thermogenic formation in laboratory experiments: Implications for the chemistry of pyrolysis and the origins of natural gases

Science.gov (United States)

Shuai, Yanhua; Douglas, Peter M. J.; Zhang, Shuichang; Stolper, Daniel A.; Ellis, Geoffrey S.; Lawson, Michael; Lewan, Michael D.; Formolo, Michael; Mi, Jingkui; He, Kun; Hu, Guoyi; Eiler, John M.

2018-02-01

Multiply isotopically substituted molecules ('clumped' isotopologues) can be used as geothermometers because their proportions at isotopic equilibrium relative to a random distribution of isotopes amongst all isotopologues are functions of temperature. This has allowed measurements of clumped-isotope abundances to be used to constrain formation temperatures of several natural materials. However, kinetic processes during generation, modification, or transport of natural materials can also affect their clumped-isotope compositions. Herein, we show that methane generated experimentally by closed-system hydrous pyrolysis of shale or nonhydrous pyrolysis of coal yields clumped-isotope compositions consistent with an equilibrium distribution of isotopologues under some experimental conditions (temperature-time conditions corresponding to 'low,' 'mature,' and 'over-mature' stages of catagenesis), but can have non-equilibrium (i.e., kinetically controlled) distributions under other experimental conditions ('high' to 'over-mature' stages), particularly for pyrolysis of coal. Non-equilibrium compositions, when present, lead the measured proportions of clumped species to be lower than expected for equilibrium at the experimental temperature, and in some cases to be lower than a random distribution of isotopes (i.e., negative Δ18 values). We propose that the consistency with equilibrium for methane formed by relatively low temperature pyrolysis reflects local reversibility of isotope exchange reactions involving a reactant or transition state species during demethylation of one or more components of kerogen. Non-equilibrium clumped-isotope compositions occur under conditions where 'secondary' cracking of retained oil in shale or wet gas hydrocarbons (C2-5, especially ethane) in coal is prominent. We suggest these non-equilibrium isotopic compositions are the result of the expression of kinetic isotope effects during the irreversible generation of methane from an alkyl

Improvements on non-equilibrium and transport Green function techniques: The next-generation TRANSIESTA

OpenAIRE

Papior, Nick Rübner; Lorente, Nicolás; Frederiksen, Thomas; García, Alberto; Brandbyge, Mads

2017-01-01

We present novel methods implemented within the non-equilibrium Green function code (NEGF) TRANSIESTA based on density functional theory (DFT). Our flexible, next-generation DFT–NEGF code handles devices with one or multiple electrodes (Ne≥1) with individual chemical potentials and electronic temperatures. We describe its novel methods for electrostatic gating, contour optimizations, and assertion of charge conservation, as well as the newly implemented algorithms for optimized and scalable m...

Approach to transverse equilibrium in axial channeling

International Nuclear Information System (INIS)

Fearick, R.W.

2000-01-01

Analytical treatments of channeling rely on the assumption of equilibrium on the transverse energy shell. The approach to equilibrium, and the nature of the equilibrium achieved, is examined using solutions of the equations of motion in the continuum multi-string model. The results show that the motion is chaotic in the absence of dissipative processes, and a complicated structure develops in phase space which prevent the development of the simple equilibrium usually assumed. The role of multiple scattering in smoothing out the equilibrium distribution is investigated

Equilibrium states for a plane incompressible perfect fluid

Energy Technology Data Exchange (ETDEWEB)

Boldrighini, C; Frigio, S [Camerino Univ. (Italy). Istituto di Matematica

1980-01-01

We associate to the plane incompressible Euler equation with periodic conditions the corresponding Hopf equation, as an equation for measures on the space of solenoidal distributions. We define equilibrium states as the solutions of the stationary Hopf equation. We find a class of equilibrium states which corresponds to a class of infinitely divisible distributions, and investigate the properties of gaussian and poissonian states. Equilibrium dynamics for a class of poissonian states is constructed by means of the Onsager vortex equations.

A Novel Derivation of the Time Evolution of the Entropy for Macroscopic Systems in Thermal Non-Equilibrium

Directory of Open Access Journals (Sweden)

Enrico Sciubba

2017-11-01

Full Text Available The paper discusses how the two thermodynamic properties, energy (U and exergy (E, can be used to solve the problem of quantifying the entropy of non-equilibrium systems. Both energy and exergy are a priori concepts, and their formal dependence on thermodynamic state variables at equilibrium is known. Exploiting the results of a previous study, we first calculate the non-equilibrium exergy En-eq can be calculated for an arbitrary temperature distributions across a macroscopic body with an accuracy that depends only on the available information about the initial distribution: the analytical results confirm that En-eq exponentially relaxes to its equilibrium value. Using the Gyftopoulos-Beretta formalism, a non-equilibrium entropy Sn-eq(x,t is then derived from En-eq(x,t and U(x,t. It is finally shown that the non-equilibrium entropy generation between two states is always larger than its equilibrium (herein referred to as “classical” counterpart. We conclude that every iso-energetic non-equilibrium state corresponds to an infinite set of non-equivalent states that can be ranked in terms of increasing entropy. Therefore, each point of the Gibbs plane corresponds therefore to a set of possible initial distributions: the non-equilibrium entropy is a multi-valued function that depends on the initial mass and energy distribution within the body. Though the concept cannot be directly extended to microscopic systems, it is argued that the present formulation is compatible with a possible reinterpretation of the existing non-equilibrium formulations, namely those of Tsallis and Grmela, and answers at least in part one of the objections set forth by Lieb and Yngvason. A systematic application of this paradigm is very convenient from a theoretical point of view and may be beneficial for meaningful future applications in the fields of nano-engineering and biological sciences.

Noncompact Equilibrium Points and Applications

Directory of Open Access Journals (Sweden)

Zahra Al-Rumaih

2012-01-01

Full Text Available We prove an equilibrium existence result for vector functions defined on noncompact domain and we give some applications in optimization and Nash equilibrium in noncooperative game.

Progress in Non-equilibrium Green's Functions (PNGF VI)

International Nuclear Information System (INIS)

2016-01-01

The sixth interdisciplinary conference 'Progress in Non-equilibrium Green's Functions' (PNGF6) took place at Lund University, Sweden, on 17-21 August 2015. The conference was attended by 60 scientists, from Europe and overseas, sharing an interest in Green's function methods and/or non-equilibrium phenomena. At the conference, 34 invited and contributed talks were given, together with a poster session with 17 contributions. As its predecessors (Rostock 1999, Dresden 2002, Kiel 2005, Glasgow 2009, Jyväskylä 2012) did, the conference succeeded in gathering different communities for the exchange of recent developments and results. Among the topics of the conference, we mention approaches for strongly correlated systems, improvements of existing perturbative many-body schemes, electron-phonon/-photon interactions in time-dependent treatments, numerical scalability of NEGF approaches, connections with other non-equilibrium methods and concrete physical applications. For the latter, we mention quantum transport, semiconductor kinetics, multiply excited states in atoms and ions, nuclear reactions, high energy physics, quantum cascade lasers, strongly correlated model systems, graphene-nanostructures, optoelectronics, superconductors, spin-dynamics, photovoltaics, excitations in atoms and ions and time-resolved spectroscopy. The present volume contains 20 articles from participants of PNGF6, devoted to these topics. Compared to previous conferences, a completely novel and successful aspect of PNGF6 was the participation of experimentalists among the invited speakers, to establish a connection between emerging experimental techniques (for example, time-dependent spectroscopies) and the theoretical NEGF community. As at the previous PNGF conferences, the atmosphere was friendly and exciting at the same time, favoring vivid and stimulating discussions among experienced scientists, young researchers and students. The conference would not have been

The out of equilibrium response function in sub-diffusive systems

International Nuclear Information System (INIS)

Gradenigo, G; Puglisi, A; Sarracino, A; Vulpiani, A; Villamaina, D

2012-01-01

We study the Einstein relation between spontaneous fluctuations and the response to an external perturbation for the comb model and the single file, which are examples of systems with sub-diffusive transport properties. The relevance of nonequilibrium conditions is investigated: when a stationary current (in the form of a drift or an energy flux) is present, the Einstein relation breaks down. In the case of the comb model, a general relation - appearing in the recent literature - between the response function and an unperturbed suitable correlation function allows us to explain the obtained results. This suggests that the relevant ingredient in breaking the Einstein formula, for stationary regimes, is not anomalous diffusion but the presence of currents driving the system out of equilibrium.

dftools: Distribution function fitting

Science.gov (United States)

Obreschkow, Danail

2018-05-01

dftools, written in R, finds the most likely P parameters of a D-dimensional distribution function (DF) generating N objects, where each object is specified by D observables with measurement uncertainties. For instance, if the objects are galaxies, it can fit a mass function (D=1), a mass-size distribution (D=2) or the mass-spin-morphology distribution (D=3). Unlike most common fitting approaches, this method accurately accounts for measurement in uncertainties and complex selection functions.

Electron energy distribution function control in gas discharge plasmas

International Nuclear Information System (INIS)

Godyak, V. A.

2013-01-01

The formation of the electron energy distribution function (EEDF) and electron temperature in low temperature gas discharge plasmas is analyzed in frames of local and non-local electron kinetics. It is shown, that contrary to the local case, typical for plasma in uniform electric field, there is the possibility for EEDF modification, at the condition of non-local electron kinetics in strongly non-uniform electric fields. Such conditions “naturally” occur in some self-organized steady state dc and rf discharge plasmas, and they suggest the variety of artificial methods for EEDF modification. EEDF modification and electron temperature control in non-equilibrium conditions occurring naturally and those stimulated by different kinds of plasma disturbances are illustrated with numerous experiments. The necessary conditions for EEDF modification in gas discharge plasmas are formulated

Analysis of the trend to equilibrium of a chemically reacting system

International Nuclear Information System (INIS)

Kremer, Gilberto M; Bianchi, Miriam Pandolfi; Soares, Ana Jacinta

2007-01-01

In this present paper, a quaternary gaseous reactive mixture, for which the chemical reaction is close to its final stage and the elastic and reactive frequencies are comparable, is modelled within the Boltzmann equation extended to reacting gases. The main objective is a detailed analysis of the non-equilibrium effects arising in the reactive system A 1 + A 2 ↔ A 3 + A 4 , in a flow regime which is considered not far away from thermal, mechanical and chemical equilibrium. A first-order perturbation solution technique is applied to the macroscopic field equations for the spatially homogeneous gas system, and the trend to equilibrium is studied in detail. Adopting elastic hard-spheres and reactive line-of-centres cross sections and an appropriate choice of the input distribution functions-which allows us to distinguish the two cases where the constituents are either at same or different temperatures-explicit computations of the linearized production terms for mass, momentum and total energy are performed for each gas species. The departures from the equilibrium states of densities, temperatures and diffusion fluxes are characterized by small perturbations of their corresponding equilibrium values. For the hydrogen-chlorine system, the perturbations are plotted as functions of time for both cases where the species are either at the same or different temperatures. Moreover, the trend to equilibrium of the reaction rates is represented for the forward and backward reaction H 2 + Cl ↔ HCl + H

Exciton correlations and input–output relations in non-equilibrium exciton superfluids

International Nuclear Information System (INIS)

Ye, Jinwu; Sun, Fadi; Yu, Yi-Xiang; Liu, Wuming

2013-01-01

The photoluminescence (PL) measurements on photons and the transport measurements on excitons are the two types of independent and complementary detection tools to search for possible exciton superfluids in electron–hole semi-conductor bilayer systems. In fact, it was believed that the transport measurements can provide more direct evidences on superfluids than the spectroscopic measurements. It is important to establish the relations between the two kinds of measurements. In this paper, using quantum Heisenberg–Langevin equations, we establish such a connection by calculating various exciton correlation functions in the putative exciton superfluids. These correlation functions include both normal and anomalous greater, lesser, advanced, retarded, and time-ordered exciton Green functions and also various two exciton correlation functions. We also evaluate the corresponding normal and anomalous spectral weights and the Keldysh distribution functions. We stress the violations of the fluctuation and dissipation theorem among these various exciton correlation functions in the non-equilibrium exciton superfluids. We also explore the input–output relations between various exciton correlation functions and those of emitted photons such as the angle resolved photon power spectrum, phase sensitive two mode squeezing spectrum and two photon correlations. Applications to possible superfluids in the exciton–polariton systems are also mentioned. For a comparison, using conventional imaginary time formalism, we also calculate all the exciton correlation functions in an equilibrium dissipative exciton superfluid in the electron–electron coupled semi-conductor bilayers at the quantum Hall regime at the total filling factor ν T =1. We stress the analogies and also important differences between the correlations functions in the two exciton superfluid systems. - Highlights: ► Establish the relations between photoluminescence and transport measurements. ► Stress the

Instability of quantum equilibrium in Bohm's dynamics.

Science.gov (United States)

Colin, Samuel; Valentini, Antony

2014-11-08

We consider Bohm's second-order dynamics for arbitrary initial conditions in phase space. In principle, Bohm's dynamics allows for 'extended' non-equilibrium, with initial momenta not equal to the gradient of phase of the wave function (as well as initial positions whose distribution departs from the Born rule). We show that extended non-equilibrium does not relax in general and is in fact unstable. This is in sharp contrast with de Broglie's first-order dynamics, for which non-standard momenta are not allowed and which shows an efficient relaxation to the Born rule for positions. On this basis, we argue that, while de Broglie's dynamics is a tenable physical theory, Bohm's dynamics is not. In a world governed by Bohm's dynamics, there would be no reason to expect to see an effective quantum theory today (even approximately), in contradiction with observation.

Equilibrium Arrival Times to Queues

DEFF Research Database (Denmark)

Breinbjerg, Jesper; Østerdal, Lars Peter

We consider a non-cooperative queueing environment where a finite number of customers independently choose when to arrive at a queueing system that opens at a given point in time and serves customers on a last-come first-serve preemptive-resume (LCFS-PR) basis. Each customer has a service time...... requirement which is identically and independently distributed according to some general probability distribution, and they want to complete service as early as possible while minimizing the time spent in the queue. In this setting, we establish the existence of an arrival time strategy that constitutes...... a symmetric (mixed) Nash equilibrium, and show that there is at most one symmetric equilibrium. We provide a numerical method to compute this equilibrium and demonstrate by a numerical example that the social effciency can be lower than the effciency induced by a similar queueing system that serves customers...

Equilibrium and Kinetic Studies of Systems of Hydrogen Isotopes, Lithium Hydrides, Aluminum and LiAlO2

International Nuclear Information System (INIS)

Owen, J.H.

2001-01-01

This paper described measurements of (1) the distribution of tritium and helium throughout both phases of irradiated Li-Al alloy, (2) the migration rate of tritium during moderate heating, (3) equilibrium pressures as functions of temperature of H2, D2, or T2 in contact with lithium hydrides + aluminum, Li-Al alloy, or irradiated Li-Al alloy, (4) the equilibrium constant for the reaction as a function of temperature, and (5) extraction rates of tritium from irradiated LiAlO2 targets at elevated temperatures

General multi-group macroscopic modeling for thermo-chemical non-equilibrium gas mixtures

Energy Technology Data Exchange (ETDEWEB)

Liu, Yen, E-mail: yen.liu@nasa.gov; Vinokur, Marcel [NASA Ames Research Center, Moffett Field, California 94035 (United States); Panesi, Marco; Sahai, Amal [University of Illinois, Urbana-Champaign, Illinois 61801 (United States)

2015-04-07

This paper opens a new door to macroscopic modeling for thermal and chemical non-equilibrium. In a game-changing approach, we discard conventional theories and practices stemming from the separation of internal energy modes and the Landau-Teller relaxation equation. Instead, we solve the fundamental microscopic equations in their moment forms but seek only optimum representations for the microscopic state distribution function that provides converged and time accurate solutions for certain macroscopic quantities at all times. The modeling makes no ad hoc assumptions or simplifications at the microscopic level and includes all possible collisional and radiative processes; it therefore retains all non-equilibrium fluid physics. We formulate the thermal and chemical non-equilibrium macroscopic equations and rate coefficients in a coupled and unified fashion for gases undergoing completely general transitions. All collisional partners can have internal structures and can change their internal energy states after transitions. The model is based on the reconstruction of the state distribution function. The internal energy space is subdivided into multiple groups in order to better describe non-equilibrium state distributions. The logarithm of the distribution function in each group is expressed as a power series in internal energy based on the maximum entropy principle. The method of weighted residuals is applied to the microscopic equations to obtain macroscopic moment equations and rate coefficients succinctly to any order. The model’s accuracy depends only on the assumed expression of the state distribution function and the number of groups used and can be self-checked for accuracy and convergence. We show that the macroscopic internal energy transfer, similar to mass and momentum transfers, occurs through nonlinear collisional processes and is not a simple relaxation process described by, e.g., the Landau-Teller equation. Unlike the classical vibrational energy

General multi-group macroscopic modeling for thermo-chemical non-equilibrium gas mixtures

Science.gov (United States)

Liu, Yen; Panesi, Marco; Sahai, Amal; Vinokur, Marcel

2015-04-01

This paper opens a new door to macroscopic modeling for thermal and chemical non-equilibrium. In a game-changing approach, we discard conventional theories and practices stemming from the separation of internal energy modes and the Landau-Teller relaxation equation. Instead, we solve the fundamental microscopic equations in their moment forms but seek only optimum representations for the microscopic state distribution function that provides converged and time accurate solutions for certain macroscopic quantities at all times. The modeling makes no ad hoc assumptions or simplifications at the microscopic level and includes all possible collisional and radiative processes; it therefore retains all non-equilibrium fluid physics. We formulate the thermal and chemical non-equilibrium macroscopic equations and rate coefficients in a coupled and unified fashion for gases undergoing completely general transitions. All collisional partners can have internal structures and can change their internal energy states after transitions. The model is based on the reconstruction of the state distribution function. The internal energy space is subdivided into multiple groups in order to better describe non-equilibrium state distributions. The logarithm of the distribution function in each group is expressed as a power series in internal energy based on the maximum entropy principle. The method of weighted residuals is applied to the microscopic equations to obtain macroscopic moment equations and rate coefficients succinctly to any order. The model's accuracy depends only on the assumed expression of the state distribution function and the number of groups used and can be self-checked for accuracy and convergence. We show that the macroscopic internal energy transfer, similar to mass and momentum transfers, occurs through nonlinear collisional processes and is not a simple relaxation process described by, e.g., the Landau-Teller equation. Unlike the classical vibrational energy

General multi-group macroscopic modeling for thermo-chemical non-equilibrium gas mixtures.

Science.gov (United States)

Liu, Yen; Panesi, Marco; Sahai, Amal; Vinokur, Marcel

2015-04-07

This paper opens a new door to macroscopic modeling for thermal and chemical non-equilibrium. In a game-changing approach, we discard conventional theories and practices stemming from the separation of internal energy modes and the Landau-Teller relaxation equation. Instead, we solve the fundamental microscopic equations in their moment forms but seek only optimum representations for the microscopic state distribution function that provides converged and time accurate solutions for certain macroscopic quantities at all times. The modeling makes no ad hoc assumptions or simplifications at the microscopic level and includes all possible collisional and radiative processes; it therefore retains all non-equilibrium fluid physics. We formulate the thermal and chemical non-equilibrium macroscopic equations and rate coefficients in a coupled and unified fashion for gases undergoing completely general transitions. All collisional partners can have internal structures and can change their internal energy states after transitions. The model is based on the reconstruction of the state distribution function. The internal energy space is subdivided into multiple groups in order to better describe non-equilibrium state distributions. The logarithm of the distribution function in each group is expressed as a power series in internal energy based on the maximum entropy principle. The method of weighted residuals is applied to the microscopic equations to obtain macroscopic moment equations and rate coefficients succinctly to any order. The model's accuracy depends only on the assumed expression of the state distribution function and the number of groups used and can be self-checked for accuracy and convergence. We show that the macroscopic internal energy transfer, similar to mass and momentum transfers, occurs through nonlinear collisional processes and is not a simple relaxation process described by, e.g., the Landau-Teller equation. Unlike the classical vibrational energy

General multi-group macroscopic modeling for thermo-chemical non-equilibrium gas mixtures

International Nuclear Information System (INIS)

Liu, Yen; Vinokur, Marcel; Panesi, Marco; Sahai, Amal

2015-01-01

This paper opens a new door to macroscopic modeling for thermal and chemical non-equilibrium. In a game-changing approach, we discard conventional theories and practices stemming from the separation of internal energy modes and the Landau-Teller relaxation equation. Instead, we solve the fundamental microscopic equations in their moment forms but seek only optimum representations for the microscopic state distribution function that provides converged and time accurate solutions for certain macroscopic quantities at all times. The modeling makes no ad hoc assumptions or simplifications at the microscopic level and includes all possible collisional and radiative processes; it therefore retains all non-equilibrium fluid physics. We formulate the thermal and chemical non-equilibrium macroscopic equations and rate coefficients in a coupled and unified fashion for gases undergoing completely general transitions. All collisional partners can have internal structures and can change their internal energy states after transitions. The model is based on the reconstruction of the state distribution function. The internal energy space is subdivided into multiple groups in order to better describe non-equilibrium state distributions. The logarithm of the distribution function in each group is expressed as a power series in internal energy based on the maximum entropy principle. The method of weighted residuals is applied to the microscopic equations to obtain macroscopic moment equations and rate coefficients succinctly to any order. The model’s accuracy depends only on the assumed expression of the state distribution function and the number of groups used and can be self-checked for accuracy and convergence. We show that the macroscopic internal energy transfer, similar to mass and momentum transfers, occurs through nonlinear collisional processes and is not a simple relaxation process described by, e.g., the Landau-Teller equation. Unlike the classical vibrational energy

Non-equilibrium versus equilibrium emission of complex fragments from hot nuclei

International Nuclear Information System (INIS)

Viola, V.E.; Kwiatkowski, K.; Yennello, S.; Fields, D.E.

1989-01-01

The relative contributions of equilibrium and non-equilibrium mechanisms for intermediate-mass fragment emission have been deduced for Z=3-14 fragments formed in 3 He- and 14 N-induced reactions on Ag and Au targets. Complete inclusive excitation function measurements have been performed for 3 He projectiles from E/A=67 to 1,200 MeV and for 14 N from E/A=20 to 50 MeV. The data are consistent with a picture in which equilibrated emission is important at the lowest energies, but with increasing bombarding energy the cross sections are increasingly dominated by non-equilibrium processes. Non-equilibrium emission is also shown to be favored for light fragments relative to heavy fragments. These results are supported by coincidence studies of intermediate-mass fragments tagged by linear momentum transfer measurements

Equilibrium and non-equilibrium controls on the abundances of clumped isotopologues of methane during thermogenic formation in laboratory experiments: Implications for the chemistry of pyrolysis and the origins of natural gases

Science.gov (United States)

Shuai, Yanhua; Douglas, Peter M.J.; Zhang, Shuichang; Stolper, Daniel A.; Ellis, Geoffrey S.; Lawson, Michael; Lewan, Michael; Formolo, Michael; Mi, Jingkui; He, Kun; Hu, Guoyi; Eiler, John M.

2018-01-01

Multiply isotopically substituted molecules (‘clumped’ isotopologues) can be used as geothermometers because their proportions at isotopic equilibrium relative to a random distribution of isotopes amongst all isotopologues are functions of temperature. This has allowed measurements of clumped-isotope abundances to be used to constrain formation temperatures of several natural materials. However, kinetic processes during generation, modification, or transport of natural materials can also affect their clumped-isotope compositions. Herein, we show that methane generated experimentally by closed-system hydrous pyrolysis of shale or nonhydrous pyrolysis of coal yields clumped-isotope compositions consistent with an equilibrium distribution of isotopologues under some experimental conditions (temperature–time conditions corresponding to ‘low,’ ‘mature,’ and ‘over-mature’ stages of catagenesis), but can have non-equilibrium (i.e., kinetically controlled) distributions under other experimental conditions (‘high’ to ‘over-mature’ stages), particularly for pyrolysis of coal. Non-equilibrium compositions, when present, lead the measured proportions of clumped species to be lower than expected for equilibrium at the experimental temperature, and in some cases to be lower than a random distribution of isotopes (i.e., negative Δ18 values). We propose that the consistency with equilibrium for methane formed by relatively low temperature pyrolysis reflects local reversibility of isotope exchange reactions involving a reactant or transition state species during demethylation of one or more components of kerogen. Non-equilibrium clumped-isotope compositions occur under conditions where ‘secondary’ cracking of retained oil in shale or wet gas hydrocarbons (C2-5, especially ethane) in coal is prominent. We suggest these non-equilibrium isotopic compositions are the result of the expression of kinetic isotope effects during the irreversible generation

Meat-based functional foods for dietary equilibrium omega-6/omega-3.

Science.gov (United States)

Reglero, Guillermo; Frial, Paloma; Cifuentes, Alejandro; García-Risco, Mónica R; Jaime, Laura; Marin, Francisco R; Palanca, Vicente; Ruiz-Rodríguez, Alejandro; Santoyo, Susana; Señoráns, Francisco J; Soler-Rivas, Cristina; Torres, Carlos; Ibañez, Elena

2008-10-01

Nutritionists encourage improving the diet by combining meat products with fish or other sea-related foods, in order to equilibrate the omega-6/omega-3 ratio. Strong scientific evidence supports the beneficial health effects of a balanced omega-6/omega-3 PUFA (poly unsaturated fatty acids) diets. In the present work, the scientific bases of new functional meat products with both a balanced omega-6/omega-3 ratio and a synergic combination of antioxidants are discussed. The aim is to contribute to the dietary equilibrium omega-6/omega-3 and to increase the antioxidant intake. Conventional meat products supplemented with a specific fatty acids and antioxidants combination led to functional foods with healthier nutritional parameters.

Statistical thermodynamics of equilibrium polymers at interfaces

NARCIS (Netherlands)

Gucht, van der J.; Besseling, N.A.M.

2002-01-01

The behavior of a solution of equilibrium polymers (or living polymers) at an interface is studied, using a Bethe-Guggenheim lattice model for molecules with orientation dependent interactions. The density profile of polymers and the chain length distribution are calculated. For equilibrium polymers

Distribution of trichloroethylene and selected aliphatic and aromatic hydrocarbons between ''weathered'' and ''unweathered'' fuel mixtures and groundwater: Equilibrium and kinetic considerations

International Nuclear Information System (INIS)

Doucette, W.J.; Dupont, R.R.

1995-01-01

The distribution of trichloroethylene and several aliphatic and aromatic fuel components between 46 weathered and 11 unweathered fuel mixtures and groundwater was investigated using a slow stirring method. The weathered fuel mixtures were obtained from several contaminated field sites. Both unlabeled and 14C-labeled test compounds were used in the distribution experiments. Analyses of the test compound concentrations over time was performed by gas chromatograph or liquid scintillation counting. The time required to reach equilibrium varied from about 24 to 72 hours. Generally, the greater the hydrophobicity of the test compounds the longer time that was required to reach equilibrium. It was also observed that the fuel/water distribution coefficients were generally larger for the weathered fuels than those measured for the unweathered fuels, in some cases by a factor of 100. The weathered fuel mixtures obtained from the field site were depleted of the more water soluble compounds over time and became significantly more enriched in long chain aliphatic hydrocarbons. The ability of several models to describe the observed distribution behavior was examined

Charge-changing processes of heavy ions in matter. Non-equilibrium charge state distribution of sulfur ions after carbon foil penetration

International Nuclear Information System (INIS)

Imai, Makoto; Shibata, Hiromi; Sataka, Masao; Sugai, Hiroyuki; Nishio, Katsuhisa; Sugiyama, Koji; Komaki, Ken-ichiro

2005-01-01

Charge state distributions of 2.0 MeV/u (64 MeV) sulfur ions of various initial charge states (6+, 10+, 11+, 13+) after passing through 0.9, 1.1, 1.5, 2.0, 3.0, 4.7, 6.9 and 10 μg/cm 2 carbon foils have been studied experimentally using the heavy ion spectrometer 'ENMA'. Measured charge state distributions do not flat off to establish equilibrium within the measured thickness, proving to be the first systematic measurement of non-equilibrium charge state distribution using solid target at this energy range. The mean charge states and their distribution widths almost saturate to 12.4 and 1.03, respectively, for all initial charge states examined. Calculation with ETACHA code, developed by Rozet et al. [Nucl. Instr. and Meth. B 107 (1996) 67], is employed, although the present impact energy is lower than the assumed energy region for this code. It was also confirmed that a certain portion of 16 O q+ (q=3, 4, 7) beam is included in 32 S q+ (q=6, 8, 14) beam provided from the Tandem Accelerator, which originates in the Negative Ion Source forming O 2 - . (author)

Equilibrium charge state distributions of high energy heavy ions

International Nuclear Information System (INIS)

Clark, R.B.; Grant, I.S.; King, R.; Eastham, D.A.; Joy, T.

1976-01-01

Equilibrium charge state fractions have been measured for N, O, Ne, S, Ar and Kr ions at 1.04 MeV/nucleon after passing through various stripping materials. Further data were obtained at higher energy for S ions (4.12 MeV/nucleon) and Ar ions (4.12 and 9.6 MeV/nucleon). The mean charge fractions can be fitted to universal curves for both solid and gaseous strippers. Measurements of the equilibrium fraction of krypton ions at 1.04 MeV/nucleon passing through heavy vapours have shown that a higher average charge state is obtained than for lighter gaseous strippers. (Auth.)

Is local equilibrium a useful concept in hadronic interactions

International Nuclear Information System (INIS)

Carruthers, P.

1984-01-01

Aspects of multiparticle production phenomena are reviewed, which bear on the existence of local equilibrium in all or part of a collision event. Several universal features of purely hadronic events, such as the p/sub perpendicular/ distribution of secondaries, the independence of multiplicities and multiplicity distributions on the quantum numbers of the colliding particles are easily interpreted by postulating the existence of local thermodynamic equilibrium for the dominant nondiffractive events. Except in the case of the multiplicity distribution, other interpretations often do not exist. Equilibration mechanisms which might establish local equilibrium are examined. We point out that several mechanisms besides the usual kinetic relaxation have not been seriously studied. These include collective instabilities, turbulence and chaos, which could be more effective in establishing equilibrium. Developments in the use of the hydrodynamic model are reviewed, with particular attention to the initial conditions appropriate to hadronic and nuclear collisions. We conclude that local equilibrium is indeed a useful concept but that much effort is needed to assess its accuracy and domain of applicability

Nuclear Statistical Equilibrium for compact stars: modelling the nuclear energy functional

International Nuclear Information System (INIS)

Aymard, Francois

2015-01-01

and beyond. At densities above two-three times saturation, other degrees of freedom are expected to appear, which potentially lead to other consistency problems but this issue will not be treated in this thesis. The thesis is divided into three parts. In part I, we present the Nuclear Statistical Equilibrium model based on the grand canonical statistics and non-relativistic Skyrme interactions. Results at β-equilibrium are shown and the importance of the clusters distribution as well as a realistic treatment for the free energy model is discussed. Part II investigates the functional behavior of the baryonic energy in the Wigner-Seitz cell within the Extended-Thomas-Fermi approximation. In particular, both bulk and surface in-medium effects are studied, and their dependence on cluster size and asymmetry as well as gas densities and asymmetry is investigated. A preliminary result of in-medium surface effects is presented within some approximations in the case of β-equilibrated matter. In part III, we develop approximations in order to obtain a reliable analytical expression of the mass formula, directly linked to the functional form and parameters of the Skyrme interaction. In this part, we mainly focus on nuclei in vacuum, and analyse the different binding energy components in terms of bulk and surface properties, as well as isovector and isoscalar properties. (author)

Modeling of the equilibrium of a tokamak plasma

International Nuclear Information System (INIS)

Grandgirard, V.

1999-12-01

The simulation and the control of a plasma discharge in a tokamak require an efficient and accurate solving of the equilibrium because this equilibrium needs to be calculated again every microsecond to simulate discharges that can last up to 1000 seconds. The purpose of this thesis is to propose numerical methods in order to calculate these equilibrium with acceptable computer time and memory size. Chapter 1 deals with hydrodynamics equation and sets up the problem. Chapter 2 gives a method to take into account the boundary conditions. Chapter 3 is dedicated to the optimization of the inversion of the system matrix. This matrix being quasi-symmetric, the Woodbury method combined with Cholesky method has been used. This direct method has been compared with 2 iterative methods: GMRES (generalized minimal residual) and BCG (bi-conjugate gradient). The 2 last chapters study the control of the plasma equilibrium, this work is presented in the formalism of the optimized control of distributed systems and leads to non-linear equations of state and quadratic functionals that are solved numerically by a quadratic sequential method. This method is based on the replacement of the initial problem with a series of control problems involving linear equations of state. (A.C.)

Dependence of equilibrium properties of channeled particles on transverse quasi temperature

International Nuclear Information System (INIS)

Kashlev, Yu.A.

2006-01-01

Quasi-equilibrium and kinetic characteristics of channeled particles are investigated by methods of nonequilibrium statistical thermodynamics. The equilibrium equation of the transverse energy of fast particles and the equilibrium equation of the transverse momentum of particles are derived. It is shown that equilibrium equations solution permits to obtain the expression for the transverse quasi-temperature of the channeled particle subsystem. The quasi-equilibrium angular distribution of particles after transmission through a thin monocrystal and the angular distribution at backscattering are studied. The evaluated data of the transverse quasi-temperature are presented for the case of iodine ion channeling through silver crystals [ru

Equilibrium prices supported by dual price functions in markets with non-convexities

International Nuclear Information System (INIS)

Bjoerndal, Mette; Joernsten, Kurt

2004-06-01

The issue of finding market clearing prices in markets with non-convexities has had a renewed interest due to the deregulation of the electricity sector. In the day-ahead electricity market, equilibrium prices are calculated based on bids from generators and consumers. In most of the existing markets, several generation technologies are present, some of which have considerable non-convexities, such as capacity limitations and large start up costs. In this paper we present equilibrium prices composed of a commodity price and an uplift charge. The prices are based on the generation of a separating valid inequality that supports the optimal resource allocation. In the case when the sub-problem generated as the integer variables are held fixed to their optimal values possess the integrality property, the generated prices are also supported by non-linear price-functions that are the basis for integer programming duality. (Author)

An entropy-variables-based formulation of residual distribution schemes for non-equilibrium flows

Science.gov (United States)

Garicano-Mena, Jesús; Lani, Andrea; Degrez, Gérard

2018-06-01

In this paper we present an extension of Residual Distribution techniques for the simulation of compressible flows in non-equilibrium conditions. The latter are modeled by means of a state-of-the-art multi-species and two-temperature model. An entropy-based variable transformation that symmetrizes the projected advective Jacobian for such a thermophysical model is introduced. Moreover, the transformed advection Jacobian matrix presents a block diagonal structure, with mass-species and electronic-vibrational energy being completely decoupled from the momentum and total energy sub-system. The advantageous structure of the transformed advective Jacobian can be exploited by contour-integration-based Residual Distribution techniques: established schemes that operate on dense matrices can be substituted by the same scheme operating on the momentum-energy subsystem matrix and repeated application of scalar scheme to the mass-species and electronic-vibrational energy terms. Finally, the performance gain of the symmetrizing-variables formulation is quantified on a selection of representative testcases, ranging from subsonic to hypersonic, in inviscid or viscous conditions.

Wigner distribution function and entropy of the damped harmonic oscillator within the theory of the open quantum systems

Science.gov (United States)

Isar, Aurelian

1995-01-01

The harmonic oscillator with dissipation is studied within the framework of the Lindblad theory for open quantum systems. By using the Wang-Uhlenbeck method, the Fokker-Planck equation, obtained from the master equation for the density operator, is solved for the Wigner distribution function, subject to either the Gaussian type or the delta-function type of initial conditions. The obtained Wigner functions are two-dimensional Gaussians with different widths. Then a closed expression for the density operator is extracted. The entropy of the system is subsequently calculated and its temporal behavior shows that this quantity relaxes to its equilibrium value.

Modeling fractal structure of city-size distributions using correlation functions.

Science.gov (United States)

Chen, Yanguang

2011-01-01

Zipf's law is one the most conspicuous empirical facts for cities, however, there is no convincing explanation for the scaling relation between rank and size and its scaling exponent. Using the idea from general fractals and scaling, I propose a dual competition hypothesis of city development to explain the value intervals and the special value, 1, of the power exponent. Zipf's law and Pareto's law can be mathematically transformed into one another, but represent different processes of urban evolution, respectively. Based on the Pareto distribution, a frequency correlation function can be constructed. By scaling analysis and multifractals spectrum, the parameter interval of Pareto exponent is derived as (0.5, 1]; Based on the Zipf distribution, a size correlation function can be built, and it is opposite to the first one. By the second correlation function and multifractals notion, the Pareto exponent interval is derived as [1, 2). Thus the process of urban evolution falls into two effects: one is the Pareto effect indicating city number increase (external complexity), and the other the Zipf effect indicating city size growth (internal complexity). Because of struggle of the two effects, the scaling exponent varies from 0.5 to 2; but if the two effects reach equilibrium with each other, the scaling exponent approaches 1. A series of mathematical experiments on hierarchical correlation are employed to verify the models and a conclusion can be drawn that if cities in a given region follow Zipf's law, the frequency and size correlations will follow the scaling law. This theory can be generalized to interpret the inverse power-law distributions in various fields of physical and social sciences.

Equilibrium and non equilibrium in fragmentation

International Nuclear Information System (INIS)

Dorso, C.O.; Chernomoretz, A.; Lopez, J.A.

2001-01-01

Full text: In this communication we present recent results regarding the interplay of equilibrium and non equilibrium in the process of fragmentation of excited finite Lennard Jones drops. Because the general features of such a potential resemble the ones of the nuclear interaction (fact that is reinforced by the similarity between the EOS of both systems) these studies are not only relevant from a fundamental point of view but also shed light on the problem of nuclear multifragmentation. We focus on the microscopic analysis of the state of the fragmenting system at fragmentation time. We show that the Caloric Curve (i e. the functional relationship between the temperature of the system and the excitation energy) is of the type rise plateau with no vapor branch. The usual rise plateau rise pattern is only recovered when equilibrium is artificially imposed. This result puts a serious question on the validity of the freeze out hypothesis. This feature is independent of the dimensionality or excitation mechanism. Moreover we explore the behavior of magnitudes which can help us determine the degree of the assumed phase transition. It is found that no clear cut criteria is presently available. (Author)

Light-induced electronic non-equilibrium in plasmonic particles.

Science.gov (United States)

Kornbluth, Mordechai; Nitzan, Abraham; Seideman, Tamar

2013-05-07

We consider the transient non-equilibrium electronic distribution that is created in a metal nanoparticle upon plasmon excitation. Following light absorption, the created plasmons decohere within a few femtoseconds, producing uncorrelated electron-hole pairs. The corresponding non-thermal electronic distribution evolves in response to the photo-exciting pulse and to subsequent relaxation processes. First, on the femtosecond timescale, the electronic subsystem relaxes to a Fermi-Dirac distribution characterized by an electronic temperature. Next, within picoseconds, thermalization with the underlying lattice phonons leads to a hot particle in internal equilibrium that subsequently equilibrates with the environment. Here we focus on the early stage of this multistep relaxation process, and on the properties of the ensuing non-equilibrium electronic distribution. We consider the form of this distribution as derived from the balance between the optical absorption and the subsequent relaxation processes, and discuss its implication for (a) heating of illuminated plasmonic particles, (b) the possibility to optically induce current in junctions, and (c) the prospect for experimental observation of such light-driven transport phenomena.

Gibbs equilibrium averages and Bogolyubov measure

International Nuclear Information System (INIS)

Sankovich, D.P.

2011-01-01

Application of the functional integration methods in equilibrium statistical mechanics of quantum Bose-systems is considered. We show that Gibbs equilibrium averages of Bose-operators can be represented as path integrals over a special Gauss measure defined in the corresponding space of continuous functions. We consider some problems related to integration with respect to this measure

Equilibrium phase-space distributions and space charge limits in linacs

International Nuclear Information System (INIS)

Lysenko, W.P.

1977-10-01

Limits on beam current and emittance in proton and heavy ion linear accelerators resulting from space charge forces are calculated. The method involves determining equilibrium distributions in phase space using a continuous focusing, no acceleration, model in two degrees of freedom using the coordinates r and z. A nonlinear Poisson equation must be solved numerically. This procedure is a matching between the longitudinal and transverse directions to minimize the effect of longitudinal-transverse coupling which is believed to be the main problem in emittance growth due to space charge in linacs. Limits on the Clinton P. Anderson Meson Physics Facility (LAMPF) accelerator performance are calculated as an example. The beam physics is described by a few space charge parameters so that accelerators with different physical parameters can be compared in a natural way. The main result of this parameter study is that the requirement of a high-intensity beam is best fulfilled with a low-frequency accelerator whereas the requirement of a high-brightness beam is best fulfilled with a high-frequency accelerator

Non-equilibrium dynamics from RPMD and CMD.

Science.gov (United States)

Welsch, Ralph; Song, Kai; Shi, Qiang; Althorpe, Stuart C; Miller, Thomas F

2016-11-28

We investigate the calculation of approximate non-equilibrium quantum time correlation functions (TCFs) using two popular path-integral-based molecular dynamics methods, ring-polymer molecular dynamics (RPMD) and centroid molecular dynamics (CMD). It is shown that for the cases of a sudden vertical excitation and an initial momentum impulse, both RPMD and CMD yield non-equilibrium TCFs for linear operators that are exact for high temperatures, in the t = 0 limit, and for harmonic potentials; the subset of these conditions that are preserved for non-equilibrium TCFs of non-linear operators is also discussed. Furthermore, it is shown that for these non-equilibrium initial conditions, both methods retain the connection to Matsubara dynamics that has previously been established for equilibrium initial conditions. Comparison of non-equilibrium TCFs from RPMD and CMD to Matsubara dynamics at short times reveals the orders in time to which the methods agree. Specifically, for the position-autocorrelation function associated with sudden vertical excitation, RPMD and CMD agree with Matsubara dynamics up to O(t 4 ) and O(t 1 ), respectively; for the position-autocorrelation function associated with an initial momentum impulse, RPMD and CMD agree with Matsubara dynamics up to O(t 5 ) and O(t 2 ), respectively. Numerical tests using model potentials for a wide range of non-equilibrium initial conditions show that RPMD and CMD yield non-equilibrium TCFs with an accuracy that is comparable to that for equilibrium TCFs. RPMD is also used to investigate excited-state proton transfer in a system-bath model, and it is compared to numerically exact calculations performed using a recently developed version of the Liouville space hierarchical equation of motion approach; again, similar accuracy is observed for non-equilibrium and equilibrium initial conditions.

Multi-period equilibrium/near-equilibrium in electricity markets based on locational marginal prices

Science.gov (United States)

Garcia Bertrand, Raquel

In this dissertation we propose an equilibrium procedure that coordinates the point of view of every market agent resulting in an equilibrium that simultaneously maximizes the independent objective of every market agent and satisfies network constraints. Therefore, the activities of the generating companies, consumers and an independent system operator are modeled: (1) The generating companies seek to maximize profits by specifying hourly step functions of productions and minimum selling prices, and bounds on productions. (2) The goals of the consumers are to maximize their economic utilities by specifying hourly step functions of demands and maximum buying prices, and bounds on demands. (3) The independent system operator then clears the market taking into account consistency conditions as well as capacity and line losses so as to achieve maximum social welfare. Then, we approach this equilibrium problem using complementarity theory in order to have the capability of imposing constraints on dual variables, i.e., on prices, such as minimum profit conditions for the generating units or maximum cost conditions for the consumers. In this way, given the form of the individual optimization problems, the Karush-Kuhn-Tucker conditions for the generating companies, the consumers and the independent system operator are both necessary and sufficient. The simultaneous solution to all these conditions constitutes a mixed linear complementarity problem. We include minimum profit constraints imposed by the units in the market equilibrium model. These constraints are added as additional constraints to the equivalent quadratic programming problem of the mixed linear complementarity problem previously described. For the sake of clarity, the proposed equilibrium or near-equilibrium is first developed for the particular case considering only one time period. Afterwards, we consider an equilibrium or near-equilibrium applied to a multi-period framework. This model embodies binary

Candidates Profile in FUVEST Exams from 2004 to 2013: Private and Public School Distribution, FUVEST Average Performance and Chemical Equilibrium Tasks Performance

Directory of Open Access Journals (Sweden)

R.S.A.P. Oliveira

2014-08-01

Full Text Available INTRODUCTION. Chemical equilibrium is recognized as a topic of several misconceptions. Its origins must be tracked from previous scholarship. Its impact on biochemistry learning is not fully described. A possible bulk of data is the FUVEST exam. OBJECTIVES: Identify students’ errors profile on chemical equilibrium tasks using public data from FUVEST exam. MATERIAL AND METHODS: Data analysis from FUVEST were: i Private and Public school distribution in Elementary and Middle School, and High School candidates of Pharmacy-Biochemistry course and total USP careers until the last call for enrollment (2004-2013; ii Average performance in 1st and 2nd parts of FUVEST exam of Pharmacy-Biochemistry, Chemistry, Engineering, Biological Sciences, Languages and Medicine courses and total enrolled candidates until 1st call for enrollment (2008- 2013; iii Performance of candidates of Pharmacy-Biochemistry, Chemistry, Engineering, Biological Sciences, Languages and Medicine courses and total USP careers in chemical equilibrium issues from 1st part of FUVEST (2011-2013. RESULTS AND DISCUSSION: i 66.2% of candidates came from private Elementary-Middle School courses and 71.8%, came from High School courses; ii Average grade over the period for 1st and 2nd FUVEST parts are respectively (in 100 points: Pharmacy-Biochemistry 66.7 and 61.2, Chemistry 65.9 and 58.9, Engineering 75.9 and 71.9, Biological Sciences 65.6 and 54.6, Languages 49.9 and 43.3, Medicine 83.5 and 79.5, total enrolled candidates 51,5 and 48.9; iii Four chemical equilibrium issues were found during 2011-2013 and the analysis of multiplechoice percentage distribution over the courses showed that there was a similar performance of students among them, except for Engineering and Medicine with higher grades, but the same proportional distribution among choices. CONCLUSION: Approved students came majorly from private schools. There was a different average performance among courses and similar on

Can elliptical galaxies be equilibrium systems

Energy Technology Data Exchange (ETDEWEB)

Caimmi, R [Padua Univ. (Italy). Ist. di Astronomia

1980-08-01

This paper deals with the question of whether elliptical galaxies can be considered as equilibrium systems (i.e., the gravitational + centrifugal potential is constant on the external surface). We find that equilibrium models such as Emden-Chandrasekhar polytropes and Roche polytropes with n = 0 can account for the main part of observations relative to the ratio of maximum rotational velocity to central velocity dispersion in elliptical systems. More complex models involving, for example, massive halos could lead to a more complete agreement. Models that are a good fit to the observed data are characterized by an inner component (where most of the mass is concentrated) and a low-density outer component. A comparison is performed between some theoretical density distributions and the density distribution observed by Young et al. (1978) in NGC 4473, but a number of limitations must be adopted. Alternative models, such as triaxial oblate non-equilibrium configurations with coaxial shells, involve a number of problems which are briefly discussed. We conclude that spheroidal oblate models describing elliptical galaxies cannot be ruled out until new analyses relative to more refined theoretical equilibrium models (involving, for example, massive halos) and more detailed observations are performed.

Relevance of equilibrium in multifragmentation

International Nuclear Information System (INIS)

Furuta, Takuya; Ono, Akira

2009-01-01

The relevance of equilibrium in a multifragmentation reaction of very central 40 Ca + 40 Ca collisions at 35 MeV/nucleon is investigated by using simulations of antisymmetrized molecular dynamics (AMD). Two types of ensembles are compared. One is the reaction ensemble of the states at each reaction time t in collision events simulated by AMD, and the other is the equilibrium ensemble prepared by solving the AMD equation of motion for a many-nucleon system confined in a container for a long time. The comparison of the ensembles is performed for the fragment charge distribution and the excitation energies. Our calculations show that there exists an equilibrium ensemble that well reproduces the reaction ensemble at each reaction time t for the investigated period 80≤t≤300 fm/c. However, there are some other observables that show discrepancies between the reaction and equilibrium ensembles. These may be interpreted as dynamical effects in the reaction. The usual static equilibrium at each instant is not realized since any equilibrium ensemble with the same volume as that of the reaction system cannot reproduce the fragment observables

Transport processes and sound velocity in vibrationally non-equilibrium gas of anharmonic oscillators

Science.gov (United States)

Rydalevskaya, Maria A.; Voroshilova, Yulia N.

2018-05-01

Vibrationally non-equilibrium flows of chemically homogeneous diatomic gases are considered under the conditions that the distribution of the molecules over vibrational levels differs significantly from the Boltzmann distribution. In such flows, molecular collisions can be divided into two groups: the first group corresponds to "rapid" microscopic processes whereas the second one corresponds to "slow" microscopic processes (their rate is comparable to or larger than that of gasdynamic parameters variation). The collisions of the first group form quasi-stationary vibrationally non-equilibrium distribution functions. The model kinetic equations are used to study the transport processes under these conditions. In these equations, the BGK-type approximation is used to model only the collision operators of the first group. It allows us to simplify derivation of the transport fluxes and calculation of the kinetic coefficients. Special attention is given to the connection between the formulae for the bulk viscosity coefficient and the sound velocity square.

Exploring Chemical and Thermal Non-equilibrium in Nitrogen Arcs

International Nuclear Information System (INIS)

Ghorui, S; Das, A K

2012-01-01

Plasma torches operating with nitrogen are of special importance as they can operate with usual tungsten based refractory electrodes and offer radical rich non-oxidizing high temperature environment for plasma chemistry. Strong gradients in temperature as well as species densities and huge convective fluxes lead to varying degrees of chemical non-equilibrium in associated regions. An axi-symmetric two-temperature chemical non-equilibrium model of a nitrogen plasma torch has been developed to understand the effects of thermal and chemical non-equilibrium in arcs. A 2-D finite volume CFD code in association with a non-equilibrium property routine enabled extraction of steady state self-consistent distributions of various plasma quantities inside the torch under various thermal and chemical non-equilibrium conditions. Chemical non-equilibrium has been incorporated through computation of diffusive and convective fluxes in each finite volume cell in every iteration and associating corresponding thermodynamic and transport properties through the scheme of 'chemical non-equilibrium parameter' introduced by Ghorui et. al. Recombination coefficient data from Nahar et. al. and radiation data from Krey and Morris have been used in the simulation. Results are presented for distributions of temperature, pressure, velocity, current density, electric potential, species densities and chemical non-equilibrium effects. Obtained results are compared with similar results under LTE.

Equilibrium statistical mechanics

CERN Document Server

Mayer, J E

1968-01-01

The International Encyclopedia of Physical Chemistry and Chemical Physics, Volume 1: Equilibrium Statistical Mechanics covers the fundamental principles and the development of theoretical aspects of equilibrium statistical mechanics. Statistical mechanical is the study of the connection between the macroscopic behavior of bulk matter and the microscopic properties of its constituent atoms and molecules. This book contains eight chapters, and begins with a presentation of the master equation used for the calculation of the fundamental thermodynamic functions. The succeeding chapters highlight t

Non-equilibrium steady states: maximization of the Shannon entropy associated with the distribution of dynamical trajectories in the presence of constraints

International Nuclear Information System (INIS)

Monthus, Cécile

2011-01-01

Filyokov and Karpov (1967 Inzh.-Fiz. Zh. 13 624) have proposed a theory of non-equilibrium steady states in direct analogy with the theory of equilibrium states: the principle is to maximize the Shannon entropy associated with the probability distribution of dynamical trajectories in the presence of constraints, including the macroscopic current of interest, via the method of Lagrange multipliers. This maximization leads directly to the generalized Gibbs distribution for the probability distribution of dynamical trajectories, and to some fluctuation relation of the integrated current. The simplest stochastic dynamics where these ideas can be applied are discrete-time Markov chains, defined by transition probabilities W i→j between configurations i and j: instead of choosing the dynamical rules W i→j a priori, one determines the transition probabilities and the associate stationary state that maximize the entropy of dynamical trajectories with the other physical constraints that one wishes to impose. We give a self-contained and unified presentation of this type of approach, both for discrete-time Markov chains and for continuous-time master equations. The obtained results are in full agreement with the Bayesian approach introduced by Evans (2004 Phys. Rev. Lett. 92 150601) under the name 'Non-equilibrium Counterpart to detailed balance', and with the 'invariant quantities' derived by Baule and Evans (2008 Phys. Rev. Lett. 101 240601), but provide a slightly different perspective via the formulation in terms of an eigenvalue problem

Non-Equilibrium Relations for Bounded Rational Decision-Making in Changing Environments

Directory of Open Access Journals (Sweden)

Jordi Grau-Moya

2017-12-01

Full Text Available Living organisms from single cells to humans need to adapt continuously to respond to changes in their environment. The process of behavioural adaptation can be thought of as improving decision-making performance according to some utility function. Here, we consider an abstract model of organisms as decision-makers with limited information-processing resources that trade off between maximization of utility and computational costs measured by a relative entropy, in a similar fashion to thermodynamic systems undergoing isothermal transformations. Such systems minimize the free energy to reach equilibrium states that balance internal energy and entropic cost. When there is a fast change in the environment, these systems evolve in a non-equilibrium fashion because they are unable to follow the path of equilibrium distributions. Here, we apply concepts from non-equilibrium thermodynamics to characterize decision-makers that adapt to changing environments under the assumption that the temporal evolution of the utility function is externally driven and does not depend on the decision-maker’s action. This allows one to quantify performance loss due to imperfect adaptation in a general manner and, additionally, to find relations for decision-making similar to Crooks’ fluctuation theorem and Jarzynski’s equality. We provide simulations of several exemplary decision and inference problems in the discrete and continuous domains to illustrate the new relations.

Scaling function, spectral function and nucleon momentum distribution in nuclei

International Nuclear Information System (INIS)

Antonov, A.N.; Ivanov, M.V.; Caballero, J.A.; Barbaro, M.B.; Udias, J.M.; Moya de Guerra, E.; Donnelly, T.W.

2010-01-01

The aim of the study is to find a good simultaneous description of the spectral function and the momentum distribution in relation to the realistic scaling function obtained from inclusive electron-nuclei scattering experiments. We start with a modified Hartree-Fock spectral function in which the energy dependent part (δ-function) is replaced by the Gaussian distributions with hole state widths as free parameters. We calculate the scaling function and the nucleon momentum distribution on the basis of the spectral function constructed in this way, trying to find a good description of the experimental data. The obtained scaling function has a weak asymmetry and the momentum distribution has not got a high-momentum tail in the case when harmonic-oscillator single-particle wave functions are used. So, to improve the behavior of the momentum distribution we used the basis of natural orbitals (NO) in which short-range correlations are partly incorporated. The results for the scaling function show again a weak asymmetry, but in this case the momentum distribution has a high-momentum tail. As a next step we include final-state interactions (FSI) in the calculations to reproduce the experimentally observed asymmetry of the scaling function. (author)

The Rate-Controlled Constrained-Equilibrium Approach to Far-From-Local-Equilibrium Thermodynamics

Directory of Open Access Journals (Sweden)

Hameed Metghalchi

2012-01-01

Full Text Available The Rate-Controlled Constrained-Equilibrium (RCCE method for the description of the time-dependent behavior of dynamical systems in non-equilibrium states is a general, effective, physically based method for model order reduction that was originally developed in the framework of thermodynamics and chemical kinetics. A generalized mathematical formulation is presented here that allows including nonlinear constraints in non-local equilibrium systems characterized by the existence of a non-increasing Lyapunov functional under the system’s internal dynamics. The generalized formulation of RCCE enables to clarify the essentials of the method and the built-in general feature of thermodynamic consistency in the chemical kinetics context. In this paper, we work out the details of the method in a generalized mathematical-physics framework, but for definiteness we detail its well-known implementation in the traditional chemical kinetics framework. We detail proofs and spell out explicit functional dependences so as to bring out and clarify each underlying assumption of the method. In the standard context of chemical kinetics of ideal gas mixtures, we discuss the relations between the validity of the detailed balance condition off-equilibrium and the thermodynamic consistency of the method. We also discuss two examples of RCCE gas-phase combustion calculations to emphasize the constraint-dependent performance of the RCCE method.

Thermodynamic theory of equilibrium fluctuations

International Nuclear Information System (INIS)

Mishin, Y.

2015-01-01

The postulational basis of classical thermodynamics has been expanded to incorporate equilibrium fluctuations. The main additional elements of the proposed thermodynamic theory are the concept of quasi-equilibrium states, a definition of non-equilibrium entropy, a fundamental equation of state in the entropy representation, and a fluctuation postulate describing the probability distribution of macroscopic parameters of an isolated system. Although these elements introduce a statistical component that does not exist in classical thermodynamics, the logical structure of the theory is different from that of statistical mechanics and represents an expanded version of thermodynamics. Based on this theory, we present a regular procedure for calculations of equilibrium fluctuations of extensive parameters, intensive parameters and densities in systems with any number of fluctuating parameters. The proposed fluctuation formalism is demonstrated by four applications: (1) derivation of the complete set of fluctuation relations for a simple fluid in three different ensembles; (2) fluctuations in finite-reservoir systems interpolating between the canonical and micro-canonical ensembles; (3) derivation of fluctuation relations for excess properties of grain boundaries in binary solid solutions, and (4) derivation of the grain boundary width distribution for pre-melted grain boundaries in alloys. The last two applications offer an efficient fluctuation-based approach to calculations of interface excess properties and extraction of the disjoining potential in pre-melted grain boundaries. Possible future extensions of the theory are outlined.

Visualising the equilibrium distribution and mobility of organic contaminants in soil using the chemical partitioning space.

Science.gov (United States)

Wong, Fiona; Wania, Frank

2011-06-01

Assessing the behaviour of organic chemicals in soil is a complex task as it is governed by the physical chemical properties of the chemicals, the characteristics of the soil as well as the ambient conditions of the environment. The chemical partitioning space, defined by the air-water partition coefficient (K(AW)) and the soil organic carbon-water partition coefficient (K(OC)), was employed to visualize the equilibrium distribution of organic contaminants between the air-filled pores, the pore water and the solid phases of the bulk soil and the relative importance of the three transport processes removing contaminants from soil (evaporation, leaching and particle erosion). The partitioning properties of twenty neutral organic chemicals (i.e. herbicides, pharmaceuticals, polychlorinated biphenyls and volatile chemicals) were estimated using poly-parameter linear free energy relationships and superimposed onto these maps. This allows instantaneous estimation of the equilibrium phase distribution and mobility of neutral organic chemicals in soil. Although there is a link between the major phase and the dominant transport process, such that chemicals found in air-filled pore space are subject to evaporation, those in water-filled pore space undergo leaching and those in the sorbed phase are associated with particle erosion, the partitioning coefficient thresholds for distribution and mobility can often deviate by many orders of magnitude. In particular, even a small fraction of chemical in pore water or pore air allows for evaporation and leaching to dominate over solid phase transport. Multiple maps that represent soils that differ in the amount and type of soil organic matter, water saturation, temperature, depth of surface soil horizon, and mineral matters were evaluated.

Use of JANAF Tables in Equilibrium Calculations and Partition Function Calculations for an Undergraduate Physical Chemistry Course

Science.gov (United States)

Cleary, David A.

2014-01-01

The usefulness of the JANAF tables is demonstrated with specific equilibrium calculations. An emphasis is placed on the nature of standard chemical potential calculations. Also, the use of the JANAF tables for calculating partition functions is examined. In the partition function calculations, the importance of the zero of energy is highlighted.

The supply function equilibrium and its policy implications for wholesale electricity auctions

International Nuclear Information System (INIS)

Holmberg, Paer; Newbery, David

2010-01-01

The supply function equilibrium provides a game-theoretic model of strategic bidding in oligopolistic wholesale electricity auctions. This paper presents an intuitive account of current understanding and shows how welfare losses depend on the number of firms in the market and their asymmetry. Previous results and general recommendations for divisible-good/multi-unit auctions provides guidance on the design of the auction format, setting the reservation price, the rationing rule, and restrictions on the offer curves in wholesale electricity auctions. (author)

Non-equilibrium scalar two point functions in AdS/CFT

Energy Technology Data Exchange (ETDEWEB)

Keränen, Ville [Rudolf Peierls Centre for Theoretical Physics, University of Oxford,1 Keble Road, Oxford OX1 3NP (United Kingdom); Kleinert, Philipp [Rudolf Peierls Centre for Theoretical Physics, University of Oxford,1 Keble Road, Oxford OX1 3NP (United Kingdom); Merton College, University of Oxford,Merton Street, Oxford OX1 4JD (United Kingdom)

2015-04-22

In the first part of the paper, we discuss different versions of the AdS/CFT dictionary out of equilibrium. We show that the Skenderis-van Rees prescription and the “extrapolate” dictionary are equivalent at the level of “in-in” two point functions of free scalar fields in arbitrary asymptotically AdS spacetimes. In the second part of the paper, we calculate two point correlation functions in dynamical spacetimes using the “extrapolate” dictionary. These calculations are performed for conformally coupled scalar fields in examples of spacetimes undergoing gravitational collapse, the AdS{sub 2}-Vaidya spacetime and the AdS{sub 3}-Vaidya spacetime, which allow us to address the problem of thermalization following a quench in the boundary field theory. The computation of the correlators is formulated as an initial value problem in the bulk spacetime. Finally, we compare our results for AdS{sub 3}-Vaidya to results in the previous literature obtained using the geodesic approximation and we find qualitative agreement.

Non-equilibrium scalar two point functions in AdS/CFT

International Nuclear Information System (INIS)

Keränen, Ville; Kleinert, Philipp

2015-01-01

In the first part of the paper, we discuss different versions of the AdS/CFT dictionary out of equilibrium. We show that the Skenderis-van Rees prescription and the “extrapolate” dictionary are equivalent at the level of “in-in” two point functions of free scalar fields in arbitrary asymptotically AdS spacetimes. In the second part of the paper, we calculate two point correlation functions in dynamical spacetimes using the “extrapolate” dictionary. These calculations are performed for conformally coupled scalar fields in examples of spacetimes undergoing gravitational collapse, the AdS 2 -Vaidya spacetime and the AdS 3 -Vaidya spacetime, which allow us to address the problem of thermalization following a quench in the boundary field theory. The computation of the correlators is formulated as an initial value problem in the bulk spacetime. Finally, we compare our results for AdS 3 -Vaidya to results in the previous literature obtained using the geodesic approximation and we find qualitative agreement.

An equilibrium-conserving taxation scheme for income from capital

Science.gov (United States)

Tempere, Jacques

2018-02-01

Under conditions of market equilibrium, the distribution of capital income follows a Pareto power law, with an exponent that characterizes the given equilibrium. Here, a simple taxation scheme is proposed such that the post-tax capital income distribution remains an equilibrium distribution, albeit with a different exponent. This taxation scheme is shown to be progressive, and its parameters can be simply derived from (i) the total amount of tax that will be levied, (ii) the threshold selected above which capital income will be taxed and (iii) the total amount of capital income. The latter can be obtained either by using Piketty's estimates of the capital/labor income ratio or by fitting the initial Pareto exponent. Both ways moreover provide a check on the amount of declared income from capital.

Non-equilibrium thermodynamics of highly rarefied neutron gas under creative and destructive reactions

International Nuclear Information System (INIS)

Hayasaka, Hideo

1978-01-01

The thermodynamic structures of non-equilibrium steady states of a highly rarefied neutron gas in various media are considered in terms of the irreversible processes due to creative and destructive reactions of neutrons with nuclei of these media and to neutrons supplied from external sources. The respective subsystems of the stationary neutron gas are regarded as imperfect equilibrium systems in the presence of the medium and the external neutron sources, and are treated like different species in a mixture. The entropy production due to neutron-nuclear reactions has a minimum value at the steady state. The distribution function of such a neutron gas is determined from the extremum condition in which entropy does not change, and is expressed as a shifted Boltzmann distribution specified by the respective values of the generalized chemical potential for each energy level. (author)

Intermittent many-body dynamics at equilibrium

Science.gov (United States)

Danieli, C.; Campbell, D. K.; Flach, S.

2017-06-01

The equilibrium value of an observable defines a manifold in the phase space of an ergodic and equipartitioned many-body system. A typical trajectory pierces that manifold infinitely often as time goes to infinity. We use these piercings to measure both the relaxation time of the lowest frequency eigenmode of the Fermi-Pasta-Ulam chain, as well as the fluctuations of the subsequent dynamics in equilibrium. The dynamics in equilibrium is characterized by a power-law distribution of excursion times far off equilibrium, with diverging variance. Long excursions arise from sticky dynamics close to q -breathers localized in normal mode space. Measuring the exponent allows one to predict the transition into nonergodic dynamics. We generalize our method to Klein-Gordon lattices where the sticky dynamics is due to discrete breathers localized in real space.

New insights for mesospheric OH: multi-quantum vibrational relaxation as a driver for non-local thermodynamic equilibrium

Directory of Open Access Journals (Sweden)

K. S. Kalogerakis

2018-01-01

Full Text Available The question of whether mesospheric OH(v rotational population distributions are in equilibrium with the local kinetic temperature has been debated over several decades. Despite several indications for the existence of non-equilibrium effects, the general consensus has been that emissions originating from low rotational levels are thermalized. Sky spectra simultaneously observing several vibrational levels demonstrated reproducible trends in the extracted OH(v rotational temperatures as a function of vibrational excitation. Laboratory experiments provided information on rotational energy transfer and direct evidence for fast multi-quantum OH(high-v vibrational relaxation by O atoms. We examine the relationship of the new relaxation pathways with the behavior exhibited by OH(v rotational population distributions. Rapid OH(high-v + O multi-quantum vibrational relaxation connects high and low vibrational levels and enhances the hot tail of the OH(low-v rotational distributions. The effective rotational temperatures of mesospheric OH(v are found to deviate from local thermodynamic equilibrium for all observed vibrational levels. Dedicated to Tom G. Slanger in celebration of his 5 decades of research in aeronomy.

Tracer disposition kinetics in the determination of local cerebral blood flow by a venous equilibrium model, tube model, and distributed model

International Nuclear Information System (INIS)

Sawada, Y.; Sugiyama, Y.; Iga, T.; Hanano, M.

1987-01-01

Tracer distribution kinetics in the determination of local cerebral blood flow (LCBF) were examined by using three models, i.e., venous equilibrium, tube, and distributed models. The technique most commonly used for measuring LCBF is the tissue uptake method, which was first developed and applied by Kety. The measurement of LCBF with the 14 C-iodoantipyrine (IAP) method is calculated by using an equation derived by Kety based on the Fick's principle and a two-compartment model of blood-tissue exchange and tissue concentration at a single data point. The procedure, in which the tissue is to be in equilibrium with venous blood, will be referred to as the tissue equilibration model. In this article, effects of the concentration gradient of tracer along the length of the capillary (tube model) and the transverse heterogeneity in the capillary transit time (distributed model) on the determination of LCBF were theoretically analyzed for the tissue sampling method. Similarities and differences among these models are explored. The rank order of the LCBF calculated by using arterial blood concentration time courses and the tissue concentration of tracer based on each model were tube model (model II) less than distributed model (model III) less than venous equilibrium model (model I). Data on 14 C-IAP kinetics reported by Ohno et al. were employed. The LCBFs calculated based on model I were 45-260% larger than those in models II or III. To discriminate among three models, we propose to examine the effect of altering the venous infusion time of tracer on the apparent tissue-to-blood concentration ratio (lambda app). A range of the ratio of the predicted lambda app in models II or III to that in model I was from 0.6 to 1.3

Relation between absorbed dose, charged particle equilibrium and nuclear transformations: A non-equilibrium thermodynamics point of view

International Nuclear Information System (INIS)

Alvarez-Romero, J. T.

2006-01-01

We present a discussion to show that the absorbed dose D is a time-dependent function. This time dependence is demonstrated based on the concepts of charged particle equilibrium and on radiation equilibrium within the context of thermodynamic non-equilibrium. In the latter, the time dependence is due to changes of the rest mass energy of the nuclei and elementary particles involved in the terms ΣQ and Q that appear in the definitions of energy imparted ε and energy deposit ε i , respectively. In fact, nothing is said about the averaging operation of the non-stochastic quantity mean energy imparted ε-bar, which is used in the definition of D according to ICRU 60. It is shown in this research that the averaging operation necessary to define the ε-bar employed to get D cannot be performed with an equilibrium statistical operator ρ(r) as could be expected. Rather, the operation has to be defined with a time-dependent non-equilibrium statistical operator (r, t) therefore, D is a time-dependent function D(r, t). (authors)

Decomposition of thermal-equilibrium states

International Nuclear Information System (INIS)

Gu Lei

2010-01-01

It is shown that a thermal-equilibrium state can be decomposed into a tensor product of the operators in subspaces of single-particle energy. On the basis of this form, a straightforward derivation of the Fermi-Dirac and the Bose-Einstein distribution is performed. The derivation can be generalized for systems with weak interaction to obtain an approximate distribution in momentum.

Equilibrium Propagation: Bridging the Gap between Energy-Based Models and Backpropagation

Directory of Open Access Journals (Sweden)

Benjamin Scellier

2017-05-01

Full Text Available We introduce Equilibrium Propagation, a learning framework for energy-based models. It involves only one kind of neural computation, performed in both the first phase (when the prediction is made and the second phase of training (after the target or prediction error is revealed. Although this algorithm computes the gradient of an objective function just like Backpropagation, it does not need a special computation or circuit for the second phase, where errors are implicitly propagated. Equilibrium Propagation shares similarities with Contrastive Hebbian Learning and Contrastive Divergence while solving the theoretical issues of both algorithms: our algorithm computes the gradient of a well-defined objective function. Because the objective function is defined in terms of local perturbations, the second phase of Equilibrium Propagation corresponds to only nudging the prediction (fixed point or stationary distribution toward a configuration that reduces prediction error. In the case of a recurrent multi-layer supervised network, the output units are slightly nudged toward their target in the second phase, and the perturbation introduced at the output layer propagates backward in the hidden layers. We show that the signal “back-propagated” during this second phase corresponds to the propagation of error derivatives and encodes the gradient of the objective function, when the synaptic update corresponds to a standard form of spike-timing dependent plasticity. This work makes it more plausible that a mechanism similar to Backpropagation could be implemented by brains, since leaky integrator neural computation performs both inference and error back-propagation in our model. The only local difference between the two phases is whether synaptic changes are allowed or not. We also show experimentally that multi-layer recurrently connected networks with 1, 2, and 3 hidden layers can be trained by Equilibrium Propagation on the permutation-invariant MNIST

Determination of equilibrium composition of thermally ionized monoatomic gas under different physical conditions

Science.gov (United States)

Romanova, M. S.; Rydalevskaya, M. A.

2017-05-01

Perfect gas mixtures that result from thermal ionization of spatially and chemically homogeneous monoatomic gases are considered. Equilibrium concentrations of the components of such mixtures are determined using integration over the momentum space and summation with respect to energy levels of the distribution functions that maximize the entropy of system under condition for constancy of the total number of nuclei and electrons. It is demonstrated that such a method allows significant simplification of the calculation of the equilibrium composition for ionized mixtures at different temperatures and makes it possible to study the degree of ionization of gas versus gas density and number in the periodic table of elements.

Distribution functions of probabilistic automata

Science.gov (United States)

Vatan, F.

2001-01-01

Each probabilistic automaton M over an alphabet A defines a probability measure Prob sub(M) on the set of all finite and infinite words over A. We can identify a k letter alphabet A with the set {0, 1,..., k-1}, and, hence, we can consider every finite or infinite word w over A as a radix k expansion of a real number X(w) in the interval [0, 1]. This makes X(w) a random variable and the distribution function of M is defined as usual: F(x) := Prob sub(M) { w: X(w) automata in detail. Automata with continuous distribution functions are characterized. By a new, and much more easier method, it is shown that the distribution function F(x) is an analytic function if it is a polynomial. Finally, answering a question posed by D. Knuth and A. Yao, we show that a polynomial distribution function F(x) on [0, 1] can be generated by a prob abilistic automaton iff all the roots of F'(x) = 0 in this interval, if any, are rational numbers. For this, we define two dynamical systems on the set of polynomial distributions and study attracting fixed points of random composition of these two systems.

Vlasov-Maxwell equilibrium solutions for Harris sheet magnetic field with Kappa velocity distribution

International Nuclear Information System (INIS)

Fu, W.-Z.; Hau, L.-N.

2005-01-01

An exact solution of the steady-state, one-dimensional Vlasov-Maxwell equations for a plasma current sheet with oppositely directed magnetic field was found by Harris in 1962. The so-called Harris magnetic field model assumes Maxwellian velocity distributions for oppositely drifting ions and electrons and has been widely used for plasma stability studies. This paper extends Harris solutions by using more general κ distribution functions that incorporate Maxwellian distribution in the limit of κ→∞. A new functional form for the plasma pressure as a function of the magnetic vector potential p(A) is found and the magnetic field is a modified tanh z function. In the extended solutions the effective temperature is no longer spatially uniform like in the Harris model and the thickness of the current layer decreases with decreasing κ

Fluid dynamics of out of equilibrium boost invariant plasmas

Science.gov (United States)

Blaizot, Jean-Paul; Yan, Li

2018-05-01

By solving a simple kinetic equation, in the relaxation time approximation, and for a particular set of moments of the distribution function, we establish a set of equations which, on the one hand, capture exactly the dynamics of the kinetic equation, and, on the other hand, coincide with the hierarchy of equations of viscous hydrodynamics, to arbitrary order in the viscous corrections. This correspondence sheds light on the underlying mechanism responsible for the apparent success of hydrodynamics in regimes that are far from local equilibrium.

Plutonium valence state distributions

International Nuclear Information System (INIS)

Silver, G.L.

1974-01-01

A calculational method for ascertaining equilibrium valence state distributions of plutonium in acid solutions as a function of the plutonium oxidation number and the solution acidity is illustrated with an example. The method may be more practical for manual use than methods based upon polynomial equations. (T.G.)

Equilibrium and off-equilibrium trap-size scaling in one-dimensional ultracold bosonic gases

International Nuclear Information System (INIS)

Campostrini, Massimo; Vicari, Ettore

2010-01-01

We study some aspects of equilibrium and off-equilibrium quantum dynamics of dilute bosonic gases in the presence of a trapping potential. We consider systems with a fixed number of particles and study their scaling behavior with increasing the trap size. We focus on one-dimensional bosonic systems, such as gases described by the Lieb-Liniger model and its Tonks-Girardeau limit of impenetrable bosons, and gases constrained in optical lattices as described by the Bose-Hubbard model. We study their quantum (zero-temperature) behavior at equilibrium and off equilibrium during the unitary time evolution arising from changes of the trapping potential, which may be instantaneous or described by a power-law time dependence, starting from the equilibrium ground state for an initial trap size. Renormalization-group scaling arguments and analytical and numerical calculations show that the trap-size dependence of the equilibrium and off-equilibrium dynamics can be cast in the form of a trap-size scaling in the low-density regime, characterized by universal power laws of the trap size, in dilute gases with repulsive contact interactions and lattice systems described by the Bose-Hubbard model. The scaling functions corresponding to several physically interesting observables are computed. Our results are of experimental relevance for systems of cold atomic gases trapped by tunable confining potentials.

Kinetic corrections from analytic non-Maxwellian distribution functions in magnetized plasmas

Energy Technology Data Exchange (ETDEWEB)

Izacard, Olivier, E-mail: izacard@llnl.gov [Lawrence Livermore National Laboratory, 7000 East Avenue, L-637, Livermore, California 94550 (United States)

2016-08-15

In magnetized plasma physics, almost all developed analytic theories assume a Maxwellian distribution function (MDF) and in some cases small deviations are described using the perturbation theory. The deviations with respect to the Maxwellian equilibrium, called kinetic effects, are required to be taken into account especially for fusion reactor plasmas. Generally, because the perturbation theory is not consistent with observed steady-state non-Maxwellians, these kinetic effects are numerically evaluated by very central processing unit (CPU)-expensive codes, avoiding the analytic complexity of velocity phase space integrals. We develop here a new method based on analytic non-Maxwellian distribution functions constructed from non-orthogonal basis sets in order to (i) use as few parameters as possible, (ii) increase the efficiency to model numerical and experimental non-Maxwellians, (iii) help to understand unsolved problems such as diagnostics discrepancies from the physical interpretation of the parameters, and (iv) obtain analytic corrections due to kinetic effects given by a small number of terms and removing the numerical error of the evaluation of velocity phase space integrals. This work does not attempt to derive new physical effects even if it could be possible to discover one from the better understandings of some unsolved problems, but here we focus on the analytic prediction of kinetic corrections from analytic non-Maxwellians. As applications, examples of analytic kinetic corrections are shown for the secondary electron emission, the Langmuir probe characteristic curve, and the entropy. This is done by using three analytic representations of the distribution function: the Kappa distribution function, the bi-modal or a new interpreted non-Maxwellian distribution function (INMDF). The existence of INMDFs is proved by new understandings of the experimental discrepancy of the measured electron temperature between two diagnostics in JET. As main results, it

Local approximation of a metapopulation's equilibrium.

Science.gov (United States)

Barbour, A D; McVinish, R; Pollett, P K

2018-04-18

We consider the approximation of the equilibrium of a metapopulation model, in which a finite number of patches are randomly distributed over a bounded subset [Formula: see text] of Euclidean space. The approximation is good when a large number of patches contribute to the colonization pressure on any given unoccupied patch, and when the quality of the patches varies little over the length scale determined by the colonization radius. If this is the case, the equilibrium probability of a patch at z being occupied is shown to be close to [Formula: see text], the equilibrium occupation probability in Levins's model, at any point [Formula: see text] not too close to the boundary, if the local colonization pressure and extinction rates appropriate to z are assumed. The approximation is justified by giving explicit upper and lower bounds for the occupation probabilities, expressed in terms of the model parameters. Since the patches are distributed randomly, the occupation probabilities are also random, and we complement our bounds with explicit bounds on the probability that they are satisfied at all patches simultaneously.

Real time equilibrium reconstruction for tokamak discharge control

International Nuclear Information System (INIS)

Ferron, J.R.; Walker, M.L.; Lao, L.L.; St John, H.E.; Humphreys, D.A.; Leuer, J.A.

1998-01-01

A practical method for performing a tokamak equilibrium reconstruction in real time for arbitrary time varying discharge shapes and current profiles is described. An approximate solution to the Grad-Shafranov equilibrium relation is found which best fits the diagnostic measurements. Thus, a solution for the spatial distribution of poloidal flux and toroidal current density is available in real time that is consistent with plasma force balance, allowing accurate evaluation of parameters such as discharge shape and safety factor profile. The equilibrium solutions are produced at a rate sufficient for discharge control. This equilibrium reconstruction algorithm has been implemented on the digital plasma control system for the DIII-D tokamak. The first application of real time equilibrium reconstruction to discharge shape control is described. (author)

Niche tracking and rapid establishment of distributional equilibrium in the house sparrow show potential responsiveness of species to climate change.

Directory of Open Access Journals (Sweden)

William B Monahan

Full Text Available The ability of species to respond to novel future climates is determined in part by their physiological capacity to tolerate climate change and the degree to which they have reached and continue to maintain distributional equilibrium with the environment. While broad-scale correlative climatic measurements of a species' niche are often described as estimating the fundamental niche, it is unclear how well these occupied portions actually approximate the fundamental niche per se, versus the fundamental niche that exists in environmental space, and what fitness values bounding the niche are necessary to maintain distributional equilibrium. Here, we investigate these questions by comparing physiological and correlative estimates of the thermal niche in the introduced North American house sparrow (Passer domesticus. Our results indicate that occupied portions of the fundamental niche derived from temperature correlations closely approximate the centroid of the existing fundamental niche calculated on a fitness threshold of 50% population mortality. Using these niche measures, a 75-year time series analysis (1930-2004 further shows that: (i existing fundamental and occupied niche centroids did not undergo directional change, (ii interannual changes in the two niche centroids were correlated, (iii temperatures in North America moved through niche space in a net centripetal fashion, and consequently, (iv most areas throughout the range of the house sparrow tracked the existing fundamental niche centroid with respect to at least one temperature gradient. Following introduction to a new continent, the house sparrow rapidly tracked its thermal niche and established continent-wide distributional equilibrium with respect to major temperature gradients. These dynamics were mediated in large part by the species' broad thermal physiological tolerances, high dispersal potential, competitive advantage in human-dominated landscapes, and climatically induced

The tensor distribution function.

Science.gov (United States)

Leow, A D; Zhu, S; Zhan, L; McMahon, K; de Zubicaray, G I; Meredith, M; Wright, M J; Toga, A W; Thompson, P M

2009-01-01

Diffusion weighted magnetic resonance imaging is a powerful tool that can be employed to study white matter microstructure by examining the 3D displacement profile of water molecules in brain tissue. By applying diffusion-sensitized gradients along a minimum of six directions, second-order tensors (represented by three-by-three positive definite matrices) can be computed to model dominant diffusion processes. However, conventional DTI is not sufficient to resolve more complicated white matter configurations, e.g., crossing fiber tracts. Recently, a number of high-angular resolution schemes with more than six gradient directions have been employed to address this issue. In this article, we introduce the tensor distribution function (TDF), a probability function defined on the space of symmetric positive definite matrices. Using the calculus of variations, we solve the TDF that optimally describes the observed data. Here, fiber crossing is modeled as an ensemble of Gaussian diffusion processes with weights specified by the TDF. Once this optimal TDF is determined, the orientation distribution function (ODF) can easily be computed by analytic integration of the resulting displacement probability function. Moreover, a tensor orientation distribution function (TOD) may also be derived from the TDF, allowing for the estimation of principal fiber directions and their corresponding eigenvalues.

Comments on equilibrium, transient equilibrium, and secular equilibrium in serial radioactive decay

International Nuclear Information System (INIS)

Prince, J.R.

1979-01-01

Equations describing serial radioactive decay are reviewed along with published descriptions or transient and secular equilibrium. It is shown that terms describing equilibrium are not used in the same way by various authors. Specific definitions are proposed; they suggest that secular equilibrium is a subset of transient equilibrium

Quasivariational Inequalities for a Dynamic Competitive Economic Equilibrium Problem

Directory of Open Access Journals (Sweden)

Carmela Vitanza

2009-01-01

Full Text Available The aim of this paper is to consider a dynamic competitive economic equilibrium problem in terms of maximization of utility functions and of excess demand functions. This equilibrium problem is studied by means of a time-dependent quasivariational inequality which is set in the Lebesgue space L2([0,T],ℝ. This approach allows us to obtain an existence result of time-dependent equilibrium solutions.

Memory loss process and non-Gibbsian equilibrium solutions of master equations

International Nuclear Information System (INIS)

Cataldo, H.M.; Hernandez, E.S.

1988-01-01

The phonon dynamics of a harmonic oscillator coupled to a steady reservoir is studied. In the Markovian limit, the equilibrium is reached through a progressive loss of memory process which involves the moments of the initial distribution. The relationship to the non-Markovian equations of motion and its resolvent poles is settled. As a particular model of the coupling mechanism is adopted, the possibility of non-Gibbsian equilibrium distribution arises, which is analyzed focusing upon the dependence of various parameters of the system on an effective equilibrium temperature

Anharmonic effects in the quantum cluster equilibrium method

Science.gov (United States)

von Domaros, Michael; Perlt, Eva

2017-03-01

The well-established quantum cluster equilibrium (QCE) model provides a statistical thermodynamic framework to apply high-level ab initio calculations of finite cluster structures to macroscopic liquid phases using the partition function. So far, the harmonic approximation has been applied throughout the calculations. In this article, we apply an important correction in the evaluation of the one-particle partition function and account for anharmonicity. Therefore, we implemented an analytical approximation to the Morse partition function and the derivatives of its logarithm with respect to temperature, which are required for the evaluation of thermodynamic quantities. This anharmonic QCE approach has been applied to liquid hydrogen chloride and cluster distributions, and the molar volume, the volumetric thermal expansion coefficient, and the isobaric heat capacity have been calculated. An improved description for all properties is observed if anharmonic effects are considered.

Mathematical models and equilibrium in irreversible microeconomics

Directory of Open Access Journals (Sweden)

Anatoly M. Tsirlin

2010-07-01

Full Text Available A set of equilibrium states in a system consisting of economic agents, economic reservoirs, and firms is considered. Methods of irreversible microeconomics are used. We show that direct sale/purchase leads to an equilibrium state which depends upon the coefficients of supply/demand functions. To reach the unique equilibrium state it is necessary to add either monetary exchange or an intermediate firm.

Electron distribution function in laser heated plasmas

International Nuclear Information System (INIS)

Fourkal, E.; Bychenkov, V. Yu.; Rozmus, W.; Sydora, R.; Kirkby, C.; Capjack, C. E.; Glenzer, S. H.; Baldis, H. A.

2001-01-01

A new electron distribution function has been found in laser heated homogeneous plasmas by an analytical solution to the kinetic equation and by particle simulations. The basic kinetic model describes inverse bremsstrahlung absorption and electron--electron collisions. The non-Maxwellian distribution function is comprised of a super-Gaussian bulk of slow electrons and a Maxwellian tail of energetic particles. The tails are heated due to electron--electron collisions and energy redistribution between superthermal particles and light absorbing slow electrons from the bulk of the distribution function. A practical fit is proposed to the new electron distribution function. Changes to the linear Landau damping of electron plasma waves are discussed. The first evidence for the existence of non-Maxwellian distribution functions has been found in the interpretation, which includes the new distribution function, of the Thomson scattering spectra in gold plasmas [Glenzer , Phys. Rev. Lett. 82, 97 (1999)

Non-equilibrium Green's functions method: Non-trivial and disordered leads

Science.gov (United States)

He, Yu; Wang, Yu; Klimeck, Gerhard; Kubis, Tillmann

2014-11-01

The non-equilibrium Green's function algorithm requires contact self-energies to model charge injection and extraction. All existing approaches assume infinitely periodic leads attached to a possibly quite complex device. This contradicts today's realistic devices in which contacts are spatially inhomogeneous, chemically disordered, and impacting the overall device characteristics. This work extends the complex absorbing potentials method for arbitrary, ideal, or non-ideal leads in atomistic tight binding representation. The algorithm is demonstrated on a Si nanowire with periodic leads, a graphene nanoribbon with trumpet shape leads, and devices with leads of randomly alloyed Si0.5Ge0.5. It is found that alloy randomness in the leads can reduce the predicted ON-state current of Si0.5Ge0.5 transistors by 45% compared to conventional lead methods.

Electronic equilibrium as a function of depth in tissue from cobalt-60 point source exposures

International Nuclear Information System (INIS)

Myrick, J.A.

1994-08-01

The Nuclear Regulatory Commission has set the basic criteria for assessing skin dose stemming from hot particle contaminations. Compliance with 10 CFR 20.101 requires that exposure to the skin be evaluated over a 1 cm 2 area at a depth of 0.007 cm. Skin exposure can arise from both the beta and gamma components of radioactive particles and gamma radiation can contribute significantly to skin doses. The gamma component of dose increases dramatically when layers of protective clothing are interposed between the hot particle source and the skin, and in cases where the hot particle is large in comparison to the range of beta particles. Once the protective clothing layer is thicker than the maximum range of the beta particles, skin dose is due solely to gamma radiation. Charged particle equilibrium is not established at shallow depths. The degree of electronic equilibrium establishment must be assessed for shallow doses to prevent the over-assessment of skin dose because conventional fluence-to-dose conversion factors are not applicable. To assess the effect of electronic equilibrium, selected thicknesses of tissue equivalent material were interposed between radiochromic dye film and a 60 Co hot particle source and dose was measured as a function of depth. These measured values were then compared to models which are used to calculate charged particle equilibrium. The Miller-Reece model was found to agree closely with the experimental data while the Lantz-Lambert model overestimated dose at shallow depths

Thermodynamic equilibrium model to predict the cobalt distribution coefficient in the CoCl2--HCl--H2O--TBP liquid--liquid extraction system

International Nuclear Information System (INIS)

Nevarez, M.; Bautista, R.G.

1976-01-01

The development of a thermodynamic equilibrium model to predict the cobalt distribution coefficient in the CoCl 2 -HCl-H 2 O-TBP system is described. The model makes use of the various aqueous phase cobaltous chloride complexes stoichiometric stability constants expressed as their degree of formation, their mechanism of extraction into the organic phase, and the equilibrium constant for the extraction reaction. The model was verified by the good agreement between the calculated cobalt distribution coefficients and those obtained experimentally both in the present study and published by other investigators. The optimum extraction of cobalt by the TBP occurred at an HCl equilibrium aqueous place concentration between 8.5 and 9.5M. The development of efficient procedures for the separation and concentration of important industrial metals from their aqueous solutions by liquid-liquid extraction has recently been given impetus by the realization of an impending shortage of energy and mineral resources. Liquid-liquid extraction is one of the few methods by which it is possible to quantitatively separate elements which are similar in properties. The use of liquid-liquid extraction to separate cobalt and nickel, which very frequently occur in nature together, is an important separation problem in nonferrous metallurgy. There is some fundamental information available in the chemical literature regarding the mechanism and equilibrium thermodynamic properties of selected liquid-liquid extraction systems. This research effort shows how this available information can be utilized to improve existing separation and concentration theory and technique. The development and application of a thermodynamic equilibrium model for describing the liquid-liquid extraction of cobaltous chloride from aqueous HCl solutions by tributyl phosphate (TBP) using experimental data obtained in this investigation and from the literature are presented

Time evolution of distribution functions in dissipative environments

International Nuclear Information System (INIS)

Hu Li-Yun; Chen Fei; Wang Zi-Sheng; Fan Hong-Yi

2011-01-01

By introducing the thermal entangled state representation, we investigate the time evolution of distribution functions in the dissipative channels by bridging the relation between the initial distribution function and the any time distribution function. We find that most of them are expressed as such integrations over the Laguerre—Gaussian function. Furthermore, as applications, we derive the time evolution of photon-counting distribution by bridging the relation between the initial distribution function and the any time photon-counting distribution, and the time evolution of R-function characteristic of nonclassicality depth. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

Distribution of nuclei in equilibrium stellar matter from the free-energy density in a Wigner-Seitz cell

Science.gov (United States)

Grams, G.; Giraud, S.; Fantina, A. F.; Gulminelli, F.

2018-03-01

The aim of the present study is to calculate the nuclear distribution associated at finite temperature to any given equation of state of stellar matter based on the Wigner-Seitz approximation, for direct applications in core-collapse simulations. The Gibbs free energy of the different configurations is explicitly calculated, with special care devoted to the calculation of rearrangement terms, ensuring thermodynamic consistency. The formalism is illustrated with two different applications. First, we work out the nuclear statistical equilibrium cluster distribution for the Lattimer and Swesty equation of state, widely employed in supernova simulations. Secondly, we explore the effect of including shell structure, and consider realistic nuclear mass tables from the Brussels-Montreal Hartree-Fock-Bogoliubov model (specifically, HFB-24). We show that the whole collapse trajectory is dominated by magic nuclei, with extremely spread and even bimodal distributions of the cluster probability around magic numbers, demonstrating the importance of cluster distributions with realistic mass models in core-collapse simulations. Simple analytical expressions are given, allowing further applications of the method to any relativistic or nonrelativistic subsaturation equation of state.

Tailoring electron energy distribution functions through energy confinement in dual radio-frequency driven atmospheric pressure plasmas

Energy Technology Data Exchange (ETDEWEB)

O' Neill, C.; Waskoenig, J. [Centre for Plasma Physics, School of Maths and Physics, Queen' s University Belfast, Belfast BT7 1NN (United Kingdom); Gans, T. [Centre for Plasma Physics, School of Maths and Physics, Queen' s University Belfast, Belfast BT7 1NN (United Kingdom); York Plasma Institute, Department of Physics, University of York, York YO10 5DD (United Kingdom)

2012-10-08

A multi-scale numerical model based on hydrodynamic equations with semi-kinetic treatment of electrons is used to investigate the influence of dual frequency excitation on the effective electron energy distribution function (EEDF) in a radio-frequency driven atmospheric pressure plasma. It is found that variations of power density, voltage ratio, and phase relationship provide separate control over the electron density and the mean electron energy. This is exploited to directly influence both the phase dependent and time averaged effective EEDF. This enables tailoring the EEDF for enhanced control of non-equilibrium plasma chemical kinetics at ambient pressure and temperature.

Strong Duality and Optimality Conditions for Generalized Equilibrium Problems

Directory of Open Access Journals (Sweden)

D. H. Fang

2013-01-01

Full Text Available We consider a generalized equilibrium problem involving DC functions. By using the properties of the epigraph of the conjugate functions, some sufficient and/or necessary conditions for the weak and strong duality results and optimality conditions for generalized equilibrium problems are provided.

Description of the approach to equilibrium in the Boltzmann equation

Energy Technology Data Exchange (ETDEWEB)

Barrachina, R.O.; Fujii, D.H.; Garibotti, C.R.

1985-06-01

An integral transform of the Boltzmann equation with a clear physical interpretation is introduced. It is applied to different interaction models and initial conditions, relevant information about the way the equilibrium is reached. This method leads quite naturally to the introduction of an N-pole approximant of the distribution function which seems to be a rather useful technique not only in view of its simplicity but also because of its capability to keep track of the temporal evolution features of the chosen interaction model. 6 references.

The critical role of logarithmic transformation in Nernstian equilibrium potential calculations.

Science.gov (United States)

Sawyer, Jemima E R; Hennebry, James E; Revill, Alexander; Brown, Angus M

2017-06-01

The membrane potential, arising from uneven distribution of ions across cell membranes containing selectively permeable ion channels, is of fundamental importance to cell signaling. The necessity of maintaining the membrane potential may be appreciated by expressing Ohm's law as current = voltage/resistance and recognizing that no current flows when voltage = 0, i.e., transmembrane voltage gradients, created by uneven transmembrane ion concentrations, are an absolute requirement for the generation of currents that precipitate the action and synaptic potentials that consume >80% of the brain's energy budget and underlie the electrical activity that defines brain function. The concept of the equilibrium potential is vital to understanding the origins of the membrane potential. The equilibrium potential defines a potential at which there is no net transmembrane ion flux, where the work created by the concentration gradient is balanced by the transmembrane voltage difference, and derives from a relationship describing the work done by the diffusion of ions down a concentration gradient. The Nernst equation predicts the equilibrium potential and, as such, is fundamental to understanding the interplay between transmembrane ion concentrations and equilibrium potentials. Logarithmic transformation of the ratio of internal and external ion concentrations lies at the heart of the Nernst equation, but most undergraduate neuroscience students have little understanding of the logarithmic function. To compound this, no current undergraduate neuroscience textbooks describe the effect of logarithmic transformation in appreciable detail, leaving the majority of students with little insight into how ion concentrations determine, or how ion perturbations alter, the membrane potential. Copyright © 2017 the American Physiological Society.

Theory of chemical equilibrium in a lattice

International Nuclear Information System (INIS)

Dietrich, K.; Dufour, M.; Balazs, N.L.

1989-01-01

The chemical equilibrium is studied for the reaction A+B↔C, assuming that, initially, the particles B form a lattice and the particles A are statistically distributed on interstices. A mass action law is derived which defines the numbers n A , n B , n C of particles A, B, C in the chemical equilibrium assuming the initial distribution to be known. It predicts a considerably larger number n C of fused particles C compared to the mass action law for the gaseous phase. The result holds for an ordinary as well as for a nuclear lattice. Its possible relevance for the production of proton-rich isotopes in the universe is discussed. (orig.)

Money Inventories in Search Equilibrium

OpenAIRE

Berentsen, Aleksander

1998-01-01

The paper relaxes the one unit storage capacity imposed in the basic search-theoretic model of fiat money with indivisible real commodities and indivisible money. Agents can accumulate as much money as they want. It characterizes the stationary distributions of money and shows that for reasonable parameter values (e.g. production cost, discounting, degree of specialization) a monetary equilibrium exists. There are multiple stationary distributions of a given amount of money, which differ in t...

COVAL, Compound Probability Distribution for Function of Probability Distribution

International Nuclear Information System (INIS)

Astolfi, M.; Elbaz, J.

1979-01-01

1 - Nature of the physical problem solved: Computation of the probability distribution of a function of variables, given the probability distribution of the variables themselves. 'COVAL' has been applied to reliability analysis of a structure subject to random loads. 2 - Method of solution: Numerical transformation of probability distributions

Nonequilibrium approach regarding metals from a linearised kappa distribution

Science.gov (United States)

Domenech-Garret, J. L.

2017-10-01

The widely used kappa distribution functions develop high-energy tails through an adjustable kappa parameter. The aim of this work is to show that such a parameter can itself be regarded as a function, which entangles information about the sources of disequilibrium. We first derive and analyse an expanded Fermi-Dirac kappa distribution. Later, we use this expanded form to obtain an explicit analytical expression for the kappa parameter of a heated metal on which an external electric field is applied. We show that such a kappa index causes departures from equilibrium depending on the physical magnitudes. Finally, we study the role of temperature and electric field on such a parameter, which characterises the electron population of a metal out of equilibrium.

Equilibrium and non-equilibrium extraction separation of rare earth metals in presence of diethylenetriaminepentaacetic acid in aqueous phase

International Nuclear Information System (INIS)

Azis, Abdul; Teramoto, Masaaki; Matsuyama, Hideto.

1995-01-01

Equilibrium and non-equilibrium extraction separations of rare earth metals were carried out in the presence of chelating agent in the aqueous phase. The separation systems of the rare earth metal mixtures used were Y/Dy, Y/Ho, Y/Er and Y/Tm, and the chelating agent and the extractant were diethylenetriaminepentaacetic acid (DTPA) and bis (2,4,4-trimethylpentyl) phosphinic acid (CYANEXR 272), respectively. For Y/Dy and Y/Ho systems, higher selectivities were obtained in equilibrium separation compared with those in non-equilibrium separation. On the other hand, the selectivities in non-equilibrium separation were higher for Y/Er and Y/Tm systems. In the separation condition suitable to each system, the addition of DTPA to the aqueous phase was found to be very effective for obtaining higher selectivities. The distribution ratios of the rare earth metals and the selectivities in the equilibrium separations obtained experimentally were thoroughly analyzed by considering various equilibria such as the extraction equilibrium and the complex formation equilibrium between rare earth metals and DTPA in the aqueous phase. Moreover, the extraction rates and the selectivities in the non-equilibrium separations were also analyzed by the extraction model considering the dissociation reactions of the rare earth metal-DTPA complexes in the aqueous stagnant layer. Based on these analyses, we presented an index which is useful for selecting the optimum operation mode. Using this index, we can predict that the selectivities under equilibrium conditions are higher than those under non-equilibrium conditions for Y/Dy and Y/Ho systems, while for Y/Er and Y/Tm systems, higher selectivities are obtained under non-equilibrium conditions. The experimental results were in agreement with predictions by this index. Further, the selectivities in various systems including other chelating agents and extractants were discussed based on this index. (J.P.N.)

Density distribution function of a self-gravitating isothermal compressible turbulent fluid in the context of molecular clouds ensembles

Science.gov (United States)

Donkov, Sava; Stefanov, Ivan Z.

2018-03-01

We have set ourselves the task of obtaining the probability distribution function of the mass density of a self-gravitating isothermal compressible turbulent fluid from its physics. We have done this in the context of a new notion: the molecular clouds ensemble. We have applied a new approach that takes into account the fractal nature of the fluid. Using the medium equations, under the assumption of steady state, we show that the total energy per unit mass is an invariant with respect to the fractal scales. As a next step we obtain a non-linear integral equation for the dimensionless scale Q which is the third root of the integral of the probability distribution function. It is solved approximately up to the leading-order term in the series expansion. We obtain two solutions. They are power-law distributions with different slopes: the first one is -1.5 at low densities, corresponding to an equilibrium between all energies at a given scale, and the second one is -2 at high densities, corresponding to a free fall at small scales.

Non-equilibrium Green function method: theory and application in simulation of nanometer electronic devices

International Nuclear Information System (INIS)

Do, Van-Nam

2014-01-01

We review fundamental aspects of the non-equilibrium Green function method in the simulation of nanometer electronic devices. The method is implemented into our recently developed computer package OPEDEVS to investigate transport properties of electrons in nano-scale devices and low-dimensional materials. Concretely, we present the definition of the four real-time Green functions, the retarded, advanced, lesser and greater functions. Basic relations among these functions and their equations of motion are also presented in detail as the basis for the performance of analytical and numerical calculations. In particular, we review in detail two recursive algorithms, which are implemented in OPEDEVS to solve the Green functions defined in finite-size opened systems and in the surface layer of semi-infinite homogeneous ones. Operation of the package is then illustrated through the simulation of the transport characteristics of a typical semiconductor device structure, the resonant tunneling diodes. (review)

Structure functions and parton distributions

International Nuclear Information System (INIS)

Olness, F.; Tung, Wu-Ki

1991-04-01

Activities of the structure functions and parton distributions group is summarized. The impact of scheme-dependence of parton distributions (especially sea-quarks and gluons) on the quantitative formulation of the QCD parton model is highlighted. Recent progress on the global analysis of parton distributions is summarized. Issues on the proper use of the next-to-leading parton distributions are stressed

Temperature relaxation in collisional non equilibrium plasmas

Energy Technology Data Exchange (ETDEWEB)

Potapenko, I.F.; Bobylev, A.V.; Azevedo, C.A.; Assis, A.S. [Universidade do Estado, Rio de Janeiro, RJ (Brazil). Inst. de Fisica

1997-12-31

Full text. We study the relaxation of a space uniform plasma composed of electrons and one species of ions. To simplified the consideration, standard approach is usually accepted: the distribution functions are considered to be a Maxwellian with time dependent electron T{sub e}(t) and ion T{sub i}(t) temperatures. This approach imposes a severe restriction on the electron/ion distributions that could be very far from the equilibrium. In the present work the problem is investigated on the basis of the nonlinear kinetic Fokker - Planck equation, which is widely used for the description of collisional plasmas. This equation has many applications in plasma physics as an intrinsic part of physical models, both analytical and numerical. A new detailed description of this classical problem of the collisional plasma kinetic theory is given. A deeper examination of the problem shows that the unusual perturbation theory can not be used. The part of the perturbation of the electron distribution has the character of a boundary layer in the neighborhood of small velocities. In this work the boundary layer is thoroughly studied. The correct distribution electron function is given. Nonmonotonic character of the distribution relaxation in the tail region is observed. The corrected formula for temperature equalization is obtained. The comparison of the calculation results with the asymptotic approach is made. We should stress the important role of the completely conservative different scheme used here, which keeps the symmetric properties of the nonlinear exact equation. This allows us to make calculations without numerical error accumulations, except for machine errors. (author)

Empirical phylogenies and species abundance distributions are consistent with pre-equilibrium dynamics of neutral community models with gene flow

KAUST Repository

Bonnet-Lebrun, Anne-Sophie

2017-03-17

Community characteristics reflect past ecological and evolutionary dynamics. Here, we investigate whether it is possible to obtain realistically shaped modelled communities - i.e., with phylogenetic trees and species abundance distributions shaped similarly to typical empirical bird and mammal communities - from neutral community models. To test the effect of gene flow, we contrasted two spatially explicit individual-based neutral models: one with protracted speciation, delayed by gene flow, and one with point mutation speciation, unaffected by gene flow. The former produced more realistic communities (shape of phylogenetic tree and species-abundance distribution), consistent with gene flow being a key process in macro-evolutionary dynamics. Earlier models struggled to capture the empirically observed branching tempo in phylogenetic trees, as measured by the gamma statistic. We show that the low gamma values typical of empirical trees can be obtained in models with protracted speciation, in pre-equilibrium communities developing from an initially abundant and widespread species. This was even more so in communities sampled incompletely, particularly if the unknown species are the youngest. Overall, our results demonstrate that the characteristics of empirical communities that we have studied can, to a large extent, be explained through a purely neutral model under pre-equilibrium conditions. This article is protected by copyright. All rights reserved.

Empirical phylogenies and species abundance distributions are consistent with pre-equilibrium dynamics of neutral community models with gene flow

KAUST Repository

Bonnet-Lebrun, Anne-Sophie; Manica, Andrea; Eriksson, Anders; Rodrigues, Ana S.L.

2017-01-01

Community characteristics reflect past ecological and evolutionary dynamics. Here, we investigate whether it is possible to obtain realistically shaped modelled communities - i.e., with phylogenetic trees and species abundance distributions shaped similarly to typical empirical bird and mammal communities - from neutral community models. To test the effect of gene flow, we contrasted two spatially explicit individual-based neutral models: one with protracted speciation, delayed by gene flow, and one with point mutation speciation, unaffected by gene flow. The former produced more realistic communities (shape of phylogenetic tree and species-abundance distribution), consistent with gene flow being a key process in macro-evolutionary dynamics. Earlier models struggled to capture the empirically observed branching tempo in phylogenetic trees, as measured by the gamma statistic. We show that the low gamma values typical of empirical trees can be obtained in models with protracted speciation, in pre-equilibrium communities developing from an initially abundant and widespread species. This was even more so in communities sampled incompletely, particularly if the unknown species are the youngest. Overall, our results demonstrate that the characteristics of empirical communities that we have studied can, to a large extent, be explained through a purely neutral model under pre-equilibrium conditions. This article is protected by copyright. All rights reserved.

Density Functional Study of Chemical Reaction Equilibrium for Dimerization Reactions in Slit and Cylindrical Nanopores

Czech Academy of Sciences Publication Activity Database

Malijevský, Alexandr; Lísal, Martin

2009-01-01

Roč. 130, č. 16 (2009), 164713-1-24 ISSN 0021-9606 R&D Projects: GA ČR GA203/05/0725; GA AV ČR 1ET400720507; GA AV ČR KAN400720701 Institutional research plan: CEZ:AV0Z40720504 Keywords : density functional theory * reaction ensemble Monte Carlo * reaction equilibrium Subject RIV: CF - Physical ; Theoretical Chemistry Impact factor: 3.093, year: 2009

Collision integral and equilibrium distributions for a bounded plasma

International Nuclear Information System (INIS)

Zagorodnij, A.G.; Usenko, A.S.; Yakimenko, I.P.

1985-01-01

A kinetic equation of Balesku-Lennard type for multicomponent system of charged particle limited by two flat-parallel surfaces is derived on the basis of the general theory of electromagnetic fluctuations in plasma. Equilibrium values of collision integral for a plasma with arbitrary configuration boundaries are calculated and general ratios describing charged particles density profiles in such systems are obtained

Equilibrium Solubility of CO2 in Alkanolamines

DEFF Research Database (Denmark)

Waseem Arshad, Muhammad; Fosbøl, Philip Loldrup; von Solms, Nicolas

2014-01-01

Equilibrium solubility of CO2 were measured in aqueous solutions of Monoethanolamine (MEA) and N,N-diethylethanolamine(DEEA). Equilibrium cells are generally used for these measurements. In this study, the equilibrium data were measured from the calorimetry. For this purpose a reaction calorimeter...... (model CPA 122 from ChemiSens AB, Sweden) was used. The advantage of this method is being the measurement of both heats of absorption and equilibrium solubility data of CO2 at the same time. The measurements were performed for 30 mass % MEA and 5M DEEA solutions as a function of CO2 loading at three...... different temperatures 40, 80 and 120 ºC. The measured 30 mass % MEA and 5M DEEA data were compared with the literature data obtained from different equilibrium cells which validated the use of calorimeters for equilibrium solubility measurements....

Positivity of time-frequency distribution functions

NARCIS (Netherlands)

Janssen, A.J.E.M.

1988-01-01

This paper deals with the question how various 'natural' conditions posed on time-frequency distribution functions prevent them to be nonnegative everywhere for all signals. The attention is restricted mainly to distribution functions that involve the signal bilinearly. This paper summarizes and

Computer simulations of equilibrium magnetization and microstructure in magnetic fluids

Science.gov (United States)

Rosa, A. P.; Abade, G. C.; Cunha, F. R.

2017-09-01

In this work, Monte Carlo and Brownian Dynamics simulations are developed to compute the equilibrium magnetization of a magnetic fluid under action of a homogeneous applied magnetic field. The particles are free of inertia and modeled as hard spheres with the same diameters. Two different periodic boundary conditions are implemented: the minimum image method and Ewald summation technique by replicating a finite number of particles throughout the suspension volume. A comparison of the equilibrium magnetization resulting from the minimum image approach and Ewald sums is performed by using Monte Carlo simulations. The Monte Carlo simulations with minimum image and lattice sums are used to investigate suspension microstructure by computing the important radial pair-distribution function go(r), which measures the probability density of finding a second particle at a distance r from a reference particle. This function provides relevant information on structure formation and its anisotropy through the suspension. The numerical results of go(r) are compared with theoretical predictions based on quite a different approach in the absence of the field and dipole-dipole interactions. A very good quantitative agreement is found for a particle volume fraction of 0.15, providing a validation of the present simulations. In general, the investigated suspensions are dominated by structures like dimmer and trimmer chains with trimmers having probability to form an order of magnitude lower than dimmers. Using Monte Carlo with lattice sums, the density distribution function g2(r) is also examined. Whenever this function is different from zero, it indicates structure-anisotropy in the suspension. The dependence of the equilibrium magnetization on the applied field, the magnetic particle volume fraction, and the magnitude of the dipole-dipole magnetic interactions for both boundary conditions are explored in this work. Results show that at dilute regimes and with moderate dipole

Distribution function of dark matter

International Nuclear Information System (INIS)

Evans, N. Wyn; An, Jin H.

2006-01-01

There is good evidence from N-body simulations that the velocity distribution in the outer parts of halos is radially anisotropic, with the kinetic energy in the radial direction roughly equal to the sum of that in the two tangential directions. We provide a simple algorithm to generate such cosmologically important distribution functions. Introducing r E (E), the radius of the largest orbit of a particle with energy E, we show how to write down almost trivially a distribution function of the form f(E,L)=L -1 g(r E ) for any spherical model - including the 'universal' halo density law (Navarro-Frenk-White profile). We in addition give the generic form of the distribution function for any model with a local density power-law index α and anisotropy parameter β and provide limiting forms appropriate for the central parts and envelopes of dark matter halos. From those, we argue that, regardless of the anisotropy, the density falloff at large radii must evolve to ρ∼r -4 or steeper ultimately

Support of the extremal measure in a vector equilibrium problem

International Nuclear Information System (INIS)

Lapik, M A

2006-01-01

A generalization of the Mhaskar-Saff functional is obtained for a vector equilibrium problem with an external field. As an application, the supports of the equilibrium measures are found in a special vector equilibrium problem with Nikishin matrix.

Asymptotic numbers, asymptotic functions and distributions

International Nuclear Information System (INIS)

Todorov, T.D.

1979-07-01

The asymptotic functions are a new type of generalized functions. But they are not functionals on some space of test-functions as the distributions of Schwartz. They are mappings of the set denoted by A into A, where A is the set of the asymptotic numbers introduced by Christov. On its part A is a totally-ordered set of generalized numbers including the system of real numbers R as well as infinitesimals and infinitely large numbers. Every two asymptotic functions can be multiplied. On the other hand, the distributions have realizations as asymptotic functions in a certain sense. (author)

On the distribution functions in the quantum mechanics and Wigner functions

International Nuclear Information System (INIS)

Kuz'menkov, L.S.; Maksimov, S.G.

2002-01-01

The problem on the distribution functions, leading to the similar local values of the particles number, pulse and energy, as in the quantum mechanics, is formulated and solved. The method is based on the quantum-mechanical determination of the probability density. The derived distribution function coincides with the Wigner function only for the spatial-homogeneous systems. The Bogolyubov equations chain, the Liouville equation for the distribution quantum functions by any number of particles in the system, the general expression for the tensor of the dielectric permittivity of the plasma electron component are obtained [ru

A generalized quantitative antibody homeostasis model: maintenance of global antibody equilibrium by effector functions.

Science.gov (United States)

Prechl, József

2017-11-01

The homeostasis of antibodies can be characterized as a balanced production, target-binding and receptor-mediated elimination regulated by an interaction network, which controls B-cell development and selection. Recently, we proposed a quantitative model to describe how the concentration and affinity of interacting partners generates a network. Here we argue that this physical, quantitative approach can be extended for the interpretation of effector functions of antibodies. We define global antibody equilibrium as the zone of molar equivalence of free antibody, free antigen and immune complex concentrations and of dissociation constant of apparent affinity: [Ab]=[Ag]=[AbAg]= K D . This zone corresponds to the biologically relevant K D range of reversible interactions. We show that thermodynamic and kinetic properties of antibody-antigen interactions correlate with immunological functions. The formation of stable, long-lived immune complexes correspond to a decrease of entropy and is a prerequisite for the generation of higher-order complexes. As the energy of formation of complexes increases, we observe a gradual shift from silent clearance to inflammatory reactions. These rules can also be applied to complement activation-related immune effector processes, linking the physicochemical principles of innate and adaptive humoral responses. Affinity of the receptors mediating effector functions shows a wide range of affinities, allowing the continuous sampling of antibody-bound antigen over the complete range of concentrations. The generation of multivalent, multicomponent complexes triggers effector functions by crosslinking these receptors on effector cells with increasing enzymatic degradation potential. Thus, antibody homeostasis is a thermodynamic system with complex network properties, nested into the host organism by proper immunoregulatory and effector pathways. Maintenance of global antibody equilibrium is achieved by innate qualitative signals modulating a

Applicability of Donnan equilibrium theory at nanochannel-reservoir interfaces.

Science.gov (United States)

Tian, Huanhuan; Zhang, Li; Wang, Moran

2015-08-15

Understanding ionic transport in nanochannels has attracted broad attention from various areas in energy and environmental fields. In most pervious research, Donnan equilibrium has been applied widely to nanofluidic systems to obtain ionic concentration and electrical potential at channel-reservoir interfaces; however, as well known that Donnan equilibrium is derived from classical thermodynamic theories with equilibrium assumptions. Therefore the applicability of the Donnan equilibrium may be questionable when the transport at nanochannel-reservoir interface is strongly non-equilibrium. In this work, the Poisson-Nernst-Planck model for ion transport is numerically solved to obtain the exact distributions of ionic concentration and electrical potential. The numerical results are quantitatively compared with the Donnan equilibrium predictions. The applicability of Donnan equilibrium is therefore justified by changing channel length, reservoir ionic concentration, surface charge density and channel height. The results indicate that the Donnan equilibrium is not applicable for short nanochannels, large concentration difference and wide openings. A non-dimensional parameter, Q factor, is proposed to measure the non-equilibrium extent and the relation between Q and the working conditions is studied in detail. Copyright © 2015 Elsevier Inc. All rights reserved.

Partition functions. I. Improved partition functions and thermodynamic quantities for normal, equilibrium, and ortho and para molecular hydrogen

Science.gov (United States)

Popovas, A.; Jørgensen, U. G.

2016-11-01

Context. Hydrogen is the most abundant molecule in the Universe. Its thermodynamic quantities dominate the physical conditions in molecular clouds, protoplanetary disks, etc. It is also of high interest in plasma physics. Therefore thermodynamic data for molecular hydrogen have to be as accurate as possible in a wide temperature range. Aims: We here rigorously show the shortcomings of various simplifications that are used to calculate the total internal partition function. These shortcomings can lead to errors of up to 40 percent or more in the estimated partition function. These errors carry on to calculations of thermodynamic quantities. Therefore a more complicated approach has to be taken. Methods: Seven possible simplifications of various complexity are described, together with advantages and disadvantages of direct summation of experimental values. These were compared to what we consider the most accurate and most complete treatment (case 8). Dunham coefficients were determined from experimental and theoretical energy levels of a number of electronically excited states of H2. Both equilibrium and normal hydrogen was taken into consideration. Results: Various shortcomings in existing calculations are demonstrated, and the reasons for them are explained. New partition functions for equilibrium, normal, and ortho and para hydrogen are calculated and thermodynamic quantities are reported for the temperature range 1-20 000 K. Our results are compared to previous estimates in the literature. The calculations are not limited to the ground electronic state, but include all bound and quasi-bound levels of excited electronic states. Dunham coefficients of these states of H2 are also reported. Conclusions: For most of the relevant astrophysical cases it is strongly advised to avoid using simplifications, such as a harmonic oscillator and rigid rotor or ad hoc summation limits of the eigenstates to estimate accurate partition functions and to be particularly careful when

Intermittent Fermi-Pasta-Ulam Dynamics at Equilibrium

Science.gov (United States)

Campbell, David; Danieli, Carlo; Flach, Sergej

The equilibrium value of an observable defines a manifold in the phase space of an ergodic and equipartitioned many-body syste. A typical trajectory pierces that manifold infinitely often as time goes to infinity. We use these piercings to measure both the relaxation time of the lowest frequency eigenmode of the Fermi-Pasta-Ulam chain, as well as the fluctuations of the subsequent dynamics in equilibrium. We show that previously obtained scaling laws for equipartition times are modified at low energy density due to an unexpected slowing down of the relaxation. The dynamics in equilibrium is characterized by a power-law distribution of excursion times far off equilibrium, with diverging variance. The long excursions arise from sticky dynamics close to regular orbits in the phase space. Our method is generalizable to large classes of many-body systems. The authors acknowledge financial support from IBS (Project Code IBS-R024-D1).

Non-equilibrium synergistic effects in atmospheric pressure plasmas.

Science.gov (United States)

Guo, Heng; Zhang, Xiao-Ning; Chen, Jian; Li, He-Ping; Ostrikov, Kostya Ken

2018-03-19

Non-equilibrium is one of the important features of an atmospheric gas discharge plasma. It involves complicated physical-chemical processes and plays a key role in various actual plasma processing. In this report, a novel complete non-equilibrium model is developed to reveal the non-equilibrium synergistic effects for the atmospheric-pressure low-temperature plasmas (AP-LTPs). It combines a thermal-chemical non-equilibrium fluid model for the quasi-neutral plasma region and a simplified sheath model for the electrode sheath region. The free-burning argon arc is selected as a model system because both the electrical-thermal-chemical equilibrium and non-equilibrium regions are involved simultaneously in this arc plasma system. The modeling results indicate for the first time that it is the strong and synergistic interactions among the mass, momentum and energy transfer processes that determine the self-consistent non-equilibrium characteristics of the AP-LTPs. An energy transfer process related to the non-uniform spatial distributions of the electron-to-heavy-particle temperature ratio has also been discovered for the first time. It has a significant influence for self-consistently predicting the transition region between the "hot" and "cold" equilibrium regions of an AP-LTP system. The modeling results would provide an instructive guidance for predicting and possibly controlling the non-equilibrium particle-energy transportation process in various AP-LTPs in future.

Equilibrium Droplets on Deformable Substrates: Equilibrium Conditions.

Science.gov (United States)

Koursari, Nektaria; Ahmed, Gulraiz; Starov, Victor M

2018-05-15

Equilibrium conditions of droplets on deformable substrates are investigated, and it is proven using Jacobi's sufficient condition that the obtained solutions really provide equilibrium profiles of both the droplet and the deformed support. At the equilibrium, the excess free energy of the system should have a minimum value, which means that both necessary and sufficient conditions of the minimum should be fulfilled. Only in this case, the obtained profiles provide the minimum of the excess free energy. The necessary condition of the equilibrium means that the first variation of the excess free energy should vanish, and the second variation should be positive. Unfortunately, the mentioned two conditions are not the proof that the obtained profiles correspond to the minimum of the excess free energy and they could not be. It is necessary to check whether the sufficient condition of the equilibrium (Jacobi's condition) is satisfied. To the best of our knowledge Jacobi's condition has never been verified for any already published equilibrium profiles of both the droplet and the deformable substrate. A simple model of the equilibrium droplet on the deformable substrate is considered, and it is shown that the deduced profiles of the equilibrium droplet and deformable substrate satisfy the Jacobi's condition, that is, really provide the minimum to the excess free energy of the system. To simplify calculations, a simplified linear disjoining/conjoining pressure isotherm is adopted for the calculations. It is shown that both necessary and sufficient conditions for equilibrium are satisfied. For the first time, validity of the Jacobi's condition is verified. The latter proves that the developed model really provides (i) the minimum of the excess free energy of the system droplet/deformable substrate and (ii) equilibrium profiles of both the droplet and the deformable substrate.

Kinetics and equilibrium modelling of lead uptake by algae Gelidium and algal waste from agar extraction industry.

Science.gov (United States)

Vilar, Vítor J P; Botelho, Cidália M S; Boaventura, Rui A R

2007-05-08

Pb(II) biosorption onto algae Gelidium, algal waste from agar extraction industry and a composite material was studied. Discrete and continuous site distribution models were used to describe the biosorption equilibrium at different pH (5.3, 4 and 3), considering competition among Pb(II) ions and protons. The affinity distribution function of Pb(II) on the active sites was calculated by the Sips distribution. The Langmuir equilibrium constant was compared with the apparent affinity calculated by the discrete model, showing higher affinity for lead ions at higher pH values. Kinetic experiments were conducted at initial Pb(II) concentrations of 29-104 mgl(-1) and data fitted to pseudo-first Lagergren and second-order models. The adsorptive behaviour of biosorbent particles was modelled using a batch mass transfer kinetic model, which successfully predicts Pb(II) concentration profiles at different initial lead concentration and pH, and provides significant insights on the biosorbents performance. Average values of homogeneous diffusivity, D(h), are 3.6 x 10(-8); 6.1 x 10(-8) and 2.4 x 10(-8)cm(2)s(-1), respectively, for Gelidium, algal waste and composite material. The concentration of lead inside biosorbent particles follows a parabolic profile that becomes linear near equilibrium.

Kinetics and equilibrium modelling of lead uptake by algae Gelidium and algal waste from agar extraction industry

International Nuclear Information System (INIS)

Vilar, Vitor J.P.; Botelho, Cidalia M.S.; Boaventura, Rui A.R.

2007-01-01

Pb(II) biosorption onto algae Gelidium, algal waste from agar extraction industry and a composite material was studied. Discrete and continuous site distribution models were used to describe the biosorption equilibrium at different pH (5.3, 4 and 3), considering competition among Pb(II) ions and protons. The affinity distribution function of Pb(II) on the active sites was calculated by the Sips distribution. The Langmuir equilibrium constant was compared with the apparent affinity calculated by the discrete model, showing higher affinity for lead ions at higher pH values. Kinetic experiments were conducted at initial Pb(II) concentrations of 29-104 mg l -1 and data fitted to pseudo-first Lagergren and second-order models. The adsorptive behaviour of biosorbent particles was modelled using a batch mass transfer kinetic model, which successfully predicts Pb(II) concentration profiles at different initial lead concentration and pH, and provides significant insights on the biosorbents performance. Average values of homogeneous diffusivity, D h , are 3.6 x 10 -8 ; 6.1 x 10 -8 and 2.4 x 10 -8 cm 2 s -1 , respectively, for Gelidium, algal waste and composite material. The concentration of lead inside biosorbent particles follows a parabolic profile that becomes linear near equilibrium

Kinetics and equilibrium modelling of lead uptake by algae Gelidium and algal waste from agar extraction industry

Energy Technology Data Exchange (ETDEWEB)

Vilar, Vitor J.P. [Laboratory of Separation and Reaction Engineering (LSRE), Departamento de Engenharia Quimica, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, 4200-465 Porto (Portugal); Botelho, Cidalia M.S. [Laboratory of Separation and Reaction Engineering (LSRE), Departamento de Engenharia Quimica, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, 4200-465 Porto (Portugal); Boaventura, Rui A.R. [Laboratory of Separation and Reaction Engineering (LSRE), Departamento de Engenharia Quimica, Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias, 4200-465 Porto (Portugal)]. E-mail: bventura@fe.up.pt

2007-05-08

Pb(II) biosorption onto algae Gelidium, algal waste from agar extraction industry and a composite material was studied. Discrete and continuous site distribution models were used to describe the biosorption equilibrium at different pH (5.3, 4 and 3), considering competition among Pb(II) ions and protons. The affinity distribution function of Pb(II) on the active sites was calculated by the Sips distribution. The Langmuir equilibrium constant was compared with the apparent affinity calculated by the discrete model, showing higher affinity for lead ions at higher pH values. Kinetic experiments were conducted at initial Pb(II) concentrations of 29-104 mg l{sup -1} and data fitted to pseudo-first Lagergren and second-order models. The adsorptive behaviour of biosorbent particles was modelled using a batch mass transfer kinetic model, which successfully predicts Pb(II) concentration profiles at different initial lead concentration and pH, and provides significant insights on the biosorbents performance. Average values of homogeneous diffusivity, D {sub h}, are 3.6 x 10{sup -8}; 6.1 x 10{sup -8} and 2.4 x 10{sup -8} cm{sup 2} s{sup -1}, respectively, for Gelidium, algal waste and composite material. The concentration of lead inside biosorbent particles follows a parabolic profile that becomes linear near equilibrium.

Multiplicity distributions and multiplicity correlations in sequential, off-equilibrium fragmentation process

International Nuclear Information System (INIS)

Botet, R.

1996-01-01

A new kinetic fragmentation model, the Fragmentation - Inactivation -Binary (FIB) model is described where a dissipative process stops randomly the sequential, conservative and off-equilibrium fragmentation process. (K.A.)

Analysis of competitive power market with constant elasticity function

International Nuclear Information System (INIS)

Nguyen, D.H.M.; Wong, K.P.

2003-01-01

A solution method, for competitive power markets formulated as a Cournot game, that allows equilibrium to be determined without an explicit model of aggregated demand is presented. The method determines market equilibrium for all feasible demand conditions and thus provides a perspective on the market, independent of representative demand function, that reveals the inherent tendencies of producers in the market. Numerical solutions are determined by use of the new controlled genetic algorithm and constraint handling techniques. The solutions give production and demand elasticity distributions of the market at any feasible equilibrium price and volume. The solution distributions evaluated for the market with unspecified demand functions, were found to be consistent with previous results obtained from markets with specific demand functions. The ability of the new approach to all, and arbitrary, solutions allow specific markets to be examined, as well as very general observations to be made. Generally it was observed that: no inherent price constraint exists; price is more volatile for low volumes and high prices; market dominance and power are unaffected by price; and inelastic demand can give rise to equilibrium with lower price than responsive demand. (Author)

Microscopic Simulation and Macroscopic Modeling for Thermal and Chemical Non-Equilibrium

Science.gov (United States)

Liu, Yen; Panesi, Marco; Vinokur, Marcel; Clarke, Peter

2013-01-01

This paper deals with the accurate microscopic simulation and macroscopic modeling of extreme non-equilibrium phenomena, such as encountered during hypersonic entry into a planetary atmosphere. The state-to-state microscopic equations involving internal excitation, de-excitation, dissociation, and recombination of nitrogen molecules due to collisions with nitrogen atoms are solved time-accurately. Strategies to increase the numerical efficiency are discussed. The problem is then modeled using a few macroscopic variables. The model is based on reconstructions of the state distribution function using the maximum entropy principle. The internal energy space is subdivided into multiple groups in order to better describe the non-equilibrium gases. The method of weighted residuals is applied to the microscopic equations to obtain macroscopic moment equations and rate coefficients. The modeling is completely physics-based, and its accuracy depends only on the assumed expression of the state distribution function and the number of groups used. The model makes no assumption at the microscopic level, and all possible collisional and radiative processes are allowed. The model is applicable to both atoms and molecules and their ions. Several limiting cases are presented to show that the model recovers the classical twotemperature models if all states are in one group and the model reduces to the microscopic equations if each group contains only one state. Numerical examples and model validations are carried out for both the uniform and linear distributions. Results show that the original over nine thousand microscopic equations can be reduced to 2 macroscopic equations using 1 to 5 groups with excellent agreement. The computer time is decreased from 18 hours to less than 1 second.

Equilibrium econophysics: A unified formalism for neoclassical economics and equilibrium thermodynamics

Science.gov (United States)

Sousa, Tânia; Domingos, Tiago

2006-11-01

We develop a unified conceptual and mathematical structure for equilibrium econophysics, i.e., the use of concepts and tools of equilibrium thermodynamics in neoclassical microeconomics and vice versa. Within this conceptual structure the results obtained in microeconomic theory are: (1) the definition of irreversibility in economic behavior; (2) the clarification that the Engel curve and the offer curve are not descriptions of real processes dictated by the maximization of utility at constant endowment; (3) the derivation of a relation between elasticities proving that economic elasticities are not all independent; (4) the proof that Giffen goods do not exist in a stable equilibrium; (5) the derivation that ‘economic integrability’ is equivalent to the generalized Le Chatelier principle and (6) the definition of a first order phase transition, i.e., a transition between separate points in the utility function. In thermodynamics the results obtained are: (1) a relation between the non-dimensional isothermal and adiabatic compressibilities and the increase or decrease in the thermodynamic potentials; (2) the distinction between mathematical integrability and optimization behavior and (3) the generalization of the Clapeyron equation.

Family of probability distributions derived from maximal entropy principle with scale invariant restrictions.

Science.gov (United States)

Sonnino, Giorgio; Steinbrecher, György; Cardinali, Alessandro; Sonnino, Alberto; Tlidi, Mustapha

2013-01-01

Using statistical thermodynamics, we derive a general expression of the stationary probability distribution for thermodynamic systems driven out of equilibrium by several thermodynamic forces. The local equilibrium is defined by imposing the minimum entropy production and the maximum entropy principle under the scale invariance restrictions. The obtained probability distribution presents a singularity that has immediate physical interpretation in terms of the intermittency models. The derived reference probability distribution function is interpreted as time and ensemble average of the real physical one. A generic family of stochastic processes describing noise-driven intermittency, where the stationary density distribution coincides exactly with the one resulted from entropy maximization, is presented.

Capability Assessment of the Equilibrium Field System in KTX

International Nuclear Information System (INIS)

Luo Bing; You Wei; Tan Mingsheng; Bai Wei; Mao Wenzhe; Li Hong; Liu Adi; Lan Tao; Xie Jinlin; Liu Wandong; Luo Zhengping; Xiao Bingjia; Guo Yong

2016-01-01

Radial equilibrium of the KTX plasma column is maintained by the vertical field which is produced by the equilibrium field coils. The equilibrium is also affected by the eddy current, which is generated by the coupling of copper shell, plasma and poloidal field coils. An equivalent circuit model is developed to analyze the dynamic performance of equilibrium field coils, without auxiliary power input to equilibrium field coils and passive conductors. Considering the coupling of poloidal field coils, copper shell and plasma, the evolution of spatial distribution of the eddy current density on the copper shell is estimated by finite element to analyze the effect of shell to balance. The simulation results show that the copper shell and equilibrium field coils can provide enough vertical field to balance 1 MA plasma current in phase 1 of a KTX discharge. Auxiliary power supply on the EQ coils is necessary to control the horizontal displacement of KTX due to the finite resistance effect of the shell. (paper)

Plasma equilibrium response modelling and validation on JT-60U

International Nuclear Information System (INIS)

Lister, J.B.; Sharma, A.; Limebeer, D.J.N.; Wainwright, J.P.; Nakamura, Y.; Yoshino, R.

2002-01-01

A systematic procedure to identify the plasma equilibrium response to the poloidal field coil voltages has been applied to the JT-60U tokamak. The required response was predicted with a high accuracy by a state-space model derived from first principles. The ab initio derivation of linearized plasma equilibrium response models is re-examined using an approach standard in analytical mechanics. A symmetric formulation is naturally obtained, removing a previous weakness in such models. RZIP, a rigid current distribution model, is re-derived using this approach and is compared with the new experimental plasma equilibrium response data obtained from Ohmic and neutral beam injection discharges in the JT-60U tokamak. In order to remove any bias from the comparison between modelled and measured plasma responses, the electromagnetic response model without plasma was first carefully tuned against experimental data, using a parametric approach, for which different cost functions for quantifying model agreement were explored. This approach additionally provides new indications of the accuracy to which various plasma parameters are known, and to the ordering of physical effects. Having taken these precautions when tuning the plasmaless model, an empirical estimate of the plasma self-inductance, the plasma resistance and its radial derivative could be established and compared with initial assumptions. Off-line tuning of the JT-60U controller is presented as an example of the improvements which might be obtained by using such a model of the plasma equilibrium response. (author)

Equilibrium-point control of human elbow-joint movement under isometric environment by using multichannel functional electrical stimulation

Directory of Open Access Journals (Sweden)

Kazuhiro eMatsui

2014-06-01

Full Text Available Functional electrical stimulation (FES is considered an effective technique for aiding quadriplegic persons. However, the human musculoskeletal system has highly nonlinearity and redundancy. It is thus difficult to stably and accurately control limbs using FES. In this paper, we propose a simple FES method that is consistent with the motion-control mechanism observed in humans. We focus on joint motion by a pair of agonist-antagonist muscles of the musculoskeletal system, and define theelectrical agonist-antagonist muscle ratio (EAA ratio and electrical agonist-antagonist muscle activity (EAA activity in light of the agonist-antagonist muscle ratio and agonist-antagonist muscle activity, respectively, to extract the equilibrium point and joint stiffness from electromyography (EMG signals. These notions, the agonist-antagonist muscle ratio and agonist-antagonist muscle activity, are based on the hypothesis that the equilibrium point and stiffness of the agonist-antagonist motion system are controlled by the central nervous system. We derived the transfer function between the input EAA ratio and force output of the end-point. We performed some experiments in an isometric environment using six subjects. This transfer-function model is expressed as a cascade-coupled dead time element and a second-order system. High-speed, high-precision, smooth control of the hand force were achieved through the agonist-antagonist muscle stimulation pattern determined by this transfer function model.

Equilibrium-point control of human elbow-joint movement under isometric environment by using multichannel functional electrical stimulation.

Science.gov (United States)

Matsui, Kazuhiro; Hishii, Yasuo; Maegaki, Kazuya; Yamashita, Yuto; Uemura, Mitsunori; Hirai, Hiroaki; Miyazaki, Fumio

2014-01-01

Functional electrical stimulation (FES) is considered an effective technique for aiding quadriplegic persons. However, the human musculoskeletal system has highly non-linearity and redundancy. It is thus difficult to stably and accurately control limbs using FES. In this paper, we propose a simple FES method that is consistent with the motion-control mechanism observed in humans. We focus on joint motion by a pair of agonist-antagonist muscles of the musculoskeletal system, and define the "electrical agonist-antagonist muscle ratio (EAA ratio)" and "electrical agonist-antagonist muscle activity (EAA activity)" in light of the agonist-antagonist muscle ratio and agonist-antagonist muscle activity, respectively, to extract the equilibrium point and joint stiffness from electromyography (EMG) signals. These notions, the agonist-antagonist muscle ratio and agonist-antagonist muscle activity, are based on the hypothesis that the equilibrium point and stiffness of the agonist-antagonist motion system are controlled by the central nervous system. We derived the transfer function between the input EAA ratio and force output of the end-point. We performed some experiments in an isometric environment using six subjects. This transfer-function model is expressed as a cascade-coupled dead time element and a second-order system. High-speed, high-precision, smooth control of the hand force were achieved through the agonist-antagonist muscle stimulation pattern determined by this transfer function model.

MHD equilibrium identification on ASDEX-Upgrade

International Nuclear Information System (INIS)

McCarthy, P.J.; Schneider, W.; Lakner, K.; Zehrfeld, H.P.; Buechl, K.; Gernhardt, J.; Gruber, O.; Kallenbach, A.; Lieder, G.; Wunderlich, R.

1992-01-01

A central activity accompanying the ASDEX-Upgrade experiment is the analysis of MHD equilibria. There are two different numerical methods available, both using magnetic measurements which reflect equilibrium states of the plasma. The first method proceeds via a function parameterization (FP) technique, which uses in-vessel magnetic measurements to calculate up to 66 equilibrium parameters. The second method applies an interpretative equilibrium code (DIVA) for a best fit to a different set of magnetic measurements. Cross-checks with the measured particle influxes from the inner heat shield and the divertor region and with visible camera images of the scrape-off layer are made. (author) 3 refs., 3 figs

Computation of thermodynamic equilibrium in systems under stress

Science.gov (United States)

Vrijmoed, Johannes C.; Podladchikov, Yuri Y.

2016-04-01

Metamorphic reactions may be partly controlled by the local stress distribution as suggested by observations of phase assemblages around garnet inclusions related to an amphibolite shear zone in granulite of the Bergen Arcs in Norway. A particular example presented in fig. 14 of Mukai et al. [1] is discussed here. A garnet crystal embedded in a plagioclase matrix is replaced on the left side by a high pressure intergrowth of kyanite and quartz and on the right side by chlorite-amphibole. This texture apparently represents disequilibrium. In this case, the minerals adapt to the low pressure ambient conditions only where fluids were present. Alternatively, here we compute that this particular low pressure and high pressure assemblage around a stressed rigid inclusion such as garnet can coexist in equilibrium. To do the computations we developed the Thermolab software package. The core of the software package consists of Matlab functions that generate Gibbs energy of minerals and melts from the Holland and Powell database [2] and aqueous species from the SUPCRT92 database [3]. Most up to date solid solutions are included in a general formulation. The user provides a Matlab script to do the desired calculations using the core functions. Gibbs energy of all minerals, solutions and species are benchmarked versus THERMOCALC, PerpleX [4] and SUPCRT92 and are reproduced within round off computer error. Multi-component phase diagrams have been calculated using Gibbs minimization to benchmark with THERMOCALC and Perple_X. The Matlab script to compute equilibrium in a stressed system needs only two modifications of the standard phase diagram script. Firstly, Gibbs energy of phases considered in the calculation is generated for multiple values of thermodynamic pressure. Secondly, for the Gibbs minimization the proportion of the system at each particular thermodynamic pressure needs to be constrained. The user decides which part of the stress tensor is input as thermodynamic

Kinetic equilibrium for an asymmetric tangential layer with rotation of the magnetic field

Science.gov (United States)

Belmont, Gérard; Dorville, Nicolas; Aunai, Nicolas; Rezeau, Laurence

2015-04-01

Finding kinetic equilibria for tangential current layers is a key issue for modeling plasma phenomena such as magnetic reconnection instabilities, for which theoretical and numerical studies have to start from steady-state current layers. Until 2012, all theoretical models -starting with the most famous "Harris" one- relied on distribution functions built as mono-valued functions of the trajectories invariants. For a coplanar anti-symmetric magnetic field and in absence of electric field, these models were only able to model symmetric variations of the plasma, so precluding any modeling of "magnetopause-like'' layers, which separate two plasmas of different densities and temperatures. Recently, the "BAS" model was presented (Belmont et al., 2012), where multi-valued functions were taken into account. This new tool is made necessary each time the magnetic field reversal occurs on scales larger than the particle Larmor radii, and therefore guaranties a logical transition with the MHD modeling of large scales. The BAS model so provides a new asymmetric equilibrium. It has been validated in a hybrid simulation by Aunai et al (2013), and more recently in a fully kinetic simulation as well. For this original equilibrium to be computed, the magnetic field had to stay coplanar inside the layer. We present here an important generalization, where the magnetic field rotates inside the layer (although restricted to a 180° rotation hitherto). The tangential layers so obtained are thus closer to those encountered at the real magnetopause. This will be necessary, in the future, for comparing directly the theoretical profiles with the experimental ones for the various physical parameters. As it was done previously, the equilibrium is presently tested with a hybrid simulation. Belmont, G.; Aunai, N.; Smets, R., Kinetic equilibrium for an asymmetric tangential layer, Physics of Plasmas, Volume 19, Issue 2, pp. 022108-022118-10, 2012 Aunai, N.; Belmont, G.; Smets, R., First

Non-equilibrium statistical theory about microscopic fatigue cracks of metal in magnetic field

International Nuclear Information System (INIS)

Zhao-Long, Liu; Hai-Yun, Hu; Tian-You, Fan; Xiu-San, Xing

2010-01-01

This paper develops the non-equilibrium statistical fatigue damage theory to study the statistical behaviour of micro-crack for metals in magnetic field. The one-dimensional homogeneous crack system is chosen for study. To investigate the effect caused by magnetic field on the statistical distribution of micro-crack in the system, the theoretical analysis on microcrack evolution equation, the average length of micro-crack, density distribution function of micro-crack and fatigue fracture probability have been performed. The derived results relate the changes of some quantities, such as average length, density distribution function and fatigue fracture probability, to the applied magnetic field, the magnetic and mechanical properties of metals. It gives a theoretical explanation on the change of fatigue damage due to magnetic fields observed by experiments, and presents an analytic approach on studying the fatigue damage of metal in magnetic field. (cross-disciplinary physics and related areas of science and technology)

Predicting the Equilibrium Deuterium-Tritium Fuel Layer Thickness Profile in an Indirect-Drive Hohlraum Capsule

International Nuclear Information System (INIS)

Sanchez, Jorge J.; Giedt, Warren H.

2004-01-01

A numerical procedure for calculating the equilibrium thickness distribution of a thin layer of deuterium and tritium on the inner surface of an indirect drive target sphere (∼2.0 mm in diameter) is described. Starting with an assumed uniform thickness layer and with specified thermal boundary conditions, the temperature distribution throughout the capsule and hohlraum (including natural convection in the hohlraum gas) is calculated. Results are used to make a first estimate of the final non-uniform thickness distribution of the layer. This thickness distribution is then used to make a second calculation of the temperature distribution with the same boundary conditions. Legendre polynomial coefficients are evaluated for the two temperature distributions and the two thickness profiles. Final equilibrium Legendre coefficients are determined by linear extrapolation. From these coefficients, the equilibrium layer thickness can be computed

Wigner distribution function for an oscillator

International Nuclear Information System (INIS)

Davies, R.W.; Davies, K.T.R.

1975-01-01

We present two new derivations of the Wigner distribution function for a simple harmonic oscillator Hamiltonian. Both methods are facilitated using a formula which expresses the Wigner function as a simple trace. The first method of derivation utilizes a modification of a theorem due to Messiah. An alternative procedure makes use of the coherent state representation of an oscillator. The Wigner distribution function gives a semiclassical joint probability for finding the system with given coordinates and momenta, and the joint probability is factorable for the special case of an oscillator. An important application of this result occurs in the theory of nuclear fission for calculating the probability distributions for the masses, kinetic energies, and vibrational energies of the fission fragments at infinite separation. (U.S.)

Equilibrium structure and Ti-catalyzed H-2 desorption in NaAlH4 nanoparticles from density functional theory

DEFF Research Database (Denmark)

Vegge, T.

2006-01-01

the kinetics significantly, the physical understanding remains elusive. Density functional theory is used to calculate the energy of the potential low energy surfaces of NaAlH4 to establish the equilibrium particle shape, and furthermore to determine the deposition energy of Ti/TiH2 and the substitutional...

Non-equilibrium Green's function calculation for GaN-based terahertz-quantum cascade laser structures

Science.gov (United States)

Yasuda, H.; Kubis, T.; Hosako, I.; Hirakawa, K.

2012-04-01

We theoretically investigated GaN-based resonant phonon terahertz-quantum cascade laser (QCL) structures for possible high-temperature operation by using the non-equilibrium Green's function method. It was found that the GaN-based THz-QCL structures do not necessarily have a gain sufficient for lasing, even though the thermal backfilling and the thermally activated phonon scattering are effectively suppressed. The main reason for this is the broadening of the subband levels caused by a very strong interaction between electrons and longitudinal optical (LO) phonons in GaN.

Equilibrium reconstruction in the TCA/Br tokamak

International Nuclear Information System (INIS)

Sa, Wanderley Pires de

1996-01-01

The accurate and rapid determination of the Magnetohydrodynamic (MHD) equilibrium configuration in tokamaks is a subject for the magnetic confinement of the plasma. With the knowledge of characteristic plasma MHD equilibrium parameters it is possible to control the plasma position during its formation using feed-back techniques. It is also necessary an on-line analysis between successive discharges to program external parameters for the subsequent discharges. In this work it is investigated the MHD equilibrium configuration reconstruction of the TCA/BR tokamak from external magnetic measurements, using a method that is able to fast determine the main parameters of discharge. The thesis has two parts. Firstly it is presented the development of an equilibrium code that solves de Grad-Shafranov equation for the TCA/BR tokamak geometry. Secondly it is presented the MHD equilibrium reconstruction process from external magnetic field and flux measurements using the Function Parametrization FP method. this method. This method is based on the statistical analysis of a database of simulated equilibrium configurations, with the goal of obtaining a simple relationship between the parameters that characterize the equilibrium and the measurements. The results from FP are compared with conventional methods. (author)

Calculation code NIRVANA for free boundary MHD equilibrium

International Nuclear Information System (INIS)

Ninomiya, Hiromasa; Suzuki, Yasuo; Kameari, Akihisa

1975-03-01

The calculation method and code of solving the free boundary problem for MHD equilibrium has been developed. Usage of the code ''NIRVANA'' is described. The toroidal plasma current density determined as a function of the flux function PSI is substituted by a group of the ring currents, whereby the equation of MHD equilibrium is transformed into an integral equation. Either of the two iterative methods is chosen to solve the integral equation, depending on the assumptions made of the plasma surface points. Calculation of the magnetic field configurations is possible when the plasma surface coincides self-consistently with the magnetic flux including the separatrix points. The code is usable in calculation of the circular or non-circular shell-less Tokamak equilibrium. (auth.)

Angular distributions in pre-equilibrium reactions

International Nuclear Information System (INIS)

Chatterjee, A.; Gupta, S.K.; Bhabha Atomic Research Centre, Bombay

1982-10-01

A new model is proposed for calculating angular distributions in preequilibrium reactions. In this model, as in the model of Feshbach et al. the system consisting of target plus projectile initially branches into two sets of states with either no particle in the continuum (multistep compound states) or with at least one particle in the continuum (multistep direct states). The two chains of states are treated independently by solving two sets of master equations. The multistep compound emission is assumed to be isotropic while the angular distribution of the multistep direct emission is described using the fast particle model of Mantzouranis et al. The angular distributions for 14.6 MeV neutrons calculated using this model are found to be in better agreement with the data than the fast particle model. (author)

Reynolds number dependency in equilibrium two-dimensional turbulence

Science.gov (United States)

Bracco, A.; McWilliams, J.

2009-04-01

We use the Navier-Stokes equations for barotropic turbulence as a zero-order approximation of chaotic space-time patterns and equilibrium distributions that mimic turbulence in geophysical flows. In this overly-simplified set-up for which smooth-solutions exist, we investigate if is possible to bound the uncertainty associated with the numerical domain discretization, i.e. with the limitation imposed by the Reynolds number range we can explore. To do so we analyze a series of stationary barotropic turbulence simulations spanning a large range of Reynolds numbers and run over a three year period for over 300,000 CPU hours. We find a persistent Reynolds number dependency in the energy power spectra and second order vorticity structure function, while distributions of dynamical quantities such as velocity, vorticity, dissipation rates and others are invariant in shape and have variances scaling with the viscosity coefficient according to simple power-laws. The relevance to this work to the possibility of conceptually reducing uncertainties in climate models will be discussed.

Non-equilibrium Quasi-Chemical Nucleation Model

Science.gov (United States)

Gorbachev, Yuriy E.

2018-04-01

Quasi-chemical model, which is widely used for nucleation description, is revised on the basis of recent results in studying of non-equilibrium effects in reacting gas mixtures (Kolesnichenko and Gorbachev in Appl Math Model 34:3778-3790, 2010; Shock Waves 23:635-648, 2013; Shock Waves 27:333-374, 2017). Non-equilibrium effects in chemical reactions are caused by the chemical reactions themselves and therefore these contributions should be taken into account in the corresponding expressions for reaction rates. Corrections to quasi-equilibrium reaction rates are of two types: (a) spatially homogeneous (caused by physical-chemical processes) and (b) spatially inhomogeneous (caused by gas expansion/compression processes and proportional to the velocity divergency). Both of these processes play an important role during the nucleation and are included into the proposed model. The method developed for solving the generalized Boltzmann equation for chemically reactive gases is applied for solving the set of equations of the revised quasi-chemical model. It is shown that non-equilibrium processes lead to essential deviation of the quasi-stationary distribution and therefore the nucleation rate from its traditional form.

Non-equilibrium scaling analysis of the Kondo model with voltage bias

International Nuclear Information System (INIS)

Fritsch, Peter; Kehrein, Stefan

2009-01-01

The quintessential description of Kondo physics in equilibrium is obtained within a scaling picture that shows the buildup of Kondo screening at low temperature. For the non-equilibrium Kondo model with a voltage bias, the key new feature are decoherence effects due to the current across the impurity. In the present paper, we show how one can develop a consistent framework for studying the non-equilibrium Kondo model within a scaling picture of infinitesimal unitary transformations (flow equations). Decoherence effects appear naturally in third order of the β-function and dominate the Hamiltonian flow for sufficiently large voltage bias. We work out the spin dynamics in non-equilibrium and compare it with finite temperature equilibrium results. In particular, we report on the behavior of the static spin susceptibility including leading logarithmic corrections and compare it with the celebrated equilibrium result as a function of temperature.

Pair distribution function and structure factor of spherical particles

International Nuclear Information System (INIS)

Howell, Rafael C.; Proffen, Thomas; Conradson, Steven D.

2006-01-01

The availability of neutron spallation-source instruments that provide total scattering powder diffraction has led to an increased application of real-space structure analysis using the pair distribution function. Currently, the analytical treatment of finite size effects within pair distribution refinement procedures is limited. To that end, an envelope function is derived which transforms the pair distribution function of an infinite solid into that of a spherical particle with the same crystal structure. Distributions of particle sizes are then considered, and the associated envelope function is used to predict the particle size distribution of an experimental sample of gold nanoparticles from its pair distribution function alone. Finally, complementing the wealth of existing diffraction analysis, the peak broadening for the structure factor of spherical particles, expressed as a convolution derived from the envelope functions, is calculated exactly for all particle size distributions considered, and peak maxima, offsets, and asymmetries are discussed

Choice of initial conditions in dynamical calculations of distributions of nuclear fission fragments

International Nuclear Information System (INIS)

Kosenko, G.I.

1993-01-01

The distribution function in the coordinates and momenta for a fissioning system traversing a barrier is determined in terms of Langevin fluctuation-dissipation dynamics. It is shown that this distribution is best described by the Kramers distribution. The equilibrium distribution can be used as the initial condition, provided that the system is in the overdamping regime. 28 refs., 5 figs., 3 tabs

Phase pupil functions for focal-depth enhancement derived from a Wigner distribution function.

Science.gov (United States)

Zalvidea, D; Sicre, E E

1998-06-10

A method for obtaining phase-retardation functions, which give rise to an increase of the image focal depth, is proposed. To this end, the Wigner distribution function corresponding to a specific aperture that has an associated small depth of focus in image space is conveniently sheared in the phase-space domain to generate a new Wigner distribution function. From this new function a more uniform on-axis image irradiance can be accomplished. This approach is illustrated by comparison of the imaging performance of both the derived phase function and a previously reported logarithmic phase distribution.

Bilinear phase-plane distribution functions and positivity

NARCIS (Netherlands)

Janssen, A.J.E.M.

1985-01-01

There is a theorem of Wigner that states that phase-plane distribution functions involving the state bilinearly and having correct marginals must take negative values for certain states. The purpose of this paper is to support the statement that these phase-plane distribution functions are for

Transition from thermal to turbulent equilibrium with a resulting electromagnetic spectrum

Energy Technology Data Exchange (ETDEWEB)

Ziebell, L. F., E-mail: luiz.ziebell@ufrgs.br [Instituto de Física, UFRGS, Porto Alegre, RS (Brazil); Yoon, P. H. [Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742 (United States); School of Space Research, Kyung Hee University, Yongin, Gyeonggi 446-701 (Korea, Republic of); Gaelzer, R. [Instituto de Física, UFRGS, Porto Alegre, RS (Brazil); Instituto de Física e Matemática, UFPel, Pelotas, RS (Brazil); Pavan, J. [Instituto de Física e Matemática, UFPel, Pelotas, RS (Brazil)

2014-01-15

A recent paper [Ziebell et al., Phys. Plasmas 21, 010701 (2014)] discusses a new type of radiation emission process for plasmas in a state of quasi-equilibrium between the particles and enhanced Langmuir turbulence. Such a system may be an example of the so-called “turbulent quasi-equilibrium.” In the present paper, it is shown on the basis of electromagnetic weak turbulence theory that an initial thermal equilibrium state (i.e., only electrostatic fluctuations and Maxwellian particle distributions) transitions toward the turbulent quasi-equilibrium state with enhanced electromagnetic radiation spectrum, thus demonstrating that the turbulent quasi-equilibrium discussed in the above paper correctly describes the weakly turbulent plasma dynamically interacting with electromagnetic fluctuations, while maintaining a dynamical steady-state in the average sense.

Distribution function in the description of relaxation phenomena

DEFF Research Database (Denmark)

Brecht, M.; Klösgen, B.; Reichle, C.

1999-01-01

adjacent to cell membranes, a distribution of correlation times has to be taken into account to describe the experimentally found additional line broadening in the absorption, the less steep slope in the dispersion curves and the loss of symmetry. Appropiate distribution functions are introduced...... and discussed as to their physical relevance. The application of these selected distribution functions results in transformed Debye equations. Thus, analogous analytical expressions are obtained that are well adapted for a numerical fitting of the parameters containing both the width and the asymmetry...... of the distribution functions....

Asymptotic functions and multiplication of distributions

International Nuclear Information System (INIS)

Todorov, T.D.

1979-01-01

Considered is a new type of generalized asymptotic functions, which are not functionals on some space of test functions as the Schwartz distributions. The definition of the generalized asymptotic functions is given. It is pointed out that in future the particular asymptotic functions will be used for solving some topics of quantum mechanics and quantum theory

The applicability of equilibrium calculations to dichlorosilane CVD

International Nuclear Information System (INIS)

Medernach, J.W.; Ho, P.

1987-01-01

Equilibrium calculations were made for the chlorosilane (Si-H-Cl) system over a wide range of temperatures, pressures and Si/Cl ratios. The Si/Cl ratios are presented as a function of the Cl/H ratio, temperature and pressure. Three-dimensional contour plots of the equilibrium Si/Cl also give a qualitative picture. Comparison of observed and equilibrium deposition rates indicate the range of applicability for the chlorosilane system. Results of this study indicate that equilibrium calculations can serve as a useful guide for silicon deposition from dichlorosilane at temperatures > 1000 0 C and pressures between 625 and 80 Torr. An application related to the silicon-on insulator (SOI) technology is presented

Dynamics and feedback control of plasma equilibrium position in a tokamak

International Nuclear Information System (INIS)

Burenko, O.

1983-01-01

A brief history of the beginnings of nuclear fusion research involving toroidal closed-system magnetic plasma containment is presented. A tokamak machine is defined mathematically for the purposes of plasma equilibrium position perturbation analysis. The perturbation equations of a tokamak plasma equilibrium position are developed. Solution of the approximated perturbation equations is carried out. A unique, simple, and useful plasma displacement dynamics transfer function of a tokamak is developed. The dominant time constants of the dynamics transfer function are determined in a symbolic form. This symbolic form of the dynamics transfer function makes it possible to study the stability of a tokamak's plasma equilibrium position. Knowledge of the dynamics transfer function permits systematic syntheses of the required plasma displacement feedback control systems

The entropy concept for non-equilibrium states.

Science.gov (United States)

Lieb, Elliott H; Yngvason, Jakob

2013-10-08

In earlier work, we presented a foundation for the second law of classical thermodynamics in terms of the entropy principle. More precisely, we provided an empirically accessible axiomatic derivation of an entropy function defined on all equilibrium states of all systems that has the appropriate additivity and scaling properties, and whose increase is a necessary and sufficient condition for an adiabatic process between two states to be possible. Here, after a brief review of this approach, we address the question of defining entropy for non-equilibrium states. Our conclusion is that it is generally not possible to find a unique entropy that has all relevant physical properties. We do show, however, that one can define two entropy functions, called S - and S + , which, taken together, delimit the range of adiabatic processes that can occur between non-equilibrium states. The concept of comparability of states with respect to adiabatic changes plays an important role in our reasoning.

Poloidal field equilibrium calculations for JET

International Nuclear Information System (INIS)

Khalafallah, A.K.

1976-01-01

The structure of the JET 2D Poloidal Field Analysis Package is discussed. The ability to cope with different plasma current density distributions (skin, flat or peaked), each with a range of Beta poloidal values and varying plasma shapes is a new feature of these calculations. It is possible to construct instant-by-instant pictures of equilibrium configurations for various plasma build up scenarios taking into account the level of flux in the iron core and return limbs. The equilibrium configurations are calculated for two possible sequences of plasma build up. Examples of the magnetic field calculations being carried out under contract to JET at the Rutherford Laboratory, using a 3D code, are also given

H-functions and mixing in violent relaxation

International Nuclear Information System (INIS)

Tremaine, S.; Henon, M.; Lynden-Bell, D.

1986-01-01

An H-function is any function of the phase space distribution function F(x,v) which is non-decreasing with time. In collisionless systems Boltzmann's H-function - integral F log F dx dv is only one of a variety of H-functions of the form - integral C(F) dx dv, where C is any convex function. Every equilibrium stellar system in which the distribution function is a decreasing function of the energy alone is a stationary point of some H-function of this form. During violent relaxation, all such H-functions must increase, and the distribution function is said to become 'more mixed'. A simple criterion is given for determining whether a given distribution function is more mixed than another; this criterion is used to show that a violently relaxed galaxy resembles observed elliptical galaxies only if the initial state is cold or clumpy. (author)

Improvements on non-equilibrium and transport Green function techniques: The next-generation TRANSIESTA

Science.gov (United States)

Papior, Nick; Lorente, Nicolás; Frederiksen, Thomas; García, Alberto; Brandbyge, Mads

2017-03-01

We present novel methods implemented within the non-equilibrium Green function code (NEGF) TRANSIESTA based on density functional theory (DFT). Our flexible, next-generation DFT-NEGF code handles devices with one or multiple electrodes (Ne ≥ 1) with individual chemical potentials and electronic temperatures. We describe its novel methods for electrostatic gating, contour optimizations, and assertion of charge conservation, as well as the newly implemented algorithms for optimized and scalable matrix inversion, performance-critical pivoting, and hybrid parallelization. Additionally, a generic NEGF "post-processing" code (TBTRANS/PHTRANS) for electron and phonon transport is presented with several novelties such as Hamiltonian interpolations, Ne ≥ 1 electrode capability, bond-currents, generalized interface for user-defined tight-binding transport, transmission projection using eigenstates of a projected Hamiltonian, and fast inversion algorithms for large-scale simulations easily exceeding 106 atoms on workstation computers. The new features of both codes are demonstrated and bench-marked for relevant test systems.

Mapping the Wigner distribution function of the Morse oscillator onto a semiclassical distribution function

International Nuclear Information System (INIS)

Bund, G W; Tijero, M C

2004-01-01

The mapping of the Wigner distribution function (WDF) for a given bound state onto a semiclassical distribution function (SDF) satisfying the Liouville equation introduced previously by us is applied to the ground state of the Morse oscillator. The purpose of the present work is to obtain values of the potential parameters represented by the number of levels in the case of the Morse oscillator, for which the SDF becomes a faithful approximation of the corresponding WDF. We find that for a Morse oscillator with one level only, the agreement between the WDF and the mapped SDF is very poor but for a Morse oscillator of ten levels it becomes satisfactory. We also discuss the limit ℎ → 0 for fixed potential parameters

Equilibrium and non-equilibrium phenomena in arcs and torches

NARCIS (Netherlands)

Mullen, van der J.J.A.M.

2000-01-01

A general treatment of non-equilibrium plasma aspects is obtained by relating transport fluxes to equilibrium restoring processes in so-called disturbed Bilateral Relations. The (non) equilibrium stage of a small microwave induced plasma serves as case study.

Non-equilibrium Green's functions method: Non-trivial and disordered leads

International Nuclear Information System (INIS)

He, Yu; Wang, Yu; Klimeck, Gerhard; Kubis, Tillmann

2014-01-01

The non-equilibrium Green's function algorithm requires contact self-energies to model charge injection and extraction. All existing approaches assume infinitely periodic leads attached to a possibly quite complex device. This contradicts today's realistic devices in which contacts are spatially inhomogeneous, chemically disordered, and impacting the overall device characteristics. This work extends the complex absorbing potentials method for arbitrary, ideal, or non-ideal leads in atomistic tight binding representation. The algorithm is demonstrated on a Si nanowire with periodic leads, a graphene nanoribbon with trumpet shape leads, and devices with leads of randomly alloyed Si 0.5 Ge 0.5 . It is found that alloy randomness in the leads can reduce the predicted ON-state current of Si 0.5 Ge 0.5 transistors by 45% compared to conventional lead methods

Computer experiments on dynamical cloud and space time fluctuations in one-dimensional meta-equilibrium plasmas

International Nuclear Information System (INIS)

Rouet, J.L.; Feix, M.R.

1996-01-01

The test particle picture is a central theory of weakly correlated plasma. While experiments and computer experiments have confirmed the validity of this theory at thermal equilibrium, the extension to meta-equilibrium distributions presents interesting and intriguing points connected to the under or over-population of the tail of these distributions (high velocity) which have not yet been tested. Moreover, the general dynamical Debye cloud (which is a generalization of the static Debye cloud supposing a plasma at thermal equilibrium and a test particle of zero velocity) for any test particle velocity and three typical velocity distributions (equilibrium plus two meta-equilibriums) are presented. The simulations deal with a one-dimensional two-component plasma and, moreover, the relevance of the check for real three-dimensional plasma is outlined. Two kinds of results are presented: the dynamical cloud itself and the more usual density (or energy) fluctuation spectrums. Special attention is paid to the behavior of long wavelengths which needs long systems with very small graininess effects and, consequently, sizable computation efforts. Finally, the divergence or absence of energy in the small wave numbers connected to the excess or lack of fast particles of the two above mentioned meta-equilibrium is exhibited. copyright 1996 American Institute of Physics

Condition of Mechanical Equilibrium at the Phase Interface with Arbitrary Geometry

Science.gov (United States)

Zubkov, V. V.; Zubkova, A. V.

2017-09-01

The authors produced an expression for the mechanical equilibrium condition at the phase interface within the force definition of surface tension. This equilibrium condition is the most general one from the mathematical standpoint and takes into account the three-dimensional aspect of surface tension. Furthermore, the formula produced allows describing equilibrium on the fractal surface of the interface. The authors used the fractional integral model of fractal distribution and took the fractional order integrals over Euclidean space instead of integrating over the fractal set.

Renormalization of boundary conditions for distribution functions of quasiparticles obeying quantum statistics at interfaces between crystalline grains

International Nuclear Information System (INIS)

Grendel, M.

1981-01-01

Boundary conditions for distribution functions of quasiparticles scattered by an interface between two crystalline grains are presented. Contrary to former formulations where Maxwell-Boltzmann statistics was considered, the present boundary conditions take into account the quantum statistics (Fermi-Dirac or Bose-Einstein) of quasiparticles. Provided that small deviations only from thermodynamic equilibrium are present, the boundary conditions are linearized, and then their ''renormalization'' is investigated in case of elastic scattering. The final results of the renormalization, which are obtained for a simplified model of an interface, sugo.est that the portion of the Fermi (Bose)-quasiparticles reflected or transmitted specularly is decreased (increased) in comparison with the case of quasiparticles obeying Maxwell-Boltzmann statistics. (author)

Theoretical method for determining particle distribution functions of classical systems

International Nuclear Information System (INIS)

Johnson, E.

1980-01-01

An equation which involves the triplet distribution function and the three-particle direct correlation function is obtained. This equation was derived using an analogue of the Ornstein--Zernike equation. The new equation is used to develop a variational method for obtaining the triplet distribution function of uniform one-component atomic fluids from the pair distribution function. The variational method may be used with the first and second equations in the YBG hierarchy to obtain pair and triplet distribution functions. It should be easy to generalize the results to the n-particle distribution function

Effective temperature of the non-equilibrium electrons in a degenerate semiconductor at low lattice temperature

Energy Technology Data Exchange (ETDEWEB)

Das, B.; Basu, A.; Das, J.; Bhattacharya, D.P., E-mail: d_p_bhattacharya@rediffmail.com

2015-10-01

The energy balance equation for the electron–phonon system is recast taking the degeneracy of the carrier ensemble into account. The effect of degeneracy on the field dependence of the temperature of the non-equilibrium carriers has been studied by solving the same equation. The high field distribution function of the carriers is assumed to be given by the Fermi Dirac function at the field dependent carrier temperature. The distribution function has been approximated in a way that facilitates analytical solution of the problem without any serious loss of accuracy. The field dependence of the electron temperature thus obtained seems to be significantly different from what follows had the degeneracy not been taken into account. The agreement of the results obtained from the present analysis with the available experimental data for Ge and InSb are quite satisfactory. The scope of further refinement of the present theory is highlighted.

Phenomenological relation between distribution and fragmentation functions

International Nuclear Information System (INIS)

Ma Boqiang; Schmidt, Ivan; Soffer, Jacques; Yang Jianjun

2002-01-01

We study the relation between the quark distribution function q(x) and the fragmentation function D q (z) based on a general form D q (x)=C(z)z α q(z) for valence and sea quarks. By adopting two known parametrizations of quark distributions for the proton, we find three simple options for the fragmentation functions that can provide a good description of the available experimental data on proton production in e + e - inelastic annihilation. These three options support the revised Gribov-Lipatov relation D q (z)=zq(z) at z→1, as an approximate relation for the connection between distribution and fragmentation functions. The three options differ in the sea contributions and lead to distinct predictions for antiproton production in the reaction p+p→p-bar+X, thus they are distinguishable in future experiments at RHIC-BNL

Equilibrium and stability of off-axis periodically focused particle beams

International Nuclear Information System (INIS)

Moraes, J.S.; Pakter, R.; Rizzato, F.B.

2004-01-01

A general equation for the centroid motion of free, continuous, intense beams propagating off axis in solenoidal periodic focusing fields is derived. The centroid equation is found to be independent of the specific beam distribution and may exhibit unstable solutions. A new Vlasov equilibrium for off-axis beam propagation is also obtained. The properties of the equilibrium and the relevance of centroid motion to beam confinement are discussed

Equilibrium in a Production Economy

Energy Technology Data Exchange (ETDEWEB)

Chiarolla, Maria B., E-mail: maria.chiarolla@uniroma1.it [Universita di Roma ' La Sapienza' , Dipartimento di Metodi e Modelli per l' Economia, il Territorio e la Finanza, Facolta di Economia (Italy); Haussmann, Ulrich G., E-mail: uhaus@math.ubc.ca [University of British Columbia, Department of Mathematics (Canada)

2011-06-15

Consider a closed production-consumption economy with multiple agents and multiple resources. The resources are used to produce the consumption good. The agents derive utility from holding resources as well as consuming the good produced. They aim to maximize their utility while the manager of the production facility aims to maximize profits. With the aid of a representative agent (who has a multivariable utility function) it is shown that an Arrow-Debreu equilibrium exists. In so doing we establish technical results that will be used to solve the stochastic dynamic problem (a case with infinite dimensional commodity space so the General Equilibrium Theory does not apply) elsewhere.

Equilibrium in a Production Economy

International Nuclear Information System (INIS)

Chiarolla, Maria B.; Haussmann, Ulrich G.

2011-01-01

Consider a closed production-consumption economy with multiple agents and multiple resources. The resources are used to produce the consumption good. The agents derive utility from holding resources as well as consuming the good produced. They aim to maximize their utility while the manager of the production facility aims to maximize profits. With the aid of a representative agent (who has a multivariable utility function) it is shown that an Arrow-Debreu equilibrium exists. In so doing we establish technical results that will be used to solve the stochastic dynamic problem (a case with infinite dimensional commodity space so the General Equilibrium Theory does not apply) elsewhere.

Nash equilibrium with lower probabilities

DEFF Research Database (Denmark)

Groes, Ebbe; Jacobsen, Hans Jørgen; Sloth, Birgitte

1998-01-01

We generalize the concept of Nash equilibrium in mixed strategies for strategic form games to allow for ambiguity in the players' expectations. In contrast to other contributions, we model ambiguity by means of so-called lower probability measures or belief functions, which makes it possible...

Distributed plant simulator with two-phase flow analysis code using drift-flux non-equilibrium model for pressurized water reactors

International Nuclear Information System (INIS)

Yamamoto, Takaya; Kitamura, Masashi; Ohi, Tadashi; Akagi, Katsumi

1999-01-01

As advanced monitoring and controlling systems, such as the advanced main control console and the operator support system have been developed, real-time simulators' simulation accuracy must be improved and simulation limits must be extended. Therefore the authors have developed a distributed simulation system to achieve high processing performance using low cost hardware. Moreover, the authors have developed a thermal-hydraulic computer code, using drift-flux non-equilibrium model, which can realize a high precision two-phase flow analysis, which is considered to have the same prediction capability as two-fluid models, while achieving high speed and stability for real-time simulators. The distributed plant simulator for PWR plants was realized as a result. The distributed simulator consists of multi-processors connected to each other by an optical fiber network. Controlling software for synchronized scheduling and memory transfer was also developed. The simulation results of the four loop PWR simulator are compared with experimental data and real plant data; the agreement is satisfactory for a plant simulator. The simulation speed is also satisfactory being twice as fast as real-time. (author)

Dynamic radial distribution function from inelastic neutron scattering

International Nuclear Information System (INIS)

McQueeney, R.J.

1998-01-01

A real-space, local dynamic structure function g(r,ω) is defined from the dynamic structure function S(Q,ω), which can be measured using inelastic neutron scattering. At any particular frequency ω, S(Q,ω) contains Q-dependent intensity oscillations which reflect the spatial distribution and relative displacement directions for the atoms vibrating at that frequency. Information about local and dynamic atomic correlations is obtained from the Fourier transform of these oscillations g(r,ω) at the particular frequency. g(r,ω) can be formulated such that the elastic and frequency-summed limits correspond to the average and instantaneous radial distribution function, respectively, and is thus called the dynamic radial distribution function. As an example, the dynamic radial distribution function is calculated for fcc nickel in a model which considers only the harmonic atomic displacements due to phonons. The results of these calculations demonstrate that the magnitude of the atomic correlations can be quantified and g(r,ω) is a well-defined correlation function. This leads to a simple prescription for investigating local lattice dynamics. copyright 1998 The American Physical Society

Inference of directional selection and mutation parameters assuming equilibrium.

Science.gov (United States)

Vogl, Claus; Bergman, Juraj

2015-12-01

In a classical study, Wright (1931) proposed a model for the evolution of a biallelic locus under the influence of mutation, directional selection and drift. He derived the equilibrium distribution of the allelic proportion conditional on the scaled mutation rate, the mutation bias and the scaled strength of directional selection. The equilibrium distribution can be used for inference of these parameters with genome-wide datasets of "site frequency spectra" (SFS). Assuming that the scaled mutation rate is low, Wright's model can be approximated by a boundary-mutation model, where mutations are introduced into the population exclusively from sites fixed for the preferred or unpreferred allelic states. With the boundary-mutation model, inference can be partitioned: (i) the shape of the SFS distribution within the polymorphic region is determined by random drift and directional selection, but not by the mutation parameters, such that inference of the selection parameter relies exclusively on the polymorphic sites in the SFS; (ii) the mutation parameters can be inferred from the amount of polymorphic and monomorphic preferred and unpreferred alleles, conditional on the selection parameter. Herein, we derive maximum likelihood estimators for the mutation and selection parameters in equilibrium and apply the method to simulated SFS data as well as empirical data from a Madagascar population of Drosophila simulans. Copyright © 2015 Elsevier Inc. All rights reserved.

Dust charging processes with a Cairns-Tsallis distribution function with negative ions

Energy Technology Data Exchange (ETDEWEB)

Abid, A. A., E-mail: abidaliabid1@hotmail.com [Applied Physics Department, Federal Urdu University of Arts, Science and Technology, Islamabad Campus, Islamabad 45320 (Pakistan); Khan, M. Z., E-mail: mzk-qau@yahoo.com [Applied Physics Department, Federal Urdu University of Arts, Science and Technology, Islamabad Campus, Islamabad 45320 (Pakistan); Plasma Technology Research Center, Department of Physics, Faculty of Science, University of Malaya, Kuala Lumpur 50603 (Malaysia); Yap, S. L. [Plasma Technology Research Center, Department of Physics, Faculty of Science, University of Malaya, Kuala Lumpur 50603 (Malaysia); Terças, H., E-mail: hugo.tercas@tecnico.ul.pt [Physics of Information Group, Instituto de Telecomunicações, Av. Rovisco Pais, Lisbon 1049-001 (Portugal); Mahmood, S. [Science Place, University of Saskatchewan, Saskatoon, Saskatchewan S7N5A2 (Canada)

2016-01-15

Dust grain charging processes are presented in a non-Maxwellian dusty plasma following the Cairns-Tsallis (q, α)–distribution, whose constituents are the electrons, as well as the positive/negative ions and negatively charged dust grains. For this purpose, we have solved the current balance equation for a negatively charged dust grain to achieve an equilibrium state value (viz., q{sub d} = constant) in the presence of Cairns-Tsallis (q, α)–distribution. In fact, the current balance equation becomes modified due to the Boltzmannian/streaming distributed negative ions. It is numerically found that the relevant plasma parameters, such as the spectral indexes q and α, the positive ion-to-electron temperature ratio, and the negative ion streaming speed (U{sub 0}) significantly affect the dust grain surface potential. It is also shown that in the limit q → 1 the Cairns-Tsallis reduces to the Cairns distribution; for α = 0 the Cairns-Tsallis distribution reduces to pure Tsallis distribution and the latter reduces to Maxwellian distribution for q → 1 and α = 0.

Dust charging processes with a Cairns-Tsallis distribution function with negative ions

International Nuclear Information System (INIS)

Abid, A. A.; Khan, M. Z.; Yap, S. L.; Terças, H.; Mahmood, S.

2016-01-01

Dust grain charging processes are presented in a non-Maxwellian dusty plasma following the Cairns-Tsallis (q, α)–distribution, whose constituents are the electrons, as well as the positive/negative ions and negatively charged dust grains. For this purpose, we have solved the current balance equation for a negatively charged dust grain to achieve an equilibrium state value (viz., q d  = constant) in the presence of Cairns-Tsallis (q, α)–distribution. In fact, the current balance equation becomes modified due to the Boltzmannian/streaming distributed negative ions. It is numerically found that the relevant plasma parameters, such as the spectral indexes q and α, the positive ion-to-electron temperature ratio, and the negative ion streaming speed (U 0 ) significantly affect the dust grain surface potential. It is also shown that in the limit q → 1 the Cairns-Tsallis reduces to the Cairns distribution; for α = 0 the Cairns-Tsallis distribution reduces to pure Tsallis distribution and the latter reduces to Maxwellian distribution for q → 1 and α = 0

Phenomenological model for non-equilibrium deuteron emission in nucleon induced reactions

International Nuclear Information System (INIS)

Broeders, C.H.M.; Konobeyev, A.Yu.

2005-01-01

A new approach is proposed for the calculation of non-equilibrium deuteron energy distributions in nuclear reactions induced by nucleons of intermediate energies. It combines the model of the nucleon pick-up, the coalescence and the deuteron knock-out. Emission and absorption rates for excited particles are described by the pre-equilibrium hybrid model. The model of Sato, Iwamoto, Harada is used to describe the nucleon pick-up and the coalescence of nucleons from the exciton configurations starting from (2p, 1h). The model of deuteron knock-out is formulated taking into account the Pauli principle for the nucleon-deuteron interaction inside a nucleus. The contribution of the direct nucleon pick-up is described phenomenologically. The multiple pre-equilibrium emission of particles is taken into account. The calculated deuteron energy distributions are compared with experimental data from 12 C to 209 Bi. (orig.)

Non-equilibrium Green's functions method: Non-trivial and disordered leads

Energy Technology Data Exchange (ETDEWEB)

He, Yu, E-mail: heyuyhe@gmail.com; Wang, Yu; Klimeck, Gerhard; Kubis, Tillmann [Network for Computational Nanotechnology, Purdue University, West Lafayette, Indiana 47907 (United States)

2014-11-24

The non-equilibrium Green's function algorithm requires contact self-energies to model charge injection and extraction. All existing approaches assume infinitely periodic leads attached to a possibly quite complex device. This contradicts today's realistic devices in which contacts are spatially inhomogeneous, chemically disordered, and impacting the overall device characteristics. This work extends the complex absorbing potentials method for arbitrary, ideal, or non-ideal leads in atomistic tight binding representation. The algorithm is demonstrated on a Si nanowire with periodic leads, a graphene nanoribbon with trumpet shape leads, and devices with leads of randomly alloyed Si{sub 0.5}Ge{sub 0.5}. It is found that alloy randomness in the leads can reduce the predicted ON-state current of Si{sub 0.5}Ge{sub 0.5} transistors by 45% compared to conventional lead methods.

Stochastic pumping of non-equilibrium steady-states: how molecules adapt to a fluctuating environment.

Science.gov (United States)

Astumian, R D

2018-01-11

In the absence of input energy, a chemical reaction in a closed system ineluctably relaxes toward an equilibrium state governed by a Boltzmann distribution. The addition of a catalyst to the system provides a way for more rapid equilibration toward this distribution, but the catalyst can never, in and of itself, drive the system away from equilibrium. In the presence of external fluctuations, however, a macromolecular catalyst (e.g., an enzyme) can absorb energy and drive the formation of a steady state between reactant and product that is not determined solely by their relative energies. Due to the ubiquity of non-equilibrium steady states in living systems, the development of a theory for the effects of external fluctuations on chemical systems has been a longstanding focus of non-equilibrium thermodynamics. The theory of stochastic pumping has provided insight into how a non-equilibrium steady-state can be formed and maintained in the presence of dissipation and kinetic asymmetry. This effort has been greatly enhanced by a confluence of experimental and theoretical work on synthetic molecular machines designed explicitly to harness external energy to drive non-equilibrium transport and self-assembly.

Rocket measurement of auroral partial parallel distribution functions

Science.gov (United States)

Lin, C.-A.

1980-01-01

The auroral partial parallel distribution functions are obtained by using the observed energy spectra of electrons. The experiment package was launched by a Nike-Tomahawk rocket from Poker Flat, Alaska over a bright auroral band and covered an altitude range of up to 180 km. Calculated partial distribution functions are presented with emphasis on their slopes. The implications of the slopes are discussed. It should be pointed out that the slope of the partial parallel distribution function obtained from one energy spectra will be changed by superposing another energy spectra on it.

Generalised partition functions: inferences on phase space distributions

Directory of Open Access Journals (Sweden)

R. A. Treumann

2016-06-01

Full Text Available It is demonstrated that the statistical mechanical partition function can be used to construct various different forms of phase space distributions. This indicates that its structure is not restricted to the Gibbs–Boltzmann factor prescription which is based on counting statistics. With the widely used replacement of the Boltzmann factor by a generalised Lorentzian (also known as the q-deformed exponential function, where κ = 1∕|q − 1|, with κ, q ∈ R both the kappa-Bose and kappa-Fermi partition functions are obtained in quite a straightforward way, from which the conventional Bose and Fermi distributions follow for κ → ∞. For κ ≠ ∞ these are subject to the restrictions that they can be used only at temperatures far from zero. They thus, as shown earlier, have little value for quantum physics. This is reasonable, because physical κ systems imply strong correlations which are absent at zero temperature where apart from stochastics all dynamical interactions are frozen. In the classical large temperature limit one obtains physically reasonable κ distributions which depend on energy respectively momentum as well as on chemical potential. Looking for other functional dependencies, we examine Bessel functions whether they can be used for obtaining valid distributions. Again and for the same reason, no Fermi and Bose distributions exist in the low temperature limit. However, a classical Bessel–Boltzmann distribution can be constructed which is a Bessel-modified Lorentzian distribution. Whether it makes any physical sense remains an open question. This is not investigated here. The choice of Bessel functions is motivated solely by their convergence properties and not by reference to any physical demands. This result suggests that the Gibbs–Boltzmann partition function is fundamental not only to Gibbs–Boltzmann but also to a large class of generalised Lorentzian distributions as well as to the

Magnetotail equilibrium theory - The general three-dimensional solution

Science.gov (United States)

Birn, J.

1987-01-01

The general magnetostatic equilibrium problem for the geomagnetic tail is reduced to the solution of ordinary differential equations and ordinary integrals. The theory allows the integration of the self-consistent magnetotail equilibrium field from the knowledge of four functions of two space variables: the neutral sheet location, the total pressure, the magnetic field strength, and the z component of the magnetic field at the neutral sheet.

Dynamical Symmetries and Causality in Non-Equilibrium Phase Transitions

Directory of Open Access Journals (Sweden)

Malte Henkel

2015-11-01

Full Text Available Dynamical symmetries are of considerable importance in elucidating the complex behaviour of strongly interacting systems with many degrees of freedom. Paradigmatic examples are cooperative phenomena as they arise in phase transitions, where conformal invariance has led to enormous progress in equilibrium phase transitions, especially in two dimensions. Non-equilibrium phase transitions can arise in much larger portions of the parameter space than equilibrium phase transitions. The state of the art of recent attempts to generalise conformal invariance to a new generic symmetry, taking into account the different scaling behaviour of space and time, will be reviewed. Particular attention will be given to the causality properties as they follow for co-variant n-point functions. These are important for the physical identification of n-point functions as responses or correlators.

Equilibrium reconstruction in stellarators: V3FIT

Energy Technology Data Exchange (ETDEWEB)

Hanson, J.D.; Knowlton, S.F. [Physics Department, Auburn University, Auburn, AL (United States); Hirshman, S.P.; Lazarus, E.A. [Oak Ridge National Laboratory, Oak Ridge, TN (United States); Lao, L.L. [General Atomics, San Diego, CA (United States)

2003-07-01

The first section describes a general response function formalism for computing stellarator magnetic diagnostic signals, which is the first step in developing a reconstruction capability. The approach parallels that used in the EFIT two-dimensional (2-D) equilibrium reconstruction code. The second section describes the two codes we have written, V3RFUN and V3POST. V3RFUN computes the response functions for a specified magnetic diagnostic coil, and V3POST uses the response functions calculated by V3RFUN, along with the plasma current information supplied by the equilibrium code VMEC, to compute the expected magnetic diagnostic signals. These two codes are currently being used to design magnetic diagnostic for the NCSX stellarator (at PPPL) and the CTH toroidal hybrid stellarator (at Auburn University). The last section of the paper describes plans for the V3FIT code. (orig.)

Structure functions and parton distributions

International Nuclear Information System (INIS)

Martin, A.D.; Stirling, W.J.; Roberts, R.G.

1995-01-01

The MRS parton distribution analysis is described. The latest sets are shown to give an excellent description of a wide range of deep-inelastic and other hard scattering data. Two important theoretical issues-the behavior of the distributions at small x and the flavor structure of the quark sea-are discussed in detail. A comparison with the new structure function data from HERA is made, and the outlook for the future is discussed

ON QUIET-TIME SOLAR WIND ELECTRON DISTRIBUTIONS IN DYNAMICAL EQUILIBRIUM WITH LANGMUIR TURBULENCE

International Nuclear Information System (INIS)

Zaheer, S.; Yoon, P. H.

2013-01-01

A recent series of papers put forth a self-consistent theory of an asymptotically steady-state electron distribution function and Langmuir turbulence intensity. The theory was developed in terms of the κ distribution which features Maxwellian low-energy electrons and a non-Maxwellian energetic power-law tail component. The present paper discusses a generalized κ distribution that features a Davydov-Druyvesteyn type of core component and an energetic power-law tail component. The physical motivation for such a generalization is so that the model may reflect the influence of low-energy electrons interacting with low-frequency kinetic Alfvénic turbulence as well as with high-frequency Langmuir turbulence. It is shown that such a solution and the accompanying Langmuir wave spectrum rigorously satisfy the balance requirement between the spontaneous and induced emission processes in both the particle and wave kinetic equations, and approximately satisfy the similar balance requirement between the spontaneous and induced scattering processes, which are nonlinear. In spite of the low velocity modification of the electron distribution function, it is shown that the resulting asymptotic velocity power-law index α, where f e ∼ v –α is close to the average index observed during the quiet-time solar wind condition, i.e., α ∼ O(6.5) whereas α average ∼ 6.69, according to observation

Dynamical Models For Prices With Distributed Delays

Directory of Open Access Journals (Sweden)

Mircea Gabriela

2015-06-01

Full Text Available In the present paper we study some models for the price dynamics of a single commodity market. The quantities of supplied and demanded are regarded as a function of time. Nonlinearities in both supply and demand functions are considered. The inventory and the level of inventory are taken into consideration. Due to the fact that the consumer behavior affects commodity demand, and the behavior is influenced not only by the instantaneous price, but also by the weighted past prices, the distributed time delay is introduced. The following kernels are taken into consideration: demand price weak kernel and demand price Dirac kernel. Only one positive equilibrium point is found and its stability analysis is presented. When the demand price kernel is weak, under some conditions of the parameters, the equilibrium point is locally asymptotically stable. When the demand price kernel is Dirac, the existence of the local oscillations is investigated. A change in local stability of the equilibrium point, from stable to unstable, implies a Hopf bifurcation. A family of periodic orbits bifurcates from the positive equilibrium point when the time delay passes through a critical value. The last part contains some numerical simulations to illustrate the effectiveness of our results and conclusions.

Social security as Markov equilibrium in OLG models: A note

DEFF Research Database (Denmark)

Gonzalez Eiras, Martin

2011-01-01

I refine and extend the Markov perfect equilibrium of the social security policy game in Forni (2005) for the special case of logarithmic utility. Under the restriction that the policy function be continuous, instead of differentiable, the equilibrium is globally well defined and its dynamics...

Kinetic and equilibrium characterization of uranium(VI) adsorption onto carboxylate-functionalized poly(hydroxyethylmethacrylate)-grafted lignocellulosics.

Science.gov (United States)

Anirudhan, T S; Divya, L; Suchithra, P S

2009-01-01

This study investigated the feasibility of using a new adsorbent prepared from coconut coir pith, CP (a coir industry-based lignocellulosic residue), for the removal of uranium [U(VI)] from aqueous solutions. The adsorbent (PGCP-COOH) having a carboxylate functional group at the chain end was synthesized by grafting poly(hydroxyethylmethacrylate) onto CP using potassium peroxydisulphate-sodium thiosulphite as a redox initiator and in the presence of N,N'-methylenebisacrylamide as a crosslinking agent. IR spectroscopy results confirm the graft copolymer formation and carboxylate functionalization. XRD studies confirm the decrease of crystallinity in PGCP-COOH compared to CP, and it favors the protrusion of the functional group into the aqueous medium. The thermal stability of the samples was studied using thermogravimetry (TG). Surface charge density of the samples as a function of pH was determined using potentiometric titration. The ability of PGCP-COOH to remove U(VI) from aqueous solutions was assessed using a batch adsorption technique. The maximum adsorption capacity was observed at the pH range 4.0-6.0. Maximum removal of 99.2% was observed for an initial concentration of 25mg/L at pH 6.0 and an adsorbent dose of 2g/L. Equilibrium was achieved in approximately 3h. The experimental kinetic data were analyzed using a first-order kinetic model. The temperature dependence indicates an endothermic process. U(VI) adsorption was found to decrease with an increase in ionic strength due to the formation of outer-sphere surface complexes on PGCP-COOH. Equilibrium data were best modeled by the Langmuir isotherm. The thermodynamic parameters such as DeltaG(0), DeltaH(0) and DeltaS(0) were derived to predict the nature of adsorption. Adsorption experiments were also conducted using a commercial cation exchanger, Ceralite IRC-50, with carboxylate functionality for comparison. Utility of the adsorbent was tested by removing U(VI) from simulated nuclear industry wastewater

Thermodynamic q-distributions that aren't

International Nuclear Information System (INIS)

Vokos, S.

1993-01-01

Bosonic q-oscillators commute with themselves and so their free distribution is Planckian. In a cavity, their emission and absorption rates may grow or shrink-and even diverge-but they nevertheless balance to yield the Planck distribution via Einstein's equilibrium method, (a careless application of which might produce spurious q-dependent distribution functions). This drives home the point that the black-body energy distribution is not a handle for distinguishing q-excitations from plain oscillators. A maximum cavity size is suggested by the inverse critical frequency of such emission/absorption rates at a given temperature, or a maximum temperature at a given frequency. To remedy fragmentation of opinion on the subject, we provide some discussion, context, and references

A New Equilibrium State for Singly Synchronous Binary Asteroids

Science.gov (United States)

Golubov, Oleksiy; Unukovych, Vladyslav; Scheeres, Daniel J.

2018-04-01

The evolution of rotation states of small asteroids is governed by the Yarkovsky–O’Keefe–Radzievskii–Paddack (YORP) effect, nonetheless some asteroids can stop their YORP evolution by attaining a stable equilibrium. The same is true for binary asteroids subjected to the binary YORP (BYORP) effect. Here we discuss a new type of equilibrium that combines these two, which is possible in a singly synchronous binary system. This equilibrium occurs when the normal YORP, the tangential YORP, and the BYORP compensate each other, and tidal torques distribute the angular momentum between the components of the system and dissipate energy. If unperturbed, such a system would remain singly synchronous in perpetuity with constant spin and orbit rates, as the tidal torques dissipate the incoming energy from impinging sunlight at the same rate. The probability of the existence of this kind of equilibrium in a binary system is found to be on the order of a few percent.

Equilibrium and kinetic studies of systems of hydrogen isotopes, lithium hydrides, aluminum, and LiAlO2

International Nuclear Information System (INIS)

Owen, J.H.; Randall, D.

1976-01-01

Tritium might be bred by the 6 Li(n,α)T reaction in a solid lithium alloy or compound in the blanket of a controlled thermonuclear reactor to avoid problems associated with molten lithium or lithium compounds. Li--Al and LiAlO 2 systems containing hydrogen, deuterium, or tritium were studied 10 to 15 years ago at the Savannah River Laboratory. This paper descibes measurements of (1) the distribution of tritium and helium throughout both α and β phases of irradiated Li--Al alloy, (2) the migration rate of tritium to the β phase during moderate heating, (3) equilibrium pressures as functions of temperature of H 2 , D 2 , or T 2 in contact with lithium hydrides + aluminum, Li--Al alloy, or irradiated Li--Al alloy, (4) the equilibrium constant for the reaction LiH + Al → LiAl + 1 / 2 H 2 as a function of temperature, and (5) extraction rates of tritium from irradiated LiAlO 2 targets at elevated temperatures

Effects of distribution function nonequilibrium tails on relaxation and transfer processes in rarefied gases

International Nuclear Information System (INIS)

Grigoryev, Yu.N.; Mikhalitsyn, A.N.; Yanenko, N.N.

1984-01-01

Quantitative characteristics of the nonmonotone relaxation process are studied in a gas of pseudo-Maxwell molecules. Basic results are obtained by a direct numerical integration of the nonlinear Boltzmann equation. The evolution of initial distributions being finite or having exponential asymptotics of tails was researched. In particular, initial data obtained by selective excitation (absorption) against the Maxwell background encountered in laser physics problems have been considered. It is shown that under conditions of a developed effect of nonmonotone relaxation the overpopulation in the velocity range 4 <= upsilon <= 10 exceeds on the average 2-3 times the equilibrium value. For the given particles energy the excitation is preserved during t = 5/6 and the total relaxation time of the overpopulation wave reaches t asymptotically equals 20. The amplitudes and the relaxation time of overpopulation in the ''cupola'' region of distribution are substantially lower than in the case of a developed effect in the tail. The influence of the effect on the kinetics of threshold chemical reaction is studied. From the results it follows that in the process of nonmonotone relaxation the mean rates of binary threshold reactions can exceed more than twice the equilibrium values. This estimate is valid for all power like intermolecular repulsive potentials from the pseudo-Maxwell model up to rigid spheres. Time intervals over which the mean reaction rate exceeds considerably the equilibrium one make from 5 to 15 mean free path times increasing with the decrease in the potential ''rigidity''. (author)

Rigorous approximation of stationary measures and convergence to equilibrium for iterated function systems

International Nuclear Information System (INIS)

Galatolo, Stefano; Monge, Maurizio; Nisoli, Isaia

2016-01-01

We study the problem of the rigorous computation of the stationary measure and of the rate of convergence to equilibrium of an iterated function system described by a stochastic mixture of two or more dynamical systems that are either all uniformly expanding on the interval, either all contracting. In the expanding case, the associated transfer operators satisfy a Lasota–Yorke inequality, we show how to compute a rigorous approximations of the stationary measure in the L "1 norm and an estimate for the rate of convergence. The rigorous computation requires a computer-aided proof of the contraction of the transfer operators for the maps, and we show that this property propagates to the transfer operators of the IFS. In the contracting case we perform a rigorous approximation of the stationary measure in the Wasserstein–Kantorovich distance and rate of convergence, using the same functional analytic approach. We show that a finite computation can produce a realistic computation of all contraction rates for the whole parameter space. We conclude with a description of the implementation and numerical experiments. (paper)

Improved Simulation of the Pre-equilibrium Triton Emission in Nuclear Reactions Induced by Nucleons

Science.gov (United States)

Konobeyev, A. Yu.; Fischer, U.; Pereslavtsev, P. E.; Blann, M.

2014-04-01

A new approach is proposed for the calculation of non-equilibrium triton energy distributions in nuclear reactions induced by nucleons of intermediate energies. It combines models describing the nucleon pick-up, the coalescence and the triton knock-out processes. Emission and absorption rates for excited particles are represented by the pre-equilibrium hybrid model. The model of Sato, Iwamoto, Harada is used to describe the nucleon pick-up and the coalescence of nucleons from exciton configurations starting from (2p,1h) states. The contribution of the direct nucleon pick-up is described phenomenologically. Multiple pre-equilibrium emission of tritons is accounted for. The calculated triton energy distributions are compared with available experimental data.

RISM theory distribution functions for Lennard--Jones interaction site fluids

International Nuclear Information System (INIS)

Johnson, E.; Hazoume, R.P.

1978-01-01

Reference interaction site model (RISM) theory distribution functions for Lennard-Jones interaction site fluids are discussed. The comparison with computer simulation results suggests that these distribution functions are as accurate as RISM distribution functions for fused hard sphere molecular fluids

Application of the Wigner distribution function in optics

NARCIS (Netherlands)

Bastiaans, M.J.; Mecklenbräuker, W.; Hlawatsch, F.

1997-01-01

This contribution presents a review of the Wigner distribution function and of some of its applications to optical problems. The Wigner distribution function describes a signal in space and (spatial) frequency simultaneously and can be considered as the local frequency spectrum of the signal.

Functional fixedness and functional reduction as common sense reasonings in chemical equilibrium and in geometry and polarity of molecules

Science.gov (United States)

Furió, C.; Calatayud, M. L.; Bárcenas, S. L.; Padilla, O. M.

2000-09-01

Many of the learning difficulties in the specific domain of chemistry are found not only in the ideas already possessed by students but in the strategic and procedural knowledge that is characteristic of everyday thinking. These defects in procedural knowledge have been described as functional fixedness and functional reduction. This article assesses the procedural difficulties of students (grade 12 and first and third year of university) based on common sense reasoning in two areas of chemistry: chemical equilibrium and geometry and polarity of molecules. In the first area, the theme of external factors affecting equilibria (temperature and concentration change) was selected because the explanations given by the students could be analyzed easily. The existence of a functional fixedness where Le Chatelier's principle was almost exclusively applied by rote could be observed, with this being the cause of the incorrect responses given to the proposed items. Functional fixedness of the Lewis structure also led to an incorrect prediction of molecular geometry. When molecular geometry was correctly determined by the students, it seemed that other methodological or procedural difficulties appeared when the task was to determine molecular polarity. The students showed a tendency, in many cases, to reduce the factors affecting molecular polarity in two possible ways: (a) assuming that polarity depends only on shape (geometric functional reduction) or (b) assuming that molecular polarity depends only on the polarity of bonds (bonding functional reduction).

Using nonequilibrium capillary electrophoresis of equilibrium mixtures (NECEEM) for simultaneous determination of concentration and equilibrium constant.

Science.gov (United States)

Kanoatov, Mirzo; Galievsky, Victor A; Krylova, Svetlana M; Cherney, Leonid T; Jankowski, Hanna K; Krylov, Sergey N

2015-03-03

Nonequilibrium capillary electrophoresis of equilibrium mixtures (NECEEM) is a versatile tool for studying affinity binding. Here we describe a NECEEM-based approach for simultaneous determination of both the equilibrium constant, K(d), and the unknown concentration of a binder that we call a target, T. In essence, NECEEM is used to measure the unbound equilibrium fraction, R, for the binder with a known concentration that we call a ligand, L. The first set of experiments is performed at varying concentrations of T, prepared by serial dilution of the stock solution, but at a constant concentration of L, which is as low as its reliable quantitation allows. The value of R is plotted as a function of the dilution coefficient, and dilution corresponding to R = 0.5 is determined. This dilution of T is used in the second set of experiments in which the concentration of T is fixed but the concentration of L is varied. The experimental dependence of R on the concentration of L is fitted with a function describing their theoretical dependence. Both K(d) and the concentration of T are used as fitting parameters, and their sought values are determined as the ones that generate the best fit. We have fully validated this approach in silico by using computer-simulated NECEEM electropherograms and then applied it to experimental determination of the unknown concentration of MutS protein and K(d) of its interactions with a DNA aptamer. The general approach described here is applicable not only to NECEEM but also to any other method that can determine a fraction of unbound molecules at equilibrium.

Automatic Functionality Assignment to AUTOSAR Multicore Distributed Architectures

DEFF Research Database (Denmark)

Maticu, Florin; Pop, Paul; Axbrink, Christian

2016-01-01

The automotive electronic architectures have moved from federated architectures, where one function is implemented in one ECU (Electronic Control Unit), to distributed architectures, where several functions may share resources on an ECU. In addition, multicore ECUs are being adopted because...... of better performance, cost, size, fault-tolerance and power consumption. In this paper we present an approach for the automatic software functionality assignment to multicore distributed architectures. We consider that the systems use the AUTomotive Open System ARchitecture (AUTOSAR). The functionality...

Equilibrium and pre-equilibrium emissions in proton-induced ...

Indian Academy of Sciences (India)

necessary for the domain of fission-reactor technology for the calculation of nuclear transmutation ... tions occur in three stages: INC, pre-equilibrium and equilibrium (or compound. 344. Pramana ... In the evaporation phase of the reaction, the.

Shape characteristics of equilibrium and non-equilibrium fractal clusters.

Science.gov (United States)

Mansfield, Marc L; Douglas, Jack F

2013-07-28

It is often difficult in practice to discriminate between equilibrium and non-equilibrium nanoparticle or colloidal-particle clusters that form through aggregation in gas or solution phases. Scattering studies often permit the determination of an apparent fractal dimension, but both equilibrium and non-equilibrium clusters in three dimensions frequently have fractal dimensions near 2, so that it is often not possible to discriminate on the basis of this geometrical property. A survey of the anisotropy of a wide variety of polymeric structures (linear and ring random and self-avoiding random walks, percolation clusters, lattice animals, diffusion-limited aggregates, and Eden clusters) based on the principal components of both the radius of gyration and electric polarizability tensor indicates, perhaps counter-intuitively, that self-similar equilibrium clusters tend to be intrinsically anisotropic at all sizes, while non-equilibrium processes such as diffusion-limited aggregation or Eden growth tend to be isotropic in the large-mass limit, providing a potential means of discriminating these clusters experimentally if anisotropy could be determined along with the fractal dimension. Equilibrium polymer structures, such as flexible polymer chains, are normally self-similar due to the existence of only a single relevant length scale, and are thus anisotropic at all length scales, while non-equilibrium polymer structures that grow irreversibly in time eventually become isotropic if there is no difference in the average growth rates in different directions. There is apparently no proof of these general trends and little theoretical insight into what controls the universal anisotropy in equilibrium polymer structures of various kinds. This is an obvious topic of theoretical investigation, as well as a matter of practical interest. To address this general problem, we consider two experimentally accessible ratios, one between the hydrodynamic and gyration radii, the other

Non-equilibrium thermodynamics, maximum entropy production and Earth-system evolution.

Science.gov (United States)

Kleidon, Axel

2010-01-13

The present-day atmosphere is in a unique state far from thermodynamic equilibrium. This uniqueness is for instance reflected in the high concentration of molecular oxygen and the low relative humidity in the atmosphere. Given that the concentration of atmospheric oxygen has likely increased throughout Earth-system history, we can ask whether this trend can be generalized to a trend of Earth-system evolution that is directed away from thermodynamic equilibrium, why we would expect such a trend to take place and what it would imply for Earth-system evolution as a whole. The justification for such a trend could be found in the proposed general principle of maximum entropy production (MEP), which states that non-equilibrium thermodynamic systems maintain steady states at which entropy production is maximized. Here, I justify and demonstrate this application of MEP to the Earth at the planetary scale. I first describe the non-equilibrium thermodynamic nature of Earth-system processes and distinguish processes that drive the system's state away from equilibrium from those that are directed towards equilibrium. I formulate the interactions among these processes from a thermodynamic perspective and then connect them to a holistic view of the planetary thermodynamic state of the Earth system. In conclusion, non-equilibrium thermodynamics and MEP have the potential to provide a simple and holistic theory of Earth-system functioning. This theory can be used to derive overall evolutionary trends of the Earth's past, identify the role that life plays in driving thermodynamic states far from equilibrium, identify habitability in other planetary environments and evaluate human impacts on Earth-system functioning. This journal is © 2010 The Royal Society

Simulations of NMR pulse sequences during equilibrium and non-equilibrium chemical exchange

International Nuclear Information System (INIS)

Helgstrand, Magnus; Haerd, Torleif; Allard, Peter

2000-01-01

The McConnell equations combine the differential equations for a simple two-state chemical exchange process with the Bloch differential equations for a classical description of the behavior of nuclear spins in a magnetic field. This equation system provides a useful starting point for the analysis of slow, intermediate and fast chemical exchange studied using a variety of NMR experiments. The McConnell equations are in the mathematical form of an inhomogeneous system of first-order differential equations. Here we rewrite the McConnell equations in a homogeneous form in order to facilitate fast and simple numerical calculation of the solution to the equation system. The McConnell equations can only treat equilibrium chemical exchange. We therefore also present a homogeneous equation system that can handle both equilibrium and non-equilibrium chemical processes correctly, as long as the kinetics is of first-order. Finally, the same method of rewriting the inhomogeneous form of the McConnell equations into a homogeneous form is applied to a quantum mechanical treatment of a spin system in chemical exchange. In order to illustrate the homogeneous McConnell equations, we have simulated pulse sequences useful for measuring exchange rates in slow, intermediate and fast chemical exchange processes. A stopped-flow NMR experiment was simulated using the equations for non-equilibrium chemical exchange. The quantum mechanical treatment was tested by the simulation of a sensitivity enhanced 15 N-HSQC with pulsed field gradients during slow chemical exchange and by the simulation of the transfer efficiency of a two-dimensional heteronuclear cross-polarization based experiment as a function of both chemical shift difference and exchange rate constants

Phylogenies support out-of-equilibrium models of biodiversity.

Science.gov (United States)

Manceau, Marc; Lambert, Amaury; Morlon, Hélène

2015-04-01

There is a long tradition in ecology of studying models of biodiversity at equilibrium. These models, including the influential Neutral Theory of Biodiversity, have been successful at predicting major macroecological patterns, such as species abundance distributions. But they have failed to predict macroevolutionary patterns, such as those captured in phylogenetic trees. Here, we develop a model of biodiversity in which all individuals have identical demographic rates, metacommunity size is allowed to vary stochastically according to population dynamics, and speciation arises naturally from the accumulation of point mutations. We show that this model generates phylogenies matching those observed in nature if the metacommunity is out of equilibrium. We develop a likelihood inference framework that allows fitting our model to empirical phylogenies, and apply this framework to various mammalian families. Our results corroborate the hypothesis that biodiversity dynamics are out of equilibrium. © 2015 John Wiley & Sons Ltd/CNRS.

Generalized Information Equilibrium Approaches to EEG Sleep Stage Discrimination

Directory of Open Access Journals (Sweden)

Todd Zorick

2016-01-01

Full Text Available Recent advances in neuroscience have raised the hypothesis that the underlying pattern of neuronal activation which results in electroencephalography (EEG signals is via power-law distributed neuronal avalanches, while EEG signals are nonstationary. Therefore, spectral analysis of EEG may miss many properties inherent in such signals. A complete understanding of such dynamical systems requires knowledge of the underlying nonequilibrium thermodynamics. In recent work by Fielitz and Borchardt (2011, 2014, the concept of information equilibrium (IE in information transfer processes has successfully characterized many different systems far from thermodynamic equilibrium. We utilized a publicly available database of polysomnogram EEG data from fourteen subjects with eight different one-minute tracings of sleep stage 2 and waking and an overlapping set of eleven subjects with eight different one-minute tracings of sleep stage 3. We applied principles of IE to model EEG as a system that transfers (equilibrates information from the time domain to scalp-recorded voltages. We find that waking consciousness is readily distinguished from sleep stages 2 and 3 by several differences in mean information transfer constants. Principles of IE applied to EEG may therefore prove to be useful in the study of changes in brain function more generally.

Unimodal tree size distributions possibly result from relatively strong conservatism in intermediate size classes.

Directory of Open Access Journals (Sweden)

Yue Bin

Full Text Available Tree size distributions have long been of interest to ecologists and foresters because they reflect fundamental demographic processes. Previous studies have assumed that size distributions are often associated with population trends or with the degree of shade tolerance. We tested these associations for 31 tree species in a 20 ha plot in a Dinghushan south subtropical forest in China. These species varied widely in growth form and shade-tolerance. We used 2005 and 2010 census data from that plot. We found that 23 species had reversed J shaped size distributions, and eight species had unimodal size distributions in 2005. On average, modal species had lower recruitment rates than reversed J species, while showing no significant difference in mortality rates, per capita population growth rates or shade-tolerance. We compared the observed size distributions with the equilibrium distributions projected from observed size-dependent growth and mortality. We found that observed distributions generally had the same shape as predicted equilibrium distributions in both unimodal and reversed J species, but there were statistically significant, important quantitative differences between observed and projected equilibrium size distributions in most species, suggesting that these populations are not at equilibrium and that this forest is changing over time. Almost all modal species had U-shaped size-dependent mortality and/or growth functions, with turning points of both mortality and growth at intermediate size classes close to the peak in the size distribution. These results show that modal size distributions do not necessarily indicate either population decline or shade-intolerance. Instead, the modal species in our study were characterized by a life history strategy of relatively strong conservatism in an intermediate size class, leading to very low growth and mortality in that size class, and thus to a peak in the size distribution at intermediate sizes.

Conceptual Integration of Chemical Equilibrium by Prospective Physical Sciences Teachers

Science.gov (United States)

Ganaras, Kostas; Dumon, Alain; Larcher, Claudine

2008-01-01

This article describes an empirical study concerning the mastering of the chemical equilibrium concept by prospective physical sciences teachers. The main objective was to check whether the concept of chemical equilibrium had become an integrating and unifying concept for them, that is to say an operational and functional knowledge to explain and…

Approach to equilibrium in high energy heavy ion collisions

International Nuclear Information System (INIS)

Zimanyi, J.

1981-01-01

With the aim to clarify somewhat the question of equilibration in the following we investigate the approach to equilibrium of particle composition and momentum distribution of the particles within the firecloud formed in the central collision of energetic heavy ions. (orig.)

Measuring productivity differences in equilibrium search models

DEFF Research Database (Denmark)

Lanot, Gauthier; Neumann, George R.

1996-01-01

Equilibrium search models require unobserved heterogeneity in productivity to fit observed wage distribution data, but provide no guidance about the location parameter of the heterogeneity. In this paper we show that the location of the productivity heterogeneity implies a mode in a kernel density...... estimate of the wage distribution. The number of such modes and their location are identified using bump hunting techniques due to Silverman (1981). These techniques are applied to Danish panel data on workers and firms. These estimates are used to assess the importance of employer wage policy....

Magnetohydrodynamic equilibrium with spheroidal plasma-vacuum interface

International Nuclear Information System (INIS)

Kaneko, Shobu; Chiyoda, Katsuji; Hirota, Isao.

1983-01-01

The Grad-Shafranov equations for an oblate and a prolate spheroidal plasmas are solved analytically under the assumptions, Bsub(phi) = 0 and dp/dpsi = constant. Here Bsub(phi) is the toroidal magnetic field, p is the kinetic pressure, and psi is the magnetic flux function. The plasmas in magnetohydrodynamic equilibrium are shown to be toroidal. The equilibrium magnetic-field configurations outside the spheroidal plasmas are considerably different from that of a spherical plasma. A line cusp or two point cusps appear outside the oblate or the prolate spheroidal plasma, respectively. (author)

A class of almost equilibrium states in Robertson-Walker spacetimes

Energy Technology Data Exchange (ETDEWEB)

Kueskue, Muharrem

2008-11-06

In quantum field theory in curved spacetimes the construction of the algebra of observables of linear fields is today well understood. However, it remains a non-trivial task to construct physically meaningful states on the algebra. For instance, we are in the unsatisfactory situation that there exist no examples of states suited to describe local thermal equilibrium in a non-stationary spacetime. In this thesis, we construct a class of states for the Klein-Gordon field in Robertson-Walker spacetimes, which seem to provide the first example of thermal states in a spacetime without time translation symmetry. More precisely, in the setting of real, linear, scalar fields in Robertson-Walker spacetimes we define on the set of homogeneous, isotropic, quasi-free states a free energy functional that is based on the averaged energy density measured by an isotropic observer along his worldline. This functional is well defined and lower bounded by a suitable quantum energy inequality. Subsequently, we minimize this functional and obtain states that we interpret as 'almost equilibrium states'. It turns out that the states of low energy are the ground states of the almost equilibrium states. Finally, we prove that the almost equilibrium states satisfy the Hadamard condition, which qualifies them as physically meaningful states. (orig.)

A class of almost equilibrium states in Robertson-Walker spacetimes

International Nuclear Information System (INIS)

Kueskue, Muharrem

2008-01-01

In quantum field theory in curved spacetimes the construction of the algebra of observables of linear fields is today well understood. However, it remains a non-trivial task to construct physically meaningful states on the algebra. For instance, we are in the unsatisfactory situation that there exist no examples of states suited to describe local thermal equilibrium in a non-stationary spacetime. In this thesis, we construct a class of states for the Klein-Gordon field in Robertson-Walker spacetimes, which seem to provide the first example of thermal states in a spacetime without time translation symmetry. More precisely, in the setting of real, linear, scalar fields in Robertson-Walker spacetimes we define on the set of homogeneous, isotropic, quasi-free states a free energy functional that is based on the averaged energy density measured by an isotropic observer along his worldline. This functional is well defined and lower bounded by a suitable quantum energy inequality. Subsequently, we minimize this functional and obtain states that we interpret as 'almost equilibrium states'. It turns out that the states of low energy are the ground states of the almost equilibrium states. Finally, we prove that the almost equilibrium states satisfy the Hadamard condition, which qualifies them as physically meaningful states. (orig.)

Specification of optical components using Wigner distribution function

International Nuclear Information System (INIS)

Xu Jiancheng; Li Haibo; Xu Qiao; Chai Liqun; Fan Changjiang

2010-01-01

In order to characterize and specify small-scale local wavefront deformation of optical component, a method based on Wigner distribution function has been proposed, which can describe wavefront deformation in spatial and spatial frequency domain. The relationship between Wigner distribution function and power spectral density is analyzed and thus the specification of small-scale local wavefront deformation is obtained by Wigner distribution function. Simulation and experiment demonstrate the effectiveness of the proposed method. The proposed method can not only identify whether the optical component meets the requirement of inertial confinement fusion (ICF), but also determine t he location where small-scale wavefront deformation is unqualified. Thus it provides an effective guide to the revision of unqualified optical components. (authors)

Equilibrium Investment Strategy for DC Pension Plan with Inflation and Stochastic Income under Heston’s SV Model

Directory of Open Access Journals (Sweden)

Jingyun Sun

2016-01-01

Full Text Available We consider a portfolio selection problem for a defined contribution (DC pension plan under the mean-variance criteria. We take into account the inflation risk and assume that the salary income process of the pension plan member is stochastic. Furthermore, the financial market consists of a risk-free asset, an inflation-linked bond, and a risky asset with Heston’s stochastic volatility (SV. Under the framework of game theory, we derive two extended Hamilton-Jacobi-Bellman (HJB equations systems and give the corresponding verification theorems in both the periods of accumulation and distribution of the DC pension plan. The explicit expressions of the equilibrium investment strategies, corresponding equilibrium value functions, and the efficient frontiers are also obtained. Finally, some numerical simulations and sensitivity analysis are presented to verify our theoretical results.

BINARY NEUTRON STARS IN QUASI-EQUILIBRIUM

International Nuclear Information System (INIS)

Taniguchi, Keisuke; Shibata, Masaru

2010-01-01

Quasi-equilibrium sequences of binary neutron stars are constructed for a variety of equations of state in general relativity. Einstein's constraint equations in the Isenberg-Wilson-Mathews approximation are solved together with the relativistic equations of hydrostationary equilibrium under the assumption of irrotational flow. We focus on unequal-mass sequences as well as equal-mass sequences, and compare those results. We investigate the behavior of the binding energy and total angular momentum along a quasi-equilibrium sequence, the endpoint of sequences, and the orbital angular velocity as a function of time, changing the mass ratio, the total mass of the binary system, and the equation of state of a neutron star. It is found that the orbital angular velocity at the mass-shedding limit can be determined by an empirical formula derived from an analytic estimation. We also provide tables for 160 sequences, which will be useful as a guideline of numerical simulations for the inspiral and merger performed in the near future.

[Clinical aspect of recent progress in phosphate metabolism. Distribution of phosphorus and its physiological roles in the body: the form, distribution, and physiological function].

Science.gov (United States)

Yano, Shozo; Sugimoto, Toshitsugu

2009-06-01

Phosphorus plays pivotal roles in the survival such as the cellular structure, genomic information, energy metabolism, and cell signaling. Total amount of phosphorus is 500-700 g in human, most of which is stored in the bone in an insoluble form of calcium salt. About 15% of phosphorus is located in the cell membrane and the intracellular fluid in the soft tissues in a form of organic phosphate. Only 0.1% is present in the extracellular fluid. This phosphate pool plays a role in the dynamic equilibrium through the gut, kidney, bone and other tissues. Most of inorganic phosphates in the extracellular fluid are present in a form of ions such as H2PO4- and HPO(4)2-, and the concentration of phosphatic acids is about 1.2 mM. The form, distribution, and physiological function of phosphorus in the body are summarized in this review.

Proposal for Modified Damage Probability Distribution Functions

DEFF Research Database (Denmark)

Pedersen, Preben Terndrup; Hansen, Peter Friis

1996-01-01

Immidiately following the Estonia disaster, the Nordic countries establishe a project entitled "Safety of Passenger/RoRo Vessels" As part of this project the present proposal for modified damage stability probability distribution functions has been developed. and submitted to "Sub-committee on st......Immidiately following the Estonia disaster, the Nordic countries establishe a project entitled "Safety of Passenger/RoRo Vessels" As part of this project the present proposal for modified damage stability probability distribution functions has been developed. and submitted to "Sub...

Kinetic Dissection of the Pre-existing Conformational Equilibrium in the Trypsin Fold*

Science.gov (United States)

Vogt, Austin D.; Chakraborty, Pradipta; Di Cera, Enrico

2015-01-01

Structural biology has recently documented the conformational plasticity of the trypsin fold for both the protease and zymogen in terms of a pre-existing equilibrium between closed (E*) and open (E) forms of the active site region. How such plasticity is manifested in solution and affects ligand recognition by the protease and zymogen is poorly understood in quantitative terms. Here we dissect the E*-E equilibrium with stopped-flow kinetics in the presence of excess ligand or macromolecule. Using the clotting protease thrombin and its zymogen precursor prethrombin-2 as relevant models we resolve the relative distribution of the E* and E forms and the underlying kinetic rates for their interconversion. In the case of thrombin, the E* and E forms are distributed in a 1:4 ratio and interconvert on a time scale of 45 ms. In the case of prethrombin-2, the equilibrium is shifted strongly (10:1 ratio) in favor of the closed E* form and unfolds over a faster time scale of 4.5 ms. The distribution of E* and E forms observed for thrombin and prethrombin-2 indicates that zymogen activation is linked to a significant shift in the pre-existing equilibrium between closed and open conformations that facilitates ligand binding to the active site. These findings broaden our mechanistic understanding of how conformational transitions control ligand recognition by thrombin and its zymogen precursor prethrombin-2 and have direct relevance to other members of the trypsin fold. PMID:26216877

Improvements for real-time magnetic equilibrium reconstruction on ASDEX Upgrade

International Nuclear Information System (INIS)

Giannone, L.; Fischer, R.; McCarthy, P.J.; Odstrcil, T.; Zammuto, I.; Bock, A.; Conway, G.; Fuchs, J.C.; Gude, A.; Igochine, V.; Kallenbach, A.; Lackner, K.; Maraschek, M.; Rapson, C.; Ruan, Q.; Schuhbeck, K.H.; Suttrop, W.; Wenzel, L.

2015-01-01

Highlights: • Spline basis current functions with second-order linear regularisation. • Perturbations of magnetic probe measurements due to ferromagnetic tiles on the inner wall and from oscillations in the fast position coil current are corrected. • A constraint of the safety factor on the magnetic axis is introduced. Soft X-ray tomography is used to assess the quality of the real-time magnetic equilibrium reconstruction. • External loop voltage measurements and magnetic probe pairs inside and outside the vessel wall were used to measure the vacuum vessel wall resistivity. - Abstract: Real-time magnetic equilibria are needed for NTM stabilization and disruption avoidance experiments on ASDEX Upgrade. Five improvements to real-time magnetic equilibrium reconstruction on ASDEX Upgrade have been investigated. The aim is to include as many features of the offline magnetic equilibrium reconstruction code in the real-time equilibrium reconstruction code. Firstly, spline current density basis functions with regularization are used in the offline equilibrium reconstruction code, CLISTE [1]. It is now possible to have the same number of spline basis functions in the real-time code. Secondly, in the presence of edge localized modes, (ELM's), it is found to be necessary to include the low pass filter effect of the vacuum vessel on the fast position control coil currents to correctly compensate the magnetic probes for current oscillations in these coils. Thirdly, the introduction of ferromagnetic tiles in ASDEX Upgrade means that a real-time algorithm for including the perturbations of the magnetic equilibrium generated by these tiles is required. A methodology based on tile surface currents is described. Fourthly, during current ramps it was seen that the difference between fitted and measured magnetic measurements in the equilibrium reconstruction were larger than in the constant current phase. External loop voltage measurements and magnetic probe pairs inside and

Improvements for real-time magnetic equilibrium reconstruction on ASDEX Upgrade

Energy Technology Data Exchange (ETDEWEB)

Giannone, L.; Fischer, R. [Max Planck Institute for Plasma Physics, 85748 Garching (Germany); McCarthy, P.J. [Department of Physics, University College Cork, Cork (Ireland); Odstrcil, T.; Zammuto, I.; Bock, A.; Conway, G.; Fuchs, J.C.; Gude, A.; Igochine, V.; Kallenbach, A.; Lackner, K.; Maraschek, M.; Rapson, C. [Max Planck Institute for Plasma Physics, 85748 Garching (Germany); Ruan, Q. [National Instruments, Austin, TX 78759-3504 (United States); Schuhbeck, K.H.; Suttrop, W. [Max Planck Institute for Plasma Physics, 85748 Garching (Germany); Wenzel, L. [National Instruments, Austin, TX 78759-3504 (United States)

2015-11-15

Highlights: • Spline basis current functions with second-order linear regularisation. • Perturbations of magnetic probe measurements due to ferromagnetic tiles on the inner wall and from oscillations in the fast position coil current are corrected. • A constraint of the safety factor on the magnetic axis is introduced. Soft X-ray tomography is used to assess the quality of the real-time magnetic equilibrium reconstruction. • External loop voltage measurements and magnetic probe pairs inside and outside the vessel wall were used to measure the vacuum vessel wall resistivity. - Abstract: Real-time magnetic equilibria are needed for NTM stabilization and disruption avoidance experiments on ASDEX Upgrade. Five improvements to real-time magnetic equilibrium reconstruction on ASDEX Upgrade have been investigated. The aim is to include as many features of the offline magnetic equilibrium reconstruction code in the real-time equilibrium reconstruction code. Firstly, spline current density basis functions with regularization are used in the offline equilibrium reconstruction code, CLISTE [1]. It is now possible to have the same number of spline basis functions in the real-time code. Secondly, in the presence of edge localized modes, (ELM's), it is found to be necessary to include the low pass filter effect of the vacuum vessel on the fast position control coil currents to correctly compensate the magnetic probes for current oscillations in these coils. Thirdly, the introduction of ferromagnetic tiles in ASDEX Upgrade means that a real-time algorithm for including the perturbations of the magnetic equilibrium generated by these tiles is required. A methodology based on tile surface currents is described. Fourthly, during current ramps it was seen that the difference between fitted and measured magnetic measurements in the equilibrium reconstruction were larger than in the constant current phase. External loop voltage measurements and magnetic probe pairs inside

[Distribution of 137Cs, 90Sr and their chemical analogues in the components of an above-ground part of a pine in a quasi-equilibrium condition].

Science.gov (United States)

Mamikhin, S V; Manakhov, D V; Shcheglov, A I

2014-01-01

The additional study of the distribution of radioactive isotopes of caesium and strontium and their chemical analogues in the above-ground components of pine in the remote from the accident period was carried out. The results of the research confirmed the existence of analogy in the distribution of these elements on the components of this type of wood vegetation in the quasi-equilibrium (relatively radionuclides) condition. Also shown is the selective possibility of using the data on the ash content of the components of forest stands of pine and oak as an information analogue.

CFD analysis of laboratory scale phase equilibrium cell operation

Science.gov (United States)

Jama, Mohamed Ali; Nikiforow, Kaj; Qureshi, Muhammad Saad; Alopaeus, Ville

2017-10-01

For the modeling of multiphase chemical reactors or separation processes, it is essential to predict accurately chemical equilibrium data, such as vapor-liquid or liquid-liquid equilibria [M. Šoóš et al., Chem. Eng. Process.: Process Intensif. 42(4), 273-284 (2003)]. The instruments used in these experiments are typically designed based on previous experiences, and their operation verified based on known equilibria of standard components. However, mass transfer limitations with different chemical systems may be very different, potentially falsifying the measured equilibrium compositions. In this work, computational fluid dynamics is utilized to design and analyze laboratory scale experimental gas-liquid equilibrium cell for the first time to augment the traditional analysis based on plug flow assumption. Two-phase dilutor cell, used for measuring limiting activity coefficients at infinite dilution, is used as a test case for the analysis. The Lagrangian discrete model is used to track each bubble and to study the residence time distribution of the carrier gas bubbles in the dilutor cell. This analysis is necessary to assess whether the gas leaving the cell is in equilibrium with the liquid, as required in traditional analysis of such apparatus. Mass transfer for six different bio-oil compounds is calculated to determine the approach equilibrium concentration. Also, residence times assuming plug flow and ideal mixing are used as reference cases to evaluate the influence of mixing on the approach to equilibrium in the dilutor. Results show that the model can be used to predict the dilutor operating conditions for which each of the studied gas-liquid systems reaches equilibrium.

CFD analysis of laboratory scale phase equilibrium cell operation.

Science.gov (United States)

Jama, Mohamed Ali; Nikiforow, Kaj; Qureshi, Muhammad Saad; Alopaeus, Ville

2017-10-01

For the modeling of multiphase chemical reactors or separation processes, it is essential to predict accurately chemical equilibrium data, such as vapor-liquid or liquid-liquid equilibria [M. Šoóš et al., Chem. Eng. Process Intensif. 42(4), 273-284 (2003)]. The instruments used in these experiments are typically designed based on previous experiences, and their operation verified based on known equilibria of standard components. However, mass transfer limitations with different chemical systems may be very different, potentially falsifying the measured equilibrium compositions. In this work, computational fluid dynamics is utilized to design and analyze laboratory scale experimental gas-liquid equilibrium cell for the first time to augment the traditional analysis based on plug flow assumption. Two-phase dilutor cell, used for measuring limiting activity coefficients at infinite dilution, is used as a test case for the analysis. The Lagrangian discrete model is used to track each bubble and to study the residence time distribution of the carrier gas bubbles in the dilutor cell. This analysis is necessary to assess whether the gas leaving the cell is in equilibrium with the liquid, as required in traditional analysis of such apparatus. Mass transfer for six different bio-oil compounds is calculated to determine the approach equilibrium concentration. Also, residence times assuming plug flow and ideal mixing are used as reference cases to evaluate the influence of mixing on the approach to equilibrium in the dilutor. Results show that the model can be used to predict the dilutor operating conditions for which each of the studied gas-liquid systems reaches equilibrium.

Isospin equilibrium and non-equilibrium in heavy-ion collisions at intermediate energies

International Nuclear Information System (INIS)

Chen Liewen; Ge Lingxiao; Zhang Xiaodong; Zhang Fengshou

1997-01-01

The equilibrium and non-equilibrium of the isospin degree of freedom are studied in terms of an isospin-dependent QMD model, which includes isospin-dependent symmetry energy, Coulomb energy, N-N cross sections and Pauli blocking. It is shown that there exists a transition from the isospin equilibrium to non-equilibrium as the incident energy from below to above a threshold energy in central, asymmetric heavy-ion collisions. Meanwhile, it is found that the phenomenon results from the co-existence and competition of different reaction mechanisms, namely, the isospin degree of freedom reaches an equilibrium if the incomplete fusion (ICF) component is dominant and does not reach equilibrium if the fragmentation component is dominant. Moreover, it is also found that the isospin-dependent N-N cross sections and symmetry energy are crucial for the equilibrium of the isospin degree of freedom in heavy-ion collisions around the Fermi energy. (author)

Deviations from excitation equilibrium in optically thick mercury arc plasmas

International Nuclear Information System (INIS)

Karabourniotis, D.; Couris, S.; Damelincourt, J.J.

1989-01-01

Up to date mercury arcs at pressure greater than 1 atm have been investigated as plasma systems in local thermodynamic equilibrium (LTE) state. These studies have been motivated by the applications of mercury arcs, e.g., in the lighting industry. The LTE-assumption simplifies the use of spectroscopic diagnostics and the performance of species-concentration calculations. A high pressure mercury arc of about 1 atm had been considered in two possibilities: excitation and gas temperatures are the same, the electron temperature is higher and excitation and electron temperatures are the same, the gas temperature is lower. Recent measurements in mercury arcs reveal the existence of severe departures from thermal equilibrium and suggest the absence of excitation equilibrium in the axis and in the periphery in such an arc. The deviation from equilibrium leads to complicated distributions, such that the system cannot be described correctly by any single temperature. This becomes quite complicated when plasma inhomogeneity and strong reabsorption of the radiation are present

Chemical bonding and the equilibrium composition of Grignard reagents in ethereal solutions.

Science.gov (United States)

Henriques, André M; Barbosa, André G H

2011-11-10

A thorough analysis of the electronic structure and thermodynamic aspects of Grignard reagents and its associated equilibrium composition in ethereal solutions is performed. Considering methylmagnesium halides containing fluorine, chlorine, and bromine, we studied the neutral, charged, and radical species associated with their chemical equilibrium in solution. The ethereal solvents considered, tetrahydrofuran (THF) and ethyl ether (Et(2)O), were modeled using the polarizable continuum model (PCM) and also by explicit coordination to the Mg atoms in a cluster. The chemical bonding of the species that constitute the Grignard reagent is analyzed in detail with generalized valence bond (GVB) wave functions. Equilibrium constants were calculated with the DFT/M06 functional and GVB wave functions, yielding similar results. According to our calculations and existing kinetic and electrochemical evidence, the species R(•), R(-), (•)MgX, and RMgX(2)(-) must be present in low concentration in the equilibrium. We conclude that depending on the halogen, a different route must be followed to produce the relevant equilibrium species in each case. Chloride and bromide must preferably follow a "radical-based" pathway, and fluoride must follow a "carbanionic-based" pathway. These different mechanisms are contrasted against the available experimental results and are proven to be consistent with the existing thermodynamic data on the Grignard reagent equilibria.

Income- and energy-taxation for redistribution in general equilibrium

International Nuclear Information System (INIS)

FitzRoy, F.R.

1993-01-01

In a 3-factor General Equilibrium (GE)-model with a continuum of ability, the employed choose optimal labour supply, and equilibrium unemployment is determined by benefits funded by wage- and energy-taxes. Aggregate labour and the net wage may increase or decrease with taxation (and unemployment), and conditions for a reduction in redistributive wage-taxes to be Pareto-improving are derived. A small energy tax always raises the net wage, providing the wage tax is reduced to maintain constant employment and a balanced budget. High ability households prefer higher energy taxes when externalities are uniformly distributed and non-distorting. (author)

An approach for generating trajectory-based dynamics which conserves the canonical distribution in the phase space formulation of quantum mechanics. II. Thermal correlation functions.

Science.gov (United States)

Liu, Jian; Miller, William H

2011-03-14

We show the exact expression of the quantum mechanical time correlation function in the phase space formulation of quantum mechanics. The trajectory-based dynamics that conserves the quantum canonical distribution-equilibrium Liouville dynamics (ELD) proposed in Paper I is then used to approximately evaluate the exact expression. It gives exact thermal correlation functions (of even nonlinear operators, i.e., nonlinear functions of position or momentum operators) in the classical, high temperature, and harmonic limits. Various methods have been presented for the implementation of ELD. Numerical tests of the ELD approach in the Wigner or Husimi phase space have been made for a harmonic oscillator and two strongly anharmonic model problems, for each potential autocorrelation functions of both linear and nonlinear operators have been calculated. It suggests ELD can be a potentially useful approach for describing quantum effects for complex systems in condense phase.

Distribution function of faint galaxy numbers

International Nuclear Information System (INIS)

Fesenko, L.M.

1981-01-01

The Lick observatory counts of galaxies are considered. The distribution of number of galaxies in elementary regions (ER) of 1 degx1 deg is investigated. Each field of 6 degx6 deg was treated separately At b>40 deg the probab+lity to observe of n galaxies in ER is an exponential decreasing function of n, if unequality n> were fulfilled. The mean apparent multiplicity of a galaxy (2.8+-0.9) was derived. The galaxy number distribution was simple model for the number of various systems of galaxies. The supperclustering of galaxies was not introduced. Based on that model the approximate expression for galaxy number distribution was considered and was compared with observed distributions. The agreement between these distributions become better with reducing of the interstellar absorption of light

MODELING COLLISIONAL CASCADES IN DEBRIS DISKS: STEEP DUST-SIZE DISTRIBUTIONS

International Nuclear Information System (INIS)

Gáspár, András; Psaltis, Dimitrios; Rieke, George H.; Özel, Feryal

2012-01-01

We explore the evolution of the mass distribution of dust in collision-dominated debris disks, using the collisional code introduced in our previous paper. We analyze the equilibrium distribution and its dependence on model parameters by evolving over 100 models to 10 Gyr. With our numerical models, we confirm that systems reach collisional equilibrium with a mass distribution that is steeper than the traditional solution by Dohnanyi. Our model yields a quasi-steady-state slope of n(m) ∼ m –1.88 [n(a) ∼ a –3.65 ] as a robust solution for a wide range of possible model parameters. We also show that a simple power-law function can be an appropriate approximation for the mass distribution of particles in certain regimes. The steeper solution has observable effects in the submillimeter and millimeter wavelength regimes of the electromagnetic spectrum. We assemble data for nine debris disks that have been observed at these wavelengths and, using a simplified absorption efficiency model, show that the predicted slope of the particle-mass distribution generates spectral energy distributions that are in agreement with the observed ones.

Energy distributions and radiation transport in uranium plasmas

International Nuclear Information System (INIS)

Miley, G.; Bathke, C.; Maceda, E.; Choi, C.

1976-01-01

Electron energy distribution functions have been calculated in a 235 U-plasma at 1 atmosphere for various plasma temperatures (5000 to 8000 0 K) and neutron fluxes (2 x 10 12 to 2 x 10 16 neutrons/(cm 2 -sec)). Two sources of energetic electrons are included; namely fission-fragment and electron-impact ionization, resulting in a high-energy tail superimposed on the thermalized electron distribution. Consequential derivations from equilibrium collision rates are of interest relative to direct pumping of lasers and radiation emission. Results suggest that non-equilibrium excitation can best be achieved with an additive gas such as helium or in lower temperature plasmas requiring UF 6 . An approximate analytic model, based on continuous electron slowing, has been used for survey calculations. Where more accuracy is required, a Monte Carlo technique is used which combines an analytic representation of Coulombic collisions with a random-walk treatment of inelastic collisions

Equilibrium finite-frequency noise of an interacting mesoscopic capacitor studied in time-dependent density functional theory

Science.gov (United States)

Dittmann, Niklas; Splettstoesser, Janine; Helbig, Nicole

2018-03-01

We calculate the frequency-dependent equilibrium noise of a mesoscopic capacitor in time-dependent density functional theory (TDDFT). The capacitor is modeled as a single-level quantum dot with on-site Coulomb interaction and tunnel coupling to a nearby reservoir. The noise spectra are derived from linear-response conductances via the fluctuation-dissipation theorem. Thereby, we analyze the performance of a recently derived exchange-correlation potential with time-nonlocal density dependence in the finite-frequency linear-response regime. We compare our TDDFT noise spectra with real-time perturbation theory and find excellent agreement for noise frequencies below the reservoir temperature.

Characteristic functions of scale mixtures of multivariate skew-normal distributions

KAUST Repository

Kim, Hyoung-Moon

2011-08-01

We obtain the characteristic function of scale mixtures of skew-normal distributions both in the univariate and multivariate cases. The derivation uses the simple stochastic relationship between skew-normal distributions and scale mixtures of skew-normal distributions. In particular, we describe the characteristic function of skew-normal, skew-t, and other related distributions. © 2011 Elsevier Inc.

Parton distribution function for quarks in an s-channel approach

CERN Document Server

Hautmann, F

2007-01-01

We use an s-channel picture of hard hadronic collisions to investigate the parton distribution function for quarks at small momentum fraction x, which corresponds to very high energy scattering. We study the renormalized quark distribution at one loop in this approach. In the high-energy picture, the quark distribution function is expressed in terms of a Wilson-line correlator that represents the cross section for a color dipole to scatter from the proton. We model this Wilson-line correlator in a saturation model. We relate this representation of the quark distribution function to the corresponding representation of the structure function F_T(x,Q^2) for deeply inelastic scattering.

Problems with the concept of plasma equilibrium in tokamaks

International Nuclear Information System (INIS)

Carreras, B.A.

1992-01-01

The equilibrium condition for a magnetically confined plasma in normally formulated in terms of macroscopic equations. In these equations, the plasma pressure is assumed to be a function of the magnetic flux with continuous derivatives. However, in three- dimensional systems this is not necessarily the case. Here, we look at the case of an intrinsically three-dimensional realistic tokamak, and we discuss the possible interconnection between the equilibrium and anomalous transport

Convolution of Distribution-Valued Functions. Applications.

OpenAIRE

BARGETZ, CHRISTIAN

2011-01-01

In this article we examine products and convolutions of vector-valued functions. For nuclear normal spaces of distributions Proposition 25 in [31,p. 120] yields a vector-valued product or convolution if there is a continuous product or convolution mapping in the range of the vector-valued functions. For specific spaces, we generalize this result to hypocontinuous bilinear maps at the expense of generality with respect to the function space. We consider holomorphic, meromorphic and differentia...

The Wigner distribution function for the one-dimensional parabose oscillator

International Nuclear Information System (INIS)

Jafarov, E; Lievens, S; Jeugt, J Van der

2008-01-01

In the beginning of the 1950s, Wigner introduced a fundamental deformation from the canonical quantum mechanical harmonic oscillator, which is nowadays sometimes called a Wigner quantum oscillator or a parabose oscillator. Also, in quantum mechanics the so-called Wigner distribution is considered to be the closest quantum analogue of the classical probability distribution over the phase space. In this paper, we consider which definition for such a distribution function could be used in the case of non-canonical quantum mechanics. We then explicitly compute two different expressions for this distribution function for the case of the parabose oscillator. Both expressions turn out to be multiple sums involving (generalized) Laguerre polynomials. Plots then show that the Wigner distribution function for the ground state of the parabose oscillator is similar in behaviour to the Wigner distribution function of the first excited state of the canonical quantum oscillator

Relations between dissipated work in non-equilibrium process and the family of Rényi divergences

International Nuclear Information System (INIS)

Wei, Bo-Bo; Plenio, M B

2017-01-01

In this paper, we establish a general relation which directly links the dissipated work done on a system driven arbitrarily far from equilibrium, a fundamental quantity in thermodynamics, and the family of Rényi divergences between two states along the forward and reversed dynamics, a fundamental concept in information theory. Specifically, we find that the generating function of the dissipated work under an arbitrary time-dependent driving is related to the family of Rényi divergences between a non-equilibrium state along the forward process and a non-equilibrium state along its time-reversed process. This relation is a consequence of the principle of conservation of information and time reversal symmetry and is universally applicable to both finite classical system and finite quantum system under arbitrary driving process. The significance of the relation between the generating function of dissipated work and the family of Rényi divergences are two fold. On the one hand, the relation establishes that the macroscopic entropy production and its fluctuations are determined by the family of Rényi divergences, a measure of distinguishability of two states, between a microscopic process and its time reversal. On the other hand, this relation tells us that we can extract the family of Renyi divergences from the work measurement in a microscopic process. For classical systems the work measurement is straightforward, from which the family of Rényi divergences can be obtained; for quantum systems under time-dependent driving the characteristic function of work distributions can be measured from Ramsey interferences of a single spin, then we can extract the family of Renyi divergences from Ramsey interferences of a single spin. (paper)

Functional and physical molecular size of the chicken hepatic lectin determined by radiation inactivation and sedimentation equilibrium analysis

International Nuclear Information System (INIS)

Steer, C.J.; Osborne, J.C. Jr.; Kempner, E.S.

1990-01-01

Radiation inactivation and sedimentation equilibrium analysis were used to determine the functional and physical size of the chicken hepatic membrane receptor that binds N-acetylglucosamine-terminated glycoproteins. Purified plasma membranes from chicken liver were irradiated with high energy electrons and assayed for 125I-agalactoorosomucoid binding. Increasing the dose of ionizing radiation resulted in a monoexponential decay in binding activity due to a progressive loss of binding sites. The molecular mass of the chicken lectin, determined in situ by target analysis, was 69,000 +/- 9,000 Da. When the same irradiated membranes were solubilized in Brij 58 and assayed, the binding protein exhibited a target size of 62,000 +/- 4,000 Da; in Triton X-100, the functional size of the receptor was 85,000 +/- 10,000 Da. Sedimentation equilibrium measurements of the purified binding protein yielded a lower limit molecular weight of 79,000 +/- 7,000. However, the solubilized lectin was detected as a heterogeneous population of oligomers with molecular weights as high as 450,000. Addition of calcium or calcium plus N-acetylglucosamine decreased the higher molecular weight species, but the lower limit molecular weights remained invariant. Similar results were determined when the chicken lectin was solubilized in Brij 58, C12E9, or 3-[(3-cholamidopropyl)dimethylammonio]-1-propane-sulfonic acid (CHAPS). Results from the present study suggest that in the plasma membrane, the functional species of the chicken hepatic lectin exists as a trimer. However, in detergent solution, the purified receptor forms a heterogeneous population of irreversible oligomers that exhibit binding activity proportional to size

Planar-channeling spatial density under statistical equilibrium

International Nuclear Information System (INIS)

Ellison, J.A.; Picraux, S.T.

1978-01-01

The phase-space density for planar channeled particles has been derived for the continuum model under statistical equilibrium. This is used to obtain the particle spatial probability density as a function of incident angle. The spatial density is shown to depend on only two parameters, a normalized incident angle and a normalized planar spacing. This normalization is used to obtain, by numerical calculation, a set of universal curves for the spatial density and also for the channeled-particle wavelength as a function of amplitude. Using these universal curves, the statistical-equilibrium spatial density and the channeled-particle wavelength can be easily obtained for any case for which the continuum model can be applied. Also, a new one-parameter analytic approximation to the spatial density is developed. This parabolic approximation is shown to give excellent agreement with the exact calculations

Molecular sieving through a graphene nanopore: non-equilibrium molecular dynamics simulation

Institute of Scientific and Technical Information of China (English)

Chengzhen Sun; Bofeng Bai

2017-01-01

Two-dimensional graphene nanopores have shown great promise as ultra-permeable molecular sieves based on their size-sieving effects.We design a nitrogen/hydrogen modified graphene nanopore and conduct a transient non-equilibrium molecular dynamics simulation on its molecular sieving effects.The distinct time-varying molecular crossing numbers show that this special nanopore can efficiently sieve CO2 and H2S molecules from CH4 molecules with high selectivity.By analyzing the molecular structure and pore functionalization-related molecular orientation and permeable zone in the nanopore,density distribution in the molecular adsorption layer on the graphene surface,as well as other features,the molecular sieving mechanisms of graphene nanopores are revealed.Finally,several implications on the design of highly-efficient graphene nanopores,especially for determining the porosity and chemical functionalization,as gas separation membranes are summarized based on the identified phenomena and mechanisms.

Non-equilibrium grain boundary segregation of boron in austenitic stainless steel - IV. Precipitation behaviour and distribution of elements at grain boundaries

International Nuclear Information System (INIS)

Karlsson, L.; Norden, H.

1988-01-01

The distribution of elements and the precipitation behaviour at grain boundaries have been studied in boron containing AISI 316L and ''Mo-free AISI 316L'' type austenitic stainless steels. A combination of microanalytical techniques was used to study the boundary regions after cooling at 0.29-530 0 C/s from 800, 1075 or 1250 0 C. Tetragonal M/sub 2/B, M/sub 5/B/sub 3/ and M/sub 3/B/sub 2/, all rich in Fe, Cr and Mo, precipitated in the ''high B'' (40 ppm) AISI 316L steel whereas orthorhombic M/sub 2/B, rich in Cr and Fe was found in the ''Mo-free steel'' with 23 ppm B. In the ''high B steel'' a thin (<2nm), continuous layer, containing B, Cr, Mo and Fe and having a stoichiometry of typically M/sub 9/B, formed at boundaries after cooling at intermediate cooling rates. For both types of steels a boundary zone was found, after all heat treatments, with a composition differing significantly from the bulk composition. The differences were most marked after cooling at intermediate cooling rates. In both types of steel boundary depletion of Cr and enrichment of B and C occurred. It was found that non-equilibrium grain boundary segregation of boron can affect the precipitation behaviour by making the boundary composition enter a new phase field ''Non-equilibrium phases'' might also form. The synergistic effect of B and Mo on the boundary composition and precipitation behaviour, and the observed indications of C non-equilibrium segregation are discussed

Electron and ion distribution functions in magnetopause reconnection

Science.gov (United States)

Wang, S.; Chen, L. J.; Bessho, N.; Hesse, M.; Kistler, L. M.; Torbert, R. B.; Mouikis, C.; Pollock, C. J.

2015-12-01

We investigate electron and ion velocity distribution functions in dayside magnetopause reconnection events observed by the Cluster and MMS spacecraft. The goal is to build a spatial map of electron and ion distribution features to enable the indication of the spacecraft location in the reconnection structure, and to understand plasma energization processes. Distribution functions, together with electromagnetic field structures, plasma densities, and bulk velocities, are organized and compared with particle-in-cell simulation results to indicate the proximities to the reconnection X-line. Anisotropic features in the distributions of magnetospheric- and magnetosheath- origin electrons at different locations in the reconnection inflow and exhaust are identified. In particular, parallel electron heating is observed in both the magnetosheath and magnetosphere inflow regions. Possible effects of the guide field strength, waves, and upstream density and temperature asymmetries on the distribution features will be discussed.

End to end distribution functions for a class of polymer models

International Nuclear Information System (INIS)

Khandekar, D.C.; Wiegel, F.W.

1988-01-01

The two point end-to-end distribution functions for a class of polymer models have been obtained within the first cumulant approximation. The trial distribution function this purpose is chosen to correspond to a general non-local quadratic functional. An Exact expression for the trial distribution function is obtained. It is pointed out that these trial distribution functions themselves can be used to study certain aspects of the configurational behaviours of polymers. These distribution functions are also used to obtain the averaged mean square size 2 > of a polymer characterized by the non-local quadratic potential energy functional. Finally, we derive an analytic expression for 2 > of a polyelectrolyte model and show that for a long polymer a weak electrostatic interaction does not change the behaviour of 2 > from that of a free polymer. (author). 16 refs

Entropy and equilibrium via games of complexity

Science.gov (United States)

Topsøe, Flemming

2004-09-01

It is suggested that thermodynamical equilibrium equals game theoretical equilibrium. Aspects of this thesis are discussed. The philosophy is consistent with maximum entropy thinking of Jaynes, but goes one step deeper by deriving the maximum entropy principle from an underlying game theoretical principle. The games introduced are based on measures of complexity. Entropy is viewed as minimal complexity. It is demonstrated that Tsallis entropy ( q-entropy) and Kaniadakis entropy ( κ-entropy) can be obtained in this way, based on suitable complexity measures. A certain unifying effect is obtained by embedding these measures in a two-parameter family of entropy functions.

Spin-dependent parton distributions and structure functions

International Nuclear Information System (INIS)

Bentz, W.; Ito, T.; Cloet, I.C.; Thomas, A.W.; Yazaki, K.

2008-01-01

Nuclear parton distributions and structure functions are determined in an effective chiral quark theory. We also discuss an extension of our model to fragmentation functions. Presented at the 20th Few-Body Conference, Pisa, Italy, 10-14 September 2007. (author)

Distribution function of excitations in systems with fractional statistics

International Nuclear Information System (INIS)

Protogenov, A.P.

1992-08-01

The distribution function of low-energy excitations in 2+1D systems has been considered. It is shown that in these systems the quantum distribution function differs from the usual one by having a finite value of the entropy of linked braids. (author). 47 refs

Optical properties (bidirectional reflectance distribution function) of shot fabric

NARCIS (Netherlands)

Lu, Rong; Koenderink, Jan J.; Kappers, Astrid M L

2000-01-01

To study the optical properties of materials, one needs a complete set of the angular distribution functions of surface scattering from the materials. Here we present a convenient method for collecting a large set of bidirectional reflectance distribution function (BRDF) samples in the hemispherical

Equilibrium and shot noise in mesoscopic systems

Energy Technology Data Exchange (ETDEWEB)

Martin, T.

1994-10-01

Within the last decade, there has been a resurgence of interest in the study of noise in Mesoscopic devices, both experimentally and theoretically. Noise in solid state devices can have different origins: there is 1/f noise, which is believed to arise from fluctuations in the resistance of the sample due to the motion of impurities. On top of this contribution is a frequency independent component associated with the stochastic nature of electron transport, which will be the focus of this paper. If the sample considered is small enough that dephasing and inelastic effects can be neglected, equilibrium (thermal) and excess noise can be completely described in terms of the elastic scattering properties of the sample. As mentioned above, noise arises as a consequence of random processes governing the transport of electrons. Here, there are two sources of randomness: first, electrons incident on the sample occupy a given energy state with a probability given by the Fermi-Dirac distribution function. Secondly, electrons can be transmitted across the sample or reflected in the same reservoir where they came from with a probability given by the quantum mechanical transmission/reflection coefficients. Equilibrium noise refers to the case where no bias voltage is applied between the leads connected to the sample, where thermal agitation alone allows the electrons close to the Fermi level to tunnel through the sample. In general, equilibrium noise is related to the conductance of the sample via the Johnson-Nyquist formula. In the presence of a bias, in the classical regime, one expects to recover the full shot noise < {Delta}{sup 2}I >= 2I{Delta}{mu} as was observed a long time ago in vacuum diodes. In the Mesoscopic regime, however, excess noise is reduced below the shot noise level. The author introduces a more intuitive picture, where the current passing through the device is a superposition of pulses, or electron wave packets, which can be transmitted or reflected.

Quantum mechanics with non-negative quantum distribution function

International Nuclear Information System (INIS)

Zorin, A.V.; Sevastianov, L.A.

2010-01-01

Full text: (author)Among numerous approaches to probabilistic interpretation of the conventional quantum mechanics the most close to the N. Bohr idea of the correspondence principle is the D.I. Blokhintzev - Ya.P. Terletsky approach using the quantum distribution function on the coordinate- momentum space. The detailed investigation of this approach has lead to the correspondence rule of V.V. Kuryshkin. Quantum mechanics of Kuryshkin (QMK) embody the program proposed by Yu.M. Shirokov for unifying classical and quantum mechanics in similar mathematical models. QMK develops and enhances Wigner's proposal concerning the calculation of quantum corrections to classical thermodynamic parameters using a phase distribution function. The main result of QMK is the possibility of description by mean of a positively-valued distribution function. This represents an important step towards a completely statistical model of quantum phenomena, compared with the quasi-probabilistic nature of Wigner distribution. Wigner's model does not permit to perform correctly the classical limit in quantum mechanics as well. On the other hand, QMK has a much more complex structure of operators of observables. One of the unsolved problems of QMK is the absence of a priori rules for establishing of auxiliary functions. Nevertheless, while it is impossible to overcome the complex form of operators, we find it quite possible to derive some methods of filing sets of auxiliary functions

Auroal electron distribution function

International Nuclear Information System (INIS)

Kaufmann, R.L.; Dusenbery, P.B.; Thomas, B.J.; Arnoldy, R.L.

1978-01-01

The electron velocity distribution function is presented in the energy range 25 eV 8 cm/s (E=300 eV) are nearly isotropic in pitch angle throughout the flight. Upgoing electrons show almost no pitch angle dependence beyond 120 0 , and their fluxes decline smoothly as energy increases, with little or no evidence of a plateau. Preliminary results of numerical integrations, to study bulk properties and stability of the plasma are presented

Finding equilibrium in the spatiotemporal chaos of the complex Ginzburg-Landau equation

Science.gov (United States)

Ballard, Christopher C.; Esty, C. Clark; Egolf, David A.

2016-11-01

Equilibrium statistical mechanics allows the prediction of collective behaviors of large numbers of interacting objects from just a few system-wide properties; however, a similar theory does not exist for far-from-equilibrium systems exhibiting complex spatial and temporal behavior. We propose a method for predicting behaviors in a broad class of such systems and apply these ideas to an archetypal example, the spatiotemporal chaotic 1D complex Ginzburg-Landau equation in the defect chaos regime. Building on the ideas of Ruelle and of Cross and Hohenberg that a spatiotemporal chaotic system can be considered a collection of weakly interacting dynamical units of a characteristic size, the chaotic length scale, we identify underlying, mesoscale, chaotic units and effective interaction potentials between them. We find that the resulting equilibrium Takahashi model accurately predicts distributions of particle numbers. These results suggest the intriguing possibility that a class of far-from-equilibrium systems may be well described at coarse-grained scales by the well-established theory of equilibrium statistical mechanics.

Adiabatic out-of-equilibrium solutions to the Boltzmann equation in warm inflation

Science.gov (United States)

Bastero-Gil, Mar; Berera, Arjun; Ramos, Rudnei O.; Rosa, João G.

2018-02-01

We show that, in warm inflation, the nearly constant Hubble rate and temperature lead to an adiabatic evolution of the number density of particles interacting with the thermal bath, even if thermal equilibrium cannot be maintained. In this case, the number density is suppressed compared to the equilibrium value but the associated phase-space distribution retains approximately an equilibrium form, with a smaller amplitude and a slightly smaller effective temperature. As an application, we explicitly construct a baryogenesis mechanism during warm inflation based on the out-of-equilibrium decay of particles in such an adiabatically evolving state. We show that this generically leads to small baryon isocurvature perturbations, within the bounds set by the Planck satellite. These are correlated with the main adiabatic curvature perturbations but exhibit a distinct spectral index, which may constitute a smoking gun for baryogenesis during warm inflation. Finally, we discuss the prospects for other applications of adiabatically evolving out-of-equilibrium states.

Equilibrium and kinetics of Sin Nombre hantavirus binding at DAF/CD55 functionalized bead surfaces.

Science.gov (United States)

Buranda, Tione; Swanson, Scarlett; Bondu, Virginie; Schaefer, Leah; Maclean, James; Mo, Zhenzhen; Wycoff, Keith; Belle, Archana; Hjelle, Brian

2014-03-10

Decay accelerating factor (DAF/CD55) is targeted by many pathogens for cell entry. It has been implicated as a co-receptor for hantaviruses. To examine the binding of hantaviruses to DAF, we describe the use of Protein G beads for binding human IgG Fc domain-functionalized DAF ((DAF)₂-Fc). When mixed with Protein G beads the resulting DAF beads can be used as a generalizable platform for measuring kinetic and equilibrium binding constants of DAF binding targets. The hantavirus interaction has high affinity (24-30 nM; k(on) ~ 10⁵ M⁻¹ s⁻¹, k(off) ~ 0.0045 s⁻¹). The bivalent (DAF)₂-Fc/SNV data agree with hantavirus binding to DAF expressed on Tanoue B cells (K(d) = 14.0 nM). Monovalent affinity interaction between SNV and recombinant DAF of 58.0 nM is determined from competition binding. This study serves a dual purpose of presenting a convenient and quantitative approach of measuring binding affinities between DAF and the many cognate viral and bacterial ligands and providing new data on the binding constant of DAF and Sin Nombre hantavirus. Knowledge of the equilibrium binding constant allows for the determination of the relative fractions of bound and free virus particles in cell entry assays. This is important for drug discovery assays for cell entry inhibitors.

On a Functional Equation for the Generating Function of the Logarithmic Series Distribution

OpenAIRE

Panaretos, John

1987-01-01

This note deals with finding the solution of a functional equation, where the function involved has the additional property of being a probability generating function. It turns out that the unique solution of this particular functional equation is the probability generating function of the logarithmic series distribution

Wireless distributed functional electrical stimulation system

Directory of Open Access Journals (Sweden)

Jovičić Nenad S

2012-08-01

Full Text Available Abstract Background The control of movement in humans is hierarchical and distributed and uses feedback. An assistive system could be best integrated into the therapy of a human with a central nervous system lesion if the system is controlled in a similar manner. Here, we present a novel wireless architecture and routing protocol for a distributed functional electrical stimulation system that enables control of movement. Methods The new system comprises a set of miniature battery-powered devices with stimulating and sensing functionality mounted on the body of the subject. The devices communicate wirelessly with one coordinator device, which is connected to a host computer. The control algorithm runs on the computer in open- or closed-loop form. A prototype of the system was designed using commercial, off-the-shelf components. The propagation characteristics of electromagnetic waves and the distributed nature of the system were considered during the development of a two-hop routing protocol, which was implemented in the prototype’s software. Results The outcomes of this research include a novel system architecture and routing protocol and a functional prototype based on commercial, off-the-shelf components. A proof-of-concept study was performed on a hemiplegic subject with paresis of the right arm. The subject was tasked with generating a fully functional palmar grasp (closing of the fingers. One node was used to provide this movement, while a second node controlled the activation of extensor muscles to eliminate undesired wrist flexion. The system was tested with the open- and closed-loop control algorithms. Conclusions The system fulfilled technical and application requirements. The novel communication protocol enabled reliable real-time use of the system in both closed- and open-loop forms. The testing on a patient showed that the multi-node system could operate effectively to generate functional movement.

Wireless distributed functional electrical stimulation system.

Science.gov (United States)

Jovičić, Nenad S; Saranovac, Lazar V; Popović, Dejan B

2012-08-09

The control of movement in humans is hierarchical and distributed and uses feedback. An assistive system could be best integrated into the therapy of a human with a central nervous system lesion if the system is controlled in a similar manner. Here, we present a novel wireless architecture and routing protocol for a distributed functional electrical stimulation system that enables control of movement. The new system comprises a set of miniature battery-powered devices with stimulating and sensing functionality mounted on the body of the subject. The devices communicate wirelessly with one coordinator device, which is connected to a host computer. The control algorithm runs on the computer in open- or closed-loop form. A prototype of the system was designed using commercial, off-the-shelf components. The propagation characteristics of electromagnetic waves and the distributed nature of the system were considered during the development of a two-hop routing protocol, which was implemented in the prototype's software. The outcomes of this research include a novel system architecture and routing protocol and a functional prototype based on commercial, off-the-shelf components. A proof-of-concept study was performed on a hemiplegic subject with paresis of the right arm. The subject was tasked with generating a fully functional palmar grasp (closing of the fingers). One node was used to provide this movement, while a second node controlled the activation of extensor muscles to eliminate undesired wrist flexion. The system was tested with the open- and closed-loop control algorithms. The system fulfilled technical and application requirements. The novel communication protocol enabled reliable real-time use of the system in both closed- and open-loop forms. The testing on a patient showed that the multi-node system could operate effectively to generate functional movement.

Convective plasma stability consistent with MHD equilibrium in magnetic confinement systems with a decreasing field

International Nuclear Information System (INIS)

Tsventoukh, M. M.

2010-01-01

A study is made of the convective (interchange, or flute) plasma stability consistent with equilibrium in magnetic confinement systems with a magnetic field decreasing outward and large curvature of magnetic field lines. Algorithms are developed which calculate convective plasma stability from the Kruskal-Oberman kinetic criterion and in which the convective stability is iteratively consistent with MHD equilibrium for a given pressure and a given type of anisotropy in actual magnetic geometry. Vacuum and equilibrium convectively stable configurations in systems with a decreasing, highly curved magnetic field are calculated. It is shown that, in convectively stable equilibrium, the possibility of achieving high plasma pressures in the central region is restricted either by the expansion of the separatrix (when there are large regions of a weak magnetic field) or by the filamentation of the gradient plasma current (when there are small regions of a weak magnetic field, in which case the pressure drops mainly near the separatrix). It is found that, from the standpoint of equilibrium and of the onset of nonpotential ballooning modes, a kinetic description of convective stability yields better plasma confinement parameters in systems with a decreasing, highly curved magnetic field than a simpler MHD model and makes it possible to substantially improve the confinement parameters for a given type of anisotropy. For the Magnetor experimental compact device, the maximum central pressure consistent with equilibrium and stability is calculated to be as high as β ∼ 30%. It is shown that, for the anisotropy of the distribution function that is typical of a background ECR plasma, the limiting pressure gradient is about two times steeper than that for an isotropic plasma. From a practical point of view, the possibility is demonstrated of achieving better confinement parameters of a hot collisionless plasma in systems with a decreasing, highly curved magnetic field than those

On the definition of equilibrium and non-equilibrium states in dynamical systems

OpenAIRE

Akimoto, Takuma

2008-01-01

We propose a definition of equilibrium and non-equilibrium states in dynamical systems on the basis of the time average. We show numerically that there exists a non-equilibrium non-stationary state in the coupled modified Bernoulli map lattice.

Deviation from local thermodynamical equilibrium in the solar atmosphere. Metodology. The line source function

International Nuclear Information System (INIS)

Shchukina, N.G.

1980-01-01

The methodology of the problem of deviation from local thermodynamical equilibrium in the solar atmosphere is presented. The difficulties of solution and methods of realization are systematized. The processes of line formation are considered which take into account velocity fields, structural inhomogeneity, radiation non-coherence etc. as applied to a quiet solar atmosphere. The conclusion is made on the regularity of deviation of the local thermodynamic equilibrium in upper layers of the solar atmosphere

Conformational stability and self-association equilibrium in biologics.

Science.gov (United States)

Clarkson, Benjamin R; Schön, Arne; Freire, Ernesto

2016-02-01

Biologics exist in equilibrium between native, partially denatured, and denatured conformational states. The population of any of these states is dictated by their Gibbs energy and can be altered by changes in physical and solution conditions. Some conformations have a tendency to self-associate and aggregate, an undesirable phenomenon in protein therapeutics. Conformational equilibrium and self-association are linked thermodynamic functions. Given that any associative reaction is concentration dependent, conformational stability studies performed at different protein concentrations can provide early clues to future aggregation problems. This analysis can be applied to the selection of protein variants or the identification of better formulation solutions. In this review, we discuss three different aggregation situations and their manifestation in the observed conformational equilibrium of a protein. Copyright © 2015 Elsevier Ltd. All rights reserved.

Equilibrium and generators

International Nuclear Information System (INIS)

Balter, H.S.

1994-01-01

This work studies the behaviour of radionuclides when it produce a desintegration activity,decay and the isotopes stable creation. It gives definitions about the equilibrium between activity of parent and activity of the daughter, radioactive decay,isotope stable and transient equilibrium and maxim activity time. Some considerations had been given to generators that permit a disgregation of two radioisotopes in equilibrium and its good performance. Tabs

Experimental approaches for studying non-equilibrium atmospheric plasma jets

Energy Technology Data Exchange (ETDEWEB)

Shashurin, A., E-mail: ashashur@purdue.edu [School of Aeronautics & Astronautics, Purdue University, West Lafayette, Indiana 47907 (United States); Keidar, M. [Department of Mechanical and Aerospace Engineering, The George Washington University, Washington, District of Columbia 20052 (United States)

2015-12-15

This work reviews recent research efforts undertaken in the area non-equilibrium atmospheric plasma jets with special focus on experimental approaches. Physics of small non-equilibrium atmospheric plasma jets operating in kHz frequency range at powers around few Watts will be analyzed, including mechanism of breakdown, process of ionization front propagation, electrical coupling of the ionization front with the discharge electrodes, distributions of excited and ionized species, discharge current spreading, transient dynamics of various plasma parameters, etc. Experimental diagnostic approaches utilized in the field will be considered, including Rayleigh microwave scattering, Thomson laser scattering, electrostatic streamer scatterers, optical emission spectroscopy, fast photographing, etc.

Electron-phonon relaxation and excited electron distribution in gallium nitride

Energy Technology Data Exchange (ETDEWEB)

Zhukov, V. P. [Institute of Solid State Chemistry, Urals Branch of the Russian Academy of Sciences, Pervomayskaya st. 91, Yekaterinburg (Russian Federation); Donostia International Physics Center (DIPC), P. Manuel de Lardizabal 4, 20018 San Sebastian (Spain); Tyuterev, V. G., E-mail: valtyut00@mail.ru [Donostia International Physics Center (DIPC), P. Manuel de Lardizabal 4, 20018 San Sebastian (Spain); Tomsk State Pedagogical University, Kievskaya st. 60, Tomsk (Russian Federation); Tomsk State University, Lenin st. 36, Tomsk (Russian Federation); Chulkov, E. V. [Donostia International Physics Center (DIPC), P. Manuel de Lardizabal 4, 20018 San Sebastian (Spain); Tomsk State University, Lenin st. 36, Tomsk (Russian Federation); Departamento de Fisica de Materiales, Facultad de Ciencias Qumicas, UPV/EHU and Centro de Fisica de Materiales CFM-MPC and Centro Mixto CSIC-UPV/EHU, Apdo. 1072, 20080 San Sebastian (Spain); Echenique, P. M. [Donostia International Physics Center (DIPC), P. Manuel de Lardizabal 4, 20018 San Sebastian (Spain); Departamento de Fisica de Materiales, Facultad de Ciencias Qumicas, UPV/EHU and Centro de Fisica de Materiales CFM-MPC and Centro Mixto CSIC-UPV/EHU, Apdo. 1072, 20080 San Sebastian (Spain)

2016-08-28

We develop a theory of energy relaxation in semiconductors and insulators highly excited by the long-acting external irradiation. We derive the equation for the non-equilibrium distribution function of excited electrons. The solution for this function breaks up into the sum of two contributions. The low-energy contribution is concentrated in a narrow range near the bottom of the conduction band. It has the typical form of a Fermi distribution with an effective temperature and chemical potential. The effective temperature and chemical potential in this low-energy term are determined by the intensity of carriers' generation, the speed of electron-phonon relaxation, rates of inter-band recombination, and electron capture on the defects. In addition, there is a substantial high-energy correction. This high-energy “tail” largely covers the conduction band. The shape of the high-energy “tail” strongly depends on the rate of electron-phonon relaxation but does not depend on the rates of recombination and trapping. We apply the theory to the calculation of a non-equilibrium distribution of electrons in an irradiated GaN. Probabilities of optical excitations from the valence to conduction band and electron-phonon coupling probabilities in GaN were calculated by the density functional perturbation theory. Our calculation of both parts of distribution function in gallium nitride shows that when the speed of the electron-phonon scattering is comparable with the rate of recombination and trapping then the contribution of the non-Fermi “tail” is comparable with that of the low-energy Fermi-like component. So the high-energy contribution can essentially affect the charge transport in the irradiated and highly doped semiconductors.

Modular reweighting software for statistical mechanical analysis of biased equilibrium data

Science.gov (United States)

Sindhikara, Daniel J.

2012-07-01

version supersede the previous version?: Yes Nature of problem: While equilibrium reweighting is ubiquitous, there are no public programs available to perform the reweighting in the general case. Further, specific programs often suffer from many library dependencies and numerical instability. Solution method: This package is written in a modular format that allows for easy applicability of reweighting in the general case. Modules are small, numerically stable, and require minimal libraries. Reasons for new version: Some minor bugs, some upgrades needed, error analysis added. analyzeweight.py/analyzeweight.py2 has been replaced by “multihist.py”. This new program performs all the functions of its predecessor while being versatile enough to handle other types of histograms and probability analysis. “bootstrap.py” was added. This script performs basic bootstrap resampling allowing for error analysis of data. “avg_dev_distribution.py” was added. This program computes the averages and standard deviations of multiple distributions, making error analysis (e.g. from bootstrap resampling) easier to visualize. WRE.cpp was slightly modified purely for cosmetic reasons. The manual was updated for clarity and to reflect version updates. Examples were removed from the manual in favor of online tutorials (packaged examples remain). Examples were updated to reflect the new format. An additional example is included to demonstrate error analysis. Running time: Preprocessing scripts 1-5 minutes, WHAM engine <1 minute, postprocess script ∼1-5 minutes.

Rationalisation of distribution functions for models of nanoparticle magnetism

International Nuclear Information System (INIS)

El-Hilo, M.; Chantrell, R.W.

2012-01-01

A formalism is presented which reconciles the use of different distribution functions of particle diameter in analytical models of the magnetic properties of nanoparticle systems. For the lognormal distribution a transformation is derived which shows that a distribution of volume fraction transforms into a lognormal distribution of particle number albeit with a modified median diameter. This transformation resolves an apparent discrepancy reported in Tournus and Tamion [Journal of Magnetism and Magnetic Materials 323 (2011) 1118]. - Highlights: ► We resolve a problem resulting from the misunderstanding of the nature. ► The nature of dispersion functions in models of nanoparticle magnetism. ► The derived transformation between distributions will be of benefit in comparing models and experimental results.

Chemical Principles Revisited: Chemical Equilibrium.

Science.gov (United States)

Mickey, Charles D.

1980-01-01

Describes: (1) Law of Mass Action; (2) equilibrium constant and ideal behavior; (3) general form of the equilibrium constant; (4) forward and reverse reactions; (5) factors influencing equilibrium; (6) Le Chatelier's principle; (7) effects of temperature, changing concentration, and pressure on equilibrium; and (8) catalysts and equilibrium. (JN)

Electron energy distribution function in a low-power Hall thruster discharge and near-field plume

Science.gov (United States)

Tichý, M.; Pétin, A.; Kudrna, P.; Horký, M.; Mazouffre, S.

2018-06-01

Electron temperature and plasma density, as well as the electron energy distribution function (EEDF), have been obtained inside and outside the dielectric channel of a 200 W permanent magnet Hall thruster. Measurements were carried out by means of a cylindrical Langmuir probe mounted onto a compact fast moving translation stage. The 3D particle-in cell numerical simulations complement experiments. The model accounts for the crossed electric and magnetic field configuration in a weakly collisional regime where only electrons are magnetized. Since only the electron dynamics is of interest in this study, an artificial mass of ions corresponding to mi = 30 000me was used to ensure ions could be assumed at rest. The simulation domain is located at the thruster exit plane and does not include the cathode. The measured EEDF evidences a high-energy electron population that is superimposed onto the low energy bulk population outside the channel. Inside the channel, the EEDF is close to Maxwellian. Both the experimental and numerical EEDF depart from an equilibrium distribution at the channel exit plane, a region of high magnetic field. We therefore conclude that the fast electron group found in the experiment corresponds to the electrons emitted by the external cathode that reach the thruster discharge without experiencing collision events.

Non-equilibrium magnetic interactions in strongly correlated systems

Energy Technology Data Exchange (ETDEWEB)

Secchi, A., E-mail: a.secchi@science.ru.nl [Institute for Molecules and Materials, Radboud University Nijmegen, 6525 AJ Nijmegen (Netherlands); Brener, S.; Lichtenstein, A.I. [Institut für Theoretische Physik, Universitat Hamburg, Jungiusstraße 9, D-20355 Hamburg (Germany); Katsnelson, M.I. [Institute for Molecules and Materials, Radboud University Nijmegen, 6525 AJ Nijmegen (Netherlands)

2013-06-15

We formulate a low-energy theory for the magnetic interactions between electrons in the multi-band Hubbard model under non-equilibrium conditions determined by an external time-dependent electric field which simulates laser-induced spin dynamics. We derive expressions for dynamical exchange parameters in terms of non-equilibrium electronic Green functions and self-energies, which can be computed, e.g., with the methods of time-dependent dynamical mean-field theory. Moreover, we find that a correct description of the system requires, in addition to exchange, a new kind of magnetic interaction, that we name twist exchange, which formally resembles Dzyaloshinskii–Moriya coupling, but is not due to spin–orbit, and is actually due to an effective three-spin interaction. Our theory allows the evaluation of the related time-dependent parameters as well. -- Highlights: •We develop a theory for magnetism of strongly correlated systems out of equilibrium. •Our theory is suitable for laser-induced ultrafast magnetization dynamics. •We write time-dependent exchange parameters in terms of electronic Green functions. •We find a new magnetic interaction, a “twist exchange”. •We give general expressions for magnetic noise in itinerant-electron systems.

The rigorous stochastic matrix multiplication scheme for the calculations of reduced equilibrium density matrices of open multilevel quantum systems

International Nuclear Information System (INIS)

Chen, Xin

2014-01-01

Understanding the roles of the temporary and spatial structures of quantum functional noise in open multilevel quantum molecular systems attracts a lot of theoretical interests. I want to establish a rigorous and general framework for functional quantum noises from the constructive and computational perspectives, i.e., how to generate the random trajectories to reproduce the kernel and path ordering of the influence functional with effective Monte Carlo methods for arbitrary spectral densities. This construction approach aims to unify the existing stochastic models to rigorously describe the temporary and spatial structure of Gaussian quantum noises. In this paper, I review the Euclidean imaginary time influence functional and propose the stochastic matrix multiplication scheme to calculate reduced equilibrium density matrices (REDM). In addition, I review and discuss the Feynman-Vernon influence functional according to the Gaussian quadratic integral, particularly its imaginary part which is critical to the rigorous description of the quantum detailed balance. As a result, I establish the conditions under which the influence functional can be interpreted as the average of exponential functional operator over real-valued Gaussian processes for open multilevel quantum systems. I also show the difference between the local and nonlocal phonons within this framework. With the stochastic matrix multiplication scheme, I compare the normalized REDM with the Boltzmann equilibrium distribution for open multilevel quantum systems

Para-equilibrium phase diagrams

International Nuclear Information System (INIS)

Pelton, Arthur D.; Koukkari, Pertti; Pajarre, Risto; Eriksson, Gunnar

2014-01-01

Highlights: • A rapidly cooled system may attain a state of para-equilibrium. • In this state rapidly diffusing elements reach equilibrium but others are immobile. • Application of the Phase Rule to para-equilibrium phase diagrams is discussed. • A general algorithm to calculate para-equilibrium phase diagrams is described. - Abstract: If an initially homogeneous system at high temperature is rapidly cooled, a temporary para-equilibrium state may result in which rapidly diffusing elements have reached equilibrium but more slowly diffusing elements have remained essentially immobile. The best known example occurs when homogeneous austenite is quenched. A para-equilibrium phase assemblage may be calculated thermodynamically by Gibbs free energy minimization under the constraint that the ratios of the slowly diffusing elements are the same in all phases. Several examples of calculated para-equilibrium phase diagram sections are presented and the application of the Phase Rule is discussed. Although the rules governing the geometry of these diagrams may appear at first to be somewhat different from those for full equilibrium phase diagrams, it is shown that in fact they obey exactly the same rules with the following provision. Since the molar ratios of non-diffusing elements are the same in all phases at para-equilibrium, these ratios act, as far as the geometry of the diagram is concerned, like “potential” variables (such as T, pressure or chemical potentials) rather than like “normal” composition variables which need not be the same in all phases. A general algorithm to calculate para-equilibrium phase diagrams is presented. In the limit, if a para-equilibrium calculation is performed under the constraint that no elements diffuse, then the resultant phase diagram shows the single phase with the minimum Gibbs free energy at any point on the diagram; such calculations are of interest in physical vapor deposition when deposition is so rapid that phase

Non-equilibrium concentration fluctuations in binary liquids with realistic boundary conditions.

Science.gov (United States)

Ortiz de Zárate, J M; Kirkpatrick, T R; Sengers, J V

2015-09-01

Because of the spatially long-ranged nature of spontaneous fluctuations in thermal non-equilibrium systems, they are affected by boundary conditions for the fluctuating hydrodynamic variables. In this paper we consider a liquid mixture between two rigid and impervious plates with a stationary concentration gradient resulting from a temperature gradient through the Soret effect. For liquid mixtures with large Lewis and Schmidt numbers, we are able to obtain explicit analytical expressions for the intensity of the non-equilibrium concentration fluctuations as a function of the frequency ω and the wave number q of the fluctuations. In addition we elucidate the spatial dependence of the intensity of the non-equilibrium fluctuations responsible for a non-equilibrium Casimir effect.

Crossover from Nonequilibrium Fractal Growth to Equilibrium Compact Growth

DEFF Research Database (Denmark)

Sørensen, Erik Schwartz; Fogedby, Hans C.; Mouritsen, Ole G.

1988-01-01

Solidification controlled by vacancy diffusion is studied by Monte Carlo simulations of a two-dimensional Ising model defined by a Hamiltonian which models a thermally driven fluid-solid phase transition. The nonequilibrium morphology of the growing solid is studied as a function of time as the s...... as the system relaxes into equilibrium described by a temperature. At low temperatures the model exhibits fractal growth at early times and crossover to compact solidification as equilibrium is approached....

The automated design of materials far from equilibrium

Science.gov (United States)

Miskin, Marc Z.

Automated design is emerging as a powerful concept in materials science. By combining computer algorithms, simulations, and experimental data, new techniques are being developed that start with high level functional requirements and identify the ideal materials that achieve them. This represents a radically different picture of how materials become functional in which technological demand drives material discovery, rather than the other way around. At the frontiers of this field, materials systems previously considered too complicated can start to be controlled and understood. Particularly promising are materials far from equilibrium. Material robustness, high strength, self-healing and memory are properties displayed by several materials systems that are intrinsically out of equilibrium. These and other properties could be revolutionary, provided they can first be controlled. This thesis conceptualizes and implements a framework for designing materials that are far from equilibrium. We show how, even in the absence of a complete physical theory, design from the top down is possible and lends itself to producing physical insight. As a prototype system, we work with granular materials: collections of athermal, macroscopic identical objects, since these materials function both as an essential component of industrial processes as well as a model system for many non-equilibrium states of matter. We show that by placing granular materials in the context of design, benefits emerge simultaneously for fundamental and applied interests. As first steps, we use our framework to design granular aggregates with extreme properties like high stiffness, and softness. We demonstrate control over nonlinear effects by producing exotic aggregates that stiffen under compression. Expanding on our framework, we conceptualize new ways of thinking about material design when automatic discovery is possible. We show how to build rules that link particle shapes to arbitrary granular packing

Non-equilibrium steady state of a driven levitated particle with feedback cooling

International Nuclear Information System (INIS)

Gieseler, Jan; Novotny, Lukas; Moritz, Clemens; Dellago, Christoph

2015-01-01

Laser trapped nanoparticles have been recently used as model systems to study fundamental relations holding far from equilibrium. Here we study a nanoscale silica sphere levitated by a laser in a low density gas. The center of mass motion of the particle is subjected, at the same time, to feedback cooling and a parametric modulation driving the system into a non-equilibrium steady state. Based on the Langevin equation of motion of the particle, we derive an analytical expression for the energy distribution of this steady state showing that the average and variance of the energy distribution can be controlled separately by appropriate choice of the friction, cooling and modulation parameters. Energy distributions determined in computer simulations and measured in a laboratory experiment agree well with the analytical predictions. We analyze the particle motion also in terms of the quadratures and find thermal squeezing depending on the degree of detuning. (paper)

Regge behaviour of distribution functions and evolution of gluon ...

Indian Academy of Sciences (India)

work we solved DGLAP evolution equation for gluon distribution function at low-x in next-to-leading order (NLO) and the t and x-evolutions of gluon distribution function thus obtained have been compared with global MRST2004 and GRV98 parametrizations. In PQCD, since the higher-order terms in the leading logarithmic.

Dynamical behaviors of inter-out-of-equilibrium state intervals in Korean futures exchange markets

Science.gov (United States)

Lim, Gyuchang; Kim, SooYong; Kim, Kyungsik; Lee, Dong-In; Scalas, Enrico

2008-05-01

A recently discovered feature of financial markets, the two-phase phenomenon, is utilized to categorize a financial time series into two phases, namely equilibrium and out-of-equilibrium states. For out-of-equilibrium states, we analyze the time intervals at which the state is revisited. The power-law distribution of inter-out-of-equilibrium state intervals is shown and we present an analogy with discrete-time heat bath dynamics, similar to random Ising systems. In the mean-field approximation, this model reduces to a one-dimensional multiplicative process. By varying global and local model parameters, the relevance between volatilities in financial markets and the interaction strengths between agents in the Ising model are investigated and discussed.

Multiscale measures of equilibrium on finite dynamic systems

International Nuclear Information System (INIS)

Bigerelle, M.; Iost, A.

2004-01-01

This article presents a new method for the study of the evolution of dynamic systems based on the notion of quantity of information. The system is divided into elementary cells and the quantity of information is studied with respect to the cell size. We have introduced an analogy between quantity of information and entropy, and defined the intrinsic entropy as the entropy of the whole system independent of the size of the cells. It is shown that the intrinsic entropy follows a Gaussian probability density function (PDF) and thereafter, the time needed by the system to reach equilibrium is a random variable. For a finite system, statistical analyses show that this entropy converges to a state of equilibrium and an algorithmic method is proposed to quantify the time needed to reach equilibrium for a given confidence interval level. A Monte-Carlo simulation of diffusion of A* atoms in A is then provided to illustrate the proposed simulation. It follows that the time to reach equilibrium for a constant error probability, t e , depends on the number, n, of elementary cells as: t e ∝n 2.22 ±0.06 . For an infinite system size (n infinite), the intrinsic entropy obtained by statistical modelling is a pertinent characteristic number of the system at the equilibrium

Bose-Einstein Condensation of Long-Lifetime Polaritons in Thermal Equilibrium.

Science.gov (United States)

Sun, Yongbao; Wen, Patrick; Yoon, Yoseob; Liu, Gangqiang; Steger, Mark; Pfeiffer, Loren N; West, Ken; Snoke, David W; Nelson, Keith A

2017-01-06

The experimental realization of Bose-Einstein condensation (BEC) with atoms and quasiparticles has triggered wide exploration of macroscopic quantum effects. Microcavity polaritons are of particular interest because quantum phenomena such as BEC and superfluidity can be observed at elevated temperatures. However, polariton lifetimes are typically too short to permit thermal equilibration. This has led to debate about whether polariton condensation is intrinsically a nonequilibrium effect. Here we report the first unambiguous observation of BEC of optically trapped polaritons in thermal equilibrium in a high-Q microcavity, evidenced by equilibrium Bose-Einstein distributions over broad ranges of polariton densities and bath temperatures. With thermal equilibrium established, we verify that polariton condensation is a phase transition with a well-defined density-temperature phase diagram. The measured phase boundary agrees well with the predictions of basic quantum gas theory.

The stationary non-equilibrium plasma of cosmic-ray electrons and positrons

Science.gov (United States)

Tomaschitz, Roman

2016-06-01

The statistical properties of the two-component plasma of cosmic-ray electrons and positrons measured by the AMS-02 experiment on the International Space Station and the HESS array of imaging atmospheric Cherenkov telescopes are analyzed. Stationary non-equilibrium distributions defining the relativistic electron-positron plasma are derived semi-empirically by performing spectral fits to the flux data and reconstructing the spectral number densities of the electronic and positronic components in phase space. These distributions are relativistic power-law densities with exponential cutoff, admitting an extensive entropy variable and converging to the Maxwell-Boltzmann or Fermi-Dirac distributions in the non-relativistic limit. Cosmic-ray electrons and positrons constitute a classical (low-density high-temperature) plasma due to the low fugacity in the quantized partition function. The positron fraction is assembled from the flux densities inferred from least-squares fits to the electron and positron spectra and is subjected to test by comparing with the AMS-02 flux ratio measured in the GeV interval. The calculated positron fraction extends to TeV energies, predicting a broad spectral peak at about 1 TeV followed by exponential decay.

Scaling studies of spheromak formation and equilibrium

International Nuclear Information System (INIS)

Geddes, C.G.; Kornack, T.W.; Brown, M.R.

1998-01-01

Formation and equilibrium studies have been performed on the Swarthmore Spheromak Experiment (SSX). Spheromaks are formed with a magnetized coaxial plasma gun and equilibrium is established in both small (d small =0.16 m) and large (d large =3d small =0.50 m) copper flux conservers. Using magnetic probe arrays it has been verified that spheromak formation is governed solely by gun physics (in particular the ratio of gun current to flux, μ 0 I gun /Φ gun ) and is independent of the flux conserver dimensions. It has also been verified that equilibrium is well described by the force free condition ∇xB=λB (λ=constant), particularly early in decay. Departures from the force-free state are due to current profile effects described by a quadratic function λ=λ(ψ). Force-free SSX spheromaks will be merged to study magnetic reconnection in simple magnetofluid structures. copyright 1998 American Institute of Physics

Nash equilibrium in differential games and the construction of the programmed iteration method

International Nuclear Information System (INIS)

Averboukh, Yurii V

2011-01-01

This work is devoted to the study of nonzero-sum differential games. The set of payoffs in a situation of Nash equilibrium is examined. It is shown that the set of payoffs in a situation of Nash equilibrium coincides with the set of values of consistent functions which are fixed points of the program absorption operator. A condition for functions to be consistent is given in terms of the weak invariance of the graph of the functions under a certain differential inclusion. Bibliography: 18 titles.

Solutions to the Cosmic Initial Entropy Problem without Equilibrium Initial Conditions

Directory of Open Access Journals (Sweden)

Vihan M. Patel

2017-08-01

Full Text Available The entropy of the observable universe is increasing. Thus, at earlier times the entropy was lower. However, the cosmic microwave background radiation reveals an apparently high entropy universe close to thermal and chemical equilibrium. A two-part solution to this cosmic initial entropy problem is proposed. Following Penrose, we argue that the evenly distributed matter of the early universe is equivalent to low gravitational entropy. There are two competing explanations for how this initial low gravitational entropy comes about. (1 Inflation and baryogenesis produce a virtually homogeneous distribution of matter with a low gravitational entropy. (2 Dissatisfied with explaining a low gravitational entropy as the product of a ‘special’ scalar field, some theorists argue (following Boltzmann for a “more natural” initial condition in which the entire universe is in an initial equilibrium state of maximum entropy. In this equilibrium model, our observable universe is an unusual low entropy fluctuation embedded in a high entropy universe. The anthropic principle and the fluctuation theorem suggest that this low entropy region should be as small as possible and have as large an entropy as possible, consistent with our existence. However, our low entropy universe is much larger than needed to produce observers, and we see no evidence for an embedding in a higher entropy background. The initial conditions of inflationary models are as natural as the equilibrium background favored by many theorists.

Wigner Function of Density Operator for Negative Binomial Distribution

International Nuclear Information System (INIS)

Xu Xinglei; Li Hongqi

2008-01-01

By using the technique of integration within an ordered product (IWOP) of operator we derive Wigner function of density operator for negative binomial distribution of radiation field in the mixed state case, then we derive the Wigner function of squeezed number state, which yields negative binomial distribution by virtue of the entangled state representation and the entangled Wigner operator

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.

New generalized functions and multiplication of distributions

International Nuclear Information System (INIS)

Colombeau, J.F.

1984-01-01

Since its conception, Quantum Field Theory is based on 'heuristic' computations (in particular products of distributions) that, despite lots of effort, remained meaningless from a mathematical viewpoint. In this book the author presents a new mathematical theory giving a rigorous mathematical sense to these heuristic computations and, from a mathematical viewpoint, to all products of distributions. This new mathematical theory is a new theory of Generalized Functions defined on any open subset Ω of Rsup(n), which are much more general than the distributions on Ω. (Auth.)

Parametric Probability Distribution Functions for Axon Diameters of Corpus Callosum

Directory of Open Access Journals (Sweden)

Farshid eSepehrband

2016-05-01

Full Text Available Axon diameter is an important neuroanatomical characteristic of the nervous system that alters in the course of neurological disorders such as multiple sclerosis. Axon diameters vary, even within a fiber bundle, and are not normally distributed. An accurate distribution function is therefore beneficial, either to describe axon diameters that are obtained from a direct measurement technique (e.g., microscopy, or to infer them indirectly (e.g., using diffusion-weighted MRI. The gamma distribution is a common choice for this purpose (particularly for the inferential approach because it resembles the distribution profile of measured axon diameters which has been consistently shown to be non-negative and right-skewed. In this study we compared a wide range of parametric probability distribution functions against empirical data obtained from electron microscopy images. We observed that the gamma distribution fails to accurately describe the main characteristics of the axon diameter distribution, such as location and scale of the mode and the profile of distribution tails. We also found that the generalized extreme value distribution consistently fitted the measured distribution better than other distribution functions. This suggests that there may be distinct subpopulations of axons in the corpus callosum, each with their own distribution profiles. In addition, we observed that several other distributions outperformed the gamma distribution, yet had the same number of unknown parameters; these were the inverse Gaussian, log normal, log logistic and Birnbaum-Saunders distributions.

Non-equilibrium Economics

Directory of Open Access Journals (Sweden)

Katalin Martinás

2007-02-01

Full Text Available A microeconomic, agent based framework to dynamic economics is formulated in a materialist approach. An axiomatic foundation of a non-equilibrium microeconomics is outlined. Economic activity is modelled as transformation and transport of commodities (materials owned by the agents. Rate of transformations (production intensity, and the rate of transport (trade are defined by the agents. Economic decision rules are derived from the observed economic behaviour. The non-linear equations are solved numerically for a model economy. Numerical solutions for simple model economies suggest that the some of the results of general equilibrium economics are consequences only of the equilibrium hypothesis. We show that perfect competition of selfish agents does not guarantee the stability of economic equilibrium, but cooperativity is needed, too.

Ion exchange equilibrium constants

CERN Document Server

Marcus, Y

2013-01-01

Ion Exchange Equilibrium Constants focuses on the test-compilation of equilibrium constants for ion exchange reactions. The book first underscores the scope of the compilation, equilibrium constants, symbols used, and arrangement of the table. The manuscript then presents the table of equilibrium constants, including polystyrene sulfonate cation exchanger, polyacrylate cation exchanger, polymethacrylate cation exchanger, polysterene phosphate cation exchanger, and zirconium phosphate cation exchanger. The text highlights zirconium oxide anion exchanger, zeolite type 13Y cation exchanger, and

Thermal equilibrium of pure electron plasmas across a central region of magnetic surfaces

Science.gov (United States)

Hahn, Michael; Pedersen, Thomas Sunn

2009-06-01

Measurements of the equilibria of plasmas created by emission from a biased filament located off the magnetic axis in the Columbia Non-neutral Torus (CNT) [T. S. Pedersen, J. P. Kremer, R. G. Lefrancois et al., Fusion Sci. Technol. 50, 372 (2006)] show that such plasmas have equilibrium properties consistent with the inner surfaces being in a state of cross-surface thermal equilibrium. Numerical solutions to the equilibrium equation were used to fit the experimental data and demonstrate consistency with cross-surface thermal equilibrium. Previous experiments in CNT showed that constant temperatures across magnetic surfaces are characteristic of CNT plasmas, implying thermal confinement times much less than particle confinement times. These results show that when emitting off axis there is a volume of inner surfaces where diffusion into that region is balanced by outward transport, producing a Boltzmann distribution of electrons. When combined with the low thermal energy confinement time this is a cross-surface thermal equilibrium.

Thermal equilibrium of pure electron plasmas across a central region of magnetic surfaces

International Nuclear Information System (INIS)

Hahn, Michael; Pedersen, Thomas Sunn

2009-01-01

Measurements of the equilibria of plasmas created by emission from a biased filament located off the magnetic axis in the Columbia Non-neutral Torus (CNT) [T. S. Pedersen, J. P. Kremer, R. G. Lefrancois et al., Fusion Sci. Technol. 50, 372 (2006)] show that such plasmas have equilibrium properties consistent with the inner surfaces being in a state of cross-surface thermal equilibrium. Numerical solutions to the equilibrium equation were used to fit the experimental data and demonstrate consistency with cross-surface thermal equilibrium. Previous experiments in CNT showed that constant temperatures across magnetic surfaces are characteristic of CNT plasmas, implying thermal confinement times much less than particle confinement times. These results show that when emitting off axis there is a volume of inner surfaces where diffusion into that region is balanced by outward transport, producing a Boltzmann distribution of electrons. When combined with the low thermal energy confinement time this is a cross-surface thermal equilibrium.

Non-equilibrium plasma kinetics of reacting CO: an improved state to state approach

Science.gov (United States)

Pietanza, L. D.; Colonna, G.; Capitelli, M.

2017-12-01

Non-equilibrium plasma kinetics of reacting CO for conditions typically met in microwave discharges have been developed based on the coupling of excited state kinetics and the Boltzmann equation for the electron energy distribution function (EEDF). Particular attention is given to the insertion in the vibrational kinetics of a complete set of electron molecule resonant processes linking the whole vibrational ladder of the CO molecule, as well as to the role of Boudouard reaction, i.e. the process of forming CO2 by two vibrationally excited CO molecules, in shaping the vibrational distribution of CO and promoting reaction channels assisted by vibrational excitation (pure vibrational mechanisms, PVM). PVM mechanisms can become competitive with electron impact dissociation processes (DEM) in the activation of CO. A case study reproducing the conditions of a microwave discharge has been considered following the coupled kinetics also in the post discharge conditions. Results include the evolution of EEDF in discharge and post discharge conditions highlighting the role of superelastic vibrational and electronic collisions in shaping the EEDF. Moreover, PVM rate coefficients and DEM ones are studied as a function of gas temperature, showing a non-Arrhenius behavior, i.e. the rate coefficients increase with decreasing gas temperature as a result of a vibrational-vibrational (V-V) pumping up mechanism able to form plateaux in the vibrational distribution function. The accuracy of the results is discussed in particular in connection to the present knowledge of the activation energy of the Boudouard process.

Sedimentation dynamics and equilibrium profiles in multicomponent mixtures of colloidal particles

International Nuclear Information System (INIS)

Spruijt, E; Biesheuvel, P M

2014-01-01

In this paper we give a general theoretical framework that describes the sedimentation of multicomponent mixtures of particles with sizes ranging from molecules to macroscopic bodies. Both equilibrium sedimentation profiles and the dynamic process of settling, or its converse, creaming, are modeled. Equilibrium profiles are found to be in perfect agreement with experiments. Our model reconciles two apparently contradicting points of view about buoyancy, thereby resolving a long-lived paradox about the correct choice of the buoyant density. On the one hand, the buoyancy force follows necessarily from the suspension density, as it relates to the hydrostatic pressure gradient. On the other hand, sedimentation profiles of colloidal suspensions can be calculated directly using the fluid density as apparent buoyant density in colloidal systems in sedimentation–diffusion equilibrium (SDE) as a result of balancing gravitational and thermodynamic forces. Surprisingly, this balance also holds in multicomponent mixtures. This analysis resolves the ongoing debate of the correct choice of buoyant density (fluid or suspension): both approaches can be used in their own domain. We present calculations of equilibrium sedimentation profiles and dynamic sedimentation that show the consequences of these insights. In bidisperse mixtures of colloids, particles with a lower mass density than the homogeneous suspension will first cream and then settle, whereas particles with a suspension-matched mass density form transient, bimodal particle distributions during sedimentation, which disappear when equilibrium is reached. In all these cases, the centers of the distributions of the particles with the lowest mass density of the two, regardless of their actual mass, will be located in equilibrium above the so-called isopycnic point, a natural consequence of their hard-sphere interactions. We include these interactions using the Boublik–Mansoori–Carnahan–Starling–Leland (BMCSL

Non-equilibrium carrier efect in the optical properties of semiconductors

International Nuclear Information System (INIS)

Teschke, O.

1980-01-01

The time-resolved reflectivity of picosecond pulses from optically excited carrier distributions can provide important information about the energy relaxation rates of hot electrons and holes in semiconductors. the basic optical properties of non-equilibrium carrier distributions of GaAs are discussed. A semi-empirical analysis of the reflectivity spectrum is presented and the contributions of different effects are estimated. The results are in qualitative agreement with recent experiments employing dye lasers. (Author) [pt

A Quantal Response Statistical Equilibrium Model of Induced Technical Change in an Interactive Factor Market: Firm-Level Evidence in the EU Economies

Directory of Open Access Journals (Sweden)

Jangho Yang

2018-02-01

Full Text Available This paper studies the pattern of technical change at the firm level by applying and extending the Quantal Response Statistical Equilibrium model (QRSE. The model assumes that a large number of cost minimizing firms decide whether to adopt a new technology based on the potential rate of cost reduction. The firm in the model is assumed to have a limited capacity to process market signals so there is a positive degree of uncertainty in adopting a new technology. The adoption decision by the firm, in turn, makes an impact on the whole market through changes in the factor-price ratio. The equilibrium distribution of the model is a unimodal probability distribution with four parameters, which is qualitatively different from the Walrasian notion of equilibrium in so far as the state of equilibrium is not a single state but a probability distribution of multiple states. This paper applies Bayesian inference to estimate the unknown parameters of the model using the firm-level data of seven advanced OECD countries over eight years and shows that the mentioned equilibrium distribution from the model can satisfactorily recover the observed pattern of technical change.

Non-equilibrium thermodynamical description of rhythmic motion patterns of active systems: a canonical-dissipative approach.

Science.gov (United States)

Dotov, D G; Kim, S; Frank, T D

2015-02-01

We derive explicit expressions for the non-equilibrium thermodynamical variables of a canonical-dissipative limit cycle oscillator describing rhythmic motion patterns of active systems. These variables are statistical entropy, non-equilibrium internal energy, and non-equilibrium free energy. In particular, the expression for the non-equilibrium free energy is derived as a function of a suitable control parameter. The control parameter determines the Hopf bifurcation point of the deterministic active system and describes the effective pumping of the oscillator. In analogy to the equilibrium free energy of the Landau theory, it is shown that the non-equilibrium free energy decays as a function of the control parameter. In doing so, a similarity between certain equilibrium and non-equilibrium phase transitions is pointed out. Data from an experiment on human rhythmic movements is presented. Estimates for pumping intensity as well as the thermodynamical variables are reported. It is shown that in the experiment the non-equilibrium free energy decayed when pumping intensity was increased, which is consistent with the theory. Moreover, pumping intensities close to zero could be observed at relatively slow intended rhythmic movements. In view of the Hopf bifurcation underlying the limit cycle oscillator model, this observation suggests that the intended limit cycle movements were actually more similar to trajectories of a randomly perturbed stable focus. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

Modeling of the equilibrium of a tokamak plasma; Modelisation de l'equilibre d'un plasma de tokamak

Energy Technology Data Exchange (ETDEWEB)

Grandgirard, V

1999-12-01

The simulation and the control of a plasma discharge in a tokamak require an efficient and accurate solving of the equilibrium because this equilibrium needs to be calculated again every microsecond to simulate discharges that can last up to 1000 seconds. The purpose of this thesis is to propose numerical methods in order to calculate these equilibrium with acceptable computer time and memory size. Chapter 1 deals with hydrodynamics equation and sets up the problem. Chapter 2 gives a method to take into account the boundary conditions. Chapter 3 is dedicated to the optimization of the inversion of the system matrix. This matrix being quasi-symmetric, the Woodbury method combined with Cholesky method has been used. This direct method has been compared with 2 iterative methods: GMRES (generalized minimal residual) and BCG (bi-conjugate gradient). The 2 last chapters study the control of the plasma equilibrium, this work is presented in the formalism of the optimized control of distributed systems and leads to non-linear equations of state and quadratic functionals that are solved numerically by a quadratic sequential method. This method is based on the replacement of the initial problem with a series of control problems involving linear equations of state. (A.C.)

Non-equilibrium fluctuation-induced interactions

International Nuclear Information System (INIS)

Dean, David S

2012-01-01

We discuss non-equilibrium aspects of fluctuation-induced interactions. While the equilibrium behavior of such interactions has been extensively studied and is relatively well understood, the study of these interactions out of equilibrium is relatively new. We discuss recent results on the non-equilibrium behavior of systems whose dynamics is of the dissipative stochastic type and identify a number of outstanding problems concerning non-equilibrium fluctuation-induced interactions.

Free energy distribution function of a random Ising ferromagnet

International Nuclear Information System (INIS)

Dotsenko, Victor; Klumov, Boris

2012-01-01

We study the free energy distribution function of a weakly disordered Ising ferromagnet in terms of the D-dimensional random temperature Ginzburg–Landau Hamiltonian. It is shown that besides the usual Gaussian 'body' this distribution function exhibits non-Gaussian tails both in the paramagnetic and in the ferromagnetic phases. Explicit asymptotic expressions for these tails are derived. It is demonstrated that the tails are strongly asymmetric: the left tail (for large negative values of the free energy) is much slower than the right one (for large positive values of the free energy). It is argued that at the critical point the free energy of the random Ising ferromagnet in dimensions D < 4 is described by a non-trivial universal distribution function which is non-self-averaging

Phase equilibrium engineering

CERN Document Server

Brignole, Esteban Alberto

2013-01-01

Traditionally, the teaching of phase equilibria emphasizes the relationships between the thermodynamic variables of each phase in equilibrium rather than its engineering applications. This book changes the focus from the use of thermodynamics relationships to compute phase equilibria to the design and control of the phase conditions that a process needs. Phase Equilibrium Engineering presents a systematic study and application of phase equilibrium tools to the development of chemical processes. The thermodynamic modeling of mixtures for process development, synthesis, simulation, design and

MHD equilibrium of toroidal fusion plasma with stationary flows

International Nuclear Information System (INIS)

Galkowski, A.

1994-01-01

Non-linear ideal MHD equilibria in axisymmetric system with flows are examined, both in 1st and 2nd ellipticity regions. Evidence of the bifurcation of solutions is provided and numerical solutions of several problems in a tokamak geometry are given, exhibiting bifurcation phenomena. Relaxation of plasma in the presence of zero-order flows is studied in a realistic toroidal geometry. The field aligned flow allows equilibria with finite pressure gradient but with homogeneous temperature distribution. Numerical calculations have been performed for the 1st and 2nd ellipticity regimes of the extended Grad-Shafranov-Schlueter equation. Numerical technique, alternative to the well-known Grad's ADM methods has been proposed to deal with slow adiabatic evolution of toroidal plasma with flows. The equilibrium problem with prescribed adiabatic constraints may be solved by simultaneous calculations of flux surface geometry and original profile functions. (author). 178 refs, 37 figs, 5 tabs

The Inefficiency of the Stock Market Equilibrium under Moral Hazard

NARCIS (Netherlands)

Calcagno, R.; Wagner, W.B.

2003-01-01

In this paper we study the constrained efficiency of a stock market equilibrium under moral hazard.We extend a standard general equilbrium framework (Magill and Quinzii (1999) and (2002)) to allow for a more general initial ownership distribution.We show that the market allocation is constrained

Static Equilibrium Configurations of Charged Metallic Bodies ...

African Journals Online (AJOL)

In this paper we developed a simple numerical scheme to determine the static equilibrium configuration of charged metallic bodies by minimizing the potential energy function. The method developed has some advantages; it combines the general theory and the physical meanings nested in the mathematical model and this ...

Kapitza thermal conductance at the interface between Lennard-Jones crystals using non-equilibrium molecular dynamics simulations

International Nuclear Information System (INIS)

Merabia, Samy; Termentzidis, Konstantinos

2012-01-01

We characterize the thermal Kapitza conductance between Lennard-Jones solids using non-equilibrium molecular dynamics simulations. We consider a series of perfect interfaces between mass-mismatched solids. We show that both the acoustic mismatch model (AMM) and the diffuse mismatch model (DMM) fail to predict the interfacial conductance even for large acoustic mismatched solids. This poor agreement may be explained by the use of equilibrium distributions of phonons in the expression of the conductance. On the other hand, we show that an extension of AMM taking into account the out-of-equilibrium phonon distribution on both sides of the interface leads to a good agreement with the simulation results, even for interfaces between almost similar materials. This opens the way to understand interfacial heat transport across real semi-conductors and dielectrics.

CT-quantified emphysema distribution is associated with lung function decline

NARCIS (Netherlands)

Hoesein, F.A.A.M.; Rikxoort, E.M. van; Ginneken, B. van; de Jong, P. A.; Prokop, M.; Lammers, J.W.; Zanen, P.

2012-01-01

Emphysema distribution is associated with COPD. It is however unknown whether CT-quantified emphysema distribution (upper/lower lobe) is associated with lung function decline in heavy (former) smokers.587 male participants underwent lung CT-scanning and pulmonary function testing at baseline and

Non-equilibrium blunt body flows in ionized gases

International Nuclear Information System (INIS)

Nishida, Michio

1981-01-01

The behaviors of electrons and electronically excited atoms in non-equilibrium and partially ionized blunt-body-flows are described. Formulation has been made separately in a shock layer and in a free stream, and then the free stream solution has been connected with the shock layer solution by matching the two solutions at the shock layer edge. The method of this matching is described here. The partially ionized gas is considered to be composed of neutral atoms, ions and electrons. Furthermore, the neutral atoms are divided into atoms in excited levels. Therefore, it is considered that electron energy released due to excitation, and that gained due to de-excitation, contribute to electron energy. Thus, the electron energy equation including these contributions is solved, coupled with the continuity equations of the excited atoms and the electrons. An electron temperature distribution from a free stream to a blunt body wall has been investigated for a case when the electrons are in thermal non-equilibrium with heavy particles in the free stream. In addition, the distributions of the excited atom density are discussed in the present analysis. (author)

DNA breathing dynamics: analytic results for distribution functions of relevant Brownian functionals.

Science.gov (United States)

Bandyopadhyay, Malay; Gupta, Shamik; Segal, Dvira

2011-03-01

We investigate DNA breathing dynamics by suggesting and examining several Brownian functionals associated with bubble lifetime and reactivity. Bubble dynamics is described as an overdamped random walk in the number of broken base pairs. The walk takes place on the Poland-Scheraga free-energy landscape. We suggest several probability distribution functions that characterize the breathing process, and adopt the recently studied backward Fokker-Planck method and the path decomposition method as elegant and flexible tools for deriving these distributions. In particular, for a bubble of an initial size x₀, we derive analytical expressions for (i) the distribution P(t{f}|x₀) of the first-passage time t{f}, characterizing the bubble lifetime, (ii) the distribution P(A|x₀) of the area A until the first-passage time, providing information about the effective reactivity of the bubble to processes within the DNA, (iii) the distribution P(M) of the maximum bubble size M attained before the first-passage time, and (iv) the joint probability distribution P(M,t{m}) of the maximum bubble size M and the time t{m} of its occurrence before the first-passage time. These distributions are analyzed in the limit of small and large bubble sizes. We supplement our analytical predictions with direct numericalsimulations of the related Langevin equation, and obtain a very good agreement in the appropriate limits. The nontrivial scaling behavior of the various quantities analyzed here can, in principle, be explored experimentally.

Determination of Thermal Equilibrium in a Sealed Cell Based on Optical Depth

Energy Technology Data Exchange (ETDEWEB)

Zou, Sheng; Zhang, Hong; Chen, Xi-yuan [Southeast University, Nanjing (China); Shan, Guang-cun; Quan, Wei [Beihang University, Beijing (China)

2017-01-15

An effective method based on optical depth (OD) is presented to measure thermal equilibrium in a cell. First, the principle of determining the temperature distribution in the cell by using the OD is demonstrated. Subsequently, relevant experiments are carried out. Original experimental results showed that some gradients of OD distributions in the cell at different wavelengths and variations of the OD increased slowly along the direction of motion of the beam at a fixed wavelength. At a wavelength of 766.6839 nm, which is about 7 GHz blue shifted with respect to the potassium resonance, the average value of the OD was about 0.764 and the maximal and the minimum inhomogeneity biases among all location points were about 6.07% and 0.56%, respectively. As for the corresponding wavelengths of 766.67785 nm and 766.73004 nm, some deviations from previous results, which were caused by different absorptions of the alkali-metal atoms at different frequencies of the laser beam, were observed. The nonuniform OD values along the direction of motion of the beam reflected an inhomogeneous distribution of the temperature in the cell, which may have been caused by layout of the oven. When the layout of the oven was modified, comparative experiments comparable to these with the previous layout of the oven demonstrated that the uniformity of the temperature distribution in the cell was improved and that thermal equilibrium time was shorter by about 10 minutes. This method played an important role in determining the thermal equilibrium time in the cell.

Non-equilibrium dynamics of open systems and fluctuation-dissipation theorems

Czech Academy of Sciences Publication Activity Database

Špička, Václav; Velický, B.; Kalvová, Anděla

2017-01-01

Roč. 65, 6-8 (2017), s. 1-23, č. článku 1700032. ISSN 0015-8208 Institutional support: RVO:68378271 Keywords : non-equilibrium * fluctuation-dissipation theorems * non-equilibrium Greens function * transient and steady state magnetic current * molecular bridge Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics ( physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 2.434, year: 2016

Equilibrium optimization code OPEQ and results of applying it to HT-7U

International Nuclear Information System (INIS)

Zha Xuejun; Zhu Sizheng; Yu Qingquan

2003-01-01

The plasma equilibrium configuration has a strong impact on the confinement and MHD stability in tokamaks. For designing a tokamak device, it is an important issue to determine the sites and currents of poloidal coils which have some constraint conditions from physics and engineering with a prescribed equilibrium shape of the plasma. In this paper, an effective method based on multi-variables equilibrium optimization is given. The method can optimize poloidal coils when the previously prescribed plasma parameters are treated as an object function. We apply it to HT-7U equilibrium calculation, and obtain good results

Equilibrium vertical field in the TBR Tokamak

International Nuclear Information System (INIS)

Ueta, A.Y.

1985-01-01

An experimental study on the influence of the vertical magnetic field of the TBR tokamak on the stability and equilibrium of plasma column, was done. Magnetic pick-up coils were built to measure plasma current and position, together with active networks, necessary fo the electronic processing of signals. Some measurements were on the space configuration of the vertical field, and on the influence due to the toroidal vessel. From the data obtained it was possible to discuss the influence of the currents induced on the vessel surface, on plasma equilibrium. Theoretical and experimental results of the vertica field, as a function of plasma current were compared, and allowed an evaluation of the plasma kinetic pressure and temperature. (Author) [pt

Study on the Seismic Active Earth Pressure by Variational Limit Equilibrium Method

Directory of Open Access Journals (Sweden)

Jiangong Chen

2016-01-01

Full Text Available In the framework of limit equilibrium theory, the isoperimetric model of functional extremum regarding the seismic active earth pressure is deduced according to the variational method. On this basis, Lagrange multipliers are introduced to convert the problem of seismic active earth pressure into the problem on the functional extremum of two undetermined function arguments. Based on the necessary conditions required for the existence of functional extremum, the function of the slip surface and the normal stress distribution on the slip surface is obtained, and the functional extremum problem is further converted into a function optimization problem with two undetermined Lagrange multipliers. The calculated results show that the slip surface is a plane and the seismic active earth pressure is minimal when the action point is at the lower limit position. As the action point moves upward, the slip surface becomes a logarithmic spiral and the corresponding value of seismic active earth pressure increases in a nonlinear manner. And the seismic active earth pressure is maximal at the upper limit position. The interval estimation constructed by the minimum and maximum values of seismic active earth pressure can provide a reference for the aseismic design of gravity retaining walls.

Quantity Constrained General Equilibrium

NARCIS (Netherlands)

Babenko, R.; Talman, A.J.J.

2006-01-01

In a standard general equilibrium model it is assumed that there are no price restrictions and that prices adjust infinitely fast to their equilibrium values.In case of price restrictions a general equilibrium may not exist and rationing on net demands or supplies is needed to clear the markets.In

Approach to equilibrium in a pure superconductor. The relaxation of the Cooper pair density

Energy Technology Data Exchange (ETDEWEB)

Schid, A

1968-01-01

Electron-phonon and electron-electron collisions are the processes which determine the relaxation time r/sub R/ of the Cooper pair density. The case is considered for which the deviation of the pair density from equilibrium is small and where the equilibrium state is homogeneous. Starting from the Eliashberg equation one is able to reduce the problem to a quadrature once the equilibrium Green functions are known.

The Wigner distribution function applied to optical signals and systems

NARCIS (Netherlands)

Bastiaans, M.J.

1978-01-01

In this paper the Wigner distribution function has been introduced for optical signals and systems. The Wigner distribution function of an optical signal appears to be in close resemblance to the ray concept in geometrical optics. This resemblance reaches even farther: although derived from Fourier

Probability distribution functions for intermittent scrape-off layer plasma fluctuations

Science.gov (United States)

Theodorsen, A.; Garcia, O. E.

2018-03-01

A stochastic model for intermittent fluctuations in the scrape-off layer of magnetically confined plasmas has been constructed based on a super-position of uncorrelated pulses arriving according to a Poisson process. In the most common applications of the model, the pulse amplitudes are assumed exponentially distributed, supported by conditional averaging of large-amplitude fluctuations in experimental measurement data. This basic assumption has two potential limitations. First, statistical analysis of measurement data using conditional averaging only reveals the tail of the amplitude distribution to be exponentially distributed. Second, exponentially distributed amplitudes leads to a positive definite signal which cannot capture fluctuations in for example electric potential and radial velocity. Assuming pulse amplitudes which are not positive definite often make finding a closed form for the probability density function (PDF) difficult, even if the characteristic function remains relatively simple. Thus estimating model parameters requires an approach based on the characteristic function, not the PDF. In this contribution, the effect of changing the amplitude distribution on the moments, PDF and characteristic function of the process is investigated and a parameter estimation method using the empirical characteristic function is presented and tested on synthetically generated data. This proves valuable for describing intermittent fluctuations of all plasma parameters in the boundary region of magnetized plasmas.

Non-equilibrium supramolecular polymerization.

Science.gov (United States)

Sorrenti, Alessandro; Leira-Iglesias, Jorge; Markvoort, Albert J; de Greef, Tom F A; Hermans, Thomas M

2017-09-18

Supramolecular polymerization has been traditionally focused on the thermodynamic equilibrium state, where one-dimensional assemblies reside at the global minimum of the Gibbs free energy. The pathway and rate to reach the equilibrium state are irrelevant, and the resulting assemblies remain unchanged over time. In the past decade, the focus has shifted to kinetically trapped (non-dissipative non-equilibrium) structures that heavily depend on the method of preparation (i.e., pathway complexity), and where the assembly rates are of key importance. Kinetic models have greatly improved our understanding of competing pathways, and shown how to steer supramolecular polymerization in the desired direction (i.e., pathway selection). The most recent innovation in the field relies on energy or mass input that is dissipated to keep the system away from the thermodynamic equilibrium (or from other non-dissipative states). This tutorial review aims to provide the reader with a set of tools to identify different types of self-assembled states that have been explored so far. In particular, we aim to clarify the often unclear use of the term "non-equilibrium self-assembly" by subdividing systems into dissipative, and non-dissipative non-equilibrium states. Examples are given for each of the states, with a focus on non-dissipative non-equilibrium states found in one-dimensional supramolecular polymerization.

Time-dependent free boundary equilibrium and resistive diffusion in a tokamak plasma

International Nuclear Information System (INIS)

Selig, G.

2012-12-01

In a Tokamak, in order to create the necessary conditions for nuclear fusion to occur, a plasma is maintained by applying magnetic fields. Under the hypothesis of an axial symmetry of the tokamak, the study of the magnetic configuration at equilibrium is done in two dimensions, and is deduced from the poloidal flux function. This function is solution of a non linear partial differential equation system, known as equilibrium problem. This thesis presents the time dependent free boundary equilibrium problem, where the circuit equations in the tokamak coils and passive conductors are solved together with the Grad-Shafranov equation to produce a dynamic simulation of the plasma. In this framework, the Finite Element equilibrium code CEDRES has been improved in order to solve the aforementioned dynamic problem. Consistency tests and comparisons with the DINA-CH code on an ITER vertical instability case have validated the results. Then, the resistive diffusion of the plasma current density has been simulated using a coupling between CEDRES and the averaged one-dimensional diffusion equation, and it has been successfully compared with the integrated modeling code CRONOS. (author)

Development of the PARVMEC Code for Rapid Analysis of 3D MHD Equilibrium

Science.gov (United States)

Seal, Sudip; Hirshman, Steven; Cianciosa, Mark; Wingen, Andreas; Unterberg, Ezekiel; Wilcox, Robert; ORNL Collaboration

2015-11-01

The VMEC three-dimensional (3D) MHD equilibrium has been used extensively for designing stellarator experiments and analyzing experimental data in such strongly 3D systems. Recent applications of VMEC include 2D systems such as tokamaks (in particular, the D3D experiment), where application of very small (delB/B ~ 10-3) 3D resonant magnetic field perturbations render the underlying assumption of axisymmetry invalid. In order to facilitate the rapid analysis of such equilibria (for example, for reconstruction purposes), we have undertaken the task of parallelizing the VMEC code (PARVMEC) to produce a scalable and temporally rapidly convergent equilibrium code for use on parallel distributed memory platforms. The parallelization task naturally splits into three distinct parts 1) radial surfaces in the fixed-boundary part of the calculation; 2) two 2D angular meshes needed to compute the Green's function integrals over the plasma boundary for the free-boundary part of the code; and 3) block tridiagonal matrix needed to compute the full (3D) pre-conditioner near the final equilibrium state. Preliminary results show that scalability is achieved for tasks 1 and 3, with task 2 still nearing completion. The impact of this work on the rapid reconstruction of D3D plasmas using PARVMEC in the V3FIT code will be discussed. Work supported by U.S. DOE under Contract DE-AC05-00OR22725 with UT-Battelle, LLC.

Isothermal equilibrium pressures of Y-Th alloy-H2 system

International Nuclear Information System (INIS)

Tanase, M.; Fisher, P.W.

1985-01-01

Isothermal equilibrium pressures of the Y 4 Th (3:2 by weight) alloy-H 2 system were measured as a function of atomic composition [H]/[Y + Th] in the temperature range 580-1160 K. The isotherms have two plateaux in the pressure range 10 -2 -10 3 Pa. The first plateau region is attributed to the formation of YH 2 , and the equilibrium pressure P in pascals was found to be log P = 12.36 - 11300/T where T is in kelvins. The second plateau is attributed to the formation of ThH 2 , and the equilibrium pressure was found to be log P = 10.66 - 6891/T. In low atomic composition region the system obeys Sieverts' law. (Auth.)

Nonclassicality indicator for the real phase-space distribution functions

International Nuclear Information System (INIS)

Sadeghi, Parvin; Khademi, Siamak; Nasiri, Sadollah

2010-01-01

Benedict et al. and Kenfack et al. advocated nonclassicality indicators based on the measurement of negativity of the Wigner distribution functions. These indicators have some applications in quantum mechanics and quantum optics. In this paper we define a nonclassicality indicator in terms of the interference in phase space, which is applicable to some real distribution functions including those of Wigner. As a special case one may reproduce the previous results using our indicator for the Wigner distribution functions. This indicator is examined for cases of the Schroedinger cat state and the thermal states and the results are compared with those obtained by previous methods. It seems that the physical behavior of nonclassicality indicators originates in the uncertainty principle. This is shown by an onto correspondence between these indicators and the uncertainty principle.

State-to-state modeling of non-equilibrium air nozzle flows

Science.gov (United States)

Nagnibeda, E.; Papina, K.; Kunova, O.

2018-05-01

One-dimensional non-equilibrium air flows in nozzles are studied on the basis of the state-to-state description of vibrational-chemical kinetics. Five-component mixture N2/O2/NO/N/O is considered taking into account Zeldovich exchange reactions of NO formation, dissociation, recombination and vibrational energy transitions. The equations for vibrational and chem-ical kinetics in a flow are coupled to the conservation equations of momentum and total energy and solved numerically for different conditions in a nozzle throat. The vibrational distributions of nitrogen and oxygen molecules, number densities of species as well as the gas temperature and flow velocity along a nozzle axis are analysed using the detailed state-to-state flow description and in the frame of the simplified one-temperature thermal equilibrium kinetic model. The comparison of the results showed the influence of non-equilibrium kinetics on macroscopic nozzle flow parameters. In the state-to-state approach, non-Boltzmann vibrational dis-tributions of N2 and O2 molecules with a plateau part at intermediate levels are found. The results are found with the use of the complete and simplified schemes of reactions and the impact of exchange reactions, dissociation and recombination on variation of vibrational level populations, mixture composition, gas velocity and temperature along a nozzle axis is shown.

Calculations of higher twist distribution functions in the MIT bag model

International Nuclear Information System (INIS)

Signal, A.I.

1997-01-01

We calculate all twist-2, -3 and -4 parton distribution functions involving two quark correlations using the wave function of the MIT bag model. The distributions are evolved up to experimental scales and combined to give the various nucleon structure functions. Comparisons with recent experimental data on higher twist structure functions at moderate values of Q 2 give good agreement with the calculated structure functions. (orig.)

Phase rule calculations and the thermodynamics of reactive systems under chemical equilibrium

Directory of Open Access Journals (Sweden)

PLATT G. M.

1999-01-01

Full Text Available In this paper, we examine the resolution of some phase rule problems within the context of multiple chemical equilibrium reactions, using cubic equations of state and an activity coefficient model. Bubble and dew reactive surfaces, reactive azeotropic loci and reactive critical loci are generated and presented in graphical form. Also isobaric bubble and dew reactive enthalpy loci, which may be useful in the modeling of reactive distillation operations, are depicted. All the formalism here employed is developed within the coordinate transformation of Ung and Doherty, which is appropriate for equilibrium reactive or multireactive systems. The major contribution of this work is the determination of critical loci for reactive or multireactive equilibrium systems. Since it is known that for some class of chemical reactions the kinetics and product distribution exhibit high sensitivity to pressure near criticality, the present study may be useful as a predicting tool in these cases if the chemical equilibrium condition is not too far from the real phenomenon.

Analysis of the proton longitudinal structure function from the gluon distribution function

International Nuclear Information System (INIS)

Boroun, G.R.; Rezaei, B.

2012-01-01

We make a critical, next-to-leading order, study of the relationship between the longitudinal structure function F L and the gluon distribution proposed in Cooper-Sarkar et al. (Z. Phys. C 39:281, 1988; Acta Phys. Pol. B 34:2911 2003), which is frequently used to extract the gluon distribution from the proton longitudinal structure function at small x. The gluon density is obtained by expanding at particular choices of the point of expansion and compared with the hard Pomeron behavior for the gluon density. Comparisons with H1 data are made and predictions for the proposed best approach are also provided. (orig.)

Left ventricular diastolic performance at rest in patients with angina and normal systolic function - assessment by equilibrium radionuclide angiography

International Nuclear Information System (INIS)

Maini, C.L.; Bonetti, M.G.; Valle, G.; Antonelli Incalzi, R.; Montenero, A.S.

1985-01-01

The aim of the study was to correlate diastolic function, as evaluated by peak filling rate (PFR) and relative time (TPFR), with the severity of ischemic heart disease, as evaluated by exercise electrocardiography. Accordingly, 83 ischemic patients with effort angina, but normal ejection function at rest and normal left ventricular size, were studied by equilibrium radionuclide angiocardiography within two weeks from the exercise ECG. Diastolic dysfunction, as determined from PFR and, to a lesser extent, from TPFR, is common in patients with ischemic heart disease and normal systolic function. The prevalence and severity of such dysfunction is related more to the severity of the ischemia, as evaluated by the exercise ECG, than to the presence of an old myocardial infarction. Such findings are consistent with the hypothesis that PFR reflects mainly the early diastolic active uncoupling process. (orig.) [de

Analytical modeling of equilibrium of strongly anisotropic plasma in tokamaks and stellarators

International Nuclear Information System (INIS)

Lepikhin, N. D.; Pustovitov, V. D.

2013-01-01

Theoretical analysis of equilibrium of anisotropic plasma in tokamaks and stellarators is presented. The anisotropy is assumed strong, which includes the cases with essentially nonuniform distributions of plasma pressure on magnetic surfaces. Such distributions can arise at neutral beam injection or at ion cyclotron resonance heating. Then the known generalizations of the standard theory of plasma equilibrium that treat p ‖ and p ⊥ (parallel and perpendicular plasma pressures) as almost constant on magnetic surfaces are not applicable anymore. Explicit analytical prescriptions of the profiles of p ‖ and p ⊥ are proposed that allow modeling of the anisotropic plasma equilibrium even with large ratios of p ‖ /p ⊥ or p ⊥ /p ‖ . A method for deriving the equation for the Shafranov shift is proposed that does not require introduction of the flux coordinates and calculation of the metric tensor. It is shown that for p ⊥ with nonuniformity described by a single poloidal harmonic, the equation for the Shafranov shift coincides with a known one derived earlier for almost constant p ⊥ on a magnetic surface. This does not happen in the other more complex case

Elements of non-equilibrium (ℎ, k)-dynamics at zero and finite temperatures

International Nuclear Information System (INIS)

Golubeva, O.N.; Sukhanov, A.D.

2011-01-01

We suggest a method which allows developing some elements of non-equilibrium (ℎ, k)-dynamics without use of Schroedinger equation. It is based on the generalization pf Fokker-Planck and Hamilton-Jacobi equations. Sequential considering of stochastic influence of vacuum is realized in the quantum heat bath model. We show that at the presence of quantum-thermal diffusion non-equilibrium wave functions describe the process of nearing to generalized state of thermal equilibrium at zero and finite temperatures. They can be used as a ground for universal description of transport phenomena

Prediction of the liquid-vapor equilibrium pressure using the quasi-Gaussian entropy theory

NARCIS (Netherlands)

Amadei, A; Roccatano, D; Apol, M.E F; Berendsen, H.J.C.; Di Nola, A.

1996-01-01

We derived a method to evaluate the liquid-vapor equilibrium pressure, with high accuracy over a large range of temperature, using the quasi-Gaussian entropy theory. The final expression that we obtain for the equilibrium pressure as a function of the temperature can be considered as a very accurate

Non-equilibrium dynamics and floral trait interactions shape extant angiosperm diversity.