Diffusion in heterogeneous lattices
Czech Academy of Sciences Publication Activity Database
Tarasenko, Alexander; Jastrabík, Lubomír
2010-01-01
Roč. 256, č. 17 (2010), s. 5137-5144 ISSN 0169-4332 R&D Projects: GA AV ČR KAN301370701; GA MŠk(CZ) 1M06002 Institutional research plan: CEZ:AV0Z10100522 Keywords : lattice- gas systems * diffusion * Monte Carlo simulations Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.795, year: 2010
Simulation of diffusion in concentrated lattice gases
International Nuclear Information System (INIS)
Kehr, K.W.
1986-01-01
Recently the diffusion of particles in lattice gases was studied extensively by theoretical methods and numerical simulations. This paper reviews work on collective and, in particular, on tracer diffusion. The diffusion of tagged particles is characterized by a correlation factor whose behavior as a function of concentration is now well understood. Also the detailed kinetics of the tracer transitions was investigated. A special case is the one-dimensional lattice gas where the tracer diffusion coefficient vanishes. An interesting extension is the case of tagged atoms with a different transition rate. This model allows to study various physical situations, including impurity diffusion, percolation, and diffusion in partially blocked lattices. Finally some recent work on diffusion in lattice gases under the influence of a drift field will be reported. (author)
Convection-diffusion lattice Boltzmann scheme for irregular lattices
Sman, van der R.G.M.; Ernst, M.H.
2000-01-01
In this paper, a lattice Boltzmann (LB) scheme for convection diffusion on irregular lattices is presented, which is free of any interpolation or coarse graining step. The scheme is derived using the axioma that the velocity moments of the equilibrium distribution equal those of the
Anomalous diffusion in a dynamical optical lattice
Zheng, Wei; Cooper, Nigel R.
2018-02-01
Motivated by experimental progress in strongly coupled atom-photon systems in optical cavities, we study theoretically the quantum dynamics of atoms coupled to a one-dimensional dynamical optical lattice. The dynamical lattice is chosen to have a period that is incommensurate with that of an underlying static lattice, leading to a dynamical version of the Aubry-André model which can cause localization of single-particle wave functions. We show that atomic wave packets in this dynamical lattice generically spread via anomalous diffusion, which can be tuned between superdiffusive and subdiffusive regimes. This anomalous diffusion arises from an interplay between Anderson localization and quantum fluctuations of the cavity field.
Holder, R. M.; Hacker, B. R.
2017-12-01
Calc-silicate rocks are often overlooked as sources of pressure-temperature-time data in granulite-UHT metamorphic terranes due to the strong dependence of calc-silicate mineral assemblages on complex fluid compositions and a lack of thermodynamic data on common high-temperature calc-silicate minerals such as scapolite. In the Ediacaran-Cambrian UHT rocks of southern Madagascar, clinopyroxene-scapolite-feldspar-quartz-zircon-titanite calc-silicate rocks are wide-spread. U-Pb dates of 540-520 Ma from unaltered portions of titanite correspond to cooling of the rocks through upper-amphibolite facies and indicate UHT metamorphism occurred before 540 Ma. Zr concentrations in these domains preserve growth temperatures of 900-950 °C, consistent with peak temperatures calculated by pseudosection modeling of nearby osumilite-bearing gneisses. Younger U-Pb dates (510-490 Ma) correspond to fluid-mediated Pb loss from titanite grains, which occurred below their diffusive Pb-closure temperature, along fractures. The extent of fluid alteration is seen clearly in back-scattered electron images and Zr-, Al-, Fe-, Ce-, and Nb-concentration maps. Laser-ablation depth profiling of idioblastic titanite grains shows preserved Pb diffusion profiles at grain rims, but there is no evidence for Zr diffusion, indicating that it was effectively immobile even at UHT.
Diffusion in Deterministic Interacting Lattice Systems
Medenjak, Marko; Klobas, Katja; Prosen, Tomaž
2017-09-01
We study reversible deterministic dynamics of classical charged particles on a lattice with hard-core interaction. It is rigorously shown that the system exhibits three types of transport phenomena, ranging from ballistic, through diffusive to insulating. By obtaining an exact expressions for the current time-autocorrelation function we are able to calculate the linear response transport coefficients, such as the diffusion constant and the Drude weight. Additionally, we calculate the long-time charge profile after an inhomogeneous quench and obtain diffusive profilewith the Green-Kubo diffusion constant. Exact analytical results are corroborated by Monte Carlo simulations.
Diffusion of particles over dynamically disordered lattice
Czech Academy of Sciences Publication Activity Database
Tarasenko, Alexander; Jastrabík, Lubomír
2011-01-01
Roč. 13, č. 6 (2011), s. 2300-2306 ISSN 1463-9076 R&D Projects: GA AV ČR KAN301370701; GA MŠk(CZ) 1M06002 Institutional research plan: CEZ:AV0Z10100522 Keywords : diffusion * Monte Carlo simulations * dynamic disordered lattice Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 3.573, year: 2011
Lattice cell diffusion coefficients. Definitions and comparisons
International Nuclear Information System (INIS)
Hughes, R.P.
1980-01-01
Definitions of equivalent diffusion coefficients for regular lattices of heterogeneous cells have been given by several authors. The paper begins by reviewing these different definitions and the unification of their derivation. This unification makes clear how accurately each definition (together with appropriate cross-section definitions to preserve the eigenvalue) represents the individual reaction rates within the cell. The approach can be extended to include asymmetric cells and whereas before, the buckling describing the macroscopic flux shape was real, here it is found to be complex. A neutron ''drift'' coefficient as well as a diffusion coefficient is necessary to produce the macroscopic flux shape. The numerical calculation of the various different diffusion coefficients requires the solutions of equations similar to the ordinary transport equation for an infinite lattice. Traditional reactor physics codes are not sufficiently flexible to solve these equations in general. However, calculations in certain simple cases are presented and the theoretical results quantified. In difficult geometries, Monte Carlo techniques can be used to calculate an effective diffusion coefficient. These methods relate to those already described provided that correlation effects between different generations of neutrons are included. Again, these effects are quantified in certain simple cases. (author)
Parallel diffusion length on thermal neutrons in rod type lattices
International Nuclear Information System (INIS)
Ahmed, T.; Siddiqui, S.A.M.M.; Khan, A.M.
1981-11-01
Calculation of diffusion lengths of thermal neutrons in lead-water and aluminum water lattices in direction parallel to the rods are performed using one group diffusion equation together with Shevelev transport correction. The formalism is then applied to two practical cases, the Kawasaki (Hitachi) and the Douglas point (Candu) reactor lattices. Our results are in good agreement with the observed values. (author)
Bulk diffusion in a kinetically constrained lattice gas
Arita, Chikashi; Krapivsky, P. L.; Mallick, Kirone
2018-03-01
In the hydrodynamic regime, the evolution of a stochastic lattice gas with symmetric hopping rules is described by a diffusion equation with density-dependent diffusion coefficient encapsulating all microscopic details of the dynamics. This diffusion coefficient is, in principle, determined by a Green-Kubo formula. In practice, even when the equilibrium properties of a lattice gas are analytically known, the diffusion coefficient cannot be computed except when a lattice gas additionally satisfies the gradient condition. We develop a procedure to systematically obtain analytical approximations for the diffusion coefficient for non-gradient lattice gases with known equilibrium. The method relies on a variational formula found by Varadhan and Spohn which is a version of the Green-Kubo formula particularly suitable for diffusive lattice gases. Restricting the variational formula to finite-dimensional sub-spaces allows one to perform the minimization and gives upper bounds for the diffusion coefficient. We apply this approach to a kinetically constrained non-gradient lattice gas in two dimensions, viz. to the Kob-Andersen model on the square lattice.
Dynamical behaviour of the coupled diffusion map lattice
International Nuclear Information System (INIS)
Wei Wang; Cerdeira, H.A.
1993-10-01
In this paper we report the dynamical study of a coupled diffusive map lattice with the coupling between the elements only through the bifurcation parameter of the mapping function. The diffusive process of the lattice from an initially random distribution state to a homogeneous one and the stable range of the diffusive homogeneous attractor are discussed. For various coupling strengths we find that there are several types of spatio-temporal structures. In addition, the evolution of the lattice into chaos is studied and a largest Lyapunov exponent is used to characterize the dynamical behaviour. (author). 22 refs, 9 figs
Diffusion on unstructured triangular grids using Lattice Boltzmann
Sman, van der R.G.M.
2004-01-01
In this paper, we present a Lattice Boltzmann scheme for diffusion on unstructured triangular grids. In this formulation there is no need for interpolation, as is required in other LB schemes on irregular grids. At the end of the propagation step, the lattice gas particles arrive exactly at
Lattice Boltzmann scheme for diffusion on triangular grids
Sman, van der R.G.M.
2003-01-01
In this paper we present a Lattice Boltzmann scheme for diffusion on it unstructured triangular grids. In this formulation of a LB for irregular grids there is no need for interpolation, which is required in other LB schemes on irregular grids. At the end of the propagation step the lattice gas
Maxwell iteration for the lattice Boltzmann method with diffusive scaling
Zhao, Weifeng; Yong, Wen-An
2017-03-01
In this work, we present an alternative derivation of the Navier-Stokes equations from Bhatnagar-Gross-Krook models of the lattice Boltzmann method with diffusive scaling. This derivation is based on the Maxwell iteration and can expose certain important features of the lattice Boltzmann solutions. Moreover, it will be seen to be much more straightforward and logically clearer than the existing approaches including the Chapman-Enskog expansion.
Lattice dynamics and thermal diffuse scattering for molecular crystals
International Nuclear Information System (INIS)
Kroon, P.A.
1977-01-01
Thermal diffuse scattering (TDS) corrections on the observed reflection intensities in the accurate determination of crystal structures by X-ray diffraction are emphasized. A lattice-dynamical model and procedure for lattice-dynamical calculations are set up. Expression for first- and second-order TDS intensity distributions are derived. A comparison with other models is made. First-order TDS corrections for naphtalene at 100 K are presented
Analytical approach for collective diffusion: one-dimensional heterogeneous lattice
Czech Academy of Sciences Publication Activity Database
Tarasenko, Alexander
2016-01-01
Roč. 144, č. 14 (2016), 1-11, č. článku 144105. ISSN 0021-9606 Institutional support: RVO:68378271 Keywords : diffusion * Monte Carlo simulations * one-dimensional heterogeneous lattice Subject RIV: BE - Theoretical Physics Impact factor: 2.965, year: 2016
Diffusion in lattice Lorentz gases with mixtures of point scatterers
International Nuclear Information System (INIS)
Acedo, L.; Santos, A.
1994-01-01
Monte Carlo simulations are carried out to evaluate the diffusion coefficient in some lattice Lorentz gases with mixtures of point scatterers in the limit of a low concentration of scatterers. Two models on a square lattice are considered: (a) right and left stochastic rotators plus pure reflectors and (b) right and left stochastic mirrors plus pure reflectors. The simulation data are compared with the repeated ring approximation (RRA). The agreement is excellent for models in the absence of pure reflectors, suggesting that the RRA gives the correct diffusion coefficient for those cases. As the fraction x B of reflectors increases, the diffusion coefficient decreases and seems to vanish at x B c congruent 0.8 (percolation threshold) with a critical exponent μ congruent 2 (stochastic model) or μ congruent 3 (deterministic rotator model)
Kimizuka, Hajime; Ogata, Shigenobu; Shiga, Motoyuki
2018-01-01
Understanding the underlying mechanism of the nanostructure-mediated high diffusivity of H in Pd is of recent scientific interest and also crucial for industrial applications. Here, we present a decisive scenario explaining the emergence of the fast lattice-diffusion mode of interstitial H in face-centered cubic Pd, based on the quantum mechanical natures of both electrons and nuclei under finite strains. Ab initio path-integral molecular dynamics was applied to predict the temperature- and strain-dependent free energy profiles for H migration in Pd over a temperature range of 150-600 K and under hydrostatic tensile strains of 0.0%-2.4%; such strain conditions are likely to occur in real systems, especially around the elastic fields induced by nanostructured defects. The simulated results revealed that, for preferential H location at octahedral sites, as in unstrained Pd, the activation barrier for H migration (Q ) was drastically increased with decreasing temperature owing to nuclear quantum effects. In contrast, as tetrahedral sites increased in stability with lattice expansion, nuclear quantum effects became less prominent and ceased impeding H migration. This implies that the nature of the diffusion mechanism gradually changes from quantum- to classical-like as the strain is increased. For H atoms in Pd at the hydrostatic strain of ˜2.4 % , we determined that the mechanism promoted fast lattice diffusion (Q =0.11 eV) of approximately 20 times the rate of conventional H diffusion (Q =0.23 eV) in unstrained Pd at a room temperature of 300 K.
Tracer concentration contours in grain lattice and grain boundary diffusion
International Nuclear Information System (INIS)
Kim, Y. S.; Olander, D. R.
1997-01-01
Grain boundary diffusion plays a significant role in fission gas release, which is one of the crucial processes dominating nuclear fuel performance. Gaseous fission products such as Xe and Kr generated during nuclear fission have to diffuse in the grain lattice and the boundary inside fuel pellets before they reach the open spaces in a fuel rod. These processes can be studied by 'tracer diffusion' techniques, by which grain boundary diffusivity can be estimated and directly used for low burn-up fission gas release analysis. However, only a few models accounting for the both processes are available and mostly handle them numerically due to mathematical complexity. Also the numerical solution has limitations in a practical use. In this paper, an approximate analytical solution in case of stationary grain boundary in a polycrystalline solid is developed for the tracer diffusion techniques. This closed-form solution is compared to available exact and numerical solutions and it turns out that it makes computation not only greatly easier but also more accurate than previous models. It can be applied to theoretical modelings for low burn-up fission gas release phenomena and experimental analyses as well, especially for PIE (post irradiation examination). (author)
Lattice diffusion of a single molecule in solution
Ruggeri, Francesca; Krishnan, Madhavi
2017-12-01
The ability to trap a single molecule in an electrostatic potential well in solution has opened up new possibilities for the use of molecular electrical charge to study macromolecular conformation and dynamics at the level of the single entity. Here we study the diffusion of a single macromolecule in a two-dimensional lattice of electrostatic traps in solution. We report the ability to measure both the size and effective electrical charge of a macromolecule by observing single-molecule transport trajectories, typically a few seconds in length, using fluorescence microscopy. While, as shown previously, the time spent by the molecule in a trap is a strong function of its effective charge, we demonstrate here that the average travel time between traps in the landscape yields its hydrodynamic radius. Tailoring the pitch of the lattice thus yields two different experimentally measurable time scales that together uniquely determine both the size and charge of the molecule. Since no information is required on the location of the molecule between consecutive departure and arrival events at lattice sites, the technique is ideally suited to measurements on weakly emitting entities such as single molecules.
Lattice animals in diffusion limited binary colloidal system
Shireen, Zakiya; Babu, Sujin B.
2017-08-01
In a soft matter system, controlling the structure of the amorphous materials has been a key challenge. In this work, we have modeled irreversible diffusion limited cluster aggregation of binary colloids, which serves as a model for chemical gels. Irreversible aggregation of binary colloidal particles leads to the formation of a percolating cluster of one species or both species which are also called bigels. Before the formation of the percolating cluster, the system forms a self-similar structure defined by a fractal dimension. For a one component system when the volume fraction is very small, the clusters are far apart from each other and the system has a fractal dimension of 1.8. Contrary to this, we will show that for the binary system, we observe the presence of lattice animals which has a fractal dimension of 2 irrespective of the volume fraction. When the clusters start inter-penetrating, we observe a fractal dimension of 2.5, which is the same as in the case of the one component system. We were also able to predict the formation of bigels using a simple inequality relation. We have also shown that the growth of clusters follows the kinetic equations introduced by Smoluchowski for diffusion limited cluster aggregation. We will also show that the chemical distance of a cluster in the flocculation regime will follow the same scaling law as predicted for the lattice animals. Further, we will also show that irreversible binary aggregation comes under the universality class of the percolation theory.
Lattice dynamical investigations on Zn diffusion in zinc oxide
Indian Academy of Sciences (India)
diffusion and that too by single vacancy mechanism. The results are compared with the .... Instantaneous relative displacement of the diffusing atom with respect to the neigh- bours in the diffusion ring is given as a reaction coordinate,. X =.
Phase transitions of titanite CaTiSiO5 from density functional perturbation theory
Malcherek, Thomas; Fischer, Michael
2018-02-01
Phonon dispersion of titanite CaTiSiO5 has been calculated using the variational density functional perturbation theory. The experimentally known out-of-center distortion of the Ti atom is confirmed. The distortion is associated with a Bu mode that is unstable for wave vectors normal to the octahedral chain direction of the C 2 /c aristotype structure. The layer of wave vectors with imaginary mode frequencies also comprises the Brillouin zone boundary point Y (0 ,1 ,0 ) , which is critical for the transition to the P 21/c ground-state structure. The phonon branch equivalent to the imaginary branch of the titanite aristotype is found to be stable in malayaite CaSnSiO5. The unstable phonon mode in titanite leads to the formation of transoriented short and long Ti-O1 bonds. The Ti as well as the connecting O1 atom exhibit strongly anomalous Born effective charges along the octahedral chain direction [001], indicative of the strong covalency in this direction. Accordingly and in contrast to malayaite, LO-TO splitting is very large in titanite. In the C 2 /c phase of titanite, the Ti-O1-Ti distortion chain is disordered with respect to neighboring distortion chains, as all chain configurations are equally unstable along the phonon branch. This result is in agreement with diffuse x-ray scattering in layers normal to the chain direction that is observed at temperatures close to the P 21/c to C 2 /c transition temperature and above. The resulting dynamic chains of correlated Ti displacements are expected to order in two dimensions to yield the P 21/c ground-state structure of titanite.
Czech Academy of Sciences Publication Activity Database
Tarasenko, Alexander; Boháč, Petr; Jastrabík, Lubomír
2015-01-01
Roč. 74, Nov (2015), s. 556-560 ISSN 1386-9477 R&D Projects: GA MŠk LO1409; GA TA ČR TA03010743 Institutional support: RVO:68378271 Keywords : surface diffusion * heterogeneous lattices * lattice-gas models * kinetic Monte Carlo simulation Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.904, year: 2015
Unified derivation of the various definitions of lattice cell diffusion coefficients
International Nuclear Information System (INIS)
Hughes, R.P.
1978-01-01
The various definitions of lattice cell diffusion coefficients are discussed within the context of a one-dimensional slab lattice in one energy group. It is shown how each definition, although originally derived in its own particular way, can be derived from a single approach. This makes clear the differences between, and the advantages of, the various definitions
Diffusion coefficients for multi-step persistent random walks on lattices
International Nuclear Information System (INIS)
Gilbert, Thomas; Sanders, David P
2010-01-01
We calculate the diffusion coefficients of persistent random walks on lattices, where the direction of a walker at a given step depends on the memory of a certain number of previous steps. In particular, we describe a simple method which enables us to obtain explicit expressions for the diffusion coefficients of walks with a two-step memory on different classes of one-, two- and higher dimensional lattices.
Quantum Lattice-Gas Model for the Diffusion Equation
National Research Council Canada - National Science Library
Yepez, J
2001-01-01
.... It is a minimal model with two qubits per node of a one-dimensional lattice and it is suitable for implementation on a large array of small quantum computers interconnected by nearest-neighbor...
Electrical conductivity and charge diffusion in thermal QCD from the lattice
Energy Technology Data Exchange (ETDEWEB)
Aarts, Gert; Allton, Chris [Department of Physics, College of Science, Swansea University Swansea SA2 8PP (United Kingdom); Amato, Alessandro [Department of Physics, College of Science, Swansea University Swansea SA2 8PP (United Kingdom); Department of Physics and Helsinki Institute of Physics P.O. Box 64, FI-00014 University of Helsinki (Finland); Giudice, Pietro [Universität Münster, Institut für Theoretische Physik Wilhelm-Klemm-Str. 9, D-48149 Münster (Germany); Hands, Simon [Department of Physics, College of Science, Swansea University Swansea SA2 8PP (United Kingdom); Skullerud, Jon-Ivar [Department of Mathematical Physics, National University of Ireland Maynooth Maynooth, Co Kildare (Ireland)
2015-02-27
We present a lattice QCD calculation of the charge diffusion coefficient, the electrical conductivity and various susceptibilities of conserved charges, for a range of temperatures below and above the deconfinement crossover. The calculations include the contributions from up, down and strange quarks. We find that the diffusion coefficient is of the order of 1/(2πT) and has a dip around the crossover temperature. Our results are obtained with lattice simulations containing 2+1 dynamical flavours on anisotropic lattices. The Maximum Entropy Method is used to construct spectral functions from correlators of the conserved vector current.
Anomalous diffusion in a lattice-gas wind-tree model
International Nuclear Information System (INIS)
Kong, X.P.; Cohen, E.G.D.
1989-01-01
Two new strictly deterministic lattice-gas automata derived from Ehrenfest's wind-tree model are studied. While in one model normal diffusion occurs, the other model exhibits abnormal diffusion in that the distribution function of the displacements of the wind particle is non-Gaussian, but its second moment, the mean-square displacement, is proportional to the time, so that a diffusion coefficient can be defined. A connection with the percolation problem and a self-avoiding random walk for the case in which the lattice is completely covered with trees is discussed
Diffusion and transport in locally disordered driven lattices
Energy Technology Data Exchange (ETDEWEB)
Wulf, Thomas, E-mail: Thomas.Wulf@physnet.uni-hamburg.de; Okupnik, Alexander [Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany); Schmelcher, Peter, E-mail: Peter.Schmelcher@physnet.uni-hamburg.de [Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany); The Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg (Germany)
2016-09-15
We study the effect of disorder on the particle density evolution in a classical Hamiltonian driven lattice setup. If the disorder is localized within a finite sub-domain of the lattice, the emergence of strong tails in the density distribution which even increases towards larger positions is shown, thus yielding a highly non-Gaussian particle density evolution. As the key underlying mechanism, we identify the conversion between different components of the unperturbed systems mixed phase space which is induced by the disorder. Based on the introduction of individual conversion rates between chaotic and regular components, a theoretical model is developed which correctly predicts the scaling of the particle density. The effect of disorder on the transport properties is studied where a significant enhancement of the transport for cases of localized disorder is shown, thereby contrasting strongly the merely weak modification of the transport for global disorder.
Diffusion and transport in locally disordered driven lattices
International Nuclear Information System (INIS)
Wulf, Thomas; Okupnik, Alexander; Schmelcher, Peter
2016-01-01
We study the effect of disorder on the particle density evolution in a classical Hamiltonian driven lattice setup. If the disorder is localized within a finite sub-domain of the lattice, the emergence of strong tails in the density distribution which even increases towards larger positions is shown, thus yielding a highly non-Gaussian particle density evolution. As the key underlying mechanism, we identify the conversion between different components of the unperturbed systems mixed phase space which is induced by the disorder. Based on the introduction of individual conversion rates between chaotic and regular components, a theoretical model is developed which correctly predicts the scaling of the particle density. The effect of disorder on the transport properties is studied where a significant enhancement of the transport for cases of localized disorder is shown, thereby contrasting strongly the merely weak modification of the transport for global disorder.
Influence of blocking effect and energetic disorder on diffusion in one-dimensional lattice
International Nuclear Information System (INIS)
Mai Thi Lan; Nguyen Van Hong; Nguyen Thu Nhan; Hoang Van Hue
2014-01-01
The diffusion in one-dimensional disordered lattice with Gaussian distribution of site and transition energies has been studied by mean of kinetic Monte-Carlo simulation. We focus on investigating the influence of energetic disorders and diffusive particle density on diffusivity. In single-particle case, we used both analytical method and kinetic Monte-Carlo simulation to calculate the quantities that relate to diffusive behavior in disordered systems such as the mean time between two consecutive jumps, correlation factor and diffusion coefficient. The calculation shows a good agreement between analytical and simulation results for all disordered lattice types. In many - particle case, the blocking effect results in decreasing correlation factor F and average time τ jump between two consecutive jumps. With increasing the number of particles, the diffusion coefficient D M decreases for site-energy and transition-energy disordered lattices due to the F-effect affect affects stronger than τ-effect. Furthermore, the blocking effect almost is temperature independent for both lattices. (author)
Concentration contours in lattics and grain boundary diffusion in a polycrystalline solid
International Nuclear Information System (INIS)
Kim, Yong Soo; Jae, Won Mok; El Saied, Usama; Olander, Donald R.
1995-01-01
Grain boundary diffusion plays significant role in the fission gas release, which is one of the crucial processes dominating nuclear fuel performance. Gaseous fission products such as Xe and Kr generated inside fuel pellet have to diffuse in the lattice and in the grain boundary before they reach open space in the fuel rod. In the mean time, the grains in the fuel pellet grow and shrink according to grain growth kinetics, especially at elevated temperature at which nuclear reactors are operating. Thus the boundary movement ascribed to the grain growth greatly influences the fission gas release rate by lengthening or shortening the lattice diffusion distance, which is the rate limiting step. Sweeping fission gases by the moving boundary contributes to the increment of the fission gas release as well. Lattice and grain boundary diffusion processes in the fission gas release can be studied by 'tracer diffusion' technique, by which grain boundary diffusivity can be estimated and used directly for low burn up fission gas release analysis. However, even for tracer diffusion analysis, taking both the intragranular grain growth and the diffusion processes simultaneously into consideration is not easy. Only a few models accounting for the both processes are available and mostly handle them numerically. Numerical solutions are limited in the practical use. Here in this paper, an approximate analytical solution of the lattice and stationary grain boundary diffusion in a polycrystalline solid is developed for the tracer diffusion techniques. This short closed form solution is compared to available exact and numerical solutions and turns out to be acceptably accurate. It can be applied to the theoretical modeling and the experimental analysis, especially PIE (post irradiation examination), of low burn up fission gas release
Marquardt, Katharina; Dohmen, Ralf; Wagner, Johannes
2014-05-01
Diffusion along interface and grain boundaries provides an efficient pathway and may control chemical transport in rocks as well as their mechanical strength. Besides the significant relevance of these diffusion processes for various geologic processes, experimental data are still very limited (e.g., Dohmen & Milke, 2010). Most of these data were measured using polycrystalline materials and the formalism of LeClaire (1951) to fit integrated concentration depth profiles. To correctly apply this formalism, certain boundary conditions of the diffusion problem need to be fulfilled, e.g., surface diffusion is ignored, and furthermore the lattice diffusion coefficient has to be known from other studies or is an additional fitting parameter, which produces some ambiguity in the derived grain boundary diffusion coefficients. We developed an experimental setup where we can measure the lattice and grain boundary diffusion coefficients simultaneously but independent and demonstrate the relevance of surface diffusion for typical grain boundary diffusion experiments. We performed Mg2SiO4 bicrystal diffusion experiments, where a single grain boundary is covered by a thin-film of pure Ni2SiO4 acting as diffusant source, produced by pulsed laser deposition. The investigated grain boundary is a 60° (011)/[100]. This specific grain boundary configuration was modeled using molecular dynamics for comparison with the experimental observations in the transmission electron microscope (TEM). Both, experiment and model are in good agreement regarding the misorientation, whereas there are still some disagreements regarding the strain fields along the grain boundary that are of outmost importance for the strengths of the material. The subsequent diffusion experiments were carried out in the temperature range between 800° and 1450° C. The inter diffusion profiles were measured using the TEMs energy dispersive x-ray spectrometer standardized using the Cliff-Lorimer equation and EMPA
The role of diffusion measurements in the study of crystal lattice defects
Energy Technology Data Exchange (ETDEWEB)
Kidson, G V
1965-07-15
Measurements of atomic mobility in solids are frequently of direct interest to those concerned with the design, development and utilization of materials in engineering. Increasing attention, however, is currently devoted to an under standing of such properties in terms of the occurrence and nature of point and line defects in the crystals. This paper reviews some recent diffusion studies conducted at C.R,N.L. that provide, in addition to data of interest in nuclear technology, a means of gaining some insight into the more fundamental nature of the lattice defects occurring in the materials. The systems discussed are (i) self diffusion in the high temperature phase of pure zirconium (ii) solute diffusion in lead and (iii) interdiffusion of aluminum and zirconium The unusual and at present incompletely understood results described in (i) are briefly reviewed. Evidence is given to suggest that diffusion occurs either through a dense dislocation network produced as a result of a martensitic phase transformation, or, alternatively, by excess vacancies introduced into the crystal by impurities. In (ii) the extraordinarily rapid diffusion of noble metal solutes in high purity lead single crystals will be discussed n terms of the state of solution of the solute atoms. It will be shown that their diffusion behaviour can be understood by assuming that a fraction f{sub i} of the dissolved solute atoms occupy interstitial sites, The measured diffusion coefficient D{sub m} is related to the interstitial diffusion coefficient by D{sub m} = f{sub i} D{sub i}. In (iii) the formation and rapid growth of single intermetallic compound ZrAl{sub 3} in the diffusion zone formed between pure zirconium and pure aluminum is described and the diffusion mechanism is interpreted in terms of the structure of the compound lattice. The results indicate that ZrAl{sub 3} forms a defect lattice, leading to the relatively rapid migration of aluminum atoms. (author)
Diffusion coefficients for periodically induced multi-step persistent walks on regular lattices
International Nuclear Information System (INIS)
Gilbert, Thomas; Sanders, David P
2012-01-01
We present a generalization of our formalism for the computation of diffusion coefficients of multi-step persistent random walks on regular lattices to walks which include zero-displacement states. This situation is especially relevant to systems where tracer particles move across potential barriers as a result of the action of a periodic forcing whose period sets the timescale between transitions. (paper)
Theory of spin-lattice relaxation of diffusing light nuclei in glasses
International Nuclear Information System (INIS)
Schirmer, A.; Schirmacher, W.
1988-01-01
NMR data of diffusion-induced spin-lattice relaxation in glasses cannot generally be interpreted in the framework of the classical theory of Bloembergen, Purcell and Pound (BPP). Since it is based on exponential density relaxation, generally bnot found in glasses, the BPP formula must be generalized. Here a combination of standard relaxation theory with a hopping model for diffusion in glasses is present. It is shown that the observed anomaties in the NMR data can be explained as a result of anomalous diffusion. 25 refs.; 1 figure
International Nuclear Information System (INIS)
Mihai, C.
1998-01-01
The present work performed in our department is related to development of safety assessment programme for the National Repository for Radioactive Waste - Baita, Bihor. The rate of radionuclide release in the proximity of National Repository for Radioactive Waste - Baita, Bihor was minimized by taking into account the multibarrier principle. This implies the uses of a complex system of natural and engineered barriers which should neutralize the main processes of radionuclide migration. In the first component of the system mentioned above, cement lattice, the migration of incorporated radionuclides takes place mainly by diffusion process. The diffusion equation is given for the particular case of cylindrical shape of the container, from which the ratio between the released fraction and the initial quantity of radionuclides is obtained. We studied the process of diffusion in three different materials (the radionuclides used were 65 Zn, 51 Cr, 82 Br). The results obtained allowed a pertinent selection of the material for improvement of retardation factors of cement lattice. (author)
U-Th-Pb systematics in zircon and titanite
International Nuclear Information System (INIS)
Zartman, R.E.; Kwak, L.M.
1990-01-01
U-Th-Pb isotopic analyses of zircon and titanite were made for two core samples of granite from borehole ATK-1 drilled into the Eye-Dashwa Lakes pluton. One of the samples from near the bottom of the hole (990.97 to 996.78 m) yielded zircon and titanite that were slightly to severely disturbed isotopically. Eight fractions of zircon give an upper concordia intercept age of 2625 ± 16 Ma (MSWD = 34), which, based on an evaluation of the more concordant data points and on other geochronological results, is interpreted as being slightly too young. The time of crystallization is probably better approximated by the 207 Pb/ 206 Pb age of 2665 Ma determined on a slightly (∼8 percent) discordant titanite. The other sample from near the surface (3.85 to 9.61 m) generally revealed even more severely disturbed isotopic systematics for both zircon and titanite. The complex nature of the disturbances probably resulted from the penetration of meteoritic water into rock already modified by post-crystallization hydrothermal alteration. Nuclide migration occurred in both minerals -- during the Middle or Late Proterozoic for the zircon and during the modern weathering cycle for the titanite. Material balance calculations are used to demonstrate a recent relative gain of radiogenic Pb and/or loss of Th and U from the freshest-looking, least-altered titanite by exchange with altered, leucoxenite-bearing titanite
Two-state random walk model of lattice diffusion - 1. Self-correlation function
International Nuclear Information System (INIS)
Balakrishnan, V.; Venkataraman, G.
1981-01-01
Diffusion with interruptions (arising from localized oscillations, or traps, or mixing between jump diffusion and fluid-like diffusion, etc.) is a very general phenomenon. Its manifestations range from superionic conductance to the behaviour of hydrogen in metals. Based on a continuous-time random walk approach, we present a comprehensive two-state random walk model for the diffusion of a particle on a lattice, incorporating arbitrary holding-time distributions for both localized residence at the sites and inter-site flights, and also the correct first-waiting-time distributions. A synthesis is thus achieved of the two extremes of jump diffusion (zero flight time) and fluid-like diffusion (zero residence time). Various earlier models emerge as special cases of our theory. Among the noteworthy results obtained are: closed-form solutions (in d dimensions, and with arbitrary directional bias) for temporarily uncorrelated jump diffusion and for the fluid diffusion counterpart; a compact, general formula for the mean square displacement; the effects of a continuous spectrum of time scales in the holding-time distributions, etc. The dynamic mobility and the structure factor for 'oscillatory diffusion' are taken up in part 2. (author)
Room temperature single-crystal diffuse scattering and ab initio lattice dynamics in CaTiSiO5.
Gutmann, M J; Refson, K; Zimmermann, M V; Swainson, I P; Dabkowski, A; Dabkowska, H
2013-08-07
Single-crystal diffuse scattering data have been collected at room temperature on synthetic titanite using both neutrons and high-energy x-rays. A simple ball-and-springs model reproduces the observed diffuse scattering well, confirming its origin to be primarily due to thermal motion of the atoms. Ab initio phonons are calculated using density-functional perturbation theory and are shown to reproduce the experimental diffuse scattering. The observed diffuse x-ray and neutron scattering patterns are consistent with a summation of mode frequencies and displacement eigenvectors associated with the entire phonon spectrum, rather than with a simple, short-range static displacement. A band gap is observed between 600 and 700 cm(-1) with only two modes crossing this region, both associated with antiferroelectric Ti-O motion along a. One of these modes (of Bu symmetry), displays a large LO-TO mode-splitting (562-701.4 cm(-1)) and has a dominant component coming from Ti-O bond-stretching and, thus, the mode-splitting is related to the polarizability of the Ti-O bonds along the chain direction. Similar mode-splitting is observed in piezo- and ferroelectric materials. The calculated phonon dispersion model may be of use to others in future to understand the phase transition at higher temperatures, as well as in the interpretation of measured phonon dispersion curves.
The Role of Lattice Vibrations in Adatom Diffusion at Metal Stepped Surfaces
International Nuclear Information System (INIS)
Durakanoglu, S.
2004-01-01
Diffusion of a single atom on metal surfaces remains a subject of continuing interest in the surface science community because of the important role it plays in several technologically important phenomena such as thin-film and eptaxial growth, catalysis and chemical reactions. Except for a few studies, most of theoretical works, ranging from molecular dynamic simulations to first principle electronic structure calculations, are devoted to determination of the characteristics of the diffusion processes and the energy barriers, neglecting the contribution of lattice vibrations in adatom diffusion. However, in a series of theoretical works on self-diffusion on the flat surfaces of Cu(100), Ag(100) and Ni(100), Ulrike et al.[1-3], showed that the vibrational contributions are important and should be included in any complete description of the temperature dependence of the diffusion coefficient. In this work, it is our aim to examine the role of lattice vibrations in adatom diffusion at stepped surfaces of Cu(100) and Ni(100) within the framework of transition state theory. Ehrlich-Shwoebel energy barriers for an adatom diffusing over a step-edge are calculated through the inclusion of vibrational internal energy. Local vibrational density of states, main ingredient to the vibrational thermodynamic functions, are calculated in the harmonic approximation, using real space Green's function method with the force constants derived from interaction potentials based on the embedded atom method. We emphasize the sensitivity of the local vibrational density of states to the local atomic environment. We, furthermore, discuss the contribution of thermodynamic functions calculated from local vibrational density of states to the prefactors in diffusion coefficient
Coarse-mesh method for multidimensional, mixed-lattice diffusion calculations
International Nuclear Information System (INIS)
Dodds, H.L. Jr.; Honeck, H.C.; Hostetler, D.E.
1977-01-01
A coarse-mesh finite difference method has been developed for multidimensional, mixed-lattice reactor diffusion calculations, both statics and kinetics, in hexagonal geometry. Results obtained with the coarse-mesh (CM) method have been compared with a conventional mesh-centered finite difference method and with experiment. The results of this comparison indicate that the accuracy of the CM method for highly heterogeneous (mixed) lattices using one point per hexagonal mesh element (''hex'') is about the same as the conventional method with six points per hex. Furthermore, the computing costs (i.e., central processor unit time and core storage requirements) of the CM method with one point per hex are about the same as the conventional method with one point per hex
Reaction-diffusion on the fully-connected lattice: A+A\\rightarrow A
Turban, Loïc; Fortin, Jean-Yves
2018-04-01
Diffusion-coagulation can be simply described by a dynamic where particles perform a random walk on a lattice and coalesce with probability unity when meeting on the same site. Such processes display non-equilibrium properties with strong fluctuations in low dimensions. In this work we study this problem on the fully-connected lattice, an infinite-dimensional system in the thermodynamic limit, for which mean-field behaviour is expected. Exact expressions for the particle density distribution at a given time and survival time distribution for a given number of particles are obtained. In particular, we show that the time needed to reach a finite number of surviving particles (vanishing density in the scaling limit) displays strong fluctuations and extreme value statistics, characterized by a universal class of non-Gaussian distributions with singular behaviour.
Lattice Boltzmann method for multi-component, non-continuum mass diffusion
International Nuclear Information System (INIS)
Joshi, Abhijit S; Peracchio, Aldo A; Grew, Kyle N; Chiu, Wilson K S
2007-01-01
Recently, there has been a great deal of interest in extending the lattice Boltzmann method (LBM) to model transport phenomena in the non-continuum regime. Most of these studies have focused on single-component flows through simple geometries. This work examines an ad hoc extension of a recently developed LBM model for multi-component mass diffusion (Joshi et al 2007 J. Phys. D: Appl. Phys. 40 2961) to model mass diffusion in the non-continuum regime. In order to validate the method, LBM results for ternary diffusion in a two-dimensional channel are compared with predictions of the dusty gas model (DGM) over a range of Knudsen numbers. A calibration factor based on the DGM is used in the LBM to correlate Knudsen diffusivity to pore size. Results indicate that the LBM can be a useful tool for predicting non-continuum mass diffusion (Kn > 0.001), but additional research is needed to extend the range of applicability of the algorithm for a larger parameter space. Guidelines are given on using the methodology described in this work to model non-continuum mass transport in more complex geometries where the DGM is not easily applicable. In addition, the non-continuum LBM methodology can be extended to three-dimensions. An envisioned application of this technique is to model non-continuum mass transport in porous solid oxide fuel cell electrodes
Lattice location of diffused Zn atoms in GaAs and InP single crystals
International Nuclear Information System (INIS)
Chan, L.Y.; Yu, K.M.; Ben-Tzur, M.; Haller, E.E.; Jaklevic, J.M.; Walukiewicz, W.; Hanson, C.M.
1991-01-01
We have investigated the saturation phenomenon of the free carrier concentration in p-type GaAs and InP single crystals doped by zinc diffusion. The free hole saturation occurs at 10 20 cm -3 for GaAs, but the maximum concentration for InP appears at mid 10 18 cm -3 . The difference in the saturation hole concentrations for these materials is investigated by studying the incorporation and the lattice location of the impurity zinc, an acceptor when located on a group III atom site. Zinc is diffused into the III-V wafers in a sealed quartz ampoule. Particle-induced x-ray emission with ion-channeling techniques are employed to determine the exact lattice location of the zinc atoms. We have found that over 90% of all zinc atoms occupy Ga sites in the diffused GaAs samples, while for the InP case, the zinc substitutionality is dependent on the cooling rate of the sample after high-temperature diffusion. For the slowly cooled sample, a large fraction (∼90%) of the zinc atoms form random precipitates of Zn 3 P 2 and elemental Zn. However, when rapidly cooled only 60% of the zinc forms such precipitates while the rest occupies specific sites in the InP. We analyze our results in terms of the amphoteric native defect model. We show that the difference in the electrical activity of the Zn atoms in GaAs and InP is a consequence of the different location of the Fermi level stabilization energy in these two materials
Analytic treatment of nuclear spin-lattice relaxation for diffusion in a cone model
Sitnitsky, A. E.
2011-12-01
We consider nuclear spin-lattice relaxation rate resulted from a diffusion equation for rotational wobbling in a cone. We show that the widespread point of view that there are no analytical expressions for correlation functions for wobbling in a cone model is invalid and prove that nuclear spin-lattice relaxation in this model is exactly tractable and amenable to full analytical description. The mechanism of relaxation is assumed to be due to dipole-dipole interaction of nuclear spins and is treated within the framework of the standard Bloemberger, Purcell, Pound-Solomon scheme. We consider the general case of arbitrary orientation of the cone axis relative the magnetic field. The BPP-Solomon scheme is shown to remain valid for systems with the distribution of the cone axes depending only on the tilt relative the magnetic field but otherwise being isotropic. We consider the case of random isotropic orientation of cone axes relative the magnetic field taking place in powders. Also we consider the cases of their predominant orientation along or opposite the magnetic field and that of their predominant orientation transverse to the magnetic field which may be relevant for, e.g., liquid crystals. Besides we treat in details the model case of the cone axis directed along the magnetic field. The latter provides direct comparison of the limiting case of our formulas with the textbook formulas for free isotropic rotational diffusion. The dependence of the spin-lattice relaxation rate on the cone half-width yields results similar to those predicted by the model-free approach.
Construction and analysis of lattice Boltzmann methods applied to a 1D convection-diffusion equation
International Nuclear Information System (INIS)
Dellacherie, Stephane
2014-01-01
To solve the 1D (linear) convection-diffusion equation, we construct and we analyze two LBM schemes built on the D1Q2 lattice. We obtain these LBM schemes by showing that the 1D convection-diffusion equation is the fluid limit of a discrete velocity kinetic system. Then, we show in the periodic case that these LBM schemes are equivalent to a finite difference type scheme named LFCCDF scheme. This allows us, firstly, to prove the convergence in L∞ of these schemes, and to obtain discrete maximum principles for any time step in the case of the 1D diffusion equation with different boundary conditions. Secondly, this allows us to obtain most of these results for the Du Fort-Frankel scheme for a particular choice of the first iterate. We also underline that these LBM schemes can be applied to the (linear) advection equation and we obtain a stability result in L∞ under a classical CFL condition. Moreover, by proposing a probabilistic interpretation of these LBM schemes, we also obtain Monte-Carlo algorithms which approach the 1D (linear) diffusion equation. At last, we present numerical applications justifying these results. (authors)
Helmers, Michael; Herrmann, Michael
2018-03-01
We consider a lattice regularization for an ill-posed diffusion equation with a trilinear constitutive law and study the dynamics of phase interfaces in the parabolic scaling limit. Our main result guarantees for a certain class of single-interface initial data that the lattice solutions satisfy asymptotically a free boundary problem with a hysteretic Stefan condition. The key challenge in the proof is to control the microscopic fluctuations that are inevitably produced by the backward diffusion when a particle passes the spinodal region.
Control of spatio-temporal on-off intermittency in random driving diffusively coupled map lattices
International Nuclear Information System (INIS)
Ziabakhsh Deilami, M.; Rahmani Cherati, Z.; Jahed Motlagh, M.R.
2009-01-01
In this paper, we propose feedback methods for controlling spatio-temporal on-off intermittency which is an aperiodic switching between an 'off' state and an 'on' state. Diffusively coupled map lattice with spatially non-uniform random driving is used for showing spatio-temporal on-off intermittency. For this purpose, we apply three different feedbacks. First, we use a linear feedback which is a simple method but has a long transient time. To overcome this problem, two nonlinear feedbacks based on prediction strategy are proposed. An important advantage of the methods is that the feedback signal is vanished when control is realized. Simulation results show that all methods have suppressed the chaotic behavior.
EXPANDA-75: one-dimensional diffusion code for multi-region plate lattice heterogeneous system
International Nuclear Information System (INIS)
Kikuchi, Yasuyuki; Katsuragi, Satoru; Suzuki, Tomoo; Ogitsu, Makoto.
1975-08-01
An advanced treatment has been developed for analyzing a multi-region plate lattice heterogeneous system using the coarse group constants set provided for a homogeneous system. The essential points of this treatment are modification of effective admixture cross sections and improvement of effective elastic removal cross sections. By this treatment the heterogeneity effects for flux distributions and effective cross sections in the unit cell can be reproduced accurately in comparison with the ultra fine group treatment which consumes huge amounts of computing time. Based on the present treatment and using the JAERI-Fast set, a one-dimensional diffusion code, EXPANDA-75, was developed for extensive use for analyses of fast critical experiments. The user's guide is also presented in this report. (auth.)
International Nuclear Information System (INIS)
Furman, G.B.; Panich, A.M.; Goren, S.D.
1998-01-01
The phenomena of spin diffusion and spin lattice relaxation of nuclear dipolar order in solids containing paramagnetic impurities (PI) is considered. We show that at the beginning of the relaxation process the diffusion vanishing regime realizes with non-exponential time dependence, R(t) ∼ exp [- (t/T 1d ) α ], where T 1d ∼ C p -1/α , C p is PI's concentration. For a homogeneous distribution of Pis and nuclear spins, α=Q/6, where Q is the sample dimensionality; for an inhomogeneous distribution, the sample is divided into q-dimensional subsystems, each containing one PI, yield- ing α= (Q + q) /6. This result coincides with experimental data for CaF 2 doped with 0.8 - 10 -3 ωt % of Mn 2+ , where the non-exponential decay of the dipolar signal with α= 0.83 has been observed [3]. Fitting the experimental data yields a good agreement with T 1d = 66 ms . For another independent check of the obtained results we use dependence of the relaxation time on impurities concentration. In accordance that 1/α=1.2 , we have T 1d ∼ C p -1 '. 2 . Exactly this dependence on impurity concentration of the relaxation time has been found in the experiment. Then the relaxation regime starts as a non-exponential time dependent, proceed asymptotically to an to an exponential function of time, to so called diffusion limited relaxation regime with relaxation time T 1d D is inversely depends on impurities concentration. This kind of relaxation behavior of the dipolar order takes place in the experiment [2]. Using experimental results [2] from this two regime we can estimate the diffusion coefficient of the nuclear dipolar order in CaF 2 , which gives for typical values of impurity concentration C p ∼ 10 18 cm 3 the diffusion coefficient of dipolar order in the interval D ∼ 10 -11 -i- 10 -12 cm 2 /sec which is coincide to the case of Zeeman energy spin diffusion
Radiocrystallographic study of titanites from Xerem, Rio de Janeiro
International Nuclear Information System (INIS)
Baptista, A.; Baptista, N.R.
1987-01-01
The conclusions of the radiocrystallographic studies in titanite crystals - CaTi[SiO 4 ] (0,0H,F) from two rocks with different petrogenesis, from Xerem, Rio de Janeiro State are described. The rocks was granite and nepheline-gneiss and the Spetrochemical analysis showed different compositions to crystals from each one of the rocks. This different composition was eough to development of comparative study using optical determination and petrographic analysis. (C.D.G.) [pt
Prowatke, S.; Klemme, S.
2003-04-01
The aim of this study is to systematically investigate the influence of melt composition on the partitioning of trace elements between titanite and different silicate melts. Titanite was chosen because of its important role as an accessory mineral, particularly with regard to intermediate to silicic alkaline and calc-alkaline magmas [e.g. 1] and of its relative constant mineral composition over a wide range of bulk compositions. Experiments at atmospheric pressure were performed at temperatures between 1150°C and 1050°C. Bulk compositions were chosen to represent a basaltic andesite (SH3 - 53% SiO2), a dacite (SH2 - 65 SiO2) and a rhyolite (SH1 - 71% SiO2). Furthermore, two additional experimental series were conducted to investigate the effect of Al-Na and the Na-K ratio of melts on partitioning. Starting materials consisted of glasses that were doped with 23 trace elements including some selected rare earth elements (La, Ce, Pr, Sm, Gd, Lu), high field strength elements (Zr, Hf, Nb, Ta) and large ion lithophile elements (Cs, Rb, Ba) and Th and U. The experimental run products were analysed for trace elements using secondary ion mass spectrometry at Heidelberg University. Preliminary results indicate a strong effect of melt composition on trace element partition coefficients. Partition coefficients for rare-earth elements uniformly show a convex-upward shape [2, 3], since titanite accommodates the middle rare-earth elements more readily than the light rare-earth elements or the heavy rare-earth elements. Partition coefficients for the rare-earth elements follow a parabolic trend when plotted against ionic radius. The shape of the parabola is very similar for all studied bulk compositions, the position of the parabola, however, is strongly dependent on bulk composition. For example, isothermal rare-earth element partition coefficients (such as La) are incompatible (D>1) in alkali-poor melt compositions. From our experimental data we present an model that combines
International Nuclear Information System (INIS)
Kara, Abdelkader; Yildirim, Handan; Rahman, Talat S; Trushin, Oleg
2009-01-01
We report developments of the kinetic Monte Carlo (KMC) method with improved accuracy and increased versatility for the description of atomic diffusivity on metal surfaces. The on-lattice constraint built into our recently proposed self-learning KMC (SLKMC) (Trushin et al 2005 Phys. Rev. B 72 115401) is released, leaving atoms free to occupy 'off-lattice' positions to accommodate several processes responsible for small-cluster diffusion, periphery atom motion and heteroepitaxial growth. This technique combines the ideas embedded in the SLKMC method with a new pattern-recognition scheme fitted to an off-lattice model in which relative atomic positions are used to characterize and store configurations. Application of a combination of the 'drag' and the repulsive bias potential (RBP) methods for saddle point searches allows the treatment of concerted cluster, and multiple- and single-atom, motions on an equal footing. This tandem approach has helped reveal several new atomic mechanisms which contribute to cluster migration. We present applications of this off-lattice SLKMC to the diffusion of 2D islands of Cu (containing 2-30 atoms) on Cu and Ag(111), using the interatomic potential from the embedded-atom method. For the hetero-system Cu/Ag(111), this technique has uncovered mechanisms involving concerted motions such as shear, breathing and commensurate-incommensurate occupancies. Although the technique introduces complexities in storage and retrieval, it does not introduce noticeable extra computational cost.
The off-center effect on the diffusion coefficient of Cu+ and Li+ in the KCl lattice
International Nuclear Information System (INIS)
Despa, F.
1994-07-01
It is well known that the diffusion coefficients of the Cu + cation in the NaCl and KCl lattices exceeds by three or four orders of magnitude the corresponding self-diffusion coefficients in the intrinsic temperature regions. This fast diffusion of the Cu + has been explained in many papers as an interstitial diffusion although the optical spectra do not confirm the existence of interstitial Cu + . In this paper we propose a new mechanism for fast diffusion. The model assumes that the equilibrium positions of the cationic impurities are noncentral and that the diffusion proceeds by hopping across the potential barrier along the nonlinear paths with the highest probability. The main result shows that the off-center position enhances considerably the diffusion. Theoretical diffusion coefficients have been obtained by modelling the potential barrier. Changes of the configuration entropy and the vibration spectra due to the presence of the noncentral impurity have been included in the model. We proceeded in the Li + cation case as in the case of Cu + cation. We emphasize the good agreement of the model with the experimental data and we show that if the impurity is placed close to the central site the due diffusion coefficient is close to that for the cationic self-diffusion. (author). 37 refs, 6 figs, 3 tabs
Theory of the diffusion coefficient of neutrons in a lattice containing cavities
International Nuclear Information System (INIS)
Benoist, P.
1964-01-01
In an previous publication, a simple and general formulation of the diffusion coefficient, which defines the mode of weighting of the mean free paths of the various media, in introducing the collision probabilities in each medium, was established. This expression is demonstrated again here through a more direct method, and the velocity is introduced; new terms are emphasised, the existence of which implies that the representation of the diffusion area as the mean square of the straight line distance from source to absorption is not correct in a lattice. However these terms are of small enough an order of magnitude to he treated as a correction. The general expression also shows the existence, for the radial coefficient, of the series of angular correlation terms, which is seen to converge very slowly for large channels. The term by term computation which was initiated in the first work was then interrupted and a global formulation, which emphasize a resemblance with the problem of the thermal utilisation factor, was adopted. An integral method, analogous to that use for the computation of this factor, gives the possibility to establish new and simple practical formulae, which require the use of a few basic functions only. These formulae are very accurate, as seen from the results of a variational method which was studied as a reference. Various correction effects are reviewed. Expressions which allow the exact treatment of fuel rod clusters are presented. The theory is confronted with various experimental results, and a new method of measuring the radial coefficient is proposed. (author) [fr
Yan, Zhifeng; Yang, Xiaofan; Li, Siliang; Hilpert, Markus
2017-11-01
The lattice Boltzmann method (LBM) based on single-relaxation-time (SRT) or multiple-relaxation-time (MRT) collision operators is widely used in simulating flow and transport phenomena. The LBM based on two-relaxation-time (TRT) collision operators possesses strengths from the SRT and MRT LBMs, such as its simple implementation and good numerical stability, although tedious mathematical derivations and presentations of the TRT LBM hinder its application to a broad range of flow and transport phenomena. This paper describes the TRT LBM clearly and provides a pseudocode for easy implementation. Various transport phenomena were simulated using the TRT LBM to illustrate its applications in subsurface environments. These phenomena include advection-diffusion in uniform flow, Taylor dispersion in a pipe, solute transport in a packed column, reactive transport in uniform flow, and bacterial chemotaxis in porous media. The TRT LBM demonstrated good numerical performance in terms of accuracy and stability in predicting these transport phenomena. Therefore, the TRT LBM is a powerful tool to simulate various geophysical and biogeochemical processes in subsurface environments.
Energy Technology Data Exchange (ETDEWEB)
Zhaoyuan Liu; Kord Smith; Benoit Forget; Javier Ortensi
2016-05-01
A new method for computing homogenized assembly neutron transport cross sections and dif- fusion coefficients that is both rigorous and computationally efficient is proposed in this paper. In the limit of a homogeneous hydrogen slab, the new method is equivalent to the long-used, and only-recently-published CASMO transport method. The rigorous method is used to demonstrate the sources of inaccuracy in the commonly applied “out-scatter” transport correction. It is also demonstrated that the newly developed method is directly applicable to lattice calculations per- formed by Monte Carlo and is capable of computing rigorous homogenized transport cross sections for arbitrarily heterogeneous lattices. Comparisons of several common transport cross section ap- proximations are presented for a simple problem of infinite medium hydrogen. The new method has also been applied in computing 2-group diffusion data for an actual PWR lattice from BEAVRS benchmark.
International Nuclear Information System (INIS)
Buckler, A.N.
1978-10-01
The report describes the theoretical basis of the methods that have been developed for correlating measurements of spatially distributed quantities taken on the reactor with the lattice constants in the diffusion equations. The method can be used with any thermal reactor system of current interest, but the first application is to provide a replacement for the SAMSON code for Winfrith SGHW studies, where the measurements of interest are channel powers. (author)
Czech Academy of Sciences Publication Activity Database
Tarasenko, Alexander
2018-01-01
Roč. 95, Jan (2018), s. 37-40 ISSN 1386-9477 R&D Projects: GA MŠk LO1409; GA MŠk LM2015088 Institutional support: RVO:68378271 Keywords : lattice gas systems * kinetic Monte Carlo simulations * diffusion and migration 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: 2.221, year: 2016
Magmatic Longevity Constrained by ID-TIMS U-Pb Dating of Zircon and Titanite
Szymanowski, D.; Wotzlaw, J. F.; Ellis, B. S.; Bachmann, O.; Von Quadt, A.
2016-12-01
Clues about the timescales and thermal conditions associated with the growth and evacuation of large silicic magma reservoirs are frequently drawn from radiometric dating, diffusion modelling, or thermomechanical modelling. A growing amount of petrological and geochronological evidence, supported by thermal modelling, suggests that many silicic magma reservoirs may exist for some 104-106 years in the form of high-crystallinity mushes at relatively low temperatures ( 700-750°C; [1-3]). Geochronological studies addressing this issue typically utilise the U-Pb system in zircon capable of recording extended periods of crystallisation, particularly in evolved calc-alkaline systems that spend most of their lifetime zircon-saturated. In this study, we integrate U-Pb dating of zircon and titanite to investigate the longevity of the magma reservoir that produced the Kneeling Nun Tuff, a 35 Ma, >900 km3 crystal-rich rhyolitic super-eruption from the Mogollon-Datil volcanic field in New Mexico (USA). High-precision ID-TIMS U-Pb dates of single crystals of both zircon and titanite independently record a continuous crystallisation history over >400,000 years. We combine the dating of both accessory phases with textural, major, trace element and isotopic studies of single crystals, placing tight constraints on the thermal conditions of magma accumulation and storage while recording differentiation and rejuvenation processes within the magma reservoir. The results suggest a protracted `cool' upper-crustal storage of magma prior to the Kneeling Nun Tuff eruption followed by a melting event which reduced the magma crystallinity and conditioned it for eruption. [1] Bachmann & Bergantz (2004), J. Petrol. 45, 1565-1582. [2] Gelman et al. (2013), Geology 41, 759-762. [3] Cooper & Kent (2014), Nature 506, 480-483.
Geochemical and Sm–Nd isotopic study of titanite from granitoid ...
Indian Academy of Sciences (India)
in granitic magmas that have equilibrated with titanite during fractional crystallization or partial melting ... Titanite; Kolar; Ramagiri; Dharwar craton; rare earth elements; Sm–Nd isotope dating. J. Earth Syst. Sci. 120, No. 2, April 2011, pp. 237–251 c Indian Academy of Sciences ... be altered by variations in temperature and/or.
Energy Technology Data Exchange (ETDEWEB)
Ellery, Adam J.; Simpson, Matthew J. [School of Mathematical Sciences, Queensland University of Technology (QUT), Brisbane (Australia); Baker, Ruth E. [Mathematical Institute, University of Oxford, Radcliffe Observatory Quarter, Woodstock Road, Oxford (United Kingdom)
2016-05-07
The motion of cells and molecules through biological environments is often hindered by the presence of other cells and molecules. A common approach to modeling this kind of hindered transport is to examine the mean squared displacement (MSD) of a motile tracer particle in a lattice-based stochastic random walk in which some lattice sites are occupied by obstacles. Unfortunately, stochastic models can be computationally expensive to analyze because we must average over a large ensemble of identically prepared realizations to obtain meaningful results. To overcome this limitation we describe an exact method for analyzing a lattice-based model of the motion of an agent moving through a crowded environment. Using our approach we calculate the exact MSD of the motile agent. Our analysis confirms the existence of a transition period where, at first, the MSD does not follow a power law with time. However, after a sufficiently long period of time, the MSD increases in proportion to time. This latter phase corresponds to Fickian diffusion with a reduced diffusivity owing to the presence of the obstacles. Our main result is to provide a mathematically motivated, reproducible, and objective estimate of the amount of time required for the transport to become Fickian. Our new method to calculate this crossover time does not rely on stochastic simulations.
International Nuclear Information System (INIS)
Ellery, Adam J.; Simpson, Matthew J.; Baker, Ruth E.
2016-01-01
The motion of cells and molecules through biological environments is often hindered by the presence of other cells and molecules. A common approach to modeling this kind of hindered transport is to examine the mean squared displacement (MSD) of a motile tracer particle in a lattice-based stochastic random walk in which some lattice sites are occupied by obstacles. Unfortunately, stochastic models can be computationally expensive to analyze because we must average over a large ensemble of identically prepared realizations to obtain meaningful results. To overcome this limitation we describe an exact method for analyzing a lattice-based model of the motion of an agent moving through a crowded environment. Using our approach we calculate the exact MSD of the motile agent. Our analysis confirms the existence of a transition period where, at first, the MSD does not follow a power law with time. However, after a sufficiently long period of time, the MSD increases in proportion to time. This latter phase corresponds to Fickian diffusion with a reduced diffusivity owing to the presence of the obstacles. Our main result is to provide a mathematically motivated, reproducible, and objective estimate of the amount of time required for the transport to become Fickian. Our new method to calculate this crossover time does not rely on stochastic simulations.
Guenthner, William R.; Reiners, Peter W.; Drake, Henrik; Tillberg, Mikael
2017-07-01
Craton cores far from plate boundaries have traditionally been viewed as stable features that experience minimal vertical motion over 100-1000 Ma time scales. Here we show that the Fennoscandian Shield in southeastern Sweden experienced several episodes of burial and exhumation from 1800 Ma to the present. Apatite, titanite, and zircon (U-Th)/He ages from surface samples and drill cores constrain the long-term, low-temperature history of the Laxemar region. Single grain titanite and zircon (U-Th)/He ages are negatively correlated (104-838 Ma for zircon and 160-945 Ma for titanite) with effective uranium (eU = U + 0.235 × Th), a measurement proportional to radiation damage. Apatite ages are 102-258 Ma and are positively correlated with eU. These correlations are interpreted with damage-diffusivity models, and the modeled zircon He age-eU correlations constrain multiple episodes of heating and cooling from 1800 Ma to the present, which we interpret in the context of foreland basin systems related to the Neoproterozoic Sveconorwegian and Paleozoic Caledonian orogens. Inverse time-temperature models constrain an average burial temperature of 217°C during the Sveconorwegian, achieved between 944 Ma and 851 Ma, and 154°C during the Caledonian, achieved between 366 Ma and 224 Ma. Subsequent cooling to near-surface temperatures in both cases could be related to long-term exhumation caused by either postorogenic collapse or mantle dynamics related to the final assembly of Rodinia and Pangaea. Our titanite He age-eU correlations cannot currently be interpreted in the same fashion; however, this study represents one of the first examples of a damage-diffusivity relationship in this system, which deserves further research attention.
Energy Technology Data Exchange (ETDEWEB)
Ryu, Seungyeob, E-mail: syryu@kaeri.re.kr [Korea Atomic Energy Research Institute (KAERI), 1045 Daeduk-daero, Yuseong-gu, Daejeon 305-353 (Korea, Republic of); Kim, Youngin; Yoon, Juhyeon [Korea Atomic Energy Research Institute (KAERI), 1045 Daeduk-daero, Yuseong-gu, Daejeon 305-353 (Korea, Republic of); Ko, Sungho, E-mail: sunghoko@cnu.ac.kr [Department of Mechanical Design Engineering, Chungnam National University, 220 Gung-dong, Yuseong-gu, Daejeon 305-764 (Korea, Republic of)
2014-01-15
Highlights: • We directly simulate circular-cap bubbles in low viscous liquids. • The counter diffusion multiphase lattice Boltzmann method is proposed. • The present method is validated through benchmark tests and experimental results. • The high-Reynolds-number bubbles can be simulated without any turbulence models. • The present method is feasible for the direct simulation of bubbly flows. -- Abstract: The counter diffusion lattice Boltzmann method (LBM) is used to directly simulate rising circular-cap bubbles in low viscous liquids. A counter diffusion model for single phase flows has been extended to multiphase flows, and the implicit formulation is converted into an explicit one for easy calculation. Bubbles at high Reynolds numbers ranging from O(10{sup 2}) to O(10{sup 4}) are simulated successfully without any turbulence models, which cannot be done for the existing LBM versions. The characteristics of the circular-cap bubbles are studied for a wide range of Morton numbers and compared with the previous literature. Calculated results agree with the theoretical and experimental data. Consequently, the wake phenomena of circular-cap bubbles and bubble induced turbulence are presented.
International Nuclear Information System (INIS)
Lee, K.R.
1992-01-01
This paper reports that when a 90Mo-10Ni alloy (by wt) liquid phase sintered at 1400 degrees C is heat-treated at 1400 degrees C after replacing the matrix with a melt of 44Ni-34Mo-22W (by wt), the liquid films between the grains migrate, leaving behind an Mo alloy enriched with W. The ratio of the lattice diffusivity of W in Mo, D, to the initial migration velocity, v. (D/v) is estimated to be between 0.03 and 0.18 angstrom. Hence it appears that there is no lattice diffusion of W ahead of the migrating liquid film, and is such a case the driving force has been suggested to be the chemical free energy. But the observed v is approximately same as that to be expected if the driving force is assumed to be diffusional coherency strain energy. Likewise, a previous study of den Broeder and Nakahara shows that the rate of chemically-induced grain boundary migration in Cu-Ni shows a smooth variation with temperature as D/v decreases from values much larger than the interatomic spacing to values much smaller with decreasing temperature. The coherency strain energy thus appears to be a general driving force for the migration even when the apparent diffusion length indicated by D/v is smaller than the interatomic spacing
An exact and efficient first passage time algorithm for reaction–diffusion processes on a 2D-lattice
International Nuclear Information System (INIS)
Bezzola, Andri; Bales, Benjamin B.; Alkire, Richard C.; Petzold, Linda R.
2014-01-01
We present an exact and efficient algorithm for reaction–diffusion–nucleation processes on a 2D-lattice. The algorithm makes use of first passage time (FPT) to replace the computationally intensive simulation of diffusion hops in KMC by larger jumps when particles are far away from step-edges or other particles. Our approach computes exact probability distributions of jump times and target locations in a closed-form formula, based on the eigenvectors and eigenvalues of the corresponding 1D transition matrix, maintaining atomic-scale resolution of resulting shapes of deposit islands. We have applied our method to three different test cases of electrodeposition: pure diffusional aggregation for large ranges of diffusivity rates and for simulation domain sizes of up to 4096×4096 sites, the effect of diffusivity on island shapes and sizes in combination with a KMC edge diffusion, and the calculation of an exclusion zone in front of a step-edge, confirming statistical equivalence to standard KMC simulations. The algorithm achieves significant speedup compared to standard KMC for cases where particles diffuse over long distances before nucleating with other particles or being captured by larger islands
An exact and efficient first passage time algorithm for reaction–diffusion processes on a 2D-lattice
Energy Technology Data Exchange (ETDEWEB)
Bezzola, Andri, E-mail: andri.bezzola@gmail.com [Mechanical Engineering Department, University of California, Santa Barbara, CA 93106 (United States); Bales, Benjamin B., E-mail: bbbales2@gmail.com [Mechanical Engineering Department, University of California, Santa Barbara, CA 93106 (United States); Alkire, Richard C., E-mail: r-alkire@uiuc.edu [Department of Chemical Engineering, University of Illinois, Urbana, IL 61801 (United States); Petzold, Linda R., E-mail: petzold@engineering.ucsb.edu [Mechanical Engineering Department and Computer Science Department, University of California, Santa Barbara, CA 93106 (United States)
2014-01-01
We present an exact and efficient algorithm for reaction–diffusion–nucleation processes on a 2D-lattice. The algorithm makes use of first passage time (FPT) to replace the computationally intensive simulation of diffusion hops in KMC by larger jumps when particles are far away from step-edges or other particles. Our approach computes exact probability distributions of jump times and target locations in a closed-form formula, based on the eigenvectors and eigenvalues of the corresponding 1D transition matrix, maintaining atomic-scale resolution of resulting shapes of deposit islands. We have applied our method to three different test cases of electrodeposition: pure diffusional aggregation for large ranges of diffusivity rates and for simulation domain sizes of up to 4096×4096 sites, the effect of diffusivity on island shapes and sizes in combination with a KMC edge diffusion, and the calculation of an exclusion zone in front of a step-edge, confirming statistical equivalence to standard KMC simulations. The algorithm achieves significant speedup compared to standard KMC for cases where particles diffuse over long distances before nucleating with other particles or being captured by larger islands.
Energy Technology Data Exchange (ETDEWEB)
Ryu, Seungyeob, E-mail: syryu@kaeri.re.kr [Korea Atomic Energy Research Institute (KAERI), 1045 Daeduk-daero, Yuseong-gu, Daejeon 305-353 (Korea, Republic of); Kim, Youngin; Kang, Hanok; Kim, Keung Koo [Korea Atomic Energy Research Institute (KAERI), 1045 Daeduk-daero, Yuseong-gu, Daejeon 305-353 (Korea, Republic of); Ko, Sungho, E-mail: sunghoko@cnu.ac.kr [Department of Mechanical Design Engineering, Chungnam National University, 220 Gung-dong, Yuseong-gu, Daejeon 305-764 (Korea, Republic of)
2016-08-15
Highlights: • We directly simulate intermediate-sized bubbles in low viscous liquids. • The path instability and shape oscillation can be successfully simulated. • The motion of a pair bubble and bubble swarm is presented. • Bubbles with high-Reynolds-number can be simulated with under-resolved grids. • The counter diffusion multiphase method is feasible for the direct simulation of bubbly flows. - Abstract: The counter diffusion lattice Boltzmann method (LBM) is used to simulate intermediate-sized bubbles in low viscous liquids. Bubbles at high Reynolds numbers ranging from hundreds to thousands are simulated successfully, which cannot be done for the existing LBM versions. The characteristics of the path instability of two rising bubbles are studied for a wide range of Eotvos and Morton numbers. Finally, the study presented how bubble swarms move within the flow and how the flow surrounding the bubbles is affected by the bubble motions.
Hu, Hao; Li, Jian-Wei; McFarlane, Christopher R. M.
2017-09-01
Uranium-lead isotopes and trace elements of titanite from the Chengchao iron skarn deposit (Daye district, Eastern China), located along the contact zones between Triassic marine carbonates and an early Cretaceous intrusive complex consisting of granite and quartz diorite, were analyzed using laser ablation inductively coupled plasma mass spectrometry to provide temporal constraints on iron mineralization and to evaluate its potential as a reference material for titanite U-Pb geochronology. Titanite grains from mineralized endoskarn have simple growth zoning patterns, exhibit intergrowth with magnetite, diopside, K-feldspar, albite and actinolite, and typically contain abundant primary two-phase fluid inclusions. These paragenetic and textural features suggest that these titanite grains are of hydrothermal origin. Hydrothermal titanite is distinct from the magmatic variety from the ore-related granitic intrusion in that it contains unusually high concentrations of U (up to 2995 ppm), low levels of Th (12.5-453 ppm), and virtually no common Pb. The REE concentrations are much lower, as are the Th/U and Lu/Hf ratios. The hydrothermal titanite grains yield reproducible uncorrected U-Pb ages ranging from 129.7 ± 0.7 to 132.1 ± 2.7 Ma (2σ), with a weighted mean of 131.2 ± 0.2 Ma [mean standard weighted deviation (MSWD) = 1.7] that is interpreted as the timing of iron skarn mineralization. This age closely corresponds to the zircon U-Pb age of 130.9 ± 0.7 Ma (MSWD = 0.7) determined for the quartz diorite, and the U-Pb ages for zircon and titanite (130.1 ± 1.0 Ma and 131.3 ± 0.3 Ma) in the granite, confirming a close temporal and likely genetic relationship between granitic magmatism and iron mineralization. Different hydrothermal titanite grains have virtually identical uncorrected U-Pb ratios suggestive of negligible common Pb in the mineral. The homogeneous textures and U-Pb characteristics of Chengchao hydrothermal titanite suggest that the mineral might be a
Diffusion Mechanisms and Lattice Locations of Thermal-Equilibrium Defects in Si-Ge Alloys
Lyutovich, K; Touboltsev, V; Laitinen, P O; Strohm, A
2002-01-01
It is generally accepted that Ge and Si differ considerably with respect to intrinsic-point-defect-mediated diffusion. In Ge, the native point defects dominating under thermal-equilibium conditions at all solid-state temperatures accessible in diffusion experiments are vacancies, and therefore Ge self-diffusion is vacancy-controlled. In Si, by contrast, self-interstitials and vacancies co-exist in thermal equilibrium. Whereas in the most thoroughly investigated temperature regime above about 1000$^\\circ$C Si self-diffusion is self-interstitial-controlled, it is vacancy-controlled at lower temperatures. According to the scenario displayed above, self-diffusion in Si-Ge alloys is expected to change from an interstitialcy mechanism on the Si side to a vacancy mechanism on the Ge side. Therefore, $^{71}$Ge self-diffusion experiments in Si$_{1- \\it y}$Ge$_{\\it y}$ as a function of composition Y are highly interesting. In a first series of experiments the diffusion of Ge in 0.4 to 10 $\\mu$m thick, relaxed, low-disl...
The effects of radiation damage accumulation and annealing on fission-track dating of titanite
International Nuclear Information System (INIS)
Enkelmann, Eva; Jonckheere, Raymond; Ratschbacher, Lothar
2005-01-01
Fission-track dating of titanite is hindered by the fact that track etching is anisotropic in fresh titanites and becomes isotropic with increasing radiation damage. Independent age determinations with the population method are problematic due to different track counting efficiencies (Q) for ρ s in unannealed and ρ i in annealed titanite. Independent age determinations with the external detector method depend on correction factors for the track registration geometries (G = 0.5), counting efficiencies (Q) and range deficit (R = 1.38); however, Q is unaffected by annealing. It was attempted to determine GQR through calculation, direct experiment and on the basis of age standards. The direct experiment involves measurements of the ratio of the induced-track densities in titanite and a co-irradiated external detector. The track densities in the internal titanite surfaces could not be measured but the results for the external surfaces confirm that this approach leads to a significant overestimation of GQR, due to prior annealing. The GQR-values determined on the basis of age standards are consistent with that obtained by calculation assuming that Q ∼ 1, although there is no experimental confirmation for this fact apart from their isotropic etching characteristics. The fact that identical GQR-factors were obtained on standards of different age and uranium content suggests that a single GQR-value is appropriate for dating titanites within a broad range of radiation damage. In terms of the ζ-calibration this implies that a single ζ-factor is also suitable for dating different titanites. These findings suggest that other factors besides the accumulation of alpha-recoil damage, such as a phase transition, could be co-responsible for the different etching characteristics of annealed and unannealed titanites
Neutron Diffusion in a Space Lattice of Fissionable and Absorbing Materials
Feynman, R. P.; Welton, T. A.
1946-08-27
Methods are developed for estimating the effect on a critical assembly of fabricating it as a lattice rather than in the more simply interpreted homogeneous manner. An idealized case is discussed supposing an infinite medium in which fission, elastic scattering and absorption can occur, neutrons of only one velocity present, and the neutron m.f.p. independent of position and equal to unity with the unit of length used.
International Nuclear Information System (INIS)
Deniz, V.C.
1980-01-01
The problem concerned with the correct definition of the homogenized diffusion coefficient of a lattice, and the concurrent problem of whether or not a homogenized diffusion equation can be formally set up, is studied by a space-energy-angle dependent treatment for a general lattice cell using an operator notation which applies to any eigen-problem. A new definition of the diffusion coefficient is given, which combines within itself the individual merits of the two definitions of Benoist. The relation between the new coefficient and the ''uncorrected'' Benoist coefficient is discussed by considering continuous-spectrum and multi-group diffusion equations. Other definitions existing in the literature are briefly discussed. It is concluded that a diffusion coefficient should represent only leakage effects. A comparison is made between the homogenization approach and the approach via eigen-coefficients, and brief indications are given of a possible scheme for the latter. (author)
Properties and recrystallization of radiation damaged pyrochlore and titanite
Energy Technology Data Exchange (ETDEWEB)
Zietlow, Peter
2016-11-02
initial state an amorphous x-ray diffraction pattern superimposed by weak Bragg-maxima that indicates the existence of ordered regions in a damaged matrix. Unlike the other studied pyrochlores, Raman spectra of the Blue River sample show the appearance of local modes above 560 K between 700 and 800 cm{sup -1} resulting from its high content of U and Ta impurities. DSC measurements confirmed the observed structural recovery upon annealing. While the annealing-induced ordering of Panda Hill begins at a lower temperature (ca. 500 K) the recovery of the highly-damaged pyrochlore from Miass occurs at 800 K. The Blue-River pyrochlore shows a multi-step recovery which is similarly seen by XRD. Thermogravimetry showed a continuous mass loss on heating for all radiation-damaged pyrochlores (Panda Hill ca. 1%, Blue River ca. 1.5%, Miass ca. 2.9%). In order to elucidate local phenomena by NMR spectroscopy, a simpler structure of a metamict mineral such as titanite has been chosen. Hence, metamict titanite from Cardiff uranium mine (M28696) in Ontario, Canada, has been analysed using {sup 29}Si magic angle spinning nuclear magnetic resonance spectroscopy (MAS NMR) (Zietlow et al., 2014). A broad Gaussian shaped NMR signal at -81 ppm occurs at room temperature resulting from the mainly short range ordered metamict structural state. NMR signals were obtained at room temperature and after annealing at 600, 950, 1220 and 1470 K. Because of increasing crystallinity the full width at half maximum (FWHM) decreased from 24 ppm to 20 ppm respectively using a Pseudo-Voigt fit. For comparison well crystalline titanite from Rauris showed an NMR signal at -79.3 ppm with FWHM of 4.1 ppm and an almost Lorentzian profile because of its good long range order. Integrating synchrotron X-ray diffraction (XRD) signals of Cardiff titanite show an increase of the long range order at annealing temperatures considerably lower than the short range ordering seen by NMR.
Effect of lattice mismatch-induced strains on coupled diffusive and displacive phase transformations
Bouville, Mathieu; Ahluwalia, Rajeev
2006-01-01
Materials which can undergo slow diffusive transformations as well as fast displacive transformations are studied using the phase-field method. The model captures the essential features of the time-temperature-transformation (TTT) diagrams, continuous cooling transformation (CCT) diagrams, and microstructure formation of these alloys. In some materials systems there can exist an intrinsic volume change associated with these transformations. We show that these coherency strains can stabilize m...
International Nuclear Information System (INIS)
Deniz, V.C.
1978-01-01
The problem concerned with the correct definition of the homogenized diffusion coefficient of a lattice, and the concurrent problem of whether or not a homogenized diffusion equation can be formally set up, is studied by a space-energy angle dependent treatment for a general lattice cell; using an operator notation which applies to any eigen-problem. It is shown that the diffusion coefficient should represent only leakage effects. A new definition of the diffusion coefficient is given, which combines within itself the individual merits of each of the two definitions of Benoist, and reduces to the 'uncorrected' Benoist coefficient in certain cases. The conditions under which a homogenized diffusion equation can be obtained are discussed. A compatison is made between the approach via a diffusion equation and the approach via the eigen-coefficients of Deniz. Previously defined diffusion coefficients are discussed, and it is shown that the transformed eigen-coefficients proposed by Gelbard and by Larsen are unsuitable as diffusion coefficients, and that the cell-edge normalization of the Bonalumi coefficient is not physically justifiable. (author)
International Nuclear Information System (INIS)
Tournarie, Max
1959-01-01
The total diffusing power for a crystallite of any form containing a centrosymmetric defect has been established. The antisymmetrical part of the deformation potential only contributes very slightly to the primary dissymmetry. We then go on to study the case of a group of defects of the same type. The calculation converges sufficiently to describe the thermal agitation of an infinite crystal. Reprint of a paper published in 'Comptes Rendus des Seances de l'Academie des Sciences', t. 248, p. 2103-2105, sitting of April 6, 1959 [fr
Thermal diffusivity and butterfly velocity in anisotropic Q-lattice models
Jeong, Hyun-Sik; Ahn, Yongjun; Ahn, Dujin; Niu, Chao; Li, Wei-Jia; Kim, Keun-Young
2018-01-01
We study a relation between the thermal diffusivity ( D T ) and two quantum chaotic properties, Lyapunov time (τ L ) and butterfly velocity ( v B ) in strongly correlated systems by using a holographic method. Recently, it was shown that E_i:={D}_{T,i}/({v}{^{B,i}}^2{τ}_L)(i=x,y) is universal in the sense that it is determined only by some scaling exponents of the IR metric in the low temperature limit regardless of the matter fields and ultraviolet data. Inspired by this observation, by analyzing the anisotropic IR scaling geometry carefully, we find the concrete expressions for E_i in terms of the critical dynamical exponents z i in each direction, E_i={z}_i/2({z}_i-1) . Furthermore, we find the lower bound of E_i is always 1 /2, which is not affected by anisotropy, contrary to the η/s case. However, there may be an upper bound determined by given fixed anisotropy.
International Nuclear Information System (INIS)
Hayward, P.J.; Doern, F.E.; Cecchetto, E.V.; Mitchell, S.L.
1983-01-01
Glass ceramics (i.e., glasses subjected to controlled crystallization) with synthetic titanite as the major crystalline phase are being considered as potential hosts for the radioactive wastes arising from possible future reprocessing of nuclear fuel in Canada. In order to assess the stability of titanite in the anticipated environment of a disposal vault sited 500-1000 m deep within a granitic pluton in the Canadian Shield, leaching experiments have been performed with natural and synthetic titanite, using a synthetic groundwater whose composition is based on findings from a recent borehole-survey. The results are in qualitative agreement with calculations of solution equilibria for titanite and its main alteration products, and indicate that titanite should be stable and suffer no net leaching under anticipated conditions in the vault
Energy Technology Data Exchange (ETDEWEB)
Hao, Liang; Cheng, Ping [Ministry of Education Key Laboratory of Power Machinery and Engineering, School of Mechanical Engineering, Shanghai Jiaotong University, DongChuan Road 800, Shanghai 200240 (China)
2010-06-15
The effect of wettability on water transport dynamics in gas diffusion layer (GDL) is investigated by simulating water invasion in an initially gas-filled GDL using the multiphase free-energy lattice Boltzmann method (LBM). The results show that wettability plays a significant role on water saturation distribution in two-phase flow in the uniform wetting GDL. For highly hydrophobicity, the water transport falls in the regime of capillary fingering, while for neutral wettability, water transport exhibits the characteristic of stable displacement, although both processes are capillary force dominated flow with same capillary numbers. In addition, the introduction of hydrophilic paths in the GDL leads the water to flow through the hydrophilic pores preferentially. The resulting water saturation distributions show that the saturation in the GDL has little change after water breaks through the GDL, and further confirm that the selective introduction of hydrophilic passages in the GDL would facilitate the removal of liquid water more effectively, thus alleviating the flooding in catalyst layer (CL) and GDL. The LBM approach presented in this study provides an effective tool to investigate water transport phenomenon in the GDL at pore-scale level with wettability distribution taken into consideration. (author)
Jinuntuya, Fontip; Whiteley, Michael; Chen, Rui; Fly, Ashley
2018-02-01
The Gas Diffusion Layer (GDL) of a Polymer Electrolyte Membrane Fuel Cell (PEMFC) plays a crucial role in overall cell performance. It is responsible for the dissemination of reactant gasses from the gas supply channels to the reactant sites at the Catalyst Layer (CL), and the adequate removal of product water from reactant sites back to the gas channels. Existing research into water transport in GDLs has been simplified to 2D estimations of GDL structures or use virtual stochastic models. This work uses X-ray computed tomography (XCT) to reconstruct three types of GDL in a model. These models are then analysed via Lattice Boltzmann methods to understand the water transport behaviours under differing contact angles and pressure differences. In this study, the three GDL samples were tested over the contact angles of 60°, 80°, 90°, 100°, 120° and 140° under applied pressure differences of 5 kPa, 10 kPa and 15 kPa. By varying the contact angle and pressure difference, it was found that the transition between stable displacement and capillary fingering is not a gradual process. Hydrophilic contact angles in the region of 60°<θ < 90° showed stable displacement properties, whereas contact angles in the region of 100°<θ < 140° displayed capillary fingering characteristics.
Colossal positive magnetoresistance in surface-passivated oxygen-deficient strontium titanite
David, Adrian; Tian, Yufeng; Yang, Ping; Gao, Xingyu; Lin, Weinan; Shah, Amish B.; Zuo, Jian-Min; Prellier, Wilfrid; Wu, Tao
2015-01-01
,000% at a temperature of 2 K and a magnetic field of 9 T) discovered in degenerate semiconducting strontium titanite (SrTiO3) single crystals capped with ultrathin SrTiO3/LaAlO3 bilayers. The low-pressure high-temperature homoepitaxial growth of several unit
Energy Technology Data Exchange (ETDEWEB)
Benoist, P [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1964-01-15
In an previous publication, a simple and general formulation of the diffusion coefficient, which defines the mode of weighting of the mean free paths of the various media, in introducing the collision probabilities in each medium, was established. This expression is demonstrated again here through a more direct method, and the velocity is introduced; new terms are emphasised, the existence of which implies that the representation of the diffusion area as the mean square of the straight line distance from source to absorption is not correct in a lattice. However these terms are of small enough an order of magnitude to he treated as a correction. The general expression also shows the existence, for the radial coefficient, of the series of angular correlation terms, which is seen to converge very slowly for large channels. The term by term computation which was initiated in the first work was then interrupted and a global formulation, which emphasize a resemblance with the problem of the thermal utilisation factor, was adopted. An integral method, analogous to that use for the computation of this factor, gives the possibility to establish new and simple practical formulae, which require the use of a few basic functions only. These formulae are very accurate, as seen from the results of a variational method which was studied as a reference. Various correction effects are reviewed. Expressions which allow the exact treatment of fuel rod clusters are presented. The theory is confronted with various experimental results, and a new method of measuring the radial coefficient is proposed. (author) [French] Dans une publication anterieure, on a etablie une formulation simple et generale du coefficient de diffusion, qui definit le mode de ponderation des libres parcours des differents milieux constituants en faisant apparaitre les probabilites de collision dans chaque milieu. On redemontre ici cette expression d'une maniere plus directe, tout en introduisant la variable
Energy Technology Data Exchange (ETDEWEB)
Benoist, P. [Commissariat a l' Energie Atomique, Saclay (France). Centre d' Etudes Nucleaires
1964-01-15
In an previous publication, a simple and general formulation of the diffusion coefficient, which defines the mode of weighting of the mean free paths of the various media, in introducing the collision probabilities in each medium, was established. This expression is demonstrated again here through a more direct method, and the velocity is introduced; new terms are emphasised, the existence of which implies that the representation of the diffusion area as the mean square of the straight line distance from source to absorption is not correct in a lattice. However these terms are of small enough an order of magnitude to he treated as a correction. The general expression also shows the existence, for the radial coefficient, of the series of angular correlation terms, which is seen to converge very slowly for large channels. The term by term computation which was initiated in the first work was then interrupted and a global formulation, which emphasize a resemblance with the problem of the thermal utilisation factor, was adopted. An integral method, analogous to that use for the computation of this factor, gives the possibility to establish new and simple practical formulae, which require the use of a few basic functions only. These formulae are very accurate, as seen from the results of a variational method which was studied as a reference. Various correction effects are reviewed. Expressions which allow the exact treatment of fuel rod clusters are presented. The theory is confronted with various experimental results, and a new method of measuring the radial coefficient is proposed. (author) [French] Dans une publication anterieure, on a etablie une formulation simple et generale du coefficient de diffusion, qui definit le mode de ponderation des libres parcours des differents milieux constituants en faisant apparaitre les probabilites de collision dans chaque milieu. On redemontre ici cette expression d'une maniere plus directe, tout en introduisant la variable
Growth and Yield Stimulation of Winter Oilseed Rape (Brasssica Napus L. by Mg-Titanit Fertiliser
Directory of Open Access Journals (Sweden)
Kováčik Peter
2014-12-01
Full Text Available The effort to achieve higher yields at the required qualitative level has led to the intensive studying the problems of the rational usage of the titanium containing fertilisers by the agricultural research in the course the previous thirty years. Therefore, the objective of the experiment was to evaluate the impact of two doses of Mg-Titanit (0.2 l/ha and 0.4 l/ha on the formation of the aboveground and underground phytomass, also on the total chlorophyll in leaves, on the titanium and nitrogen content in the seeds and straw, on the quantity and quality of winter rape yield. The doses were applied two or three times on the leaves of winter rape (BBCH 50-52, BBCH 59, BBCH 66-67. The experiment was realized on the Haplic Chernozem (48°42´ N, 17°70´ E - Western Slovakia during two farming years (2009/2010 and 2010/2011. The results showed that all three applications of Mg-Titanit in both doses stimulated the formation of aboveground and underground phytomass of winter rape. The highest growth of phytomass was detected after the second application. The application of Mg-Titanit in the growth phases BBCH 50-52 and BBCH 59 increased the contents of both chlorophylls (a and b, where the growth of chlorophyll b content was more considerable than the growth of chlorophyll a content. The third spraying by Mg-Titanit decreased the content of the total chlorophyll. The application of Mg-Titanit had the positive impact on the yield of seeds, straw and fat content in the winter oilseed rape seeds.
Using titanite petrochronology to monitor CO2-degassing episodes from the Himalayas
Rapa, Giulia; Groppo, Chiara; Rolfo, Franco; Petrelli, Maurizio; Mosca, Pietro
2017-04-01
Metamorphic degassing from active collisional orogens supplies a significant fraction of CO2 to the atmosphere, playing a fundamental role in the long-term (> 1 Ma) global carbon cycle (Gaillardet & Galy, 2008). The petro-chronologic study of the CO2-source rocks (e.g. calc-silicate rocks) in collisional settings is therefore fundamental to understand the nature, timing, duration and magnitude of the orogenic carbon cycle. So far, the incomplete knowledge of these systems hindered a reliable quantitative modelling of metamorphic CO2 fluxes. A detailed petrological modelling of a clinopyroxene + scapolite + K-feldspar + plagioclase + biotite + zoisite ± calcite calc-silicate rock from central Nepal Himalaya allowed us to identify and fully characterize - for the first time - different metamorphic reactions that led to the simultaneous growth of titanite and production of CO2. These reactions involve biotite (rather than rutile) as the Ti-bearing reactant counterpart of titanite. The results of petrological modelling combined with Zr-in-Ttn thermometry and U-Pb geochronology suggest that in the studied sample, most titanite grains grew during two nearly continuous episodes of titanite formation: a near-peak event at 730-740°C, 10 kbar, 25.5±1.5 Ma, and a peak event at 740-765°C, 10.5 kbar, 22±3 Ma. Both episodes of titanite growth are correlated to specific CO2-producing reactions, thus allowing to constrain the timing, duration and P-T conditions of the main CO2-producing events, as well as the amounts of CO2 produced. Assuming that fluids released at a depth of ca. 30 km are able to reach the Earth's surface 10 Ma after their production, it is therefore possible to speculate on the role exerted by the Himalayan orogenesis on the climate in the past. Gaillardet J. & Galy A. (2008): Himalaya-carbon sink or source? Science, 320, 1727-1728.
Ginzburg, Irina
2017-01-01
The effect of the heterogeneity in the soil structure or the nonuniformity of the velocity field on the modeled resident time distribution (RTD) and breakthrough curves is quantified by their moments. While the first moment provides the effective velocity, the second moment is related to the longitudinal dispersion coefficient (kT) in the developed Taylor regime; the third and fourth moments are characterized by their normalized values skewness (Sk) and kurtosis (Ku), respectively. The purpose of this investigation is to examine the role of the truncation corrections of the numerical scheme in kT, Sk, and Ku because of their interference with the second moment, in the form of the numerical dispersion, and in the higher-order moments, by their definition. Our symbolic procedure is based on the recently proposed extended method of moments (EMM). Originally, the EMM restores any-order physical moments of the RTD or averaged distributions assuming that the solute concentration obeys the advection-diffusion equation in multidimensional steady-state velocity field, in streamwise-periodic heterogeneous structure. In our work, the EMM is generalized to the fourth-order-accurate apparent mass-conservation equation in two- and three-dimensional duct flows. The method looks for the solution of the transport equation as the product of a long harmonic wave and a spatially periodic oscillating component; the moments of the given numerical scheme are derived from a chain of the steady-state fourth-order equations at a single cell. This mathematical technique is exemplified for the truncation terms of the two-relaxation-time lattice Boltzmann scheme, using plug and parabolic flow in straight channel and cylindrical capillary with the d2Q9 and d3Q15 discrete velocity sets as simple but illustrative examples. The derived symbolic dependencies can be readily extended for advection by another, Newtonian or non-Newtonian, flow profile in any-shape open-tabular conduits. It is
Asinari, Pietro
2009-11-01
A finite difference lattice Boltzmann scheme for homogeneous mixture modeling, which recovers Maxwell-Stefan diffusion model in the continuum limit, without the restriction of the mixture-averaged diffusion approximation, was recently proposed [P. Asinari, Phys. Rev. E 77, 056706 (2008)]. The theoretical basis is the Bhatnagar-Gross-Krook-type kinetic model for gas mixtures [P. Andries, K. Aoki, and B. Perthame, J. Stat. Phys. 106, 993 (2002)]. In the present paper, the recovered macroscopic equations in the continuum limit are systematically investigated by varying the ratio between the characteristic diffusion speed and the characteristic barycentric speed. It comes out that the diffusion speed must be at least one order of magnitude (in terms of Knudsen number) smaller than the barycentric speed, in order to recover the Navier-Stokes equations for mixtures in the incompressible limit. Some further numerical tests are also reported. In particular, (1) the solvent and dilute test cases are considered, because they are limiting cases in which the Maxwell-Stefan model reduces automatically to Fickian cases. Moreover, (2) some tests based on the Stefan diffusion tube are reported for proving the complete capabilities of the proposed scheme in solving Maxwell-Stefan diffusion problems. The proposed scheme agrees well with the expected theoretical results.
Ifland, Benedikt; Hoffmann, Joerg; Kressdorf, Birte; Roddatis, Vladimir; Seibt, Michael; Jooss, Christian
2017-06-01
The effect of correlation effects on photovoltaic energy conversion at manganite/titanite heterojunctions is investigated. As a model system we choose a heterostructure consisting of the small polaron absorber Pr0.66Ca0.34MnO3 (PCMO) epitaxially grown on single-crystalline Nb-doped SrTi0.998Nb0.002O3 (STNO) substrates. The high structural and chemical quality of the interfaces is proved by detailed characterization using high-resolution transmission electron microscopy (TEM) and electron energy loss spectroscopy (EELS) studies. Spectrally resolved and temperature-dependent photovoltaic measurements show pronounced contributions of both the Jahn-Teller (JT) excitations and the charge transfer (CT) transitions to the photovoltaic effect at different photon energies. A linear temperature dependence of the open-circuit voltage for an excitation in the PCMO manganite is only observed below the charge-ordering temperature, indicating that the diffusion length of the photocarrier exceeds the size of the space charge region. The photovoltaic response is compared to that of a heterojunction of lightly doped Pr0.05Ca0.95MnO3 (CMO)/STNO, where the JT transition is absent. Here, significant contributions of the CT transition to the photovoltaic effect set in below the Neel temperature. We conclude that polaronic correlations and ordering effects are essentials for photovoltaic energy conversion in manganites.
International Nuclear Information System (INIS)
Kubaschewski, O.
1983-01-01
The diffusion rate values of titanium, its compounds and alloys are summarized and tabulated. The individual chemical diffusion coefficients and self-diffusion coefficients of certain isotopes are given. Experimental methods are listed which were used for the determination of diffusion coefficients. Some values have been taken over from other studies. Also given are graphs showing the temperature dependences of diffusion and changes in the diffusion coefficient with concentration changes
Kuentz, M
2003-01-01
A two-dimensional lattice gas automaton (LGA) is used for simulating concentration-dependent diffusion in a microscopically random heterogeneous structure. The heterogeneous medium is initialized at a low density rho sub 0 and then submitted to a steep concentration gradient by continuous injection of particles at a concentration rho sub 1 >rho sub 0 from a one-dimensional source to model spreading of a density front. Whereas the nonlinear diffusion equation generally used to describe concentration-dependent diffusion processes predicts a scaling law of the type phi = xt sup - sup 1 sup / sup 2 in one dimension, the spreading process is shown to deviate from the expected t sup 1 sup / sup 2 scaling. The time exponent is found to be larger than 1/2, i.e. diffusion of the density front is enhanced with respect to standard Fickian diffusion. It is also established that the anomalous time exponent decreases as time elapses: anomalous spreading is thus not a timescaling process. We demonstrate that occurrence of a...
Skokos, C.; Bountis, T.; Antonopoulos, C.
2008-12-01
The recently introduced GALI method is used for rapidly detecting chaos, determining the dimensionality of regular motion and predicting slow diffusion in multi-dimensional Hamiltonian systems. We propose an efficient computation of the GALIk indices, which represent volume elements of k randomly chosen deviation vectors from a given orbit, based on the Singular Value Decomposition (SVD) algorithm. We obtain theoretically and verify numerically asymptotic estimates of GALIs long-time behavior in the case of regular orbits lying on low-dimensional tori. The GALIk indices are applied to rapidly detect chaotic oscillations, identify low-dimensional tori of Fermi-Pasta-Ulam (FPU) lattices at low energies and predict weak diffusion away from quasiperiodic motion, long before it is actually observed in the oscillations.
The effect of diffusion induced lattice stress on the open-circuit voltage in silicon solar cells
Weizer, V. G.; Godlewski, M. P.
1984-01-01
It is demonstrated that diffusion induced stresses in low resistivity silicon solar cells can significantly reduce both the open-circuit voltage and collection efficiency. The degradation mechanism involves stress induced changes in both the minority carrier mobility and the diffusion length. Thermal recovery characteristics indicate that the stresses are relieved at higher temperatures by divacancy flow (silicon self diffusion). The level of residual stress in as-fabricated cells was found to be negligible in the cells tested.
Frenkel, D.; Ernst, M.H.
1989-01-01
We compute the velocity autocorrelation function of a tagged particle in a two-dimensional lattice-gas cellular automaton using a method that is about a million times more efficient than existing techniques. A t-1 algebraic tail in the tagged-particle velocity autocorrelation function is clearly
International Nuclear Information System (INIS)
Williams, M.M.R.; Hall, S.K.; Eaton, M.D.
2014-01-01
Highlights: • A rectangular reactor cell with an elliptical fuel element. • Solution of transport and diffusion equations by Fourier expansion. • Numerical examples showing convergence. • Two group cell problems. - Abstract: A method for solving the diffusion and transport equations in a rectangular lattice cell with an elliptical fuel element has been developed using a Fourier expansion of the neutron flux. The method is applied to a one group model with a source in the moderator. The cell flux is obtained and also the associated disadvantage factor. In addition to the one speed case, we also consider the two group equations in the cell which now become an eigenvalue problem for the lattice multiplication factor. The method of solution relies upon an efficient procedure to solve a large set of simultaneous linear equations and for this we use the IMSL library routines. Our method is compared with the results from a finite element code. The main drawback of the problem arises from the very large number of terms required in the Fourier series which taxes the storage and speed of the computer. Nevertheless, useful solutions are obtained in geometries that would normally require the use of finite element or analogous methods, for this reason the Fourier method is useful for comparison with that type of numerical approach. Extension of the method to more intricate fuel shapes, such as stars and cruciforms as well as superpositions of these, is possible
International Nuclear Information System (INIS)
Polley, M.V.
1981-02-01
Diffusion in type 316 stainless steel was studied by depositing 60 Co and 54 Mn on flat polished surfaces and heating. Diffusion profiles, obtained after gamma-counting slices removed by hand grinding, were analysed using Suzuoka's ''instantaneous source'' model. (author)
Current–voltage characteristics of manganite–titanite perovskite junctions
Directory of Open Access Journals (Sweden)
Benedikt Ifland
2015-07-01
Full Text Available After a general introduction into the Shockley theory of current voltage (J–V characteristics of inorganic and organic semiconductor junctions of different bandwidth, we apply the Shockley theory-based, one diode model to a new type of perovskite junctions with polaronic charge carriers. In particular, we studied manganite–titanate p–n heterojunctions made of n-doped SrTi1−yNbyO3, y = 0.002 and p-doped Pr1−xCaxMnO3, x = 0.34 having a strongly correlated electron system. The diffusion length of the polaron carriers was analyzed by electron beam-induced current (EBIC in a thin cross plane lamella of the junction. In the J–V characteristics, the polaronic nature of the charge carriers is exhibited mainly by the temperature dependence of the microscopic parameters, such as the hopping mobility of the series resistance and a colossal electro-resistance (CER effect in the parallel resistance. We conclude that a modification of the Shockley equation incorporating voltage-dependent microscopic polaron parameters is required. Specifically, the voltage dependence of the reverse saturation current density is analyzed and interpreted as a voltage-dependent electron–polaron hole–polaron pair generation and separation at the interface.
International Nuclear Information System (INIS)
Santos, Camila M. dos; Rios, Francisco Javier; Amorim, Lucas E.D.; Palmieri, Helena E.
2017-01-01
The Lagoa Real Uranium Province (LRUP) is located in northwest of Bahia state and is the major uranium deposit of Brazil. Titanite is a common accessory mineral in rocks of LRUP and usually is part of uranium ore assemblage. Thirty three polished thin sections of F10 drill-hole located in Gameleira I deposit (anomaly 35) were petrographically studied and used for mineral chemistry study. Petrographically, titanite can be differentiated according to texture between granular and prismatic. Granular titanite is generally associated with magmatic assemblage (alkali feldspar hypersolvus granite) and it is present in some albitites (barren magnetite albitite). Prismatic titanite is restricted to albitite (garnet and mineralized magnetite albitite) and is associated with metamorphic assemblage. Microprobe analyses shows a trend from granites to mineralized albitites and do not cluster titanite by its texture, but by its host rocks. On the other hand, trace elements can distinguish titanite generation according to texture. Granular titanite is characterized by some highest high field strength elements (HFSE) values, like Hf, Pb, Th, U and HREE+Y, and the lowest V content. Vanadium has positive correlation with Zr/Hf ratio and inverse with U. Vanadium versus U relationship is inverse to the previously found by literature in LRUP what indicates that titanite was submitted to complexes processes of uranium loss after its crystallization. In addition, hafnium loss can be related to precipitation of hydrothermal zircon as it is strongly partitioned to this mineral. (author)
Energy Technology Data Exchange (ETDEWEB)
Santos, Camila M. dos; Rios, Francisco Javier; Amorim, Lucas E.D.; Palmieri, Helena E., E-mail: cms@cdtn.br [Centro de Desenvolvimento da Tecnologia Nuclear (CDTN/CNEN-MG), Belo Horizonte, MG (Brazil)
2017-11-01
The Lagoa Real Uranium Province (LRUP) is located in northwest of Bahia state and is the major uranium deposit of Brazil. Titanite is a common accessory mineral in rocks of LRUP and usually is part of uranium ore assemblage. Thirty three polished thin sections of F10 drill-hole located in Gameleira I deposit (anomaly 35) were petrographically studied and used for mineral chemistry study. Petrographically, titanite can be differentiated according to texture between granular and prismatic. Granular titanite is generally associated with magmatic assemblage (alkali feldspar hypersolvus granite) and it is present in some albitites (barren magnetite albitite). Prismatic titanite is restricted to albitite (garnet and mineralized magnetite albitite) and is associated with metamorphic assemblage. Microprobe analyses shows a trend from granites to mineralized albitites and do not cluster titanite by its texture, but by its host rocks. On the other hand, trace elements can distinguish titanite generation according to texture. Granular titanite is characterized by some highest high field strength elements (HFSE) values, like Hf, Pb, Th, U and HREE+Y, and the lowest V content. Vanadium has positive correlation with Zr/Hf ratio and inverse with U. Vanadium versus U relationship is inverse to the previously found by literature in LRUP what indicates that titanite was submitted to complexes processes of uranium loss after its crystallization. In addition, hafnium loss can be related to precipitation of hydrothermal zircon as it is strongly partitioned to this mineral. (author)
International Nuclear Information System (INIS)
Brito, P.E. de; Nazareno, H.N.
2012-01-01
The object of the present work is to analyze the effect of nonlinearity on wave packet propagation in a square lattice subject to a magnetic and an electric field in the Hall configuration, by using the Discrete Nonlinear Schrödinger Equation (DNLSE). In previous works we have shown that without the nonlinear term, the presence of the magnetic field induces the formation of vortices that remain stationary, while a wave packet is introduced in the system. As for the effect of an applied electric field, it was shown that the vortices propagate in a direction perpendicular to the electric field, similar behavior as presented in the classical treatment, we provide a quantum mechanics explanation for that. We have performed the calculations considering first the action of the magnetic field as well as the nonlinearity. The results indicate that for low values of the nonlinear parameter U the vortices remain stationary while preserving the form. For greater values of the parameter the picture gets distorted, the more so, the greater the nonlinearity. As for the inclusion of the electric field, we note that for small U, the wave packet propagates perpendicular to the applied field, until for greater values of U the wave gets partially localized in a definite region of the lattice. That is, for strong nonlinearity the wave packet gets partially trapped, while the tail of it can propagate through the lattice. Note that this tail propagation is responsible for the over-diffusion for long times of the wave packet under the action of an electric field. We have produced short films that show clearly the time evolution of the wave packet, which can add to the understanding of the dynamics.
Blumenthal, V. H.; Linnen, R. L.
2009-05-01
Copper mineralization in central Yukon is well known, but the metallogeny of the Ruby Range batholith, west of the copper belt, is poorly understood. The Hopper property, situated in the south western part of the Yukon in the Yukon-Tanana terrane, contains copper mineralization hosted by granodiorite and quartz feldspar porphyry of cal-alkaline affinity. These rock units, interpreted to be part of the Ruby Range batholith, intruded metasediments of the Ashihik Metamorphic Suite rocks. Mafic dykes cross cut the intrusion followed by aplite dykes. Small occurrences of skarn also occur in the area and some of these contain copper mineralization. The copper mineralization at the Hopper property appears to have a porphyry-type affinity. However, it is associated with a shear zone and propylitic alteration unlike other typical copper porphyry-type deposits. This raises the question whether or not the mineralization is orthomagmatic in origin, i.e., whether or not this is a true porphyry system. The main zone of mineralization is 1 kilometer long and 0.5 kilometer wide. It is characterized by disseminated chalcopyrite and pyrite, which also occur along fractures. Molybdenite mineralization was found to be associated with slickensides. Alteration minerals associated with the copper mineralization are chlorite, epidote-clinozoisite, carbonate and titanite. Chlorite and epidote-clinozoisite are concentrated in the mineralized zone, whereas an earlier potassic alteration shows a weaker spatial correlation with the mineralization. The association of the mineralization with propylitic alteration leads us to believe the mineralization is shear related, although a deeper porphyritic system may be present at depth. Two populations of titanite at the Hopper property are recognized based on their shape, size and association with other minerals. The first population, defined by a length of 100 micrometers to 1 centimeter, euhedral boundaries, and planar contacts with other magmatic
Energy Technology Data Exchange (ETDEWEB)
Molaeimanesh, Golamreza; Akbari, Mohammad Hadi [Shiraz University, Shiraz (Iran, Islamic Republic of)
2014-04-15
A major challenge in the application of proton exchange membrane fuel cells (PEMFCs) is water management, with the flooding of electrodes as the main issue. The Lattice-Boltzmann method (LBM) is a relatively new technique that is superior in modeling the dynamic interface of multiphase fluid flow in complex microstructures such as non-homogeneous and anisotropic porous media of PEMFC electrodes. In this study, the dynamic behavior of a water droplet during removal from gas diffusion layer (GDL) of a PEMFC electrode with interdigitated flow field is simulated using LBM. The effects of GDL wettability and its spanwise and transverse gradients on the removal process are investigated. The results demonstrate great influence of wettability and its spanwise and transverse gradients on the dynamic behavior of droplets during the removal process. Although increasing the hydrophobicity of GDL results in better droplet removal, its increase beyond a critical value does not show a significant effect.
Yang, Xuguang; Shi, Baochang; Chai, Zhenhua
2014-07-01
In this paper, two modified lattice Boltzmann Bhatnagar-Gross-Krook (LBGK) models for incompressible Navier-Stokes equations and convection-diffusion equations are proposed via the addition of correction terms in the evolution equations. Utilizing this modification, the value of the dimensionless relaxation time in the LBGK model can be kept in a proper range, and thus the stability of the LBGK model can be improved. Although some gradient operators are included in the correction terms, they can be computed efficiently using local computational schemes such that the present LBGK models still retain the intrinsic parallelism characteristic of the lattice Boltzmann method. Numerical studies of the steady Poiseuille flow and unsteady Womersley flow show that the modified LBGK model has a second-order convergence rate in space, and the compressibility effect in the common LBGK model can be eliminated. In addition, to test the stability of the present models, we also performed some simulations of the natural convection in a square cavity, and we found that the results agree well with those reported in the previous work, even at a very high Rayleigh number (Ra = 10(12)).
Yu, Ruizhi; Zhang, Zhijuan; Jamil, Sidra; Chen, Jiancheng; Zhang, Xiaohui; Wang, Xianyou; Yang, Zhenhua; Shu, Hongbo; Yang, Xiukang
2018-05-07
Li-rich layered oxides (LLOs) with high specific capacities are favorable cathode materials with high-energy density. Unfortunately, the drawbacks of LLOs such as oxygen release, low conductivity, and depressed kinetics for lithium ion transport during cycling can affect the safety and rate capability. Moreover, they suffer severe capacity and voltage fading, which are major challenges for the commercializing development. To cure these issues, herein, the synthesis of high-performance antimony-doped LLO nanofibers by an electrospinning process is put forward. On the basis of the combination of theoretical analyses and experimental approaches, it can be found that the one-dimensional porous micro-/nanomorphology is in favor of lithium-ion diffusion, and the antimony doping can expand the layered phase lattice and further improve the lithium ion diffusion coefficient. Moreover, the antimony doping can decrease the band gap and contribute extra electrons to O within the Li 2 MnO 3 phase, thereby enhancing electronic conductivity and stabilizing lattice oxygen. Benefitting from the unique architecture, reformative electronic structure, and enhanced kinetics, the antimony-doped LLO nanofibers possess a high reversible capacity (272.8 mA h g -1 ) and initial coulombic efficiency (87.8%) at 0.1 C. Moreover, the antimony-doped LLO nanofibers show excellent cycling performance, rate capability, and suppressed voltage fading. The capacity retention can reach 86.9% after 200 cycles at 1 C, and even cycling at a high rate of 10 C, a capacity of 172.3 mA h g -1 can still be obtained. The favorable results can assist in developing the LLO material with outstanding electrochemical properties.
International Nuclear Information System (INIS)
Chełminiak, Przemysław
2012-01-01
A new approach to the assemblage of complex networks displaying the scale-free architecture is proposed. While the growth and the preferential attachment of incoming nodes assure an emergence of such networks according to the Barabási–Albert model, it is argued here that the preferential linking condition needs not to be a principal rule. To assert this statement a simple computer model based on random walks on fractal lattices is introduced. It is shown that the model successfully reproduces the degree distributions, the ultra-small-worldness and the high clustering arising from the topology of scale-free networks. -- Highlights: ► A new mechanism of evolution for scale-free complex networks is proposed. ► The preferential attachment rule is not necessary to construct such networks. ► It is shown that they reveal some basic properties of classical scale-free nets.
Directory of Open Access Journals (Sweden)
Yoshihisa Suzuki
2016-07-01
Full Text Available Good model systems are required in order to understand crystal growth processes because, in many cases, precise incorporation processes of atoms or molecules cannot be visualized easily at the atomic or molecular level. Using a transmission-type optical microscope, we have successfully observed in situ adsorption, desorption, surface diffusion, lattice defect formation, and kink incorporation of particles on growth interfaces of colloidal crystals of polystyrene particles in aqueous sodium polyacrylate solutions. Precise surface transportation and kink incorporation processes of the particles into the colloidal crystals with attractive interactions were observed in situ at the particle level. In particular, contrary to the conventional expectations, the diffusion of particles along steps around a two-dimensional island of the growth interface was not the main route for kink incorporation. This is probably due to the number of bonds between adsorbed particles and particles in a crystal; the number exceeds the limit at which a particle easily exchanges its position to the adjacent one along the step. We also found novel desorption processes of particles from steps to terraces, attributing them to the assistance of attractive forces from additionally adsorbing particles to the particles on the steps.
Jiang, P.; Yang, K. F.; Fan, H. R.; Liu, X.
2016-12-01
The grain-scale textural and in-situ compositional analyses on accessory minerals (such as titanite, rutile, apatite, monazite, etc.) have recently been a hot topic for geologists, through which a detailed information on magmatic, metamorphic or hydrothermal process can be extracted. As an attempt to unravel the petrogenesis of Early Cretaceous Guojialing-type granodiorites and their bearing dioritic enclaves, we accomplished an integrated geochronological and geochemical study on titanites within these rocks. Three types of titanites, with distinguishable textural and geochemical features, are identified. G-type titanites (from granodiorites) and E-type-I titanites (from plagioclase-rich dioritic enclaves) yield identical U-Pb age of 130 Ma, but reveal distinct back-scattered electron (BSE) zonings. G-type titanites are characterized by oscillatory zonings whereas E-type-I titanites are marked by core-mantle-rim zonings, exhibiting drastic but contrary variation trends for several key elements (such as LREEs, Zr, Hf and F) among their transition BSE zones. These two types of titanites are interpreted to crystallize coevally, and record a notable temperature and compositional change of two corresponding melts, as a response to magma mixing. E-type-II titanites (from plagioclase-poor dioritic enclaves) yield a relatively younger U-Pb age at 128 Ma, and show typical interstitial growth with narrower and lower range of Zr, total REEs contents, but higher F content and Nb/Ta ratios. Such titanites are perceived to record late-stage mingling, during which F-rich and REE-poor hybrid granodioritic magma squeezed into the incompletely consolidated dioritic enclaves with accompanying fluid-rock interaction. Unlike the dramatic elemental changes in these differentiated titanites, in-situ Nd isotopic compositions are relatively homogeneous, which in our view is a good sign of showing that isotopic equilibrium among two magma systems was more easily reached compared to
Energy Technology Data Exchange (ETDEWEB)
Benoist, P [Commissariat a l' Energie Atomique, Saclay (France).Centre d' Etudes Nucleaires
1959-07-01
The calculation of diffusion coefficients in a lattice necessitates the knowledge of a correct method of weighting the free paths of the different constituents. An unambiguous definition of this weighting method is given here, based on the calculation of leakages from a zone of a reactor. The formulation obtained, which is both simple and general, reduces the calculation of diffusion coefficients to that of collision probabilities in the different media; it reveals in the expression for the radial coefficient the series of the terms of angular correlation (cross terms) recently shown by several authors. This formulation is then used to calculate the practical case of a classical type of lattice composed of a moderator and a fuel element surrounded by an empty space. Analytical and numerical comparison of the expressions obtained with those inferred from the theory of BEHRENS shows up the importance of several new terms some of which are linked with the transparency of the fuel element. Cross terms up to the second order are evaluated. A practical formulary is given at the end of the paper. (author) [French] Le calcul des coefficients de diffusion dans un reseau suppose la connaissance d'un mode de ponderation correct des libres parcours des differents constituants. On definit ici sans ambiguite ce mode de ponderation a partir du calcul des fuites hors d'une zone de reacteur. La formulation obtenue, simple et generale, ramene le calcul des coefficients de diffusion a celui des probabilites de collision dans les differents milieux; elle fait apparaitre dans l'expression du coefficient radial la serie des termes de correlation angulaire (termes rectangles), mis en evidence recemment par plusieurs auteurs. Cette formulation est ensuite appliquee au calcul pratique d'un reseau classique, compose d'un moderateur et d'un element combustible entoure d'une cavite; la comparaison analytique et numerique des expressions obtenues avec celles deduites de la theorie de BEHRENS
Two modes of orogenic collapse of the Pamir plateau recorded by titanite
Stearns, M. A.; Hacker, B. R.; Ratschbacher, L.; Rutte, D.; Kylander-Clark, A. R.
2013-12-01
Processes that operate in the mid- to lower crust during and following continent-continent collision are important for understanding how orogenic plateaux transition from thickening to collapse. In the central and southern Pamir, mid- to lower crustal rocks crop out in two belts of extensional domes. The central Pamir domes were exhumed by symmetrical N-S extension. In contrast, the southern Pamir domes were exhumed by asymmetrical top to the south (NNW-SSE) extension via a rolling-hinge detachment. To investigate the high-temperature exhumation history, titanites were dated using LASS (laser ablation split stream-ICP-MS). A multi-collector ICP was used to collect U-Pb isotopic ratios and a single collector ICP-MS was used to measure trace-element abundances. The data indicate that the central Pamir domes began exhumation synchronously at ~17 Ma. Titanite from the southern Pamir record two periods of protracted (re)crystallization: older metamorphic dates ranging from ~35-18 Ma and younger igneous and metamorphic dates from ~15-7 Ma. Samples with single populations of titanite dates are present throughout both groups. Samples with more-complex date populations typically have distinct trace-element (e.g., Sr, Y, Zr, and Nb) groups that can be used to distinguish different date populations (e.g., older dates may have higher Zr and younger dates lower Zr). The distinct early exhumation histories of the north and south Pamir require either a diachronous single process or two semi-independent processes. The N to S sequence of exhumation, ranges of dates, and overall extension directions may be related to two important plate-tectonic events inferred from seismic data: 1) breakoff of the northward subducting Indian slab around ~20 Ma, and 2) southward subduction and northwestward rollback of the Asian lithosphere between ~15-10 Ma based on geodetic convergence rates and Benioff zone length. We interpret these two lithospheric-detachment events to have driven the
International Nuclear Information System (INIS)
Li, Huidong; Wu, Lang; Xu, Dong; Wang, Xin; Teng, Yuancheng; Li, Yuxiang
2015-01-01
In order to increase the solubility of actinides in the glass matrix, the effects of CaO, TiO 2 , and ZrSiO 4 addition (abbreviated as CTZ, in the mole ratio of 2:2:1) on crystalline phases, microstructure, and chemical durability of barium borosilicate glass–ceramics were investigated. The results show that the samples possess both zirconolite-2M and titanite phase when the CTZ content is greater than or equal to 45 wt.%. For the glass–ceramics with 45 wt.% CTZ (CTZ-45), only zirconolite-2M phase is observed after annealing at 680–740 °C for 2 h. The CTZ-45 possess zirconolite-2M and titanite phases after annealing at 700 °C first, and then annealing at 900–1050 °C for 2 h. Furthermore, the zirconolite-2M and titanite grains show a strip and brick shape, respectively. The CTZ-45 annealing at 950 °C shows the lower normalized leaching rates of B, Na and Nd when compared to that of CTZ-0 and CTZ-55. - Highlights: • CaO, TiO 2 , ZrSiO 4 (CTZ) as nucleating agents were added to barium borosilicate glass. • The samples with 45–55 wt% CTZ possess CaZrTi 2 O 7 -2M and CaTiSiO 5 crystalline phases. • CTZ-45 (45wt% CTZ) possesses only CaZrTi 2 O 7 -2M phase after annealing at 680–740 °C. • CTZ-45 possesses CaZrTi 2 O 7 -2M and CaTiSiO 5 phases after annealing at 900–1050 °C. • CTZ-45 annealing at 950 °C shows the lower leaching rates of B, Na and Nd than CTZ-0 and CTZ-55.
Energy Technology Data Exchange (ETDEWEB)
Volgmann, Kai Tristan
2016-07-29
Low-dimensional diffusion was investigated to improve the understanding of the fundamentals of ion movement in condensed matter. Different model systems with different dimensionality of cation migration pathways were investigated using solidstate nuclear magnetic resonance (NMR) spectroscopy and impedance spectroscopy. Both experimental methods made it possible to complementarily study both Li and Na mobility over a wide range of jump rates. Metallic lithium as a well-known model system for isotropic diffusion was investigated using {sup 7}Li field-cycling NMR. The spin-lattice relaxation (SLR) rates were separated into an electronic contribution and a diffusion-induced contribution. The Korringa product was calculated from the actual measurements. The main focus was the comparison of different theoretical models describing the Li motion in metallic lithium. The well-known model by Bloembergen, Purcell and Pound already reproduced the data well, but two models by Sholl improved the results taking into account the type of crystal lattice and jump correlation effects. A single-vacancy diffusion mechanism was observed, but a double-vacancy mechanism was not excluded as elevated temperatures near the melting point of lithium were not available. Li{sub 0.7}Nb{sub 3}S{sub 4} is isostructural to Li{sub 0.7}Nb{sub 3}Se{sub 4} which was reported as possible 1D Li ion conductor due to its channel structure. Thus, Li{sub 0.7}Nb{sub 3}S{sub 4} was investigated as 1D model system using solid-state NMR spectroscopy. Multinuclear NMR spectroscopy gave insights into structural properties. Li dynamics was observed by several NMR methods over a wide temperature range. {sup 7}Li NMR motional narrowing led to an estimate of the activation energy for local Li hopping. {sup 7}Li NMR spin-alignment echo (SAE) was used for the determination of Li jump rates on a macroscopic scale. Possible dimensionality effects were investigated by {sup 7}Li NMR SLR. Out of the phase system Li{sub 2}O
Sakaida, Satoshi; Tabe, Yutaka; Chikahisa, Takemi
2017-09-01
A method for the large-scale simulation with the lattice Boltzmann method (LBM) is proposed for liquid water movement in a gas diffusion layer (GDL) of polymer electrolyte membrane fuel cells. The LBM is able to analyze two-phase flows in complex structures, however the simulation domain is limited due to heavy computational loads. This study investigates a variety means to reduce computational loads and increase the simulation areas. One is applying an LBM treating two-phases as having the same density, together with keeping numerical stability with large time steps. The applicability of this approach is confirmed by comparing the results with rigorous simulations using actual density. The second is establishing the maximum limit of the Capillary number that maintains flow patterns similar to the precise simulation; this is attempted as the computational load is inversely proportional to the Capillary number. The results show that the Capillary number can be increased to 3.0 × 10-3, where the actual operation corresponds to Ca = 10-5∼10-8. The limit is also investigated experimentally using an enlarged scale model satisfying similarity conditions for the flow. Finally, a demonstration is made of the effects of pore uniformity in GDL as an example of a large-scale simulation covering a channel.
International Nuclear Information System (INIS)
Hasenfratz, P.
1983-01-01
The author presents a general introduction to lattice gauge theories and discusses non-perturbative methods in the gauge sector. He then shows how the lattice works in obtaining the string tension in SU(2). Lattice QCD at finite physical temperature is discussed. Universality tests in SU(2) lattice QCD are presented. SU(3) pure gauge theory is briefly dealt with. Finally, fermions on the lattice are considered. (Auth.)
Ginzburg, Irina
2017-01-01
Impact of the unphysical tangential advective-diffusion constraint of the bounce-back (BB) reflection on the impermeable solid surface is examined for the first four moments of concentration. Despite the number of recent improvements for the Neumann condition in the lattice Boltzmann method-advection-diffusion equation, the BB rule remains the only known local mass-conserving no-flux condition suitable for staircase porous geometry. We examine the closure relation of the BB rule in straight channel and cylindrical capillary analytically, and show that it excites the Knudsen-type boundary layers in the nonequilibrium solution for full-weight equilibrium stencil. Although the d2Q5 and d3Q7 coordinate schemes are sufficient for the modeling of isotropic diffusion, the full-weight stencils are appealing for their advanced stability, isotropy, anisotropy and anti-numerical-diffusion ability. The boundary layers are not covered by the Chapman-Enskog expansion around the expected equilibrium, but they accommodate the Chapman-Enskog expansion in the bulk with the closure relation of the bounce-back rule. We show that the induced boundary layers introduce first-order errors in two primary transport properties, namely, mean velocity (first moment) and molecular diffusion coefficient (second moment). As a side effect, the Taylor-dispersion coefficient (second moment), skewness (third moment), and kurtosis (fourth moment) deviate from their physical values and predictions of the fourth-order Chapman-Enskog analysis, even though the kurtosis error in pure diffusion does not depend on grid resolution. In two- and three-dimensional grid-aligned channels and open-tubular conduits, the errors of velocity and diffusion are proportional to the diagonal weight values of the corresponding equilibrium terms. The d2Q5 and d3Q7 schemes do not suffer from this deficiency in grid-aligned geometries but they cannot avoid it if the boundaries are not parallel to the coordinate lines. In order
Colossal positive magnetoresistance in surface-passivated oxygen-deficient strontium titanite
David, Adrian
2015-05-15
Modulation of resistance by an external magnetic field, i.e. magnetoresistance effect, has been a long-lived theme of research due to both fundamental science and device applications. Here we report colossal positive magnetoresistance (CPMR) (>30,000% at a temperature of 2 K and a magnetic field of 9 T) discovered in degenerate semiconducting strontium titanite (SrTiO3) single crystals capped with ultrathin SrTiO3/LaAlO3 bilayers. The low-pressure high-temperature homoepitaxial growth of several unit cells of SrTiO3 introduces oxygen vacancies and high-mobility carriers in the bulk SrTiO3, and the three-unit-cell LaAlO3 capping layer passivates the surface and improves carrier mobility by suppressing surface-defect-related scattering. The coexistence of multiple types of carriers and inhomogeneous transport lead to the emergence of CPMR. This unit-cell-level surface engineering approach is promising to be generalized to others oxides, and to realize devices with high-mobility carriers and interesting magnetoelectronic properties.
Homogenization theory in reactor lattices
International Nuclear Information System (INIS)
Benoist, P.
1986-02-01
The purpose of the theory of homogenization of reactor lattices is to determine, by the mean of transport theory, the constants of a homogeneous medium equivalent to a given lattice, which allows to treat the reactor as a whole by diffusion theory. In this note, the problem is presented by laying emphasis on simplicity, as far as possible [fr
Mazdab, F.K.
2009-01-01
Crystals of titanite can be readily grown under ambient pressure from a mixture of CaO, TiO2 and SiO2 in the presence of molten sodium tetraborate. The crystals produced are euhedral and prismatic, lustrous and transparent, and up to 5 mm in length. Titanite obtained by this method contains approximately 4300 ppm Na and 220 ppm B contributed from the flux. In addition to dopant-free material, titanite containing trace alkali and alkaline earth metals (K, Sr, Ba), transition metals (Sc, Cr, Ni, Y, Zr, Nb, Hf and Ta), rare-earth elements (REE), actinides (Th, U) and p-block elements (F, S, Cl, Ge, Sn and Pb) have been prepared using the same procedure. Back-scattered electron (BSE) imaging accompanied by ion-microprobe (SHRIMP-RG) analysis confirms significant incorporation of selected trace-elements at structural sites. Regardless of some zonation, the large size of the crystals and broad regions of chemical homogeneity make these crystals useful as experimental starting material, and as matrix-matched trace-element standards for a variety of microbeam analytical techniques where amorphous titanite glass, heterogeneous natural titanite or a non-titanite standard may be less than satisfactory. Trace-element-doped synthetic crystals can also provide a convenient proxy for a better understanding of trace-element incorporation in natural titanite. Comparisons with igneous, authigenic and high-temperature metasomatic titanite are examined. The use of high-mass-resolution SIMS also demonstrates the analytical challenges inherent to any in situ mass-spectrometry-based analysis of titanite, owing to the production of difficult-to-resolve molecular interferences. These interferences are dominated by Ca-Ca, Ca-Ti and Ti-Ti dimers that are significant in the mass range of 80-100, affecting all isotopes of Sr and Zr, as well as 89Y and 93Nb. Methods do exist for the evaluation of interferences by these dimers and of polyatomic interferences on the LREE.
Paul, Andre N.; Spikings, Richard A.; Ulianov, Alexey; Ovtcharova, Maria
2018-05-01
Quantitative reconstruction of thermal histories can be a powerful tool to study numerous natural processes such as tectonic plate interaction, cratonic stability and extra-terrestrial phenomena such as asteroid ejection. A majority of thermochronological studies have focused on temperatures lower than 300 °C. Few previous studies have demonstrated that U-Pb data from apatite and other accessory phases can be used to recover thermal history information at T > 350 °C. We present U-Pb data from apatite, to constrain the thermal histories of Triassic peralluminous anatectites from the Northern Andes between the temperatures of ∼350-550 °C. The accuracy of the thermal history models is assessed by comparisons with previous geological models, and comparisons with pre-existing and newly acquired U/Pb (titanite and rutile), 40Ar/39Ar (muscovite) and low temperature thermochronological data. This study also examines the feasibility of using a large, regionally dispersed apatite U-Pb data set to obtain continuous thermal history paths along a long-lived (>500 Ma) active margin. A second aim of this study is to further test the hypothesis that the dominant mechanism for Pb displacement through apatite is volume diffusion, as opposed to aqueous fluid interaction. The thermal history models derived from the Triassic anatectites exposed in the Andes of Colombia and Ecuador are entirely consistent with lower temperature thermochronological constraints, and previously established geochronological and geochemical constraints. They reveal and quantify trench parallel changes in the amount of Jurassic - Early Cretaceous extension, significantly bolstering and adding to previous tectonic interpretations. Confirmation of the utility of U-Pb thermochronology provides geologists with a powerful tool for investigating the high-temperature thermal evolution of accessory minerals.
International Nuclear Information System (INIS)
Chadderton, L.T.; Johnson, E.; Wohlenberg, T.
1976-01-01
Void lattices in metals apparently owe their stability to elastically anisotropic interactions. An ordered array of voids on the anion sublattice in fluorite does not fit so neatly into this scheme of things. Crowdions may play a part in the formation of the void lattice, and stability may derive from other sources. (Auth.)
International Nuclear Information System (INIS)
Randjbar-Daemi, S.
1995-12-01
The so-called doubling problem in the lattice description of fermions led to a proof that under certain circumstances chiral gauge theories cannot be defined on the lattice. This is called the no-go theorem. It implies that if Γ/sub/A is defined on a lattice then its infrared limit, which should correspond to the quantum description of the classical action for the slowly varying fields on lattice scale, is inevitably a vector like theory. In particular, if not circumvented, the no-go theorem implies that there is no lattice formulation of the Standard Weinberg-Salam theory or SU(5) GUT, even though the fermions belong to anomaly-free representations of the gauge group. This talk aims to explain one possible attempt at bypassing the no-go theorem. 20 refs
Energy Technology Data Exchange (ETDEWEB)
Randjbar-Daemi, S
1995-12-01
The so-called doubling problem in the lattice description of fermions led to a proof that under certain circumstances chiral gauge theories cannot be defined on the lattice. This is called the no-go theorem. It implies that if {Gamma}/sub/A is defined on a lattice then its infrared limit, which should correspond to the quantum description of the classical action for the slowly varying fields on lattice scale, is inevitably a vector like theory. In particular, if not circumvented, the no-go theorem implies that there is no lattice formulation of the Standard Weinberg-Salam theory or SU(5) GUT, even though the fermions belong to anomaly-free representations of the gauge group. This talk aims to explain one possible attempt at bypassing the no-go theorem. 20 refs.
International Nuclear Information System (INIS)
Thorn, C.B.
1988-01-01
The possibility of studying non-perturbative effects in string theory using a world sheet lattice is discussed. The light-cone lattice string model of Giles and Thorn is studied numerically to assess the accuracy of ''coarse lattice'' approximations. For free strings a 5 by 15 lattice seems sufficient to obtain better than 10% accuracy for the bosonic string tachyon mass squared. In addition a crude lattice model simulating string like interactions is studied to find out how easily a coarse lattice calculation can pick out effects such as bound states which would qualitatively alter the spectrum of the free theory. The role of the critical dimension in obtaining a finite continuum limit is discussed. Instead of the ''gaussian'' lattice model one could use one of the vertex models, whose continuum limit is the same as a gaussian model on a torus of any radius. Indeed, any critical 2 dimensional statistical system will have a stringy continuum limit in the absence of string interactions. 8 refs., 1 fig. , 9 tabs
International Nuclear Information System (INIS)
Smith, L.
1975-01-01
An analysis is given of a number of variants of the basic lattice of the planned ISABELLE storage rings. The variants were formed by removing cells from the normal part of the lattice and juggling the lengths of magnets, cells, and insertions in order to maintain a rational relation of circumference to that of the AGS and approximately the same dispersion. Special insertions, correction windings, and the working line with nonlinear resonances are discussed
Kalleson, E.; Corfu, F.; Dypvik, H.
2009-05-01
Zircon and titanite were investigated in impactites of the Gardnos structure, a crater formed in Sveconorwegian (ca. 1 Ga) crust, which was then overridden in the Devonian by Caledonian nappes. Observed deformation features in zircons are granular texture, planar microstructures, and likely the incorporation of organic carbon during impact causing black staining of the zircon grains. The grains were studied by scanning electron microscopy (SEM) and cathode luminescence (CL) and dated by U-Pb isotope dilution - thermo-ionization mass spectrometry (ID-TIMS). Zircon grains without impact related features have U-Pb data showing moderate discordance (5-13%) and indicating formation ages mostly in the range of 1600-1000 Ma, except detrital zircon ages as old as >2481 Ma, reflecting the diversity of target rocks in the area. Titanite with concordant ages of 995-999 Ma dates metamorphism during final juxtaposition of the Telemarkia on the Idefjorden terrane to the east. Zircon grains with demonstrated or presumed shock features yield highly discordant (14-40%) U-Pb data, with a majority of them plotting along an array with a lower intercept of about 340 Ma reflecting the influence of the Caledonian orogeny and recent Pb-loss. One zircon grain was totally reset at 379 Ma during late Caledonian metamorphism, which also caused local growth of new titanite. A specific group of zircon grains yields data with relatively high discordance for moderate U contents, and five of these analyses, including that of a grain with proven granular or aggregate texture, fit a discordia line with an upper intercept of 546 ± 5 Ma. These features are interpreted as indicating zircon break-down to an amorphous state during impact, with subsequent recrystallization into microcrystalline aggregates causing extensive to complete Pb loss. We further suggest that their crystallinity prevented Pb loss during the Caledonian orogeny, while the small subgrain size and increasing metamictisation allowed
International Nuclear Information System (INIS)
Catterall, Simon
2013-01-01
Discretization of supersymmetric theories is an old problem in lattice field theory. It has resisted solution until quite recently when new ideas drawn from orbifold constructions and topological field theory have been brought to bear on the question. The result has been the creation of a new class of lattice gauge theory in which the lattice action is invariant under one or more supersymmetries. The resultant theories are local and free of doublers and in the case of Yang-Mills theories also possess exact gauge invariance. In principle they form the basis for a truly non-perturbative definition of the continuum supersymmetric field theory. In this talk these ideas are reviewed with particular emphasis being placed on N = 4 super Yang-Mills theory.
International Nuclear Information System (INIS)
Creutz, M.
1984-01-01
After reviewing some recent developments in supercomputer access, the author discusses a few areas where perturbation theory and lattice gauge simulations make contact. The author concludes with a brief discussion of a deterministic dynamics for the Ising model. This may be useful for numerical studies of nonequilibrium phenomena. 13 references
Lattice continuum and diffusional creep.
Mesarovic, Sinisa Dj
2016-04-01
Diffusional creep is characterized by growth/disappearance of lattice planes at the crystal boundaries that serve as sources/sinks of vacancies, and by diffusion of vacancies. The lattice continuum theory developed here represents a natural and intuitive framework for the analysis of diffusion in crystals and lattice growth/loss at the boundaries. The formulation includes the definition of the Lagrangian reference configuration for the newly created lattice, the transport theorem and the definition of the creep rate tensor for a polycrystal as a piecewise uniform, discontinuous field. The values associated with each crystalline grain are related to the normal diffusional flux at grain boundaries. The governing equations for Nabarro-Herring creep are derived with coupled diffusion and elasticity with compositional eigenstrain. Both, bulk diffusional dissipation and boundary dissipation accompanying vacancy nucleation and absorption, are considered, but the latter is found to be negligible. For periodic arrangements of grains, diffusion formally decouples from elasticity but at the cost of a complicated boundary condition. The equilibrium of deviatorically stressed polycrystals is impossible without inclusion of interface energies. The secondary creep rate estimates correspond to the standard Nabarro-Herring model, and the volumetric creep is small. The initial (primary) creep rate is estimated to be much larger than the secondary creep rate.
Energy Technology Data Exchange (ETDEWEB)
Schaefer, Stefan [DESY (Germany). Neumann Inst. for Computing
2016-11-01
These configurations are currently in use in many on-going projects carried out by researchers throughout Europe. In particular this data will serve as an essential input into the computation of the coupling constant of QCD, where some of the simulations are still on-going. But also projects computing the masses of hadrons and investigating their structure are underway as well as activities in the physics of heavy quarks. As this initial project of gauge field generation has been successful, it is worthwhile to extend the currently available ensembles with further points in parameter space. These will allow to further study and control systematic effects like the ones introduced by the finite volume, the non-physical quark masses and the finite lattice spacing. In particular certain compromises have still been made in the region where pion masses and lattice spacing are both small. This is because physical pion masses require larger lattices to keep the effects of the finite volume under control. At light pion masses, a precise control of the continuum extrapolation is therefore difficult, but certainly a main goal of future simulations. To reach this goal, algorithmic developments as well as faster hardware will be needed.
Sman, van der R.G.M.
2006-01-01
In this paper we present lattice Boltzmann (LB) schemes for convection diffusion coupled to fluid flow on two-dimensional rectangular lattices. Via inverse Chapman-Enskog analysis of LB schemes including source terms, we show that for consistency with physics it is required that the moments of the
Scott, Paul
2006-01-01
A lattice is a (rectangular) grid of points, usually pictured as occurring at the intersections of two orthogonal sets of parallel, equally spaced lines. Polygons that have lattice points as vertices are called lattice polygons. It is clear that lattice polygons come in various shapes and sizes. A very small lattice triangle may cover just 3…
LATTICE: an interactive lattice computer code
International Nuclear Information System (INIS)
Staples, J.
1976-10-01
LATTICE is a computer code which enables an interactive user to calculate the functions of a synchrotron lattice. This program satisfies the requirements at LBL for a simple interactive lattice program by borrowing ideas from both TRANSPORT and SYNCH. A fitting routine is included
Hu, Hao; Li, Jian-Wei; McFarlane, Christopher R. M.; Luo, Yan; McCarron, Travis
2017-07-01
The Mangling granitoid pluton, located along the southern margin of the North China Craton, consists mainly of monzogranite with minor amounts of diorite. The monzogranite contains abundant mafic microgranular enclaves (MMEs) and is intruded by numerous mafic dikes, providing an opportunity to study magma mixing and its role in the formation of the granitioid pluton. In this paper, we present in situ analysis of U-Pb isotopes and trace element compositions of titanite from the MMEs and the host monzogranite using Laser Ablation-Inductively Coupled Plasma-Mass Spectrometry to document the role of magma mixing in the formation of the Mangling granitoid pluton. Titanite grains from the MMEs (type 1) are euhedral with patchy zoning, whereas the varieties from the closely associated host monzogranite are euhedral and consist of two types (type 2 and type 3). Type 2 titanite is more abundant and has oscillatory zoning without Fe-Ti oxide inclusions, whereas type 3 grains commonly have Fe-Ti oxide inclusions in the core that is rimmed by inclusion-free overgrowths with weak oscillatory zoning. Titanite from monzogranite without MMEs (type 4) is euhedal and has weak oscillatory zoning, with rare ilmenite inclusions in the core. Titanite from a mafic dike intruding the monzogranite (type 5) is anhedral and has sector zoning. Titanite grains from MMEs and the monzogranite (type 1, 2 and 3) have U-Pb ages that are indistinguishable (149 ± 1 Ma, 148 ± 1 Ma and 148 ± 2 Ma, respectively). These ages agree well with zircon U-Pb ages of 150 ± 1 Ma, 150 ± 1 Ma and 149 ± 1 Ma for the MMEs, host monzogranite, and mafic dike, respectively. The age consistency thus confirms coeval formation of the MMEs, the host monzogranite, and the mafic dikes, demonstrating a mafic magmatic, rather than extraneous or restitic origin for the MMEs. Titanite grains from the MMEs (type 1) and mafic dike (type 5) have much lower Al2O3, REE, Nb/Zr, Y/Zr, and Lu/Hf, but higher (Ce + Nd)/Y and La
International Nuclear Information System (INIS)
Mack, G.
1982-01-01
After a description of a pure Yang-Mills theory on a lattice, the author considers a three-dimensional pure U(1) lattice gauge theory. Thereafter he discusses the exact relation between lattice gauge theories with the gauge groups SU(2) and SO(3). Finally he presents Monte Carlo data on phase transitions in SU(2) and SO(3) lattice gauge models. (HSI)
Spectral tunneling of lattice nonlocal solitons
International Nuclear Information System (INIS)
Kartashov, Yaroslav V.; Torner, Lluis; Vysloukh, Victor A.
2010-01-01
We address spectral tunneling of walking spatial solitons in photorefractive media with nonlocal diffusion component of the nonlinear response and an imprinted shallow optical lattice. In contrast to materials with local nonlinearities, where solitons traveling across the lattice close to the Bragg angle suffer large radiative losses, in photorefractive media with diffusion nonlinearity resulting in self-bending, solitons survive when their propagation angle approaches and even exceeds the Bragg angle. In the spatial frequency domain this effect can be considered as tunneling through the band of spatial frequencies centered around the Bragg frequency where the spatial group velocity dispersion is positive.
Lattices with unique complements
Saliĭ, V N
1988-01-01
The class of uniquely complemented lattices properly contains all Boolean lattices. However, no explicit example of a non-Boolean lattice of this class has been found. In addition, the question of whether this class contains any complete non-Boolean lattices remains unanswered. This book focuses on these classical problems of lattice theory and the various attempts to solve them. Requiring no specialized knowledge, the book is directed at researchers and students interested in general algebra and mathematical logic.
Directory of Open Access Journals (Sweden)
Hanna Jordt-Evangelista
Full Text Available ABSTRACT: In the Itabira-Nova Era Emerald District, southeast Brazil, gemological emerald is extracted from underground mines found in schist-type deposits at the contact zone of the Archean Metavolcanosedimentary Sequence of the Guanhães Complex and Paleoproterozoic anorogenic granites of the Borrachudos Suite. Schist-type deposits are commonly generated by reactions enhanced by deformation and heat during regional metamorphism. The age of the mineralization in the region has been a matter of debate for decades: Ages ranging from the Archean to the Neoproterozoic are mentioned in the literature. In the mineralized zone from the Piteiras mine fluorine-aluminum-bearing titanite is found in metamafic rocks. The fluorine content was probably derived from the Borrachudos granites and pegmatites like the beryllium for emerald, thus both minerals could have been generated during the same event. U-Pb titanite geochronology via laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS was performed on a thin section of a phlogopite-plagioclase-hornblende schist from the Piteiras mine. The determined age of 576 ± 7 Ma is also the probable age for emerald generation during the Brasiliano cycle, which was the only tectonometamorphic event postdating the intrusion of the granites. This event provided heat and fluids necessary for reactions between the Be- and the Cr-bearing rocks, thus enabling the formation of emeralds.
Energy Technology Data Exchange (ETDEWEB)
Kidson, G. V. [Chalk River Nuclear Laboratories, ON (Canada)
1966-02-15
Measurements of atomic mobility in solids are frequently of direct interest to those concerned with the design, development and utilization of materials in engineering. Increasing attention, however, is currently devoted to an understanding of such properties in terms of the occurrence and nature of point and line defects in the crystals. This paper reviews some recent diffusion studies conducted at CRNL that provide, in addition to data of interest in nuclear technology, a means of gaining some insight into the more fundamental nature of the lattice defects occurring in the materials. The systems discussed are (i) self diffusion in the high temperature phase of pure zirconium, (ii) solute diffusion in lead, and (iii) interdiffusion of aluminium and zirconium. The unusual and at present incompletely understood results described in (i) are briefly reviewed. Evidence is given to suggest that diffusion occurs either through a dense dislocation network produced as a result of a martensitic phase transformation, or, alternatively, by excess vacancies introduced into the crystal by impurities. In (ii) the extraordinarily rapid diffusion of noble metal solutes in high-purity lead single crystals will be discussed in terms of the state of solution of the solute atoms. It will be shown that their diffusion behaviour can be understood by assuming that a fraction f{sub i} of the dissolved solute atoms occupy interstitial sites. The measured diffusion coefficient D{sub m} is related to the interstitial diffusion coefficient by D{sub m} = f{sub i}D{sub i}. In (iii) the formation and rapid growth of a single intermetallic compound ZrAl{sub 3} in the diffusion zone formed between pure zirconium and pure aluminium is described and the diffusion mechanism is interpreted in terms of the structure of the compound lattice. The results indicate that ZrAl{sub 3} forms a defect lattice, leading to the relatively rapid migration of aluminium atoms. (author) [French] Les mesures du
New integrable lattice hierarchies
International Nuclear Information System (INIS)
Pickering, Andrew; Zhu Zuonong
2006-01-01
In this Letter we give a new integrable four-field lattice hierarchy, associated to a new discrete spectral problem. We obtain our hierarchy as the compatibility condition of this spectral problem and an associated equation, constructed herein, for the time-evolution of eigenfunctions. We consider reductions of our hierarchy, which also of course admit discrete zero curvature representations, in detail. We find that our hierarchy includes many well-known integrable hierarchies as special cases, including the Toda lattice hierarchy, the modified Toda lattice hierarchy, the relativistic Toda lattice hierarchy, and the Volterra lattice hierarchy. We also obtain here a new integrable two-field lattice hierarchy, to which we give the name of Suris lattice hierarchy, since the first equation of this hierarchy has previously been given by Suris. The Hamiltonian structure of the Suris lattice hierarchy is obtained by means of a trace identity formula
Generalized isothermic lattices
International Nuclear Information System (INIS)
Doliwa, Adam
2007-01-01
We study multi-dimensional quadrilateral lattices satisfying simultaneously two integrable constraints: a quadratic constraint and the projective Moutard constraint. When the lattice is two dimensional and the quadric under consideration is the Moebius sphere one obtains, after the stereographic projection, the discrete isothermic surfaces defined by Bobenko and Pinkall by an algebraic constraint imposed on the (complex) cross-ratio of the circular lattice. We derive the analogous condition for our generalized isothermic lattices using Steiner's projective structure of conics, and we present basic geometric constructions which encode integrability of the lattice. In particular, we introduce the Darboux transformation of the generalized isothermic lattice and we derive the corresponding Bianchi permutability principle. Finally, we study two-dimensional generalized isothermic lattices, in particular geometry of their initial boundary value problem
Lattice theory for nonspecialists
International Nuclear Information System (INIS)
Hari Dass, N.D.
1984-01-01
These lectures were delivered as part of the academic training programme at the NIKHEF-H. These lectures were intended primarily for experimentalists, and theorists not specializing in lattice methods. The goal was to present the essential spirit behind the lattice approach and consequently the author has concentrated mostly on issues of principle rather than on presenting a large amount of detail. In particular, the author emphasizes the deep theoretical infra-structure that has made lattice studies meaningful. At the same time, he has avoided the use of heavy formalisms as they tend to obscure the basic issues for people trying to approach this subject for the first time. The essential ideas are illustrated with elementary soluble examples not involving complicated mathematics. The following subjects are discussed: three ways of solving the harmonic oscillator problem; latticization; gauge fields on a lattice; QCD observables; how to solve lattice theories. (Auth.)
International Nuclear Information System (INIS)
Creutz, M.
1983-04-01
In the last few years lattice gauge theory has become the primary tool for the study of nonperturbative phenomena in gauge theories. The lattice serves as an ultraviolet cutoff, rendering the theory well defined and amenable to numerical and analytical work. Of course, as with any cutoff, at the end of a calculation one must consider the limit of vanishing lattice spacing in order to draw conclusions on the physical continuum limit theory. The lattice has the advantage over other regulators that it is not tied to the Feynman expansion. This opens the possibility of other approximation schemes than conventional perturbation theory. Thus Wilson used a high temperature expansion to demonstrate confinement in the strong coupling limit. Monte Carlo simulations have dominated the research in lattice gauge theory for the last four years, giving first principle calculations of nonperturbative parameters characterizing the continuum limit. Some of the recent results with lattice calculations are reviewed
On Traveling Waves in Lattices: The Case of Riccati Lattices
Dimitrova, Zlatinka
2012-09-01
The method of simplest equation is applied for analysis of a class of lattices described by differential-difference equations that admit traveling-wave solutions constructed on the basis of the solution of the Riccati equation. We denote such lattices as Riccati lattices. We search for Riccati lattices within two classes of lattices: generalized Lotka-Volterra lattices and generalized Holling lattices. We show that from the class of generalized Lotka-Volterra lattices only the Wadati lattice belongs to the class of Riccati lattices. Opposite to this many lattices from the Holling class are Riccati lattices. We construct exact traveling wave solutions on the basis of the solution of Riccati equation for three members of the class of generalized Holling lattices.
Lattice degeneracies of fermions
International Nuclear Information System (INIS)
Raszillier, H.
1983-10-01
We present a detailed description of the minimal degeneracies of geometric (Kaehler) fermions on all the lattices of maximal symmetries in n = 1, ..., 4 dimensions. We also determine the isolated orbits of the maximal symmetry groups, which are related to the minimal numbers of ''naive'' fermions on the reciprocals of these lattices. It turns out that on the self-reciprocal lattices the minimal numbers of naive fermions are equal to the minimal numbers of degrees of freedom of geometric fermions. The description we give relies on the close connection of the maximal lattice symmetry groups with (affine) Weyl groups of root systems of (semi-) simple Lie algebras. (orig.)
International Nuclear Information System (INIS)
Shindler, A.
2007-07-01
I review the theoretical foundations, properties as well as the simulation results obtained so far of a variant of the Wilson lattice QCD formulation: Wilson twisted mass lattice QCD. Emphasis is put on the discretization errors and on the effects of these discretization errors on the phase structure for Wilson-like fermions in the chiral limit. The possibility to use in lattice simulations different lattice actions for sea and valence quarks to ease the renormalization patterns of phenomenologically relevant local operators, is also discussed. (orig.)
Energy Technology Data Exchange (ETDEWEB)
Shindler, A. [Deutsches Elektronen-Synchrotron (DESY), Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2007-07-15
I review the theoretical foundations, properties as well as the simulation results obtained so far of a variant of the Wilson lattice QCD formulation: Wilson twisted mass lattice QCD. Emphasis is put on the discretization errors and on the effects of these discretization errors on the phase structure for Wilson-like fermions in the chiral limit. The possibility to use in lattice simulations different lattice actions for sea and valence quarks to ease the renormalization patterns of phenomenologically relevant local operators, is also discussed. (orig.)
Diffusion in Coulomb crystals.
Hughto, J; Schneider, A S; Horowitz, C J; Berry, D K
2011-07-01
Diffusion in Coulomb crystals can be important for the structure of neutron star crusts. We determine diffusion constants D from molecular dynamics simulations. We find that D for Coulomb crystals with relatively soft-core 1/r interactions may be larger than D for Lennard-Jones or other solids with harder-core interactions. Diffusion, for simulations of nearly perfect body-centered-cubic lattices, involves the exchange of ions in ringlike configurations. Here ions "hop" in unison without the formation of long lived vacancies. Diffusion, for imperfect crystals, involves the motion of defects. Finally, we find that diffusion, for an amorphous system rapidly quenched from Coulomb parameter Γ=175 to Coulomb parameters up to Γ=1750, is fast enough that the system starts to crystalize during long simulation runs. These results strongly suggest that Coulomb solids in cold white dwarf stars, and the crust of neutron stars, will be crystalline and not amorphous.
Directory of Open Access Journals (Sweden)
Epelbaum E.
2010-04-01
Full Text Available We review recent progress on nuclear lattice simulations using chiral eﬀective ﬁeld theory. We discuss lattice results for dilute neutron matter at next-to-leading order, three-body forces at next-to-next-toleading order, isospin-breaking and Coulomb eﬀects, and the binding energy of light nuclei.
International Nuclear Information System (INIS)
Jersak, J.
1986-01-01
This year has brought a sudden interest in lattice Higgs models. After five years of only modest activity we now have many new results obtained both by analytic and Monte Carlo methods. This talk is a review of the present state of lattice Higgs models with particular emphasis on the recent development
Lattice Boltzmann model for numerical relativity.
Ilseven, E; Mendoza, M
2016-02-01
In the Z4 formulation, Einstein equations are written as a set of flux conservative first-order hyperbolic equations that resemble fluid dynamics equations. Based on this formulation, we construct a lattice Boltzmann model for numerical relativity and validate it with well-established tests, also known as "apples with apples." Furthermore, we find that by increasing the relaxation time, we gain stability at the cost of losing accuracy, and by decreasing the lattice spacings while keeping a constant numerical diffusivity, the accuracy and stability of our simulations improve. Finally, in order to show the potential of our approach, a linear scaling law for parallelization with respect to number of CPU cores is demonstrated. Our model represents the first step in using lattice kinetic theory to solve gravitational problems.
Beirau, Tobias; Murawski, Dawid; Behrens, Harald; Salje, Ekhard K. H.; Groat, Lee A.; Kaden, Ronny; Pöllmann, Herbert; Bismayer, Ulrich
2018-01-01
In situ temperature-dependent laser-induced photoluminescence and dielectric measurements provide new evidence for the local occurrence of the α → β phase transition near 500 K in the preserved crystalline parts of natural radiation-damaged titanite (sample E2335 with ~24% amorphous fraction, containing Fe and Al impurities). Photoluminescence spectroscopic measurements show an anomaly in the vicinity of 500 K. The temperature-dependent evolution of the real part of the electrical conductivity (σ) and the real (ɛ‧) and the imaginary (ɛ″) part of the complex dielectric permittivity (ɛ *) of titanite have been measured at various AC frequencies (~1.2-96.8 kHz). Despite the masking and smearing effect of impurities and defects, the temperature-dependent behaviour of ɛ‧ and ɛ″ around the transition temperature of the investigated natural titanite E2335 shows a remarkable similarity to that of the synthetic end-member material (see Zhang et al (1995 Phys. Chem. Miner. 22 41-9)). This study indicates the suitability of photoluminescence and impedance spectroscopy for the detection of phase transitions, even in heavily disordered systems.
Quantum diffusion in semi-infinite periodic and quasiperiodic systems
International Nuclear Information System (INIS)
Zhang Kaiwang
2008-01-01
This paper studies quantum diffusion in semi-infinite one-dimensional periodic lattice and quasiperiodic Fibonacci lattice. It finds that the quantum diffusion in the semi-infinite periodic lattice shows the same properties as that for the infinite periodic lattice. Different behaviour is found for the semi-infinite Fibonacci lattice. In this case, there are still C(t) ∼ t −δ and d(t) ∼ t β . However, it finds that 0 < δ < 1 for smaller time, and δ = 0 for larger time due to the influence of surface localized states. Moreover, β for the semi-infinite Fibonacci lattice is much smaller than that for the infinite Fibonacci lattice. Effects of disorder on the quantum diffusion are also discussed
On singularities of lattice varieties
Mukherjee, Himadri
2013-01-01
Toric varieties associated with distributive lattices arise as a fibre of a flat degeneration of a Schubert variety in a minuscule. The singular locus of these varieties has been studied by various authors. In this article we prove that the number of diamonds incident on a lattice point $\\a$ in a product of chain lattices is more than or equal to the codimension of the lattice. Using this we also show that the lattice varieties associated with product of chain lattices is smooth.
On techniques of ATR lattice computation
International Nuclear Information System (INIS)
1997-08-01
Lattice computation is to compute the average nuclear constants of unit fuel lattice which are required for computing core nuclear characteristics such as core power distribution and reactivity characteristics. The main nuclear constants are infinite multiplying rate, neutron movement area, cross section for diffusion computation, local power distribution and isotope composition. As for the lattice computation code, WIMS-ATR is used, which is based on the WIMS-D code developed in U.K., and for the purpose of heightening the accuracy of analysis, which was improved by adding heavy water scattering cross section considering the temperature dependence by Honeck model. For the computation of the neutron absorption by control rods, LOIEL BLUE code is used. The extrapolation distance of neutron flux on control rod surfaces is computed by using THERMOS and DTF codes, and the lattice constants of adjoining lattices are computed by using the WIMS-ATR code. As for the WIMS-ATR code, the computation flow and nuclear data library, and as for the LOIEL BLUE code, the computation flow are explained. The local power distribution in fuel assemblies determined by the WIMS-ATR code was verified with the measured data, and the results are reported. (K.I.)
Diffusion between evolving interfaces
International Nuclear Information System (INIS)
Juntunen, Janne; Merikoski, Juha
2010-01-01
Diffusion in an evolving environment is studied by continuous-time Monte Carlo simulations. Diffusion is modeled by continuous-time random walkers on a lattice, in a dynamic environment provided by bubbles between two one-dimensional interfaces driven symmetrically towards each other. For one-dimensional random walkers constrained by the interfaces, the bubble size distribution dominates diffusion. For two-dimensional random walkers, it is also controlled by the topography and dynamics of the interfaces. The results of the one-dimensional case are recovered in the limit where the interfaces are strongly driven. Even with simple hard-core repulsion between the interfaces and the particles, diffusion is found to depend strongly on the details of the dynamical rules of particles close to the interfaces.
International Nuclear Information System (INIS)
Mackenzie, Paul
1989-01-01
The forty-year dream of understanding the properties of the strongly interacting particles from first principles is now approaching reality. Quantum chromodynamics (QCD - the field theory of the quark and gluon constituents of strongly interacting particles) was initially handicapped by the severe limitations of the conventional (perturbation) approach in this picture, but Ken Wilson's inventions of lattice gauge theory and renormalization group methods opened new doors, making calculations of masses and other particle properties possible. Lattice gauge theory became a major industry around 1980, when Monte Carlo methods were introduced, and the first prototype calculations yielded qualitatively reasonable results. The promising developments over the past year were highlighted at the 1988 Symposium on Lattice Field Theory - Lattice 88 - held at Fermilab
DEFF Research Database (Denmark)
Risager, Morten S.; Södergren, Carl Anders
2017-01-01
It is well known that the angles in a lattice acting on hyperbolic n -space become equidistributed. In this paper we determine a formula for the pair correlation density for angles in such hyperbolic lattices. Using this formula we determine, among other things, the asymptotic behavior of the den......It is well known that the angles in a lattice acting on hyperbolic n -space become equidistributed. In this paper we determine a formula for the pair correlation density for angles in such hyperbolic lattices. Using this formula we determine, among other things, the asymptotic behavior...... of the density function in both the small and large variable limits. This extends earlier results by Boca, Pasol, Popa and Zaharescu and Kelmer and Kontorovich in dimension 2 to general dimension n . Our proofs use the decay of matrix coefficients together with a number of careful estimates, and lead...
International Nuclear Information System (INIS)
Kulikowska, T.
1999-01-01
The present lecture has a main goal to show how the transport lattice calculations are realised in a standard computer code. This is illustrated on the example of the WIMSD code, belonging to the most popular tools for reactor calculations. Most of the approaches discussed here can be easily modified to any other lattice code. The description of the code assumes the basic knowledge of reactor lattice, on the level given in the lecture on 'Reactor lattice transport calculations'. For more advanced explanation of the WIMSD code the reader is directed to the detailed descriptions of the code cited in References. The discussion of the methods and models included in the code is followed by the generally used homogenisation procedure and several numerical examples of discrepancies in calculated multiplication factors based on different sources of library data. (author)
Energy Technology Data Exchange (ETDEWEB)
Mackenzie, Paul
1989-03-15
The forty-year dream of understanding the properties of the strongly interacting particles from first principles is now approaching reality. Quantum chromodynamics (QCD - the field theory of the quark and gluon constituents of strongly interacting particles) was initially handicapped by the severe limitations of the conventional (perturbation) approach in this picture, but Ken Wilson's inventions of lattice gauge theory and renormalization group methods opened new doors, making calculations of masses and other particle properties possible. Lattice gauge theory became a major industry around 1980, when Monte Carlo methods were introduced, and the first prototype calculations yielded qualitatively reasonable results. The promising developments over the past year were highlighted at the 1988 Symposium on Lattice Field Theory - Lattice 88 - held at Fermilab.
International Nuclear Information System (INIS)
Christ, Norman H
2000-01-01
The architecture and capabilities of the computers currently in use for large-scale lattice QCD calculations are described and compared. Based on this present experience, possible future directions are discussed
International Nuclear Information System (INIS)
Kulikowska, T.
2001-01-01
The description of reactor lattice codes is carried out on the example of the WIMSD-5B code. The WIMS code in its various version is the most recognised lattice code. It is used in all parts of the world for calculations of research and power reactors. The version WIMSD-5B is distributed free of charge by NEA Data Bank. The description of its main features given in the present lecture follows the aspects defined previously for lattice calculations in the lecture on Reactor Lattice Transport Calculations. The spatial models are described, and the approach to the energy treatment is given. Finally the specific algorithm applied in fuel depletion calculations is outlined. (author)
International Nuclear Information System (INIS)
Petronzio, R.
1992-01-01
Lattice gauge theories are about fifteen years old and I will report on the present status of the field without making the elementary introduction that can be found in the proceedings of the last two conferences. The talk covers briefly the following subjects: the determination of α s , the status of spectroscopy, heavy quark physics and in particular the calculation of their hadronic weak matrix elements, high temperature QCD, non perturbative Higgs bounds, chiral theories on the lattice and induced theories
Kiefel, Martin; Jampani, Varun; Gehler, Peter V.
2014-01-01
This paper presents a convolutional layer that is able to process sparse input features. As an example, for image recognition problems this allows an efficient filtering of signals that do not lie on a dense grid (like pixel position), but of more general features (such as color values). The presented algorithm makes use of the permutohedral lattice data structure. The permutohedral lattice was introduced to efficiently implement a bilateral filter, a commonly used image processing operation....
Castle, Toen; Sussman, Daniel M; Tanis, Michael; Kamien, Randall D
2016-09-01
Kirigami uses bending, folding, cutting, and pasting to create complex three-dimensional (3D) structures from a flat sheet. In the case of lattice kirigami, this cutting and rejoining introduces defects into an underlying 2D lattice in the form of points of nonzero Gaussian curvature. A set of simple rules was previously used to generate a wide variety of stepped structures; we now pare back these rules to their minimum. This allows us to describe a set of techniques that unify a wide variety of cut-and-paste actions under the rubric of lattice kirigami, including adding new material and rejoining material across arbitrary cuts in the sheet. We also explore the use of more complex lattices and the different structures that consequently arise. Regardless of the choice of lattice, creating complex structures may require multiple overlapping kirigami cuts, where subsequent cuts are not performed on a locally flat lattice. Our additive kirigami method describes such cuts, providing a simple methodology and a set of techniques to build a huge variety of complex 3D shapes.
Displacive stability of a void in a void lattice
International Nuclear Information System (INIS)
Brailsford, A.D.
1977-01-01
It has recently been suggested that the stability of the void-lattice structure in irradiated metals may be attributed to the effect of the overlapping of the point-defect diffusion fields associated with each void. It is shown here, however, that the effect is much too weak. When one void is displaced from its lattice site, the displacement is shown to relax to zero as proposed, but a conservative estimate indicates that the characteristic time is equivalent to an irradiation dose of the order of 300 displacements per atom which is generally much greater than the dose necessary for void-lattice formation
Entire solutions for bistable lattice differential equations with obstacles
Hoffman, Aaron; Vleck, E S Van
2018-01-01
The authors consider scalar lattice differential equations posed on square lattices in two space dimensions. Under certain natural conditions they show that wave-like solutions exist when obstacles (characterized by "holes") are present in the lattice. Their work generalizes to the discrete spatial setting the results obtained in Berestycki, Hamel, and Matuno (2009) for the propagation of waves around obstacles in continuous spatial domains. The analysis hinges upon the development of sub and super-solutions for a class of discrete bistable reaction-diffusion problems and on a generalization of a classical result due to Aronson and Weinberger that concerns the spreading of localized disturbances.
Lattice regularized chiral perturbation theory
International Nuclear Information System (INIS)
Borasoy, Bugra; Lewis, Randy; Ouimet, Pierre-Philippe A.
2004-01-01
Chiral perturbation theory can be defined and regularized on a spacetime lattice. A few motivations are discussed here, and an explicit lattice Lagrangian is reviewed. A particular aspect of the connection between lattice chiral perturbation theory and lattice QCD is explored through a study of the Wess-Zumino-Witten term
Vortex lattices in layered superconductors
International Nuclear Information System (INIS)
Prokic, V.; Davidovic, D.; Dobrosavljevic-Grujic, L.
1995-01-01
We study vortex lattices in a superconductor--normal-metal superlattice in a parallel magnetic field. Distorted lattices, resulting from the shear deformations along the layers, are found to be unstable. Under field variation, nonequilibrium configurations undergo an infinite sequence of continuous transitions, typical for soft lattices. The equilibrium vortex arrangement is always a lattice of isocell triangles, without shear
Diffusion processes and memory effects
International Nuclear Information System (INIS)
Mokshin, Anatolii V; Yulmetyev, Renat M; Haenggi, Peter
2005-01-01
We report the results of the numerical estimation of statistical memory effects in diffusion for two various systems: Lennard-Jones fluids and the model of the Brownian particle in a one-dimensional harmonic lattice. We have found the relation between the diffusion coefficient and the non-Markovity parameter, which is linear for the Lennard-Jones systems in liquid state. The relation between the memory measure and the excess entropy is also discussed here
Anomalous diffusion in niobium. Study of solute diffusion mechanism of iron in niobium
International Nuclear Information System (INIS)
Ablitzer, D.
1977-01-01
In order to explain anomalously high diffusion velocities observed for iron diffusion in niobium, the following parameters were measured: isotope effect, b factor (which expresses the effect of iron on niobium self-diffusion), self-diffusion coefficient of niobium, solute diffusion coefficient of iron in niobium. The results obtained show that neither pure vacancy models, nor diffusion in the lattice defects (dislocations, sub-boundaries, grain boundaries), nor pure interstitialy mechanisms, nor simple or cyclic exchange mechanisms agree with experiments. A mechanism is proposed which considers an equilibrium between substitution iron atoms and interstitial iron atoms. The diffusion of iron then occurs through interstitial vancancy pairs [fr
Low-energy scattering on the lattice
International Nuclear Information System (INIS)
Bour Bour, Shahin
2014-01-01
In this thesis we present precision benchmark calculations for two-component fermions in the unitarity limit using an ab initio method, namely Hamiltonian lattice formalism. We calculate the ground state energy for unpolarized four particles (Fermi gas) in a periodic cube as a fraction of the ground state energy of the non-interacting system for two independent representations of the lattice Hamiltonians. We obtain the values 0.211(2) and 0.210(2). These results are in full agreement with the Euclidean lattice and fixed-node diffusion Monte Carlo calculations. We also give an expression for the energy corrections to the binding energy of a bound state in a moving frame. These corrections contain information about the mass and number of the constituents and are topological in origin and will have a broad applications to the lattice calculations of nucleons, nuclei, hadronic molecules and cold atoms. As one of its applications we use this expression and determine the low-energy parameters for the fermion dimer elastic scattering in shallow binding limit. For our lattice calculations we use Luescher's finite volume method. From the lattice calculations we find κa fd =1.174(9) and κr fd =-0.029(13), where κ represents the binding momentum of dimer and a fd (r fd ) denotes the scattering length (effective-range). These results are confirmed by the continuum calculations using the Skorniakov-Ter-Martirosian integral equation which gives 1.17907(1) and -0.0383(3) for the scattering length and effective range, respectively.
Stochastic reaction-diffusion algorithms for macromolecular crowding
Sturrock, Marc
2016-06-01
Compartment-based (lattice-based) reaction-diffusion algorithms are often used for studying complex stochastic spatio-temporal processes inside cells. In this paper the influence of macromolecular crowding on stochastic reaction-diffusion simulations is investigated. Reaction-diffusion processes are considered on two different kinds of compartmental lattice, a cubic lattice and a hexagonal close packed lattice, and solved using two different algorithms, the stochastic simulation algorithm and the spatiocyte algorithm (Arjunan and Tomita 2010 Syst. Synth. Biol. 4, 35-53). Obstacles (modelling macromolecular crowding) are shown to have substantial effects on the mean squared displacement and average number of molecules in the domain but the nature of these effects is dependent on the choice of lattice, with the cubic lattice being more susceptible to the effects of the obstacles. Finally, improvements for both algorithms are presented.
International Nuclear Information System (INIS)
Chodos, A.
1978-01-01
A version of lattice gauge theory is presented in which the shape of the lattice is not assumed at the outset but is a consequence of the dynamics. Other related features which are not specified a priori include the internal and space-time symmetry groups and the dimensionality of space-time. The theory possesses a much larger invariance group than the usual gauge group on a lattice, and has associated with it an integer k 0 analogous to the topological quantum numer of quantum chromodynamics. Families of semiclassical solutions are found which are labeled by k 0 and a second integer x, but the analysis is not carried far enough to determine which space-time and internal symmetry groups characterize the lowest-lying states of the theory
Graphene antidot lattice waveguides
DEFF Research Database (Denmark)
Pedersen, Jesper Goor; Gunst, Tue; Markussen, Troels
2012-01-01
We introduce graphene antidot lattice waveguides: nanostructured graphene where a region of pristine graphene is sandwiched between regions of graphene antidot lattices. The band gaps in the surrounding antidot lattices enable localized states to emerge in the central waveguide region. We model...... the waveguides via a position-dependent mass term in the Dirac approximation of graphene and arrive at analytical results for the dispersion relation and spinor eigenstates of the localized waveguide modes. To include atomistic details we also use a tight-binding model, which is in excellent agreement...... with the analytical results. The waveguides resemble graphene nanoribbons, but without the particular properties of ribbons that emerge due to the details of the edge. We show that electrons can be guided through kinks without additional resistance and that transport through the waveguides is robust against...
Energy Technology Data Exchange (ETDEWEB)
Catterall, Simon; Kaplan, David B.; Unsal, Mithat
2009-03-31
We provide an introduction to recent lattice formulations of supersymmetric theories which are invariant under one or more real supersymmetries at nonzero lattice spacing. These include the especially interesting case of N = 4 SYM in four dimensions. We discuss approaches based both on twisted supersymmetry and orbifold-deconstruction techniques and show their equivalence in the case of gauge theories. The presence of an exact supersymmetry reduces and in some cases eliminates the need for fine tuning to achieve a continuum limit invariant under the full supersymmetry of the target theory. We discuss open problems.
International Nuclear Information System (INIS)
Jones, D.B.
1986-01-01
EPRI-LATTICE is a multigroup neutron transport computer code for the analysis of light water reactor fuel assemblies. It can solve the two-dimensional neutron transport problem by two distinct methods: (a) the method of collision probabilities and (b) the method of discrete ordinates. The code was developed by S. Levy Inc. as an account of work sponsored by the Electric Power Research Institute (EPRI). The collision probabilities calculation in EPRI-LATTICE (L-CP) is based on the same methodology that exists in the lattice codes CPM-2 and EPRI-CPM. Certain extensions have been made to the data representations of the CPM programs to improve the overall accuracy of the calculation. The important extensions include unique representations of scattering matrices and fission fractions (chi) for each composition in the problem. A new capability specifically developed for the EPRI-LATTICE code is a discrete ordinates methodology. The discrete ordinates calculation in EPRI-LATTICE (L-SN) is based on the discrete S/sub n/ methodology that exists in the TWODANT program. In contrast to TWODANT, which utilizes synthetic diffusion acceleration and supports multiple geometries, only the transport equations are solved by L-SN and only the data representations for the two-dimensional geometry are treated
Muon diffusion in noble metals
International Nuclear Information System (INIS)
Schillaci, M.E.; Bokema, C.; Heffner, R.H.; Hutson, R.L.; Leon, M.; Olsen, C.E.; Dodds, S.A.; MacLaughlin, D.E.; Richards, P.M.
1983-01-01
Diffusion-induced muon depolarization in dilute AgGd and AgEr were measured in the temperature range 200-700 K and have thereby determined the muon diffusion parameters in Ag. The diffusion parameters for μ + in Cu, Ag, and Au are compared with those of hydrogen. For Ag and Au, the μ + parameters are similar to those of hydrogen, whereas for Cu, the μ + parameters are much smaller. Lattice-activated tunneling and over-barrier hopping are investigated with computational models. 15 references, 1 figure, 2 tables
Muon diffusion in noble metals
International Nuclear Information System (INIS)
Schillaci, M.E.; Boekema, C.; Heffner, R.H.; Hutson, R.L.; Leon, M.; Olsen, C.E.; Dodds, S.A.; MacLaughlin, D.E.; Richards, P.M.
1982-01-01
Diffusion-induced muon depolarization was measured in dilute AgGd and AgEr in the temperature range 200 to 700 0 K and have thereby determined the muon diffusion parameters in Ag. The diffusion parameters for μ + in Cu, Ag, and Au are compared with those of hydrogen. For Ag and Au, the μ + parameters are similar to those of hydrogen, whereas for Cu, the μ + parameters are much smaller. Lattice-activated tunneling and over-barrier hopping are investigated with computational models
Lattice-Boltzmann simulations of droplet evaporation
Ledesma-Aguilar, Rodrigo; Vella, Dominic; Yeomans, Julia M.
2014-01-01
© the Partner Organisations 2014. We study the utility and validity of lattice-Boltzmann (LB) simulations to explore droplet evaporation driven by a concentration gradient. Using a binary-fluid lattice-Boltzmann algorithm based on Cahn-Hilliard dynamics, we study the evaporation of planar films and 3D sessile droplets from smooth solid surfaces. Our results show that LB simulations accurately reproduce the classical regime of quasi-static dynamics. Beyond this limit, we show that the algorithm can be used to explore regimes where the evaporative and diffusive timescales are not widely separated, and to include the effect of boundaries of prescribed driving concentration. We illustrate the method by considering the evaporation of a droplet from a solid surface that is chemically patterned with hydrophilic and hydrophobic stripes. This journal is
Lattice-Boltzmann simulations of droplet evaporation
Ledesma-Aguilar, Rodrigo
2014-09-04
© the Partner Organisations 2014. We study the utility and validity of lattice-Boltzmann (LB) simulations to explore droplet evaporation driven by a concentration gradient. Using a binary-fluid lattice-Boltzmann algorithm based on Cahn-Hilliard dynamics, we study the evaporation of planar films and 3D sessile droplets from smooth solid surfaces. Our results show that LB simulations accurately reproduce the classical regime of quasi-static dynamics. Beyond this limit, we show that the algorithm can be used to explore regimes where the evaporative and diffusive timescales are not widely separated, and to include the effect of boundaries of prescribed driving concentration. We illustrate the method by considering the evaporation of a droplet from a solid surface that is chemically patterned with hydrophilic and hydrophobic stripes. This journal is
International Nuclear Information System (INIS)
Krojts, M.
1987-01-01
The book by the known american physicist-theoretist M.Kreuts represents the first monography in world literature, where a new perspective direction in elementary particle physics and quantum field theory - lattice formulation of gauge theories is stated systematically. Practically all main ideas of this direction are given. Material is stated in systematic and understandable form
Phenomenology Using Lattice QCD
Gupta, R.
2005-08-01
This talk provides a brief summary of the status of lattice QCD calculations of the light quark masses and the kaon bag parameter BK. Precise estimates of these four fundamental parameters of the standard model, i.e., mu, md, ms and the CP violating parameter η, help constrain grand unified models and could provide a window to new physics.
International Nuclear Information System (INIS)
Bali, G.S.
2005-01-01
I comment on progress of lattice QCD techniques and calculations. Recent results on pentaquark masses as well as of the spectrum of excited baryons are summarized and interpreted. The present state of calculations of quantities related to the nucleon structure and of electromagnetic transition form factors is surveyed
Finite lattice extrapolation algorithms
International Nuclear Information System (INIS)
Henkel, M.; Schuetz, G.
1987-08-01
Two algorithms for sequence extrapolation, due to von den Broeck and Schwartz and Bulirsch and Stoer are reviewed and critically compared. Applications to three states and six states quantum chains and to the (2+1)D Ising model show that the algorithm of Bulirsch and Stoer is superior, in particular if only very few finite lattice data are available. (orig.)
Williamson, S. Gill
2010-01-01
Will the cosmological multiverse, when described mathematically, have easily stated properties that are impossible to prove or disprove using mathematical physics? We explore this question by constructing lattice multiverses which exhibit such behavior even though they are much simpler mathematically than any likely cosmological multiverse.
de Raedt, Hans; von der Linden, W.; Binder, K
1995-01-01
In this chapter we review methods currently used to perform Monte Carlo calculations for quantum lattice models. A detailed exposition is given of the formalism underlying the construction of the simulation algorithms. We discuss the fundamental and technical difficulties that are encountered and
Scott, Paul
2006-01-01
A "convex" polygon is one with no re-entrant angles. Alternatively one can use the standard convexity definition, asserting that for any two points of the convex polygon, the line segment joining them is contained completely within the polygon. In this article, the author provides a solution to a problem involving convex lattice polygons.
International Nuclear Information System (INIS)
Autin, B.
1984-01-01
After a description of the constraints imposed by the cooling of Antiprotons on the lattice of the rings, the reasons which motivate the shape and the structure of these machines are surveyed. Linear and non-linear beam optics properties are treated with a special amplification to the Antiproton Accumulator. (orig.)
Unquenched lattice upsilon spectroscopy
International Nuclear Information System (INIS)
Marcantonio, L.M.
2001-03-01
A non-relativistic effective theory of QCD (NRQCD) is used in calculations of the upsilon spectrum. Simultaneous multi-correlation fitting routines are used to yield lattice channel energies and amplitudes. The lattice configurations used were both dynamical, with two flavours of sea quarks included in the action; and quenched, with no sea quarks. These configurations were generated by the UKQCD collaboration. The dynamical configurations used were ''matched'', having the same lattice spacing, but differing in the sea quark mass. Thus, it was possible to analyse trends of observables with sea quark mass, in the certainty that the trend isn't partially due to varying lattice spacing. The lattice spacing used for spectroscopy was derived from the lattice 1 1 P 1 - 1 3 S 1 splitting. On each set of configurations two lattice bare b quark masses were used, giving kinetic masses bracketing the physical Υ mass. The only quantity showing a strong dependence on these masses was the hyperfine splitting, so it was interpolated to the real Υ mass. The radial and orbital splittings gave good agreement with experiment. The hyperfine splitting results showed a clear signal for unquenching and the dynamical hyperfine splitting results were extrapolated to a physical sea quark mass. This result, combined with the quenched result yielded a value for the hyperfine splitting at n f = 3, predicting an η b mass of 9.517(4) GeV. The NRQCD technique for obtaining a value of the strong coupling constant in the M-barS-bar scheme was followed. Using quenched and dynamical results a value was extrapolated to n f = 3. Employing a three loop beta function to run the coupling, with suitable matching conditions at heavy quark thresholds, the final result was obtained for n f = 5 at a scale equal to the Z boson mass. This result was α(5)/MS(Mz)=0.110(4). Two methods for finding the mass of the b quark in the MS scheme were employed. The results of both methods agree within error but the
Determination of D2O - 2% enriched uranium lattice parameters by means of a critical system
International Nuclear Information System (INIS)
Raisic, N.; Takac, S.; Markovic, H.; Bosevski, T.
1963-01-01
In order to specify experimental procedures for few standard measurements sufficient to provide consistent set of lattice parameters, a series of experiments were performed at the RB reactor using 2% enriched tubular fuel elements. Obtained results were compared to standard two-group diffusion calculation indicating high degree of accuracy for a broad variety of reactor lattice configurations
Anomalous diffusion of fermions in superlattices
International Nuclear Information System (INIS)
Drozdz, S.; Okolowicz, J.; Srokowski, T.; Ploszajczak, M.
1996-03-01
Diffusion of fermions in the periodic two-dimensional lattice of fermions is studied. It is shown that effects connected with antisymmetrization of the wave function increase chaoticness of motion. Various types of anomalous diffusion, characterized by a power spectral analysis are found. The nonlocality of the Pauli potential destroys cantori in the phase space. Consequently, the diffusion process is dominated by long free paths and the power spectrum is logarithmic at small frequency limit. (author)
New definition of the cell diffusion coefficient
International Nuclear Information System (INIS)
Koehler, P.
1975-01-01
As was shown in a recent work by Gelbard, the usually applied Benoist definition of the cell diffusion coefficient gives two different values if two different definitions of the cell are made. A new definition is proposed that preserves the neutron balance for the homogenized lattice and that is independent of the cell definition. The resulting diffusion coefficient is identical with the main term of Benoist's diffusion coefficient
Quark–gluon plasma phenomenology from anisotropic lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Skullerud, Jon-Ivar; Kelly, Aoife [Department of Mathematical Physics, Maynooth University, Maynooth, Co Kildare (Ireland); Aarts, Gert; Allton, Chris; Amato, Alessandro; Evans, P. Wynne M.; Hands, Simon [Department of Physics, Swansea University, Swansea SA2 8PP, Wales (United Kingdom); Burnier, Yannis [Institut de Théorie des Phénomènes Physiques, Ecole Polytechnique Fédérale de Lausanne, CH–1015 Lausanne (Switzerland); Giudice, Pietro [Institut für Theoretische Physik, Universität Münster, D–48149 Münster (Germany); Harris, Tim; Ryan, Sinéad M. [School of Mathematics, Trinity College, Dublin 2 (Ireland); Kim, Seyong [Department of Physics, Sejong University, Seoul 143-747 (Korea, Republic of); Lombardo, Maria Paola [INFN–Laboratori Nazionali di Frascati, I–00044 Frascati (RM) (Italy); Oktay, Mehmet B. [Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa 52242 (United States); Rothkopf, Alexander [Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, D–69120 Heidelberg (Germany)
2016-01-22
The FASTSUM collaboration has been carrying out simulations of N{sub f} = 2 + 1 QCD at nonzero temperature in the fixed-scale approach using anisotropic lattices. Here we present the status of these studies, including recent results for electrical conductivity and charge diffusion, and heavy quarkonium (charm and beauty) physics.
Superspace approach to lattice supersymmetry
International Nuclear Information System (INIS)
Kostelecky, V.A.; Rabin, J.M.
1984-01-01
We construct a cubic lattice of discrete points in superspace, as well as a discrete subgroup of the supersymmetry group which maps this ''superlattice'' into itself. We discuss the connection between this structure and previous versions of lattice supersymmetry. Our approach clarifies the mathematical problems of formulating supersymmetric lattice field theories and suggests new methods for attacking them
Basis reduction for layered lattices
Torreão Dassen, Erwin
2011-01-01
We develop the theory of layered Euclidean spaces and layered lattices. We present algorithms to compute both Gram-Schmidt and reduced bases in this generalized setting. A layered lattice can be seen as lattices where certain directions have infinite weight. It can also be
International Nuclear Information System (INIS)
Woloshyn, R.M.
1988-03-01
The basic concepts of the Lagrangian formulation of lattice field theory are discussed. The Wilson and staggered schemes for dealing with fermions on the lattice are described. Some recent results for hadron masses and vector and axial vector current matrix elements in lattice QCD are reviewed. (Author) (118 refs., 16 figs.)
Basis reduction for layered lattices
E.L. Torreão Dassen (Erwin)
2011-01-01
htmlabstractWe develop the theory of layered Euclidean spaces and layered lattices. With this new theory certain problems that usually are solved by using classical lattices with a "weighting" gain a new, more natural form. Using the layered lattice basis reduction algorithms introduced here these
Lattice gas simulations of replicating domains
International Nuclear Information System (INIS)
Dawson, S.P.; Hasslacher, B.; Pearson, J.E.
1993-01-01
We use the lattice gas cellular automation (LGCA) developed to simulate a process of pattern-formation recently observed in reaction-diffusion systems. We study the reaction mechanism, which is an extension of the Selkov model for glycolytic oscillations. We are able to reproduce the self-replicating domains observed in this work. We use the LGCA simulation to estimate the smallest length-scale on which this process can occur under conditions encountered in the cell. These estimates are similar to those obtained for Turing patterns in the same setting
Lattice gas simulations of replicating domains
Energy Technology Data Exchange (ETDEWEB)
Dawson, S.P.; Hasslacher, B.; Pearson, J.E.
1993-12-31
We use the lattice gas cellular automation (LGCA) developed to simulate a process of pattern-formation recently observed in reaction-diffusion systems. We study the reaction mechanism, which is an extension of the Selkov model for glycolytic oscillations. We are able to reproduce the self-replicating domains observed in this work. We use the LGCA simulation to estimate the smallest length-scale on which this process can occur under conditions encountered in the cell. These estimates are similar to those obtained for Turing patterns in the same setting.
Nonlinear lattice waves in heterogeneous media
International Nuclear Information System (INIS)
Laptyeva, T V; Ivanchenko, M V; Flach, S
2014-01-01
We discuss recent advances in the understanding of the dynamics of nonlinear lattice waves in heterogeneous media, which enforce complete wave localization in the linear wave equation limit, especially Anderson localization for random potentials, and Aubry–André localization for quasiperiodic potentials. Additional nonlinear terms in the wave equations can either preserve the phase-coherent localization of waves, or destroy it through nonintegrability and deterministic chaos. Spreading wave packets are observed to show universal features in their dynamics which are related to properties of nonlinear diffusion equations. (topical review)
Energy Technology Data Exchange (ETDEWEB)
Buechner, O. [Zentralinstitut fuer Angewandte Mathematik ZAM, 52425 Juelich (Germany); Ernst, M. [Deutsches Elektronen-Synchrotron DESY, 22603 Hamburg (Germany); Jansen, K. [John von Neumann-Institut fuer Computing NIC/DESY, 15738 Zeuthen (Germany); Lippert, Th. [Zentralinstitut fuer Angewandte Mathematik ZAM, 52425 Juelich (Germany); Melkumyan, D. [Deutsches Elektronen-Synchrotron DESY, 15738 Zeuthen (Germany); Orth, B. [Zentralinstitut fuer Angewandte Mathematik ZAM, 52425 Juelich (Germany); Pleiter, D. [John von Neumann-Institut fuer Computing NIC/DESY, 15738 Zeuthen (Germany)]. E-mail: dirk.pleiter@desy.de; Stueben, H. [Konrad-Zuse-Institut fuer Informationstechnik ZIB, 14195 Berlin (Germany); Wegner, P. [Deutsches Elektronen-Synchrotron DESY, 15738 Zeuthen (Germany); Wollny, S. [Konrad-Zuse-Institut fuer Informationstechnik ZIB, 14195 Berlin (Germany)
2006-04-01
As the need for computing resources to carry out numerical simulations of Quantum Chromodynamics (QCD) formulated on a lattice has increased significantly, efficient use of the generated data has become a major concern. To improve on this, groups plan to share their configurations on a worldwide level within the International Lattice DataGrid (ILDG). Doing so requires standardized description of the configurations, standards on binary file formats and common middleware interfaces. We describe the requirements and problems, and discuss solutions. Furthermore, an overview is given on the implementation of the LatFor DataGrid [http://www-zeuthen.desy.de/latfor/ldg], a France/German/Italian grid that will be one of the regional grids within the ILDG grid-of-grids concept.
International Nuclear Information System (INIS)
Borsanyi, Sz.; Kampert, K.H.; Fodor, Z.; Forschungszentrum Juelich; Eoetvoes Univ., Budapest
2016-06-01
We present a full result for the equation of state (EoS) in 2+1+1 (up/down, strange and charm quarks are present) flavour lattice QCD. We extend this analysis and give the equation of state in 2+1+1+1 flavour QCD. In order to describe the evolution of the universe from temperatures several hundreds of GeV to the MeV scale we also include the known effects of the electroweak theory and give the effective degree of freedoms. As another application of lattice QCD we calculate the topological susceptibility (χ) up to the few GeV temperature region. These two results, EoS and χ, can be used to predict the dark matter axion's mass in the post-inflation scenario and/or give the relationship between the axion's mass and the universal axionic angle, which acts as a initial condition of our universe.
International Nuclear Information System (INIS)
Lutz, H.D.; Willich, P.
1977-01-01
The FIR absorption spectra of pyrite type compounds RuS 2 , RuSsub(2-x)Sesub(x), RuSe 2 , RuTe 2 , OsS 2 , OsSe 2 , and PtP 2 as well as loellingite type phosphides FeP 2 , RuP 2 , and OsP 2 are reported. For RuS 2 , RuSe 2 , RuTe 2 , OsS 2 , and PtP 2 all of the five infrared allowed modes (k = 0) are observed. As a first result of a numerical normal coordinate treatment vibration forms of pyrite structure are communicated. The spectra show that lattice forces of corresponding sulfides, tellurides, and phosphides are about the same strength, but increase strongly by substitution of iron by ruthenium and especially of ruthenium by osmium. The lattice constants of the RuSsub(2-x)Sesub(x) solid solution obey Vegard's rule. (author)
Solórzano, S.; Mendoza, M.; Succi, S.; Herrmann, H. J.
2018-01-01
We present a numerical scheme to solve the Wigner equation, based on a lattice discretization of momentum space. The moments of the Wigner function are recovered exactly, up to the desired order given by the number of discrete momenta retained in the discretization, which also determines the accuracy of the method. The Wigner equation is equipped with an additional collision operator, designed in such a way as to ensure numerical stability without affecting the evolution of the relevant moments of the Wigner function. The lattice Wigner scheme is validated for the case of quantum harmonic and anharmonic potentials, showing good agreement with theoretical results. It is further applied to the study of the transport properties of one- and two-dimensional open quantum systems with potential barriers. Finally, the computational viability of the scheme for the case of three-dimensional open systems is also illustrated.
Lattice Quantum Chromodynamics
Sachrajda, C T
2016-01-01
I review the the application of the lattice formulation of QCD and large-scale numerical simulations to the evaluation of non-perturbative hadronic effects in Standard Model Phenomenology. I present an introduction to the elements of the calculations and discuss the limitations both in the range of quantities which can be studied and in the precision of the results. I focus particularly on the extraction of the QCD parameters, i.e. the quark masses and the strong coupling constant, and on important quantities in flavour physics. Lattice QCD is playing a central role in quantifying the hadronic effects necessary for the development of precision flavour physics and its use in exploring the limits of the Standard Model and in searches for inconsistencies which would signal the presence of new physics.
Lattices of dielectric resonators
Trubin, Alexander
2016-01-01
This book provides the analytical theory of complex systems composed of a large number of high-Q dielectric resonators. Spherical and cylindrical dielectric resonators with inferior and also whispering gallery oscillations allocated in various lattices are considered. A new approach to S-matrix parameter calculations based on perturbation theory of Maxwell equations, developed for a number of high-Q dielectric bodies, is introduced. All physical relationships are obtained in analytical form and are suitable for further computations. Essential attention is given to a new unified formalism of the description of scattering processes. The general scattering task for coupled eigen oscillations of the whole system of dielectric resonators is described. The equations for the expansion coefficients are explained in an applicable way. The temporal Green functions for the dielectric resonator are presented. The scattering process of short pulses in dielectric filter structures, dielectric antennas and lattices of d...
International Nuclear Information System (INIS)
Hasenfratz, A.; Hasenfratz, P.
1985-01-01
This paper deals almost exclusively with applications in QCD. Presumably QCD will remain in the center of lattice calculations in the near future. The existing techniques and the available computer resources should be able to produce trustworthy results in pure SU(3) gauge theory and in quenched hadron spectroscopy. Going beyond the quenched approximation might require some technical breakthrough or exceptional computer resources, or both. Computational physics has entered high-energy physics. From this point of view, lattice QCD is only one (although the most important, at present) of the research fields. Increasing attention is devoted to the study of other QFTs. It is certain that the investigation of nonasymptotically free theories, the Higgs phenomenon, or field theories that are not perturbatively renormalizable will be important research areas in the future
Lattice degeneracies of geometric fermions
International Nuclear Information System (INIS)
Raszillier, H.
1983-05-01
We give the minimal numbers of degrees of freedom carried by geometric fermions on all lattices of maximal symmetries in d = 2, 3, and 4 dimensions. These numbers are lattice dependent, but in the (free) continuum limit, part of the degrees of freedom have to escape to infinity by a Wilson mechanism built in, and 2sup(d) survive for any lattice. On self-reciprocal lattices we compare the minimal numbers of degrees of freedom of geometric fermions with the minimal numbers of naive fermions on these lattices and argue that these numbers are equal. (orig.)
Anderson localization in bipartite lattices
International Nuclear Information System (INIS)
Fabrizio, Michele; Castellani, Claudio
2000-01-01
We study the localization properties of a disordered tight-binding Hamiltonian on a generic bipartite lattice close to the band center. By means of a fermionic replica trick method, we derive the effective non-linear σ-model describing the diffusive modes, which we analyse by using the Wilson-Polyakov renormalization group. In addition to the standard parameters which define the non-linear σ-model, namely, the conductance and the external frequency, a new parameter enters, which may be related to the fluctuations of the staggered density of states. We find that, when both the regular hopping and the disorder only couple one sublattice to the other, the quantum corrections to the Kubo conductivity vanish at the band center, thus implying the existence of delocalized states. In two dimensions, the RG equations predict that the conductance flows to a finite value, while both the density of states and the staggered density of states fluctuations diverge. In three dimensions, we find that, sufficiently close to the band center, all states are extended, independently of the disorder strength. We also discuss the role of various symmetry breaking terms, as a regular hopping between same sublattices, or an on-site disorder
Anderson localization in bipartite lattices
International Nuclear Information System (INIS)
Fabrizio, M.; Castellani, C.
2000-04-01
We study the localization properties of a disordered tight-binding Hamiltonian on a generic bipartite lattice close to the band center. By means of a fermionic replica trick method, we derive the effective non-linear σ-model describing the diffusive modes, which we analyse by using the Wilson-Polyakov renormalization group. In addition to the standard parameters which define the non-linear σ-model, namely the conductance and the external frequency, a new parameter enters, which may be related to the fluctuations of the staggered density of states. We find that, when both the regular hopping and the disorder only couple one sublattice to the other, the quantum corrections to the Kubo conductivity vanish at the band center, thus implying the existence of delocalized states. In two dimensions, the RG equations predict that the conductance flows to a finite value, while both the density of states and the staggered density of states fluctuations diverge. In three dimensions, we find that, sufficiently close to the band center, all states are extended, independently of the disorder strength. We also discuss the role of various symmetry breaking terms, as a regular hopping between same sublattices, or an on-site disorder. (author)
International Nuclear Information System (INIS)
1962-01-01
The panel was attended by prominent physicists from most of the well-known laboratories in the field of light-water lattices, who exchanged the latest information on the status of work in their countries and discussed both the theoretical and the experimental aspects of the subjects. The supporting papers covered most problems, including criticality, resonance absorption, thermal utilization, spectrum calculations and the physics of plutonium bearing systems. Refs, figs and tabs
Automated lattice data generation
Directory of Open Access Journals (Sweden)
Ayyar Venkitesh
2018-01-01
Full Text Available The process of generating ensembles of gauge configurations (and measuring various observables over them can be tedious and error-prone when done “by hand”. In practice, most of this procedure can be automated with the use of a workflow manager. We discuss how this automation can be accomplished using Taxi, a minimal Python-based workflow manager built for generating lattice data. We present a case study demonstrating this technology.
Automated lattice data generation
Ayyar, Venkitesh; Hackett, Daniel C.; Jay, William I.; Neil, Ethan T.
2018-03-01
The process of generating ensembles of gauge configurations (and measuring various observables over them) can be tedious and error-prone when done "by hand". In practice, most of this procedure can be automated with the use of a workflow manager. We discuss how this automation can be accomplished using Taxi, a minimal Python-based workflow manager built for generating lattice data. We present a case study demonstrating this technology.
Energy Technology Data Exchange (ETDEWEB)
Kumar, J [Agra Coll. (India). Dept. of Physics
1977-03-01
In the present work, a local model pseudopotential has been proposed to study the lattice dynamics of thorium. The model potential depends on the core and ionic radii, and accounts for the s-d-f hybridization effects in a phenomenological way. When this form of potential is applied to derive the photon dispersion curves of Th, sufficiently good agreement is found between the computed and experimental results.
International Nuclear Information System (INIS)
Bowler, Ken
1990-01-01
One of the major recent developments in particle theory has been the use of very high performance computers to obtain approximate numerical solutions of quantum field theories by formulating them on a finite space-time lattice. The great virtue of this new technique is that it avoids the straitjacket of perturbation theory and can thus attack new, but very fundamental problems, such as the calculation of hadron masses in quark-gluon field theory (quantum chromodynamics - QCD)
Adamatzky, Andrew
2015-01-01
The book gives a comprehensive overview of the state-of-the-art research and engineering in theory and application of Lattice Automata in design and control of autonomous Robots. Automata and robots share the same notional meaning. Automata (originated from the latinization of the Greek word “αυτόματον”) as self-operating autonomous machines invented from ancient years can be easily considered the first steps of robotic-like efforts. Automata are mathematical models of Robots and also they are integral parts of robotic control systems. A Lattice Automaton is a regular array or a collective of finite state machines, or automata. The Automata update their states by the same rules depending on states of their immediate neighbours. In the context of this book, Lattice Automata are used in developing modular reconfigurable robotic systems, path planning and map exploration for robots, as robot controllers, synchronisation of robot collectives, robot vision, parallel robotic actuators. All chapters are...
Digital lattice gauge theories
Zohar, Erez; Farace, Alessandro; Reznik, Benni; Cirac, J. Ignacio
2017-02-01
We propose a general scheme for a digital construction of lattice gauge theories with dynamical fermions. In this method, the four-body interactions arising in models with 2 +1 dimensions and higher are obtained stroboscopically, through a sequence of two-body interactions with ancillary degrees of freedom. This yields stronger interactions than the ones obtained through perturbative methods, as typically done in previous proposals, and removes an important bottleneck in the road towards experimental realizations. The scheme applies to generic gauge theories with Lie or finite symmetry groups, both Abelian and non-Abelian. As a concrete example, we present the construction of a digital quantum simulator for a Z3 lattice gauge theory with dynamical fermionic matter in 2 +1 dimensions, using ultracold atoms in optical lattices, involving three atomic species, representing the matter, gauge, and auxiliary degrees of freedom, that are separated in three different layers. By moving the ancilla atoms with a proper sequence of steps, we show how we can obtain the desired evolution in a clean, controlled way.
Dielectric lattice gauge theory
International Nuclear Information System (INIS)
Mack, G.
1983-06-01
Dielectric lattice gauge theory models are introduced. They involve variables PHI(b)epsilong that are attached to the links b = (x+esub(μ),x) of the lattice and take their values in the linear space g which consists of real linear combinations of matrices in the gauge group G. The polar decomposition PHI(b)=U(b)osub(μ)(x) specifies an ordinary lattice gauge field U(b) and a kind of dielectric field epsilonsub(ij)proportionalosub(i)osub(j)sup(*)deltasub(ij). A gauge invariant positive semidefinite kinetic term for the PHI-field is found, and it is shown how to incorporate Wilson fermions in a way which preserves Osterwalder Schrader positivity. Theories with G = SU(2) and without matter fields are studied in some detail. It is proved that confinement holds, in the sense that Wilson loop expectation values show an area law decay, if the Euclidean action has certain qualitative features which imply that PHI = 0 (i.e. dielectric field identical 0) is the unique maximum of the action. (orig.)
Dielectric lattice gauge theory
International Nuclear Information System (INIS)
Mack, G.
1984-01-01
Dielectric lattice gauge theory models are introduced. They involve variables PHI(b)element ofG that are attached to the links b = (x+esub(μ), x) of the lattice and take their values in the linear space G which consists of real linear combinations of matrices in the gauge group G. The polar decomposition PHI(b)=U(b)sigmasub(μ)(x) specifies an ordinary lattice gauge field U(b) and a kind of dielectric field epsilonsub(ij)proportional sigmasub(i)sigmasub(j)sup(*)deltasub(ij). A gauge invariant positive semidefinite kinetic term for the PHI-field is found, and it is shown how to incorporate Wilson fermions in a way which preserves Osterwalder-Schrader positivity. Theories with G = SU(2) and without matter fields are studied in some detail. It is proved that confinement holds, in the sense that Wilson-loop expectation values show an area law decay, if the euclidean action has certain qualitative features which imply that PHI=0 (i.e. dielectric field identical 0) is the unique maximum of the action. (orig.)
Toward lattice fractional vector calculus
Tarasov, Vasily E.
2014-09-01
An analog of fractional vector calculus for physical lattice models is suggested. We use an approach based on the models of three-dimensional lattices with long-range inter-particle interactions. The lattice analogs of fractional partial derivatives are represented by kernels of lattice long-range interactions, where the Fourier series transformations of these kernels have a power-law form with respect to wave vector components. In the continuum limit, these lattice partial derivatives give derivatives of non-integer order with respect to coordinates. In the three-dimensional description of the non-local continuum, the fractional differential operators have the form of fractional partial derivatives of the Riesz type. As examples of the applications of the suggested lattice fractional vector calculus, we give lattice models with long-range interactions for the fractional Maxwell equations of non-local continuous media and for the fractional generalization of the Mindlin and Aifantis continuum models of gradient elasticity.
Directory of Open Access Journals (Sweden)
R.T. DeHoff
2002-09-01
Full Text Available The phenomenological formalism, which yields Fick's Laws for diffusion in single phase multicomponent systems, is widely accepted as the basis for the mathematical description of diffusion. This paper focuses on problems associated with this formalism. This mode of description of the process is cumbersome, defining as it does matrices of interdiffusion coefficients (the central material properties that require a large experimental investment for their evaluation in three component systems, and, indeed cannot be evaluated for systems with more than three components. It is also argued that the physical meaning of the numerical values of these properties with respect to the atom motions in the system remains unknown. The attempt to understand the physical content of the diffusion coefficients in the phenomenological formalism has been the central fundamental problem in the theory of diffusion in crystalline alloys. The observation by Kirkendall that the crystal lattice moves during diffusion led Darken to develop the concept of intrinsic diffusion, i.e., atom motion relative to the crystal lattice. Darken and his successors sought to relate the diffusion coefficients computed for intrinsic fluxes to those obtained from the motion of radioactive tracers in chemically homogeneous samples which directly report the jump frequencies of the atoms as a function of composition and temperature. This theoretical connection between tracer, intrinsic and interdiffusion behavior would provide the basis for understanding the physical content of interdiffusion coefficients. Definitive tests of the resulting theoretical connection have been carried out for a number of binary systems for which all three kinds of observations are available. In a number of systems predictions of intrinsic coefficients from tracer data do not agree with measured values although predictions of interdiffusion coefficients appear to give reasonable agreement. Thus, the complete
Quantum diffusion in a dynamically disordered medium
International Nuclear Information System (INIS)
Jayannavar, A.M.
1983-07-01
For a particle moving in a dynamically disordered continuum it is found that the exact quantum mechanical mean squared displacement 2 (t)> is proportional to t 3 , for t→infinity. The result differs qualitatively from the diffusive behaviour well known for the one-band lattice Hamiltonian, and is understandable in terms of momentum cut-off inherent in the lattice. Finally treatment for incorporating the friction in a quantum transport is given. (author)
Numerical modelling of random walk one-dimensional diffusion
International Nuclear Information System (INIS)
Vamos, C.; Suciu, N.; Peculea, M.
1996-01-01
The evolution of a particle which moves on a discrete one-dimensional lattice, according to a random walk low, approximates better the diffusion process smaller the steps of the spatial lattice and time are. For a sufficiently large assembly of particles one can assume that their relative frequency at lattice knots approximates the distribution function of the diffusion process. This assumption has been tested by simulating on computer two analytical solutions of the diffusion equation: the Brownian motion and the steady state linear distribution. To evaluate quantitatively the similarity between the numerical and analytical solutions we have used a norm given by the absolute value of the difference of the two solutions. Also, a diffusion coefficient at any lattice knots and moment of time has been calculated, by using the numerical solution both from the diffusion equation and the particle flux given by Fick's low. The difference between diffusion coefficient of analytical solution and the spatial lattice mean coefficient of numerical solution constitutes another quantitative indication of the similarity of the two solutions. The results obtained show that the approximation depends first on the number of particles at each knot of the spatial lattice. In conclusion, the random walk is a microscopic process of the molecular dynamics type which permits simulations precision of the diffusion processes with given precision. The numerical method presented in this work may be useful both in the analysis of real experiments and for theoretical studies
Lattice-induced nonadiabatic frequency shifts in optical lattice clocks
International Nuclear Information System (INIS)
Beloy, K.
2010-01-01
We consider the frequency shift in optical lattice clocks which arises from the coupling of the electronic motion to the atomic motion within the lattice. For the simplest of three-dimensional lattice geometries this coupling is shown to affect only clocks based on blue-detuned lattices. We have estimated the size of this shift for the prospective strontium lattice clock operating at the 390-nm blue-detuned magic wavelength. The resulting fractional frequency shift is found to be on the order of 10 -18 and is largely overshadowed by the electric quadrupole shift. For lattice clocks based on more complex geometries or other atomic systems, this shift could potentially be a limiting factor in clock accuracy.
Lattice topology dictates photon statistics.
Kondakci, H Esat; Abouraddy, Ayman F; Saleh, Bahaa E A
2017-08-21
Propagation of coherent light through a disordered network is accompanied by randomization and possible conversion into thermal light. Here, we show that network topology plays a decisive role in determining the statistics of the emerging field if the underlying lattice is endowed with chiral symmetry. In such lattices, eigenmode pairs come in skew-symmetric pairs with oppositely signed eigenvalues. By examining one-dimensional arrays of randomly coupled waveguides arranged on linear and ring topologies, we are led to a remarkable prediction: the field circularity and the photon statistics in ring lattices are dictated by its parity while the same quantities are insensitive to the parity of a linear lattice. For a ring lattice, adding or subtracting a single lattice site can switch the photon statistics from super-thermal to sub-thermal, or vice versa. This behavior is understood by examining the real and imaginary fields on a lattice exhibiting chiral symmetry, which form two strands that interleave along the lattice sites. These strands can be fully braided around an even-sited ring lattice thereby producing super-thermal photon statistics, while an odd-sited lattice is incommensurate with such an arrangement and the statistics become sub-thermal.
On the geometrical factor in the off-centre diffusion
International Nuclear Information System (INIS)
Despa, F.; Apostol, M.
1995-07-01
The geometrical factor of the off-centre diffusion coefficient is computed for certain two- and three-dimensional cubic lattice, and a method is indicated for estimating this factor in more general cases. (author). 7 refs, 4 figs
International Nuclear Information System (INIS)
Kilcup, G.
1986-01-01
A progress report on a lattice project at Los Alamos is presented. The projects are basically of two sorts: approaching the continuum (determination of MCRG flows under the blocking transformation, and beta-function along Wilson and improved action lines); and arriving at the continuum (hadron spectrum, coupling constants, and matrix elements). Since the ultimate goal is to determine matrix elements for which chiral symmetry is very relevant, the authors choose the formalism whose chiral properties are easier to understand, i.e., staggered fermions
Lattice of quantum predictions
Drieschner, Michael
1993-10-01
What is the structure of reality? Physics is supposed to answer this question, but a purely empiristic view is not sufficient to explain its ability to do so. Quantum mechanics has forced us to think more deeply about what a physical theory is. There are preconditions every physical theory must fulfill. It has to contain, e.g., rules for empirically testable predictions. Those preconditions give physics a structure that is “a priori” in the Kantian sense. An example is given how the lattice structure of quantum mechanics can be understood along these lines.
Lattice Vibrations in Chlorobenzenes:
DEFF Research Database (Denmark)
Reynolds, P. A.; Kjems, Jørgen; White, J. W.
1974-01-01
Lattice vibrational dispersion curves for the ``intermolecular'' modes in the triclinic, one molecule per unit cell β phase of p‐C6D4Cl2 and p‐C6H4Cl2 have been obtained by inelastic neutron scattering. The deuterated sample was investigated at 295 and at 90°K and a linear extrapolation to 0°K...... was applied in order to correct for anharmonic effects. Calculations based on the atom‐atom model for van der Waals' interaction and on general potential parameters for the aromatic compounds agree reasonably well with the experimental observations. There is no substantial improvement in fit obtained either...
Diamond lattice Heisenberg antiferromagnet
Oitmaa, J.
2018-04-01
We investigate ground-state and high-temperature properties of the nearest-neighbour Heisenberg antiferromagnet on the three-dimensional diamond lattice, using series expansion methods. The ground-state energy and magnetization, as well as the magnon spectrum, are calculated and found to be in good agreement with first-order spin-wave theory, with a quantum renormalization factor of about 1.13. High-temperature series are derived for the free energy, and physical and staggered susceptibilities for spin S = 1/2, 1 and 3/2, and analysed to obtain the corresponding Curie and Néel temperatures.
Lattice cell burnup calculation
International Nuclear Information System (INIS)
Pop-Jordanov, J.
1977-01-01
Accurate burnup prediction is a key item for design and operation of a power reactor. It should supply information on isotopic changes at each point in the reactor core and the consequences of these changes on the reactivity, power distribution, kinetic characters, control rod patterns, fuel cycles and operating strategy. A basic stage in the burnup prediction is the lattice cell burnup calculation. This series of lectures attempts to give a review of the general principles and calculational methods developed and applied in this area of burnup physics
Crisafulli, M.; Martinelli, G.; Sachrajda, Christopher T.; Crisafulli, M; Gimenez, V; Martinelli, G; Sachrajda, C T
1994-01-01
We present the first lattice calculation of the B-meson binding energy \\labar and of the kinetic energy \\lambda_1/2 m_Q of the heavy-quark inside the pseudoscalar B-meson. In order to cancel the ambiguities due to the ultraviolet renormalons present in the operator matrix elements, this calculation has required the non-perturbative subtraction of the power divergences present in the Lagrangian operator \\energy and in the kinetic energy operator \\kkinetic. The non-perturbative renormalization of the relevant operators has been implemented by imposing suitable renormalization conditions on quark matrix elements in the Landau gauge.
International Nuclear Information System (INIS)
Vidovsky, I.; Kereszturi, A.
1991-11-01
The results of experiments and calculations on Gd lattices are presented, and a comparison of experimental and calculational data is given. This latter can be divided into four groups. The first belongs to the comparison of criticality parameters, the second group is related with the comparison of 2D distributions, the third one relates the comparison of intra-macrocell distributions, whereas the fourth group is devoted for the comparison of spectral parameters. For comparison, the computer code RFIT based on strict statistical criteria has been used. The calculated and measured results agree, in most cases, sufficiently. (R.P.) 11 refs.; 13 figs.; 9 tabs
Lattice Transparency of Graphene.
Chae, Sieun; Jang, Seunghun; Choi, Won Jin; Kim, Youn Sang; Chang, Hyunju; Lee, Tae Il; Lee, Jeong-O
2017-03-08
Here, we demonstrated the transparency of graphene to the atomic arrangement of a substrate surface, i.e., the "lattice transparency" of graphene, by using hydrothermally grown ZnO nanorods as a model system. The growth behaviors of ZnO nanocrystals on graphene-coated and uncoated substrates with various crystal structures were investigated. The atomic arrangements of the nucleating ZnO nanocrystals exhibited a close match with those of the respective substrates despite the substrates being bound to the other side of the graphene. By using first-principles calculations based on density functional theory, we confirmed the energetic favorability of the nucleating phase following the atomic arrangement of the substrate even with the graphene layer present in between. In addition to transmitting information about the atomic lattice of the substrate, graphene also protected its surface. This dual role enabled the hydrothermal growth of ZnO nanorods on a Cu substrate, which otherwise dissolved in the reaction conditions when graphene was absent.
Introduction to lattice gauge theories
International Nuclear Information System (INIS)
La Cock, P.
1988-03-01
A general introduction to Lattice Gauge Theory (LGT) is given. The theory is discussed from first principles to facilitate an understanding of the techniques used in LGT. These include lattice formalism, gauge invariance, fermions on the lattice, group theory and integration, strong coupling methods and mean field techniques. A review of quantum chromodynamics on the lattice at finite temperature and density is also given. Monte Carlo results and analytical methods are discussed. An attempt has been made to include most relevant data up to the end of 1987, and to update some earlier reviews existing on the subject. 224 refs., 33 figs., 14 tabs
Hadron structure from lattice QCD
International Nuclear Information System (INIS)
Schaefer, Andreas
2008-01-01
Some elements and current developments of lattice QCD are reviewed, with special emphasis on hadron structure observables. In principle, high precision experimental and lattice data provide nowadays a very detailled picture of the internal structure of hadrons. However, to relate both, a very good controle of perturbative QCD is needed in many cases. Finally chiral perturbation theory is extremely helpful to boost the precision of lattice calculations. The mutual need and benefit of all four elements: experiment, lattice QCD, perturbative QCD and chiral perturbation theory is the main topic of this review
Lattice formulations of reggeon interactions
International Nuclear Information System (INIS)
Brower, R.C.; Ellis, J.; Savit, R.; Zinn-Justin, J.
1976-01-01
A class of lattice analogues to reggeon field theory is examined. First the transition from a continuum to a lattice field theory is discussed, emphasizing the necessity of a Wick rotation and the consideration of symmetry properties. Next the theory is transformed to a discrete system with two spins at each lattice site, and the problems of the triple-reggeon interaction and the reggeon energy gap are discussed. It is pointed out that transferring the theory from the continuum to a lattice necesarily introduces new relevant operators not normally present in reggeon field theory. (Auth.)
Huang diffuse scattering of neutrons
International Nuclear Information System (INIS)
Burkel, E.; Guerard, B. v.; Metzger, H.; Peisl, J.
1979-01-01
Huang diffuse neutron scattering was measured for the first time on niobium with interstitially dissolved deuterium as well as on MgO after neutron irradiation and Li 7 F after γ-irradiation. With Huang diffuse scattering the strength and symmetry of the distortion field around lattice defects can be determined. Our results clearly demonstrate that this method is feasible with neutrons. The present results are compared with X-ray experiments and the advantages of using neutrons is discussed in some detail. (orig.)
Elimination of spurious lattice fermion solutions and noncompact lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Lee, T.D.
1997-09-22
It is well known that the Dirac equation on a discrete hyper-cubic lattice in D dimension has 2{sup D} degenerate solutions. The usual method of removing these spurious solutions encounters difficulties with chiral symmetry when the lattice spacing l {ne} 0, as exemplified by the persistent problem of the pion mass. On the other hand, we recall that in any crystal in nature, all the electrons do move in a lattice and satisfy the Dirac equation; yet there is not a single physical result that has ever been entangled with a spurious fermion solution. Therefore it should not be difficult to eliminate these unphysical elements. On a discrete lattice, particle hop from point to point, whereas in a real crystal the lattice structure in embedded in a continuum and electrons move continuously from lattice cell to lattice cell. In a discrete system, the lattice functions are defined only on individual points (or links as in the case of gauge fields). However, in a crystal the electron state vector is represented by the Bloch wave functions which are continuous functions in {rvec {gamma}}, and herein lies one of the essential differences.
Lattice quantum chromodynamics
International Nuclear Information System (INIS)
Hassenfratz, P.
1983-01-01
It is generally accepted that relativistic field theory is relevant in high energy physics. It is also recognized that even in QCD, which is asymptotically free, the scope of perturbation theory is very limited. Despite the tremendous theoretical and experimental effort to study scaling, scaling violations, e + e - , lepton pair creation, jets, etc., the answer to the question whether and to what extent is QCD the theory of strong interactions is vague. At present-day energies it is difficult to disentangle perturbative and non-perturbative effects. The author states that QCD must be understood and that quantitative non-perturbative methods are needed. He states that the lattice formulation of field theories is a promising approach to meeting this need and discusses the formulation in detail in this paper
Geometry of lattice field theory
International Nuclear Information System (INIS)
Honan, T.J.
1986-01-01
Using some tools of algebraic topology, a general formalism for lattice field theory is presented. The lattice is taken to be a simplicial complex that is also a manifold and is referred to as a simplicial manifold. The fields on this lattice are cochains, that are called lattice forms to emphasize the connections with differential forms in the continuum. This connection provides a new bridge between lattice and continuum field theory. A metric can be put onto this simplicial manifold by assigning lengths to every link or I-simplex of the lattice. Regge calculus is a way of defining general relativity on this lattice. A geometric discussion of Regge calculus is presented. The Regge action, which is a discrete form of the Hilbert action, is derived from the Hilbert action using distribution valued forms. This is a new derivation that emphasizes the underlying geometry. Kramers-Wannier duality in statistical mechanics is discussed in this general setting. Nonlinear field theories, which include gauge theories and nonlinear sigma models are discussed in the continuum and then are put onto a lattice. The main new result here is the generalization to curved spacetime, which consists of making the theory compatible with Regge calculus
Remarks on lattice gauge models
International Nuclear Information System (INIS)
Grosse, H.
1981-01-01
The author reports a study of the phase structure of lattice gauge models where one takes as a gauge group a non-abelian discrete subgroup of SU(3). In addition he comments on a lattice action proposed recently by Manton and observes that it violates a positivity property. (Auth.)
Remarks on lattice gauge models
International Nuclear Information System (INIS)
Grosse, H.
1981-01-01
The author reports on a study of the phase structure of lattice gauge models where one takes as a gauge group a non-abelian discrete subgroup of SU(3). In addition he comments on a lattice action proposed recently by Manton (1980) and observes that it violates a positivity property. (Auth.)
Lattices, supersymmetry and Kaehler fermions
International Nuclear Information System (INIS)
Scott, D.M.
1984-01-01
It is shown that a graded extension of the space group of a (generalised) simple cubic lattice exists in any space dimension, D. The fermionic variables which arise admit a Kaehlerian interpretation. Each graded space group is a subgroup of a graded extension of the appropriate Euclidean group, E(D). The relevance of this to the construction of lattice theories is discussed. (author)
Lattice polytopes in coding theory
Directory of Open Access Journals (Sweden)
Ivan Soprunov
2015-05-01
Full Text Available In this paper we discuss combinatorial questions about lattice polytopes motivated by recent results on minimum distance estimation for toric codes. We also include a new inductive bound for the minimum distance of generalized toric codes. As an application, we give new formulas for the minimum distance of generalized toric codes for special lattice point configurations.
Description of the lattice code POWDERPUFS-V
International Nuclear Information System (INIS)
Rouben, B.; Tin, E.S.Y.; Loken, P.C.
1995-10-01
POWDERPUFS-V is a lattice code written specifically for CANDU lattices. The moderator is limited to reactor-grade heavy water, while the coolant may be light water, heavy water, air or HB-40 (organic fluid). The fuel can by UO 2 , U, U 3 Si, U-C or U-Zr, in the form of either a single rod or a cluster of pins. The program calculates the four-factor parameters and also provides lattice nuclear cross sections for use in finite-core neutron-diffusion codes. A burnup calculation is included. In this report, the general capabilities of the program are discussed. (author) 24 refs., 4 tabs., 12 figs
Stabilizing the thermal lattice Boltzmann method by spatial filtering.
Gillissen, J J J
2016-10-01
We propose to stabilize the thermal lattice Boltzmann method by filtering the second- and third-order moments of the collision operator. By means of the Chapman-Enskog expansion, we show that the additional numerical diffusivity diminishes in the low-wavnumber limit. To demonstrate the enhanced stability, we consider a three-dimensional thermal lattice Boltzmann system involving 33 discrete velocities. Filtering extends the linear stability of this thermal lattice Boltzmann method to 10-fold smaller transport coefficients. We further demonstrate that the filtering does not compromise the accuracy of the hydrodynamics by comparing simulation results to reference solutions for a number of standardized test cases, including natural convection in two dimensions.
Engineering self-organising helium bubble lattices in tungsten.
Harrison, R W; Greaves, G; Hinks, J A; Donnelly, S E
2017-08-10
The self-organisation of void and gas bubbles in solids into superlattices is an intriguing nanoscale phenomenon. Despite the discovery of these lattices 45 years ago, the atomistics behind the ordering mechanisms responsible for the formation of these nanostructures are yet to be fully elucidated. Here we report on the direct observation via transmission electron microscopy of the formation of bubble lattices under He ion bombardment. By careful control of the irradiation conditions, it has been possible to engineer the bubble size and spacing of the superlattice leading to important conclusions about the significance of vacancy supply in determining the physical characteristics of the system. Furthermore, no bubble lattice alignment was observed in the directions pointing to a key driving mechanism for the formation of these ordered nanostructures being the two-dimensional diffusion of self-interstitial atoms.
Computing the writhe on lattices
International Nuclear Information System (INIS)
Laing, C; Sumners, D W
2006-01-01
Given a polygonal closed curve on a lattice or space group, we describe a method for computing the writhe of the curve as the average of weighted projected writhing numbers of the polygon in a few directions. These directions are determined by the lattice geometry, the weights are determined by areas of regions on the unit 2-sphere, and the regions are formed by the tangent indicatrix to the polygonal curve. We give a new formula for the writhe of polygons on the face centred cubic lattice and prove that the writhe of polygons on the body centred cubic lattice, the hexagonal simple lattice, and the diamond space group is always a rational number, and discuss applications to ring polymers
Reis, Tim; Dellar, Paul J.
2012-01-01
lattice Boltzmann formulations cannot capture Knudsen boundary layers, we replace the usual discrete analogs of the specular diffuse reflection conditions from continuous kinetic theory with a moment-based implementation of the first-order Navier
Determination of D{sub 2}O - 2% enriched uranium lattice parameters by means of a critical system
Energy Technology Data Exchange (ETDEWEB)
Raisic, N; Takac, S; Markovic, H; Bosevski, T [Boris Kidric Institute of Nuclear Sciences Belgrade (Yugoslavia)
1963-07-01
In order to specify experimental procedures for few standard measurements sufficient to provide consistent set of lattice parameters, a series of experiments were performed at the RB reactor using 2% enriched tubular fuel elements. Obtained results were compared to standard two-group diffusion calculation indicating high degree of accuracy for a broad variety of reactor lattice configurations.
Size-dependent homogenized diffusion parameters for a finite lattice
International Nuclear Information System (INIS)
Premuda, F.
1980-01-01
A numerical technique is reported for solving the transcendental equation for unknown Ysub(n+1). The solution is expressed in terms of quantities related to Ysub(n). This is an iterative reversion technique which has already been proven to converge rapidly in the homogeneous slab problem considered herein. (author)
An approach to box homogenisation-lattice properties
International Nuclear Information System (INIS)
Paul, O.P.K.
1978-01-01
A computer code has been developed to solve two group coupled neutron diffusion equations in x, y geometry for a lattice cell of a thermal reactor comprising an array of fuel pins (cellules) regularly spaced in a square box. The method uses finite difference approximation considering four neighbours of a mesh point and successive iteration technique. To simulate the current vanishing boundary condition at the cell boundary, the code uses an hypothesis that the thermal neutron flux increases exponentially beyond the pin cellules boundary while the fast neutron flux follows the reverse behaviour and the flux across the cell boundary follows the mirror image distribution. The code requires two group diffusion properties of pin cellules as input data and it calculates Ksub(infinity), L 2 , Lsub(infinity)sup(2), Dsub(th), and Df of the system. This code coupled with lattice pin and global calculation codes has been used for IRT - 2000 reactor and the results are quite reasonable. (author)
Lattice gas cellular automata and lattice Boltzmann models an introduction
Wolf-Gladrow, Dieter A
2000-01-01
Lattice-gas cellular automata (LGCA) and lattice Boltzmann models (LBM) are relatively new and promising methods for the numerical solution of nonlinear partial differential equations. The book provides an introduction for graduate students and researchers. Working knowledge of calculus is required and experience in PDEs and fluid dynamics is recommended. Some peculiarities of cellular automata are outlined in Chapter 2. The properties of various LGCA and special coding techniques are discussed in Chapter 3. Concepts from statistical mechanics (Chapter 4) provide the necessary theoretical background for LGCA and LBM. The properties of lattice Boltzmann models and a method for their construction are presented in Chapter 5.
SLAROM, Neutron Flux Distribution and Spectra in Lattice Cell
International Nuclear Information System (INIS)
Nakagawa, M.; Tsuchihashi, K.
2002-01-01
1 - Description of program or function: SLAROM solves the neutron integral transport equations to determine flux distribution and spectra in a lattice and calculates cell averaged effective cross sections. 2 - Method of solution: Collision probability method for cell calculation and 1D diffusion for core calculation. 3 - Restrictions on the complexity of the problem: Variable dimensions are used throughout the program so that computer core requirements depend on a variety of program parameters
The properties of tagged lattice fluids: II. Velocity correlation functions
International Nuclear Information System (INIS)
Binder, P.M.; d'Humieres, D.; Poujol, L.
1988-01-01
We report preliminary measurements of the velocity autocorrelation function for a tagged particle in a lattice gas. These measurements agree with the Boltzmann-level theory. The Green-Kubo integration of these measurements agrees with theoretical predictions for the diffusion coefficient. To within the error bars of the simulations (3 /times/ 10/sup /minus/3/) we observe no long-time tails. 9 refs., 1 fig., 1 tab
Irreversible stochastic processes on lattices
International Nuclear Information System (INIS)
Nord, R.S.
1986-01-01
Models for irreversible random or cooperative filling of lattices are required to describe many processes in chemistry and physics. Since the filling is assumed to be irreversible, even the stationary, saturation state is not in equilibrium. The kinetics and statistics of these processes are described by recasting the master equations in infinite hierarchical form. Solutions can be obtained by implementing various techniques: refinements in these solution techniques are presented. Programs considered include random dimer, trimer, and tetramer filling of 2D lattices, random dimer filling of a cubic lattice, competitive filling of two or more species, and the effect of a random distribution of inactive sites on the filling. Also considered is monomer filling of a linear lattice with nearest neighbor cooperative effects and solve for the exact cluster-size distribution for cluster sizes up to the asymptotic regime. Additionally, a technique is developed to directly determine the asymptotic properties of the cluster size distribution. Finally cluster growth is considered via irreversible aggregation involving random walkers. In particular, explicit results are provided for the large-lattice-size asymptotic behavior of trapping probabilities and average walk lengths for a single walker on a lattice with multiple traps. Procedures for exact calculation of these quantities on finite lattices are also developed
Toward lattice fractional vector calculus
International Nuclear Information System (INIS)
Tarasov, Vasily E
2014-01-01
An analog of fractional vector calculus for physical lattice models is suggested. We use an approach based on the models of three-dimensional lattices with long-range inter-particle interactions. The lattice analogs of fractional partial derivatives are represented by kernels of lattice long-range interactions, where the Fourier series transformations of these kernels have a power-law form with respect to wave vector components. In the continuum limit, these lattice partial derivatives give derivatives of non-integer order with respect to coordinates. In the three-dimensional description of the non-local continuum, the fractional differential operators have the form of fractional partial derivatives of the Riesz type. As examples of the applications of the suggested lattice fractional vector calculus, we give lattice models with long-range interactions for the fractional Maxwell equations of non-local continuous media and for the fractional generalization of the Mindlin and Aifantis continuum models of gradient elasticity. (papers)
Diffusion of particles adsorbed on reconstructive surface
Czech Academy of Sciences Publication Activity Database
Tarasenko A., Nataliya; Tarasenko, Alexander; Jastrabík, Lubomír
2005-01-01
Roč. 11, č. 1 (2005), s. 485-489 ISSN 0929-5607 R&D Projects: GA MŠk LN00A015 Institutional research plan: CEZ:AV0Z10100522 Keywords : lattice gas * surface reconstruction * surface diffusion * phase transitions Subject RIV: BM - Solid Matter Physics ; Magnetism Impact factor: 1.323, year: 2005
Introduction to lattice gauge theory
International Nuclear Information System (INIS)
Gupta, R.
1987-01-01
The lattice formulation of Quantum Field Theory (QFT) can be exploited in many ways. We can derive the lattice Feynman rules and carry out weak coupling perturbation expansions. The lattice then serves as a manifestly gauge invariant regularization scheme, albeit one that is more complicated than standard continuum schemes. Strong coupling expansions: these give us useful qualitative information, but unfortunately no hard numbers. The lattice theory is amenable to numerical simulations by which one calculates the long distance properties of a strongly interacting theory from first principles. The observables are measured as a function of the bare coupling g and a gauge invariant cut-off ≅ 1/α, where α is the lattice spacing. The continuum (physical) behavior is recovered in the limit α → 0, at which point the lattice artifacts go to zero. This is the more powerful use of lattice formulation, so in these lectures the author focuses on setting up the theory for the purpose of numerical simulations to get hard numbers. The numerical techniques used in Lattice Gauge Theories have their roots in statistical mechanics, so it is important to develop an intuition for the interconnection between quantum mechanics and statistical mechanics. This will be the emphasis of the first lecture. In the second lecture, the author reviews the essential ingredients of formulating QCD on the lattice and discusses scaling and the continuum limit. In the last lecture the author summarizes the status of some of the main results. He also mentions the bottlenecks and possible directions for research. 88 refs
Lattice Methods for Quantum Chromodynamics
DeGrand, Thomas
2006-01-01
Numerical simulation of lattice-regulated QCD has become an important source of information about strong interactions. In the last few years there has been an explosion of techniques for performing ever more accurate studies on the properties of strongly interacting particles. Lattice predictions directly impact many areas of particle and nuclear physics theory and phenomenology. This book provides a thorough introduction to the specialized techniques needed to carry out numerical simulations of QCD: a description of lattice discretizations of fermions and gauge fields, methods for actually do
Localized structures in Kagome lattices
Energy Technology Data Exchange (ETDEWEB)
Saxena, Avadh B [Los Alamos National Laboratory; Bishop, Alan R [Los Alamos National Laboratory; Law, K J H [UNIV OF MASSACHUSETTS; Kevrekidis, P G [UNIV OF MASSACHUSETTS
2009-01-01
We investigate the existence and stability of gap vortices and multi-pole gap solitons in a Kagome lattice with a defocusing nonlinearity both in a discrete case and in a continuum one with periodic external modulation. In particular, predictions are made based on expansion around a simple and analytically tractable anti-continuum (zero coupling) limit. These predictions are then confirmed for a continuum model of an optically-induced Kagome lattice in a photorefractive crystal obtained by a continuous transformation of a honeycomb lattice.
Lattice QCD: Status and Prospect
International Nuclear Information System (INIS)
Ukawa, Akira
2006-01-01
A brief review is given of the current status and near-future prospect of lattice QCD studies of the Standard Model. After summarizing a bit of history, we describe current attempts toward inclusion of dynamical up, down and strange quarks. Recent results on the light hadron mass spectrum as well as those on the heavy quark quantities are described. Recent work on lattice pentaquark search is summarized. We touch upon the PACS-CS Project for building our next machine for lattice QCD, and conclude with a summary of computer situation and the physics possibilities over the next several years
Borwein, J M; McPhedran, R C
2013-01-01
The study of lattice sums began when early investigators wanted to go from mechanical properties of crystals to the properties of the atoms and ions from which they were built (the literature of Madelung's constant). A parallel literature was built around the optical properties of regular lattices of atoms (initiated by Lord Rayleigh, Lorentz and Lorenz). For over a century many famous scientists and mathematicians have delved into the properties of lattices, sometimes unwittingly duplicating the work of their predecessors. Here, at last, is a comprehensive overview of the substantial body of
International Nuclear Information System (INIS)
Carlen, E.A.
1984-01-01
In Nelson's stochastic mechanics, quantum phenomena are described in terms of diffusions instead of wave functions. These diffusions are formally given by stochastic differential equations with extremely singular coefficients. Using PDE methods, we prove the existence of solutions. This reult provides a rigorous basis for stochastic mechanics. (orig.)
Flux Limiter Lattice Boltzmann for Compressible Flows
International Nuclear Information System (INIS)
Chen Feng; Li Yingjun; Xu Aiguo; Zhang Guangcai
2011-01-01
In this paper, a new flux limiter scheme with the splitting technique is successfully incorporated into a multiple-relaxation-time lattice Boltzmann (LB) model for shacked compressible flows. The proposed flux limiter scheme is efficient in decreasing the artificial oscillations and numerical diffusion around the interface. Due to the kinetic nature, some interface problems being difficult to handle at the macroscopic level can be modeled more naturally through the LB method. Numerical simulations for the Richtmyer-Meshkov instability show that with the new model the computed interfaces are smoother and more consistent with physical analysis. The growth rates of bubble and spike present a satisfying agreement with the theoretical predictions and other numerical simulations. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)
Phase transitions in a lattice population model
International Nuclear Information System (INIS)
Windus, Alastair; Jensen, Henrik J
2007-01-01
We introduce a model for a population on a lattice with diffusion and birth/death according to 2A→3A and A→Φ for a particle A. We find that the model displays a phase transition from an active to an absorbing state which is continuous in 1 + 1 dimensions and of first-order in higher dimensions in agreement with the mean field equation. For the (1 + 1)-dimensional case, we examine the critical exponents and a scaling function for the survival probability and show that it belongs to the universality class of directed percolation. In higher dimensions, we look at the first-order phase transition by plotting a histogram of the population density and use the presence of phase coexistence to find an accurate value for the critical point in 2 + 1 dimensions
Nitrogen diffusion in zirconium nitride
International Nuclear Information System (INIS)
Desmaison, J.G.; Smeltzer, W.W.
1977-01-01
Nitrogen diffusion in polycrystalline ZrN/sub 0.71-0.79/ spheres, 60 and 90 μm diameter, was studied by the gas-solid exchange technique using 15 N as a tracer at a nitrogen pressure of 220 torr and 1000 to 1200 0 C. These specimens were characterized by chemical analyses, density, lattice parameter, and structural measurements. The tracer diffusion coefficient can be expressed as D* (cm 2 /S) = 3.0 x 10 -10 exp (-23,000/RT). This result, when compared to a previous determination obtained in the same conditions with 254 μm thick plates, confirms that nitrogen transport in this polycrystalline solid at temperatures less than 1200 0 C is associated with a short-circuit diffusion mechanism
Tallarita, Gianni; Peterson, Adam
2018-04-01
We perform a numerical study of the phase diagram of the model proposed in [M. Shifman, Phys. Rev. D 87, 025025 (2013)., 10.1103/PhysRevD.87.025025], which is a simple model containing non-Abelian vortices. As per the case of Abrikosov vortices, we map out a region of parameter space in which the system prefers the formation of vortices in ordered lattice structures. These are generalizations of Abrikosov vortex lattices with extra orientational moduli in the vortex cores. At sufficiently large lattice spacing the low energy theory is described by a sum of C P (1 ) theories, each located on a vortex site. As the lattice spacing becomes smaller, when the self-interaction of the orientational field becomes relevant, only an overall rotation in internal space survives.
Diffuse scattering of neutrons
International Nuclear Information System (INIS)
Novion, C.H. de.
1981-02-01
The use of neutron scattering to study atomic disorder in metals and alloys is described. The diffuse elastic scattering of neutrons by a perfect crystal lattice leads to a diffraction spectrum with only Bragg spreads. the existence of disorder in the crystal results in intensity and position modifications to these spreads, and above all, to the appearance of a low intensity scatter between Bragg peaks. The elastic scattering of neutrons is treated in this text, i.e. by measuring the number of scattered neutrons having the same energy as the incident neutrons. Such measurements yield information on the static disorder in the crystal and time average fluctuations in composition and atomic displacements [fr
Lattice Studies of Hyperon Spectroscopy
Energy Technology Data Exchange (ETDEWEB)
Richards, David G. [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States)
2016-04-01
I describe recent progress at studying the spectrum of hadrons containing the strange quark through lattice QCD calculations. I emphasise in particular the richness of the spectrum revealed by lattice studies, with a spectrum of states at least as rich as that of the quark model. I conclude by prospects for future calculations, including in particular the determination of the decay amplitudes for the excited states.
Harmonic oscillator on a lattice
International Nuclear Information System (INIS)
Ader, J.P.; Bonnier, B.; Hontebeyrie, M.; Meyers, C.
1983-01-01
The continuum limit of the ground state energy for the harmonic oscillator with discrete time is derived for all possible choices of the lattice derivative. The occurrence of unphysical values is shown to arise whenever the lattice laplacian is not strictly positive on its Brillouin zone. These undesirable limits can either be finite and arbitrary (multiple spectrum) or infinite (overlapping sublattices with multiple spectrum). (orig.)
International Nuclear Information System (INIS)
DeGrand, T.
1997-01-01
These lectures provide an introduction to lattice methods for nonperturbative studies of Quantum Chromodynamics. Lecture 1: Basic techniques for QCD and results for hadron spectroscopy using the simplest discretizations; lecture 2: Improved actions--what they are and how well they work; lecture 3: SLAC physics from the lattice-structure functions, the mass of the glueball, heavy quarks and α s (M z ), and B-anti B mixing. 67 refs., 36 figs
Takami, A.; Hashimoto, T.; Horibe, M.; Hayashi, A.
2000-01-01
The Wigner functions on the one dimensional lattice are studied. Contrary to the previous claim in literature, Wigner functions exist on the lattice with any number of sites, whether it is even or odd. There are infinitely many solutions satisfying the conditions which reasonable Wigner functions should respect. After presenting a heuristic method to obtain Wigner functions, we give the general form of the solutions. Quantum mechanical expectation values in terms of Wigner functions are also ...
Energy Technology Data Exchange (ETDEWEB)
DeGrand, T. [Univ. of Colorado, Boulder, CO (United States). Dept. of Physics
1997-06-01
These lectures provide an introduction to lattice methods for nonperturbative studies of Quantum Chromodynamics. Lecture 1: Basic techniques for QCD and results for hadron spectroscopy using the simplest discretizations; lecture 2: Improved actions--what they are and how well they work; lecture 3: SLAC physics from the lattice-structure functions, the mass of the glueball, heavy quarks and {alpha}{sub s} (M{sub z}), and B-{anti B} mixing. 67 refs., 36 figs.
Random walks on a fluctuating lattice: A renormalization group approach applied in one dimension
International Nuclear Information System (INIS)
Levermore, C.D.; Nadler, W.; Stein, D.L.
1995-01-01
We study the problem of a random walk on a lattice in which bonds connecting nearest-neighbor sites open and close randomly in time, a situation often encountered in fluctuating media. We present a simple renormalization group technique to solve for the effective diffusive behavior at long times. For one-dimensional lattices we obtain better quantitative agreement with simulation data than earlier effective medium results. Our technique works in principle in any dimension, although the amount of computation required rises with the dimensionality of the lattice
Quantum mechanics of lattice gas automata: One-particle plane waves and potentials
International Nuclear Information System (INIS)
Meyer, D.A.
1997-01-01
Classical lattice gas automata effectively simulate physical processes, such as diffusion and fluid flow (in certain parameter regimes), despite their simplicity at the microscale. Motivated by current interest in quantum computation we recently defined quantum lattice gas automata; in this paper we initiate a project to analyze which physical processes these models can effectively simulate. Studying the single particle sector of a one-dimensional quantum lattice gas we find discrete analogs of plane waves and wave packets, and then investigate their behavior in the presence of inhomogeneous potentials. copyright 1997 The American Physical Society
Racetrack lattices for the TRIUMF KAON factory
International Nuclear Information System (INIS)
Servranckx, R.V.; Wienands, U.; Craddock, M.K.; Rees, G.H.
1989-03-01
Separated-function racetrack lattices have been developed for the KAON Factory accelerators that have more flexibility than the old circular lattices. Straight sections with zero dispersion are provided for rf cavities and fast injection and extraction, and with controlled dispersion for H - injection and slow extraction. In addition the new lattices have fewer depolarizing resonances than the old circular lattices
Real depletion in nodal diffusion codes
International Nuclear Information System (INIS)
Petkov, P.T.
2002-01-01
The fuel depletion is described by more than one hundred fuel isotopes in the advanced lattice codes like HELIOS, but only a few fuel isotopes are accounted for even in the advanced steady-state diffusion codes. The general assumption that the number densities of the majority of the fuel isotopes depend only on the fuel burnup is seriously in error if high burnup is considered. The real depletion conditions in the reactor core differ from the asymptotic ones at the stage of lattice depletion calculations. This study reveals which fuel isotopes should be explicitly accounted for in the diffusion codes in order to predict adequately the real depletion effects in the core. A somewhat strange conclusion is that if the real number densities of the main fissionable isotopes are not explicitly accounted for in the diffusion code, then Sm-149 should not be accounted for either, because the net error in k-inf is smaller (Authors)
Lattice gauge theory using parallel processors
International Nuclear Information System (INIS)
Lee, T.D.; Chou, K.C.; Zichichi, A.
1987-01-01
The book's contents include: Lattice Gauge Theory Lectures: Introduction and Current Fermion Simulations; Monte Carlo Algorithms for Lattice Gauge Theory; Specialized Computers for Lattice Gauge Theory; Lattice Gauge Theory at Finite Temperature: A Monte Carlo Study; Computational Method - An Elementary Introduction to the Langevin Equation, Present Status of Numerical Quantum Chromodynamics; Random Lattice Field Theory; The GF11 Processor and Compiler; and The APE Computer and First Physics Results; Columbia Supercomputer Project: Parallel Supercomputer for Lattice QCD; Statistical and Systematic Errors in Numerical Simulations; Monte Carlo Simulation for LGT and Programming Techniques on the Columbia Supercomputer; Food for Thought: Five Lectures on Lattice Gauge Theory
Calculation Of A Lattice Physics Parameter For SBWR Fuel Bundle Design
International Nuclear Information System (INIS)
Sardjono, Y.
1996-01-01
The maximum power peaking factor for Nuclear Power Plant SBWR type is 1.5. The precision for that calculation is related with the result of unit cell analysis each rod in the fuel bundles. This analysis consist of lattice eigenvalue, lattice average diffusion cross section as well as relative power peaking factor in the fuel rod for each fuel bundles. The calculation by using TGBLA computer code which is based on the transport and 168 group diffusion theory. From this calculation can be concluded that the maximum relative power peaking factor is 1.304 and lower than design limit
Embedded Lattice and Properties of Gram Matrix
Directory of Open Access Journals (Sweden)
Futa Yuichi
2017-03-01
Full Text Available In this article, we formalize in Mizar [14] the definition of embedding of lattice and its properties. We formally define an inner product on an embedded module. We also formalize properties of Gram matrix. We formally prove that an inverse of Gram matrix for a rational lattice exists. Lattice of Z-module is necessary for lattice problems, LLL (Lenstra, Lenstra and Lov´asz base reduction algorithm [16] and cryptographic systems with lattice [17].
Logarithmic Superdiffusion in Two Dimensional Driven Lattice Gases
Krug, J.; Neiss, R. A.; Schadschneider, A.; Schmidt, J.
2018-03-01
The spreading of density fluctuations in two-dimensional driven diffusive systems is marginally anomalous. Mode coupling theory predicts that the diffusivity in the direction of the drive diverges with time as (ln t)^{2/3} with a prefactor depending on the macroscopic current-density relation and the diffusion tensor of the fluctuating hydrodynamic field equation. Here we present the first numerical verification of this behavior for a particular version of the two-dimensional asymmetric exclusion process. Particles jump strictly asymmetrically along one of the lattice directions and symmetrically along the other, and an anisotropy parameter p governs the ratio between the two rates. Using a novel massively parallel coupling algorithm that strongly reduces the fluctuations in the numerical estimate of the two-point correlation function, we are able to accurately determine the exponent of the logarithmic correction. In addition, the variation of the prefactor with p provides a stringent test of mode coupling theory.
Fractional Diffusion Equations and Anomalous Diffusion
Evangelista, Luiz Roberto; Kaminski Lenzi, Ervin
2018-01-01
Preface; 1. Mathematical preliminaries; 2. A survey of the fractional calculus; 3. From normal to anomalous diffusion; 4. Fractional diffusion equations: elementary applications; 5. Fractional diffusion equations: surface effects; 6. Fractional nonlinear diffusion equation; 7. Anomalous diffusion: anisotropic case; 8. Fractional Schrödinger equations; 9. Anomalous diffusion and impedance spectroscopy; 10. The Poisson–Nernst–Planck anomalous (PNPA) models; References; Index.
Finite-lattice-spacing corrections to masses and g factors on a lattice
International Nuclear Information System (INIS)
Roskies, R.; Wu, J.C.
1986-01-01
We suggest an alternative method for extracting masses and g factors from lattice calculations. Our method takes account of more of the infrared and ultraviolet lattice effects. It leads to more reasonable results in simulations of QED on a lattice
Terrien's marginal degeneration accompanied by latticed stromal opacities.
Zhang, Yibing; Jia, Hui
2014-05-01
We report a case of Terrien's marginal degeneration (TMD) with a unilaterally typical narrow band of peripheral corneal stroma thinning, accompanied by the presence of an unusual network of opacities diffusing throughout the anterior stroma layers. A 43-year-old woman presented with superior nasal peripheral corneal thinning and an unusual network of polygonal stromal opacities in the anterior corneal stroma of the right eye. Latticed corneal changes were unusually extensive and distributed diffusely in the stroma. No abnormalities were found in the corneal epithelium and in the basal epithelial cells. No noticeable changes were found in the left eye. Because of a progressively worse ocular irritation of the right eye, a diagnosis of TMD was made for this patient. This case of TMD accompanied by keratopathy was unusual. The branching stromal lattice pattern of the corneal opacities was difficult to distinguish from lattice corneal dystrophy. In this case, the polygonal stromal opacities were located in the anterior corneal stroma and therefore were distinguished from a similar manifestation in posterior crocodile shagreen.
Terrien’s Marginal Degeneration Accompanied by Latticed Stromal Opacities
Zhang, Yibing; Jia, Hui
2014-01-01
ABSTRACT Purpose We report a case of Terrien’s marginal degeneration (TMD) with a unilaterally typical narrow band of peripheral corneal stroma thinning, accompanied by the presence of an unusual network of opacities diffusing throughout the anterior stroma layers. Case Report A 43-year-old woman presented with superior nasal peripheral corneal thinning and an unusual network of polygonal stromal opacities in the anterior corneal stroma of the right eye. Latticed corneal changes were unusually extensive and distributed diffusely in the stroma. No abnormalities were found in the corneal epithelium and in the basal epithelial cells. No noticeable changes were found in the left eye. Because of a progressively worse ocular irritation of the right eye, a diagnosis of TMD was made for this patient. Conclusions This case of TMD accompanied by keratopathy was unusual. The branching stromal lattice pattern of the corneal opacities was difficult to distinguish from lattice corneal dystrophy. In this case, the polygonal stromal opacities were located in the anterior corneal stroma and therefore were distinguished from a similar manifestation in posterior crocodile shagreen. PMID:24681833
Quantum lattice model solver HΦ
Kawamura, Mitsuaki; Yoshimi, Kazuyoshi; Misawa, Takahiro; Yamaji, Youhei; Todo, Synge; Kawashima, Naoki
2017-08-01
HΦ [aitch-phi ] is a program package based on the Lanczos-type eigenvalue solution applicable to a broad range of quantum lattice models, i.e., arbitrary quantum lattice models with two-body interactions, including the Heisenberg model, the Kitaev model, the Hubbard model and the Kondo-lattice model. While it works well on PCs and PC-clusters, HΦ also runs efficiently on massively parallel computers, which considerably extends the tractable range of the system size. In addition, unlike most existing packages, HΦ supports finite-temperature calculations through the method of thermal pure quantum (TPQ) states. In this paper, we explain theoretical background and user-interface of HΦ. We also show the benchmark results of HΦ on supercomputers such as the K computer at RIKEN Advanced Institute for Computational Science (AICS) and SGI ICE XA (Sekirei) at the Institute for the Solid State Physics (ISSP).
Frustrated lattices of Ising chains
International Nuclear Information System (INIS)
Kudasov, Yurii B; Korshunov, Aleksei S; Pavlov, V N; Maslov, Dmitrii A
2012-01-01
The magnetic structure and magnetization dynamics of systems of plane frustrated Ising chain lattices are reviewed for three groups of compounds: Ca 3 Co 2 O 6 , CsCoCl 3 , and Sr 5 Rh 4 O 12 . The available experimental data are analyzed and compared in detail. It is shown that a high-temperature magnetic phase on a triangle lattice is normally and universally a partially disordered antiferromagnetic (PDA) structure. The diversity of low-temperature phases results from weak interactions that lift the degeneracy of a 2D antiferromagnetic Ising model on the triangle lattice. Mean-field models, Monte Carlo simulation results on the static magnetization curve, and results on slow magnetization dynamics obtained with Glauber's theory are discussed in detail. (reviews of topical problems)
Lattice QCD for nuclear physics
Meyer, Harvey
2015-01-01
With ever increasing computational resources and improvements in algorithms, new opportunities are emerging for lattice gauge theory to address key questions in strongly interacting systems, such as nuclear matter. Calculations today use dynamical gauge-field ensembles with degenerate light up/down quarks and the strange quark and it is possible now to consider including charm-quark degrees of freedom in the QCD vacuum. Pion masses and other sources of systematic error, such as finite-volume and discretization effects, are beginning to be quantified systematically. Altogether, an era of precision calculation has begun, and many new observables will be calculated at the new computational facilities. The aim of this set of lectures is to provide graduate students with a grounding in the application of lattice gauge theory methods to strongly interacting systems, and in particular to nuclear physics. A wide variety of topics are covered, including continuum field theory, lattice discretizations, hadron spect...
Nucleon structure from lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Dinter, Simon
2012-11-13
In this thesis we compute within lattice QCD observables related to the structure of the nucleon. One part of this thesis is concerned with moments of parton distribution functions (PDFs). Those moments are essential elements for the understanding of nucleon structure and can be extracted from a global analysis of deep inelastic scattering experiments. On the theoretical side they can be computed non-perturbatively by means of lattice QCD. However, since the time lattice calculations of moments of PDFs are available, there is a tension between these lattice calculations and the results from a global analysis of experimental data. We examine whether systematic effects are responsible for this tension, and study particularly intensively the effects of excited states by a dedicated high precision computation. Moreover, we carry out a first computation with four dynamical flavors. Another aspect of this thesis is a feasibility study of a lattice QCD computation of the scalar quark content of the nucleon, which is an important element in the cross-section of a heavy particle with the nucleon mediated by a scalar particle (e.g. Higgs particle) and can therefore have an impact on Dark Matter searches. Existing lattice QCD calculations of this quantity usually have a large error and thus a low significance for phenomenological applications. We use a variance-reduction technique for quark-disconnected diagrams to obtain a precise result. Furthermore, we introduce a new stochastic method for the calculation of connected 3-point correlation functions, which are needed to compute nucleon structure observables, as an alternative to the usual sequential propagator method. In an explorative study we check whether this new method is competitive to the standard one. We use Wilson twisted mass fermions at maximal twist in all our calculations, such that all observables considered here have only O(a{sup 2}) discretization effects.
Nucleon structure from lattice QCD
International Nuclear Information System (INIS)
Dinter, Simon
2012-01-01
In this thesis we compute within lattice QCD observables related to the structure of the nucleon. One part of this thesis is concerned with moments of parton distribution functions (PDFs). Those moments are essential elements for the understanding of nucleon structure and can be extracted from a global analysis of deep inelastic scattering experiments. On the theoretical side they can be computed non-perturbatively by means of lattice QCD. However, since the time lattice calculations of moments of PDFs are available, there is a tension between these lattice calculations and the results from a global analysis of experimental data. We examine whether systematic effects are responsible for this tension, and study particularly intensively the effects of excited states by a dedicated high precision computation. Moreover, we carry out a first computation with four dynamical flavors. Another aspect of this thesis is a feasibility study of a lattice QCD computation of the scalar quark content of the nucleon, which is an important element in the cross-section of a heavy particle with the nucleon mediated by a scalar particle (e.g. Higgs particle) and can therefore have an impact on Dark Matter searches. Existing lattice QCD calculations of this quantity usually have a large error and thus a low significance for phenomenological applications. We use a variance-reduction technique for quark-disconnected diagrams to obtain a precise result. Furthermore, we introduce a new stochastic method for the calculation of connected 3-point correlation functions, which are needed to compute nucleon structure observables, as an alternative to the usual sequential propagator method. In an explorative study we check whether this new method is competitive to the standard one. We use Wilson twisted mass fermions at maximal twist in all our calculations, such that all observables considered here have only O(a 2 ) discretization effects.
Kondo length in bosonic lattices
Giuliano, Domenico; Sodano, Pasquale; Trombettoni, Andrea
2017-09-01
Motivated by the fact that the low-energy properties of the Kondo model can be effectively simulated in spin chains, we study the realization of the effect with bond impurities in ultracold bosonic lattices at half filling. After presenting a discussion of the effective theory and of the mapping of the bosonic chain onto a lattice spin Hamiltonian, we provide estimates for the Kondo length as a function of the parameters of the bosonic model. We point out that the Kondo length can be extracted from the integrated real-space correlation functions, which are experimentally accessible quantities in experiments with cold atoms.
Supersymmetry on the noncommutative lattice
International Nuclear Information System (INIS)
Nishimura, Jun; Rey, Soo-Jong; Sugino, Fumihiko
2003-01-01
Built upon the proposal of Kaplan et al. (heplat{0206109}), we construct noncommutative lattice gauge theory with manifest supersymmetry. We show that such theory is naturally implementable via orbifold conditions generalizing those used by Kaplan et al. We present the prescription in detail and illustrate it for noncommutative gauge theories latticized partially in two dimensions. We point out a deformation freedom in the defining theory by a complex-parameter, reminiscent of discrete torsion in string theory. We show that, in the continuum limit, the supersymmetry is enhanced only at a particular value of the deformation parameter, determined solely by the size of the noncommutativity. (author)
Machines for lattice gauge theory
International Nuclear Information System (INIS)
Mackenzie, P.B.
1989-05-01
The most promising approach to the solution of the theory of strong interactions is large scale numerical simulation using the techniques of lattice gauge theory. At the present time, computing requirements for convincing calculations of the properties of hadrons exceed the capabilities of even the most powerful commercial supercomputers. This has led to the development of massively parallel computers dedicated to lattice gauge theory. This talk will discuss the computing requirements behind these machines, and general features of the components and architectures of the half dozen major projects now in existence. 20 refs., 1 fig
Graphene on graphene antidot lattices
DEFF Research Database (Denmark)
Gregersen, Søren Schou; Pedersen, Jesper Goor; Power, Stephen
2015-01-01
Graphene bilayer systems are known to exhibit a band gap when the layer symmetry is broken by applying a perpendicular electric field. The resulting band structure resembles that of a conventional semiconductor with a parabolic dispersion. Here, we introduce a bilayer graphene heterostructure......, where single-layer graphene is placed on top of another layer of graphene with a regular lattice of antidots. We dub this class of graphene systems GOAL: graphene on graphene antidot lattice. By varying the structure geometry, band-structure engineering can be performed to obtain linearly dispersing...
Unconventional superconductivity in honeycomb lattice
Directory of Open Access Journals (Sweden)
P Sahebsara
2013-03-01
Full Text Available The possibility of symmetrical s-wave superconductivity in the honeycomb lattice is studied within a strongly correlated regime, using the Hubbard model. The superconducting order parameter is defined by introducing the Green function, which is obtained by calculating the density of the electrons . In this study showed that the superconducting order parameter appears in doping interval between 0 and 0.5, and x=0.25 is the optimum doping for the s-wave superconductivity in honeycomb lattice.
[Lattice degeneration of the retina].
Boĭko, E V; Suetov, A A; Mal'tsev, D S
2014-01-01
Lattice degeneration of the retina is a clinically important type of peripheral retinal dystrophies due to its participation in the pathogenesis of rhegmatogenous retinal detachment. In spite of extensive epidemiological, morphological, and clinical data, the question on causes of this particular type of retinal dystrophies currently remains debatable. Existing hypotheses on pathogenesis of retinal structural changes in lattice degeneration explain it to a certain extent. In clinical ophthalmology it is necessary to pay close attention to this kind of degenerations and distinguish between cases requiring preventive treatment and those requiring monitoring.
Lattice calculations in gauge theory
International Nuclear Information System (INIS)
Rebbi, C.
1985-01-01
The lattice formulation of quantum gauge theories is discussed as a viable technique for quantitative studies of nonperturbative effects in QCD. Evidence is presented to ascertain that whole classes of lattice actions produce a universal continuum limit. Discrepancies between numerical results from Monto Carlo simulations for the pure gauge system and for the system with gauge and quark fields are discussed. Numerical calculations for QCD require very substantial computational resources. The use of powerful vector processors of special purpose machines, in extending the scope and magnitude or the calculations is considered, and one may reasonably expect that in the near future good quantitative predictions will be obtained for QCD
Chiral symmetry on the lattice
International Nuclear Information System (INIS)
Creutz, M.
1994-11-01
The author reviews some of the difficulties associated with chiral symmetry in the context of a lattice regulator. The author discusses the structure of Wilson Fermions when the hopping parameter is in the vicinity of its critical value. Here one flavor contrasts sharply with the case of more, where a residual chiral symmetry survives anomalies. The author briefly discusses the surface mode approach, the use of mirror Fermions to cancel anomalies, and finally speculates on the problems with lattice versions of the standard model
Nuclear Physics from Lattice QCD
Energy Technology Data Exchange (ETDEWEB)
William Detmold, Silas Beane, Konstantinos Orginos, Martin Savage
2011-01-01
We review recent progress toward establishing lattice Quantum Chromodynamics as a predictive calculational framework for nuclear physics. A survey of the current techniques that are used to extract low-energy hadronic scattering amplitudes and interactions is followed by a review of recent two-body and few-body calculations by the NPLQCD collaboration and others. An outline of the nuclear physics that is expected to be accomplished with Lattice QCD in the next decade, along with estimates of the required computational resources, is presented.
Representation theory of lattice current algebras
International Nuclear Information System (INIS)
Alekseev, A.Yu.; Eidgenoessische Technische Hochschule, Zurich; Faddeev, L.D.; Froehlich, L.D.; Schomerus, V.; Kyoto Univ.
1996-04-01
Lattice current algebras were introduced as a regularization of the left-and right moving degrees of freedom in the WZNW model. They provide examples of lattice theories with a local quantum symmetry U q (G). Their representation theory is studied in detail. In particular, we construct all irreducible representations along with a lattice analogue of the fusion product for representations of the lattice current algebra. It is shown that for an arbitrary number of lattice sites, the representation categories of the lattice current algebras agree with their continuum counterparts. (orig.)
Analytical solution to the hybrid diffusion-transport equation
International Nuclear Information System (INIS)
Nanneh, M.M.; Williams, M.M.R.
1986-01-01
A special integral equation was derived in previous work using a hybrid diffusion-transport theory method for calculating the flux distribution in slab lattices. In this paper an analytical solution of this equation has been carried out on a finite reactor lattice. The analytical results of disadvantage factors are shown to be accurate in comparison with the numerical results and accurate transport theory calculations. (author)
WIMSD5, Deterministic Multigroup Reactor Lattice Calculations
International Nuclear Information System (INIS)
2004-01-01
1 - Description of program or function: The Winfrith improved multigroup scheme (WIMS) is a general code for reactor lattice cell calculation on a wide range of reactor systems. In particular, the code will accept rod or plate fuel geometries in either regular arrays or in clusters and the energy group structure has been chosen primarily for thermal calculations. The basic library has been compiled with 14 fast groups, 13 resonance groups and 42 thermal groups, but the user is offered the choice of accurate solutions in many groups or rapid calculations in few groups. Temperature dependent thermal scattering matrices for a variety of scattering laws are included in the library for the principal moderators which include hydrogen, deuterium, graphite, beryllium and oxygen. WIMSD5 is a successor version of WIMS-D/4. 2 - Method of solution: The treatment of resonances is based on the use of equivalence theorems with a library of accurately evaluated resonance integrals for equivalent homogeneous systems at a variety of temperatures. The collision theory procedure gives accurate spectrum computations in the 69 groups of the library for the principal regions of the lattice using a simplified geometric representation of complicated lattice cells. The computed spectra are then used for the condensation of cross-sections to the number of groups selected for solution of the transport equation in detailed geometry. Solution of the transport equation is provided either by use of the Carlson DSN method or by collision probability methods. Leakage calculations including an allowance for streaming asymmetries may be made using either diffusion theory or the more elaborate B1-method. The output of the code provides Eigenvalues for the cases where a simple buckling mode is applicable or cell-averaged parameters for use in overall reactor calculations. Various reaction rate edits are provided for direct comparison with experimental measurements. 3 - Restrictions on the complexity of
Devil's in the (diffuse) detail
International Nuclear Information System (INIS)
Welberry, R.
2006-07-01
X-ray crystallography is an important workhorse in the world of solid-state chemistry. However, while it's a powerful tool in determining the average structure in a crystal lattice, conventional crystallography is very limited when it comes to understanding nano-scale disorder within that crystal structure. And when it comes to understanding the properties of many important materials, the devil is in the detail. X-ray diffraction is still one of the keys to understanding this finer scale structure but using it requires a capacity to read between the lines - to understand the diffuse diffraction that most crystallography ignores. Scientists at the Research School of Chemistry are leading the world in this field. Their work on modelling nano-scaled disorder using diffuse diffraction is opening up new possibilities in understanding and modifying many of our most important materials
Computers for lattice field theories
International Nuclear Information System (INIS)
Iwasaki, Y.
1994-01-01
Parallel computers dedicated to lattice field theories are reviewed with emphasis on the three recent projects, the Teraflops project in the US, the CP-PACS project in Japan and the 0.5-Teraflops project in the US. Some new commercial parallel computers are also discussed. Recent development of semiconductor technologies is briefly surveyed in relation to possible approaches toward Teraflops computers. (orig.)
Synthesis of spatially variant lattices.
Rumpf, Raymond C; Pazos, Javier
2012-07-02
It is often desired to functionally grade and/or spatially vary a periodic structure like a photonic crystal or metamaterial, yet no general method for doing this has been offered in the literature. A straightforward procedure is described here that allows many properties of the lattice to be spatially varied at the same time while producing a final lattice that is still smooth and continuous. Properties include unit cell orientation, lattice spacing, fill fraction, and more. This adds many degrees of freedom to a design such as spatially varying the orientation to exploit directional phenomena. The method is not a coordinate transformation technique so it can more easily produce complicated and arbitrary spatial variance. To demonstrate, the algorithm is used to synthesize a spatially variant self-collimating photonic crystal to flow a Gaussian beam around a 90° bend. The performance of the structure was confirmed through simulation and it showed virtually no scattering around the bend that would have arisen if the lattice had defects or discontinuities.
From lattice gases to polymers
Frenkel, D.
1990-01-01
The modification of a technique that was developed to study time correlations in lattice-gas cellular automata to facilitate the numerical simulation of chain molecules is described. As an example, the calculation of the excess chemical potential of an ideal polymer in a dense colloidal
Flavor extrapolation in lattice QCD
International Nuclear Information System (INIS)
Duffy, W.C.
1984-01-01
Explicit calculation of the effect of virtual quark-antiquark pairs in lattice QCD has eluded researchers. To include their effect explicitly one must calculate the determinant of the fermion-fermion coupling matrix. Owing to the large number of sites in a continuum limit size lattice, direct evaluation of this term requires an unrealistic amount of computer time. The effect of the virtual pairs can be approximated by ignoring this term and adjusting lattice couplings to reproduce experimental results. This procedure is called the valence approximation since it ignores all but the minimal number of quarks needed to describe hadrons. In this work the effect of the quark-antiquark pairs has been incorporated in a theory with an effective negative number of quark flavors contributing to the closed loops. Various particle masses and decay constants have been calculated for this theory and for one with no virtual pairs. The author attempts to extrapolate results towards positive numbers of quark flavors. The results show approximate agreement with experimental measurements and demonstrate the smoothness of lattice expectations in the number of quark flavors
Nuclear physics on the lattice?
International Nuclear Information System (INIS)
Koonin, S.E.
1985-01-01
The goal of the paper is to try to adapt lattice gauge theory to build in some biases in order for being applicable to nuclear physics. In so doing the calculations are made more precise, and the author can address questions like the size of the nucleon, the nucleon-nucleon potential, the modifications of the nucleon in the nuclear medium, etc. (Auth.)
Differential geometry of group lattices
International Nuclear Information System (INIS)
Dimakis, Aristophanes; Mueller-Hoissen, Folkert
2003-01-01
In a series of publications we developed ''differential geometry'' on discrete sets based on concepts of noncommutative geometry. In particular, it turned out that first-order differential calculi (over the algebra of functions) on a discrete set are in bijective correspondence with digraph structures where the vertices are given by the elements of the set. A particular class of digraphs are Cayley graphs, also known as group lattices. They are determined by a discrete group G and a finite subset S. There is a distinguished subclass of ''bicovariant'' Cayley graphs with the property ad(S)S subset of S. We explore the properties of differential calculi which arise from Cayley graphs via the above correspondence. The first-order calculi extend to higher orders and then allow us to introduce further differential geometric structures. Furthermore, we explore the properties of ''discrete'' vector fields which describe deterministic flows on group lattices. A Lie derivative with respect to a discrete vector field and an inner product with forms is defined. The Lie-Cartan identity then holds on all forms for a certain subclass of discrete vector fields. We develop elements of gauge theory and construct an analog of the lattice gauge theory (Yang-Mills) action on an arbitrary group lattice. Also linear connections are considered and a simple geometric interpretation of the torsion is established. By taking a quotient with respect to some subgroup of the discrete group, generalized differential calculi associated with so-called Schreier diagrams are obtained
Lattice dynamics of lithium oxide
Indian Academy of Sciences (India)
Abstract. Li2O finds several important technological applications, as it is used in solid- state batteries, can be used as a blanket breeding material in nuclear fusion reactors, etc. Li2O exhibits a fast ion phase, characterized by a thermally induced dynamic disorder in the anionic sub-lattice of Li+, at elevated temperatures ...
Lattice fields and strong interactions
International Nuclear Information System (INIS)
Creutz, M.
1989-06-01
I review the lattice formulation of gauge theories and the use of numerical methods to investigate nonperturbative phenomena. These methods are directly applicable to studying hadronic matter at high temperatures. Considerable recent progress has been made in numerical algorithms for including dynamical fermions in such calculations. Dealing with a nonvanishing baryon density adds new unsolved challenges. 33 refs
Borgs, C.; Chayes, J.T.; Hofstad, van der R.W.; Slade, G.
1999-01-01
We introduce a mean-field model of lattice trees based on embeddings into d of abstract trees having a critical Poisson offspring distribution. This model provides a combinatorial interpretation for the self-consistent mean-field model introduced previously by Derbez and Slade [9], and provides an
Lattice quantum chromodynamics: Some topics
Indian Academy of Sciences (India)
I will begin with a lightning quick overview of the basic lattice gauge theory and then go on to .... The Monte Carlo technique to evaluate C(t), or the expectation value of any other observable ... x }occurs with a probability proportional to. 890.
International Nuclear Information System (INIS)
Itzykson, C.
1983-10-01
We review the formulation of field theory and statistical mechanics on a Poissonian random lattice. Topics discussed include random geometry, the construction of field equations for arbitrary spin, the free field spectrum and the question of localization illustrated in the one dimensional case
Collective diffusion and quantum chaos in holography
Wu, Shao-Feng; Wang, Bin; Ge, Xian-Hui; Tian, Yu
2018-05-01
We define a particular combination of charge and heat currents that is decoupled with the heat current. This "heat-decoupled" (HD) current can be transported by diffusion at long distances, when some thermoelectric conductivities and susceptibilities satisfy a simple condition. Using the diffusion condition together with the Kelvin formula, we show that the HD diffusivity can be same as the charge diffusivity and also the heat diffusivity. We illustrate that such mechanism is implemented in a strongly coupled field theory, which is dual to a Lifshitz gravity with the dynamical critical index z =2 . In particular, it is exhibited that both charge and heat diffusivities build the relationship to the quantum chaos. Moreover, we study the HD diffusivity without imposing the diffusion condition. In some homogeneous holographic lattices, it is found that the diffusivity/chaos relation holds independently of any parameters, including the strength of momentum relaxation, chemical potential, or temperature. We also show a counter example of the relation and discuss its limited universality.
Disconnected Diagrams in Lattice QCD
Gambhir, Arjun Singh
In this work, we present state-of-the-art numerical methods and their applications for computing a particular class of observables using lattice quantum chromodynamics (Lattice QCD), a discretized version of the fundamental theory of quarks and gluons. These observables require calculating so called "disconnected diagrams" and are important for understanding many aspects of hadron structure, such as the strange content of the proton. We begin by introducing the reader to the key concepts of Lattice QCD and rigorously define the meaning of disconnected diagrams through an example of the Wick contractions of the nucleon. Subsequently, the calculation of observables requiring disconnected diagrams is posed as the computationally challenging problem of finding the trace of the inverse of an incredibly large, sparse matrix. This is followed by a brief primer of numerical sparse matrix techniques that overviews broadly used methods in Lattice QCD and builds the background for the novel algorithm presented in this work. We then introduce singular value deflation as a method to improve convergence of trace estimation and analyze its effects on matrices from a variety of fields, including chemical transport modeling, magnetohydrodynamics, and QCD. Finally, we apply this method to compute observables such as the strange axial charge of the proton and strange sigma terms in light nuclei. The work in this thesis is innovative for four reasons. First, we analyze the effects of deflation with a model that makes qualitative predictions about its effectiveness, taking only the singular value spectrum as input, and compare deflated variance with different types of trace estimator noise. Second, the synergy between probing methods and deflation is investigated both experimentally and theoretically. Third, we use the synergistic combination of deflation and a graph coloring algorithm known as hierarchical probing to conduct a lattice calculation of light disconnected matrix elements
Disconnected Diagrams in Lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Gambhir, Arjun [College of William and Mary, Williamsburg, VA (United States)
2017-08-01
In this work, we present state-of-the-art numerical methods and their applications for computing a particular class of observables using lattice quantum chromodynamics (Lattice QCD), a discretized version of the fundamental theory of quarks and gluons. These observables require calculating so called \\disconnected diagrams" and are important for understanding many aspects of hadron structure, such as the strange content of the proton. We begin by introducing the reader to the key concepts of Lattice QCD and rigorously define the meaning of disconnected diagrams through an example of the Wick contractions of the nucleon. Subsequently, the calculation of observables requiring disconnected diagrams is posed as the computationally challenging problem of finding the trace of the inverse of an incredibly large, sparse matrix. This is followed by a brief primer of numerical sparse matrix techniques that overviews broadly used methods in Lattice QCD and builds the background for the novel algorithm presented in this work. We then introduce singular value deflation as a method to improve convergence of trace estimation and analyze its effects on matrices from a variety of fields, including chemical transport modeling, magnetohydrodynamics, and QCD. Finally, we apply this method to compute observables such as the strange axial charge of the proton and strange sigma terms in light nuclei. The work in this thesis is innovative for four reasons. First, we analyze the effects of deflation with a model that makes qualitative predictions about its effectiveness, taking only the singular value spectrum as input, and compare deflated variance with different types of trace estimator noise. Second, the synergy between probing methods and deflation is investigated both experimentally and theoretically. Third, we use the synergistic combination of deflation and a graph coloring algorithm known as hierarchical probing to conduct a lattice calculation of light disconnected matrix elements
Ultrafast palladium diffusion in germanium
Tahini, Hassan Ali
2015-01-01
The slow transport of dopants through crystal lattices has hindered the development of novel devices. Typically atoms are contained within deep potential energy wells which necessitates multiple attempts to hop between minimum energy positions. This is because the bonds that constrain atoms are strongest at the minimum positions. As they hop between sites the bonds must be broken, only to re-form as the atoms slide into adjacent minima. Here we demonstrate that the Pd atoms introduced into the Ge lattice behave differently. They retain bonds as the atoms shift across so that at the energy maximum between sites Pd still exhibits strong bonding characteristics. This reduces the energy maximum to almost nothing (a migration energy of only 0.03 eV) and means that the transport of Pd through the Ge lattice is ultrafast. We scrutinize the bonding characteristics at the atomic level using quantum mechanical simulation tools and demonstrate why Pd behaves so differently to other metals we investigated (i.e. Li, Cu, Ag, Pt and Au). Consequently, this fundamental understanding can be extended to systems where extremely rapid diffusion is desired, such as radiation sensors, batteries and solid oxide fuel cells.
Random attractors for stochastic lattice reversible Gray-Scott systems with additive noise
Directory of Open Access Journals (Sweden)
Hongyan Li
2015-10-01
Full Text Available In this article, we prove the existence of a random attractor of the stochastic three-component reversible Gray-Scott system on infinite lattice with additive noise. We use a transformation of addition involved with Ornstein-Uhlenbeck process, for proving the pullback absorbing property and the pullback asymptotic compactness of the reaction diffusion system with cubic nonlinearity.
Statistical hydrodynamics of lattice-gas automata
Grosfils, Patrick; Boon, Jean-Pierre; Brito López, Ricardo; Ernst, M. H.
1993-01-01
We investigate the space and time behavior of spontaneous thermohydrodynamic fluctuations in a simple fluid modeled by a lattice-gas automaton and develop the statistical-mechanical theory of thermal lattice gases to compute the dynamical structure factor, i.e., the power spectrum of the density correlation function. A comparative analysis of the theoretical predictions with our lattice gas simulations is presented. The main results are (i) the spectral function of the lattice-gas fluctuation...
International Nuclear Information System (INIS)
Anderson, R.C.
1976-01-01
A method is described for joining beryllium to beryllium by diffusion bonding. At least one surface portion of at least two beryllium pieces is coated with nickel. A coated surface portion is positioned in a contiguous relationship with another surface portion and subjected to an environment having an atmosphere at a pressure lower than ambient pressure. A force is applied on the beryllium pieces for causing the contiguous surface portions to abut against each other. The contiguous surface portions are heated to a maximum temperature less than the melting temperature of the beryllium, and the applied force is decreased while increasing the temperature after attaining a temperature substantially above room temperature. A portion of the applied force is maintained at a temperature corresponding to about maximum temperature for a duration sufficient to effect the diffusion bond between the contiguous surface portions
An extended fractal growth regime in the diffusion limited aggregation including edge diffusion
Directory of Open Access Journals (Sweden)
Aritra Ghosh
2016-01-01
Full Text Available We have investigated on-lattice diffusion limited aggregation (DLA involving edge diffusion and compared the results with the standard DLA model. For both cases, we observe the existence of a crossover from the fractal to the compact regime as a function of sticking coefficient. However, our modified DLA model including edge diffusion shows an extended fractal growth regime like an earlier theoretical result using realistic growth models and physical parameters [Zhang et al., Phys. Rev. Lett. 73 (1994 1829]. While the results of Zhang et al. showed the existence of the extended fractal growth regime only on triangular but not on square lattices, we find its existence on the square lattice. There is experimental evidence of this growth regime on a square lattice. The standard DLA model cannot characterize fractal morphology as the fractal dimension (Hausdorff dimension, DH is insensitive to morphology. It also predicts DH = DP (the perimeter dimension. For the usual fractal structures, observed in growth experiments on surfaces, the perimeter dimension can differ significantly (DH ≠ DP depending on the morphology. Our modified DLA model shows minor sensitivity to this difference.
Lattice QCD. A critical status report
Energy Technology Data Exchange (ETDEWEB)
Jansen, Karl
2008-10-15
The substantial progress that has been achieved in lattice QCD in the last years is pointed out. I compare the simulation cost and systematic effects of several lattice QCD formulations and discuss a number of topics such as lattice spacing scaling, applications of chiral perturbation theory, non-perturbative renormalization and finite volume effects. Additionally, the importance of demonstrating universality is emphasized. (orig.)
Lattice QCD. A critical status report
International Nuclear Information System (INIS)
Jansen, Karl
2008-10-01
The substantial progress that has been achieved in lattice QCD in the last years is pointed out. I compare the simulation cost and systematic effects of several lattice QCD formulations and discuss a number of topics such as lattice spacing scaling, applications of chiral perturbation theory, non-perturbative renormalization and finite volume effects. Additionally, the importance of demonstrating universality is emphasized. (orig.)
Gauge theories on a small lattice
International Nuclear Information System (INIS)
Robson, D.; Webber, D.M.
1980-01-01
We present exact solutions to U(1), SU(2), and SU(3) lattice gauge theories on a Kogut-Susskind lattice consisting of a single plaquette. We demonstrate precise equivalence between the U(1) theory and the harmonic oscillator on an infinite one-dimensional lattice, and between the SU(N) theory and an N-fermion Schroedinger equation. (orig.)
Spatiotemporal complexity in coupled map lattices
International Nuclear Information System (INIS)
Kaneko, Kunihiko
1986-01-01
Some spatiotemporal patterns of couple map lattices are presented. The chaotic kink-like motions are shown for the phase motion of the coupled circle lattices. An extension of the couple map lattice approach to Hamiltonian dynamics is briefly reported. An attempt to characterize the high-dimensional attractor by the extension of the correlation dimension is discussed. (author)
Clar sextets in square graphene antidot lattices
DEFF Research Database (Denmark)
Petersen, Rene; Pedersen, Thomas Garm; Jauho, Antti-Pekka
2011-01-01
A periodic array of holes transforms graphene from a semimetal into a semiconductor with a band gap tuneable by varying the parameters of the lattice. In earlier work only hexagonal lattices have been treated. Using atomistic models we here investigate the size of the band gap of a square lattice...
Spatial classification with fuzzy lattice reasoning
Mavridis, Constantinos; Athanasiadis, I.N.
2017-01-01
This work extends the Fuzzy Lattice Reasoning (FLR) Classifier to manage spatial attributes, and spatial relationships. Specifically, we concentrate on spatial entities, as countries, cities, or states. Lattice Theory requires the elements of a Lattice to be partially ordered. To match such
International Nuclear Information System (INIS)
Najsh, V.E.; Novoselova, T.V.; Sagaradze, I.V.; Kvyatkovskij, B.E.; Fedorov, V.I.; Chernenkov, Yu.P.
1994-01-01
With the use of X-ray diffractometer a study was made into the intensity of diffuse scattering in Ni crystals with FCC lattice. Earlier accomplished quantitative analysis for BCC crystals was extended to FCC lattices. Comparative evaluation was made for cooperative thermal oscillation patterns and corresponding diffuse scattering in crystals of various structures. Measurements on FCC crystals were carried out at room temperature using AgK a lpha-radiation in 96 points of Ni crystal. 8 refs., 4 figs
Determination of axial diffusion coefficients by the Monte-Carlo method
International Nuclear Information System (INIS)
Milgram, M.
1994-01-01
A simple method to calculate the homogenized diffusion coefficient for a lattice cell using Monte-Carlo techniques is demonstrated. The method relies on modelling a finite reactor volume to induce a curvature in the flux distribution, and then follows a large number of histories to obtain sufficient statistics for a meaningful result. The goal is to determine the diffusion coefficient with sufficient accuracy to test approximate methods built into deterministic lattice codes. Numerical results are given. (author). 4 refs., 8 figs
International Nuclear Information System (INIS)
Lalis, A.; Rouviere, R.; Simon, G.
1976-01-01
A multipassage diffuser having 2p passages comprises a leak-tight cylindrical enclosure closed by a top cover and a bottom end-wall, parallel porous tubes which are rigidly assembled in sectors between tube plates and through which the gas mixture flows, the tube sectors being disposed at uniform intervals on the periphery of the enclosure. The top tube plates are rigidly fixed to an annular header having the shape of a half-torus and adapted to communicate with the tubes of the corresponding sector. Each passage is constituted by a plurality of juxtaposed sectors in which the mixture circulates in the same direction, the header being divided into p portions limited by radial partition-walls and each constituting two adjacent passages. The diffuser is provided beneath the bottom end-wall with p-1 leak-tight chambers each adapted to open into two different portions of the header, and with two collector-chambers each fitted with a nozzle for introducing the gas mixture and discharging the fraction of the undiffused mixture. By means of a central orifice formed in the bottom end-wall the enclosure communicates with a shaft for discharging the diffused fraction of the gas mixture
Inexpensive chirality on the lattice
International Nuclear Information System (INIS)
Kamleh, W.; Williams, A.G.; Adams, D.
2000-01-01
Full text: Implementing lattice fermions that resemble as closely as possible continuum fermions is one of the main goals of the theoretical physics community. Aside from a lack of infinitely powerful computers, one of the main impediments to this is the Nielsen-Ninomiya No-Go theorem for chirality on the lattice. One of the consequences of this theorem is that exact chiral symmetry and a lack of fermion doublers cannot be simultaneously satisfied for fermions on the lattice. In the commonly used Wilson fermion formulation, chiral symmetry is explicitly sacrificed on the lattice to avoid fermion doubling. Recently, an alternative has come forward, namely, the Ginsparg-Wilson relation and one of its solutions, the Overlap fermion. The Ginsparg-Wilson relation is a statement of lattice-deformed chirality. The Overlap-Dirac operator is a member of the family of solutions of the Ginsparg-Wilson relation. In recent times, Overlap fermions have been of great interest to the community due to their excellent chiral properties. However, they are significantly more expensive to implement than Wilson fermions. This expense is primarily due to the fact that the Overlap implementation requires an evaluation of the sign function for the Wilson-Dirac operator. The sign function is approximated by a high order rational polynomial function, but this approximation is poor close to the origin. The less near-zero modes that the Wilson- Dirac operator possesses, the cheaper the Overlap operator will be to implement. A means of improving the eigenvalue properties of the Wilson-Dirac operator by the addition of a so-called 'Clover' term is put forward. Numerical results are given that demonstrate this improvement. The Nielsen-Ninomiya no-go theorem and chirality on the lattice are reviewed. The general form of solutions of the Ginsparg-Wilson relation are given, and the Overlap solution is discussed. Properties of the Overlap-Dirac operator are given, including locality and analytic
Lattice Boltzmann method for weakly ionized isothermal plasmas
International Nuclear Information System (INIS)
Li Huayu; Ki, Hyungson
2007-01-01
In this paper, a lattice Boltzmann method (LBM) for weakly ionized isothermal plasmas is presented by introducing a rescaling scheme for the Boltzmann transport equation. Without using this rescaling, we found that the nondimensional relaxation time used in the LBM is too large and the LBM does not produce physically realistic results. The developed model was applied to the electrostatic wave problem and the diffusion process of singly ionized helium plasmas with a 1-3% degree of ionization under an electric field. The obtained results agree well with theoretical values
One-dimensional map lattices: Synchronization, bifurcations, and chaotic structures
DEFF Research Database (Denmark)
Belykh, Vladimir N.; Mosekilde, Erik
1996-01-01
The paper presents a qualitative analysis of coupled map lattices (CMLs) for the case of arbitrary nonlinearity of the local map and with space-shift as well as diffusion coupling. The effect of synchronization where, independently of the initial conditions, all elements of a CML acquire uniform...... dynamics is investigated and stable chaotic time behaviors, steady structures, and traveling waves are described. Finally, the bifurcations occurring under the transition from spatiotemporal chaos to chaotic synchronization and the peculiarities of CMLs with specific symmetries are discussed....
A critical review of homogenization techniques in reactor lattices
International Nuclear Information System (INIS)
Benoist, P.
1983-01-01
The determination of the shape of the neutron flux in a whole reactor is, at the time being, a much too complex problem to be treated by transport theory. Since the earlier times of reactor theory, the necessity appeared to solve the problem in two steps. First the reactor is divided into zones, each of them forming a regular lattice. In each of these zones, homogenized parameters are determined by transport theory, in order to define an equivalent smeared medium. In a second step, these parameters are introduced in a diffusion theory scheme in order to treat the reactor as a whole. This is the homogenization procedure. 14 refs
A critical review of homogenization techniques in reactor lattices
International Nuclear Information System (INIS)
Benoist, P.
1983-01-01
The determination of the shape of the neutron flux in a whole reactor is, at the time being, a much too complex problem to be treated by transport theory. Since the earlier times of reactor theory, the necessity appeared to solve the problem in two steps. First the reactor is divided into zones, each of them forming a regular lattice. In each of these zones, homogenized parameters are determined by transport theory, in order to define an equivalent smeared medium. In a second step, these parameters are introduced in a diffusion theory scheme in order to treat the reactor as a whole. This is the homogenization procedure
Deterministic diffusion in flower-shaped billiards.
Harayama, Takahisa; Klages, Rainer; Gaspard, Pierre
2002-08-01
We propose a flower-shaped billiard in order to study the irregular parameter dependence of chaotic normal diffusion. Our model is an open system consisting of periodically distributed obstacles in the shape of a flower, and it is strongly chaotic for almost all parameter values. We compute the parameter dependent diffusion coefficient of this model from computer simulations and analyze its functional form using different schemes, all generalizing the simple random walk approximation of Machta and Zwanzig. The improved methods we use are based either on heuristic higher-order corrections to the simple random walk model, on lattice gas simulation methods, or they start from a suitable Green-Kubo formula for diffusion. We show that dynamical correlations, or memory effects, are of crucial importance in reproducing the precise parameter dependence of the diffusion coefficent.
Radiation enhanced diffusion in FCC alloys
International Nuclear Information System (INIS)
Schuele, W.
1982-01-01
In many alloys vacancies and interstitials can be identified in a straight forward way by measurements of radiation enhanced diffusion. In some alloys, however, quenching experiments are also necessary for the identification of these defects. Results for two characteristic alloys in which the transformation rate during high energy particle irradiation is determined by an interstitialcy and by a vacancy diffusion mechanism only, are discussed. It is also shown that a decrease of the migration energy of defects due to an interaction of the high energy particles with the lattice atoms must be taken into account in the interpretation of the results. (author)
Monte Carlo based diffusion coefficients for LMFBR analysis
International Nuclear Information System (INIS)
Van Rooijen, Willem F.G.; Takeda, Toshikazu; Hazama, Taira
2010-01-01
A method based on Monte Carlo calculations is developed to estimate the diffusion coefficient of unit cells. The method uses a geometrical model similar to that used in lattice theory, but does not use the assumption of a separable fundamental mode used in lattice theory. The method uses standard Monte Carlo flux and current tallies, and the continuous energy Monte Carlo code MVP was used without modifications. Four models are presented to derive the diffusion coefficient from tally results of flux and partial currents. In this paper the method is applied to the calculation of a plate cell of the fast-spectrum critical facility ZEBRA. Conventional calculations of the diffusion coefficient diverge in the presence of planar voids in the lattice, but our Monte Carlo method can treat this situation without any problem. The Monte Carlo method was used to investigate the influence of geometrical modeling as well as the directional dependence of the diffusion coefficient. The method can be used to estimate the diffusion coefficient of complicated unit cells, the limitation being the capabilities of the Monte Carlo code. The method will be used in the future to confirm results for the diffusion coefficient obtained of the Monte Carlo code. The method will be used in the future to confirm results for the diffusion coefficient obtained with deterministic codes. (author)
Chiral fermions on the lattice
International Nuclear Information System (INIS)
Randjbar Daemi, S.; Strathdee, J.
1995-01-01
The overlap approach to chiral gauge theories on arbitrary D-dimensional lattices is studied. The doubling problem and its relation to chiral anomalies for D = 2 and 4 is examined. In each case it is shown that the doublers can be eliminated and the well known perturbative results for chiral anomalies can be recovered. We also consider the multi-flavour case and give the general criteria for the construction of anomaly free chiral gauge theories on arbitrary lattices. We calculate the second order terms in a continuum approximation to the overlap formula in D dimensions and show that they coincide with the bilinear part of the effective action of D-dimensional Weyl fermions coupled to a background gauge field. Finally, using the same formalism we reproduce the correct Lorentz, diffeomorphism and gauge anomalies in the coupling of a Weyl fermion to 2-dimensional gravitation and Maxwell fields. (author). 15 refs
Entropy favours open colloidal lattices
Mao, Xiaoming; Chen, Qian; Granick, Steve
2013-03-01
Burgeoning experimental and simulation activity seeks to understand the existence of self-assembled colloidal structures that are not close-packed. Here we describe an analytical theory based on lattice dynamics and supported by experiments that reveals the fundamental role entropy can play in stabilizing open lattices. The entropy we consider is associated with the rotational and vibrational modes unique to colloids interacting through extended attractive patches. The theory makes predictions of the implied temperature, pressure and patch-size dependence of the phase diagram of open and close-packed structures. More generally, it provides guidance for the conditions at which targeted patchy colloidal assemblies in two and three dimensions are stable, thus overcoming the difficulty in exploring by experiment or simulation the full range of conceivable parameters.
Electroweak interactions on the lattice
International Nuclear Information System (INIS)
Kieu, T.D.
1994-07-01
It is shown that the lattice fermion doubling phenomenon is connected to the chiral anomaly which is unique to the electroweak interactions. The chiral anomaly is the breaking of chiral gauge symmetry at the quantum level due to the quantum fluctuations. Such breaking, however, is undesirable and to be avoided. The preservation of gauge symmetry imposes stringent constraints on acceptable chiral gauge theory. It is argued that the constraints are unnecessary because the conventional quantization of chiral gauge theory has missed out some crucial contributions of the chiral interactions. The corrected quantization yields consistent theory in which there is no gauge anomaly and in which various mass terms can be introduced with neither the loss of gauge invariance nor the need for the Higgs mechanism. The new quantization also provide a solution to the difficulty of how to model the electroweak interactions on the lattice. 9 refs. 1 fig
Entanglement scaling in lattice systems
Energy Technology Data Exchange (ETDEWEB)
Audenaert, K M R [Institute for Mathematical Sciences, Imperial College London, 53 Prince' s Gate, Exhibition Road, London SW7 2PG (United Kingdom); Cramer, M [QOLS, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2BW (United Kingdom); Eisert, J [Institute for Mathematical Sciences, Imperial College London, 53 Prince' s Gate, Exhibition Road, London SW7 2PG (United Kingdom); Plenio, M B [Institute for Mathematical Sciences, Imperial College London, 53 Prince' s Gate, Exhibition Road, London SW7 2PG (United Kingdom)
2007-05-15
We review some recent rigorous results on scaling laws of entanglement properties in quantum many body systems. More specifically, we study the entanglement of a region with its surrounding and determine its scaling behaviour with its size for systems in the ground and thermal states of bosonic and fermionic lattice systems. A theorem connecting entanglement between a region and the rest of the lattice with the surface area of the boundary between the two regions is presented for non-critical systems in arbitrary spatial dimensions. The entanglement scaling in the field limit exhibits a peculiar difference between fermionic and bosonic systems. In one-spatial dimension a logarithmic divergence is recovered for both bosonic and fermionic systems. In two spatial dimensions in the setting of half-spaces however we observe strict area scaling for bosonic systems and a multiplicative logarithmic correction to such an area scaling in fermionic systems. Similar questions may be posed and answered in classical systems.
Transitionless lattices for LAMPF II
International Nuclear Information System (INIS)
Franczak, B.J.
1984-10-01
Some techniques are described for the design of synchrotron lattices that have zero dispersion in the straight sections and/or imaginary transition energy (negative momentum-compaction factor) but no excessive amplitudes of the dispersion function. Included as an application is a single-stage synchrotron, with variable optics, that has different ion-optical properties at injection and extraction but requires a complex way of programming the quadrupoles. In addition, a two-stage facility consisting of a 45-GeV synchrotron of 1100-m circumference and a 9-GeV booster of half that size is presented. As alternates to these separated-function lattices, some combined-function modules are given that can be used to construct a synchrotron with similar properties
Graphene antidot lattice transport measurements
DEFF Research Database (Denmark)
Mackenzie, David; Cagliani, Alberto; Gammelgaard, Lene
2017-01-01
We investigate graphene devices patterned with a narrow band of holes perpendicular to the current flow, a few-row graphene antidot lattice (FR-GAL). Theoretical reports suggest that a FR-GAL can have a bandgap with a relatively small reduction of the transmission compared to what is typical...... for antidot arrays devices. Graphene devices were fabricated using 100 keV electron beam lithography (EBL) for nanopatterning as well as for defining electrical contacts. Patterns with hole diameter and neck widths of order 30 nm were produced, which is the highest reported pattern density of antidot lattices...... in graphene reported defined by EBL. Electrical measurements showed that devices with one and five rows exhibited field effect mobility of ∼100 cm2/Vs, while a larger number of rows, around 40, led to a significant reduction of field effect mobility (
Cellular automata in cytoskeletal lattices
Energy Technology Data Exchange (ETDEWEB)
Smith, S A; Watt, R C; Hameroff, S R
1984-01-01
Cellular automata (CA) activities could mediate biological regulation and information processing via nonlinear electrodynamic effects in cytoskeletal lattice arrays. Frohlich coherent oscillations and other nonlinear mechanisms may effect discrete 10/sup -10/ to 10/sup -11/ s interval events which result in dynamic patterns in biolattices such as cylindrical protein polymers: microtubules (MT). Structural geometry and electrostatic forces of MT subunit dipole oscillations suggest neighbor rules among the hexagonally packed protein subunits. Computer simulations using these suggested rules and MT structural geometry demonstrate CA activities including dynamical and stable self-organizing patterns, oscillators, and traveling gliders. CA activities in MT and other cytoskeletal lattices may have important biological regulatory functions. 23 references, 6 figures, 1 table.
Innovations in lattice QCD algorithms
International Nuclear Information System (INIS)
Orginos, Konstantinos
2006-01-01
Lattice QCD calculations demand a substantial amount of computing power in order to achieve the high precision results needed to better understand the nature of strong interactions, assist experiment to discover new physics, and predict the behavior of a diverse set of physical systems ranging from the proton itself to astrophysical objects such as neutron stars. However, computer power alone is clearly not enough to tackle the calculations we need to be doing today. A steady stream of recent algorithmic developments has made an important impact on the kinds of calculations we can currently perform. In this talk I am reviewing these algorithms and their impact on the nature of lattice QCD calculations performed today
Baryon structure from lattice QCD
International Nuclear Information System (INIS)
Alexandrou, C.
2009-01-01
We present recent lattice results on the baryon spectrum, nucleon electromagnetic and axial form factors, nucleon to Δ transition form factors as well as the Δ electromagnetic form factors. The masses of the low lying baryons and the nucleon form factors are calculated using two degenerate flavors of twisted mass fermions down to pion mass of about 270 MeV. We compare to the results of other collaborations. The nucleon to Δ transition and Δ form factors are calculated in a hybrid scheme, which uses staggered sea quarks and domain wall valence quarks. The dominant magnetic dipole nucleon to Δ transition form factor is also evaluated using dynamical domain wall fermions. The transverse density distributions of the Δ in the infinite momentum frame are extracted using the form factors determined from lattice QCD. (author)
Multigrid for Staggered Lattice Fermions
Energy Technology Data Exchange (ETDEWEB)
Brower, Richard C. [Boston U.; Clark, M. A. [Unlisted, US; Strelchenko, Alexei [Fermilab; Weinberg, Evan [Boston U.
2018-01-23
Critical slowing down in Krylov methods for the Dirac operator presents a major obstacle to further advances in lattice field theory as it approaches the continuum solution. Here we formulate a multi-grid algorithm for the Kogut-Susskind (or staggered) fermion discretization which has proven difficult relative to Wilson multigrid due to its first-order anti-Hermitian structure. The solution is to introduce a novel spectral transformation by the K\\"ahler-Dirac spin structure prior to the Galerkin projection. We present numerical results for the two-dimensional, two-flavor Schwinger model, however, the general formalism is agnostic to dimension and is directly applicable to four-dimensional lattice QCD.
Computing nucleon EDM on a lattice
Abramczyk, Michael; Aoki, Sinya; Blum, Tom; Izubuchi, Taku; Ohki, Hiroshi; Syritsyn, Sergey
2018-03-01
I will discuss briefly recent changes in the methodology of computing the baryon EDM on a lattice. The associated correction substantially reduces presently existing lattice values for the proton and neutron theta-induced EDMs, so that even the most precise previous lattice results become consistent with zero. On one hand, this change removes previous disagreements between these lattice results and the phenomenological estimates of the nucleon EDM. On the other hand, the nucleon EDM becomes much harder to compute on a lattice. In addition, I will review the progress in computing quark chromo-EDM-induced nucleon EDM using chiral quark action.
Heavy water critical experiments on plutonium lattice
International Nuclear Information System (INIS)
Miyawaki, Yoshio; Shiba, Kiminori
1975-06-01
This report is the summary of physics study on plutonium lattice made in Heavy Water Critical Experiment Section of PNC. By using Deuterium Critical Assembly, physics study on plutonium lattice has been carried out since 1972. Experiments on following items were performed in a core having 22.5 cm square lattice pitch. (1) Material buckling (2) Lattice parameters (3) Local power distribution factor (4) Gross flux distribution in two region core (5) Control rod worth. Experimental results were compared with theoretical ones calculated by METHUSELAH II code. It is concluded from this study that calculation by METHUSELAH II code has acceptable accuracy in the prediction on plutonium lattice. (author)
Computing nucleon EDM on a lattice
Energy Technology Data Exchange (ETDEWEB)
Abramczyk, Michael; Izubuchi, Taku
2017-06-18
I will discuss briefly recent changes in the methodology of computing the baryon EDM on a lattice. The associated correction substantially reduces presently existing lattice values for the proton and neutron theta-induced EDMs, so that even the most precise previous lattice results become consistent with zero. On one hand, this change removes previous disagreements between these lattice results and the phenomenological estimates of the nucleon EDM. On the other hand, the nucleon EDM becomes much harder to compute on a lattice. In addition, I will review the progress in computing quark chromo-EDM-induced nucleon EDM using chiral quark action.
Aliasing modes in the lattice Schwinger model
International Nuclear Information System (INIS)
Campos, Rafael G.; Tututi, Eduardo S.
2007-01-01
We study the Schwinger model on a lattice consisting of zeros of the Hermite polynomials that incorporates a lattice derivative and a discrete Fourier transform with many properties. Such a lattice produces a Klein-Gordon equation for the boson field and the exact value of the mass in the asymptotic limit if the boundaries are not taken into account. On the contrary, if the lattice is considered with boundaries new modes appear due to aliasing effects. In the continuum limit, however, this lattice yields also a Klein-Gordon equation with a reduced mass
International Nuclear Information System (INIS)
Sommer, Rainer
2014-02-01
The principles of scale setting in lattice QCD as well as the advantages and disadvantages of various commonly used scales are discussed. After listing criteria for good scales, I concentrate on the main presently used ones with an emphasis on scales derived from the Yang-Mills gradient flow. For these I discuss discretisation errors, statistical precision and mass effects. A short review on numerical results also brings me to an unpleasant disagreement which remains to be explained.
Apiary B Factory lattice design
International Nuclear Information System (INIS)
Donald, M.H.R.; Garren, A.A.
1991-04-01
The Apiary B Factory is a proposed high-intensity electron-positron collider. This paper will present the lattice design for this facility, which envisions two rings with unequal energies in the PEP tunnel. The design has many interesting optical and geometrical features due to the needs to conform to the existing tunnel, and to achieve the necessary emittances, damping times and vacuum. Existing hardware is used to a maximum extent. 8 figs. 1 tab
BROOKHAVEN: Lattice gauge theory symposium
Energy Technology Data Exchange (ETDEWEB)
Anon.
1986-12-15
Originally introduced by Kenneth Wilson in the early 70s, the lattice formulation of a quantum gauge theory became a hot topic of investigation after Mike Creutz, Laurence Jacobs and Claudio Rebbi demonstrated in 1979 the feasibility of meaningful computer simulations. The initial enthusiasm led gradually to a mature research effort, with continual attempts to improve upon previous results, to develop better computational techniques and to find new domains of application.
Harmonic Lattice Dynamics of Germanium
Energy Technology Data Exchange (ETDEWEB)
Nelin, G
1974-07-01
The phonon dispersion relations of the DELTA-, LAMBDA-, and SIGMA-directions of germanium at 80 K are analysed in terms of current harmonic lattice dynamical models. On the basis of this experience, a new model is proposed which gives a unified account of the strong points of the previous models. The principal elements of the presented theory are quasiparticle bond charges combined with a valence force field.
Screening in graphene antidot lattices
DEFF Research Database (Denmark)
Schultz, Marco Haller; Jauho, A. P.; Pedersen, T. G.
2011-01-01
We compute the dynamical polarization function for a graphene antidot lattice in the random-phase approximation. The computed polarization functions display a much more complicated structure than what is found for pristine graphene (even when evaluated beyond the Dirac-cone approximation...... the plasmon dispersion law and find an approximate square-root dependence with a suppressed plasmon frequency as compared to doped graphene. The plasmon dispersion is nearly isotropic and the developed approximation schemes agree well with the full calculation....
Symplectic maps for accelerator lattices
International Nuclear Information System (INIS)
Warnock, R.L.; Ruth, R.; Gabella, W.
1988-05-01
We describe a method for numerical construction of a symplectic map for particle propagation in a general accelerator lattice. The generating function of the map is obtained by integrating the Hamilton-Jacobi equation as an initial-value problem on a finite time interval. Given the generating function, the map is put in explicit form by means of a Fourier inversion technique. We give an example which suggests that the method has promise. 9 refs., 9 figs
Harmonic Lattice Dynamics of Germanium
International Nuclear Information System (INIS)
Nelin, G.
1974-01-01
The phonon dispersion relations of the Δ-, Λ-, and Σ-directions of germanium at 80 K are analysed in terms of current harmonic lattice dynamical models. On the basis of this experience, a new model is proposed which gives a unified account of the strong points of the previous models. The principal elements of the presented theory are quasiparticle bond charges combined with a valence force field
Energy Technology Data Exchange (ETDEWEB)
Sommer, Rainer [DESY, Zeuthen (Germany). John von Neumann-Inst. fuer Computing NIC
2014-02-15
The principles of scale setting in lattice QCD as well as the advantages and disadvantages of various commonly used scales are discussed. After listing criteria for good scales, I concentrate on the main presently used ones with an emphasis on scales derived from the Yang-Mills gradient flow. For these I discuss discretisation errors, statistical precision and mass effects. A short review on numerical results also brings me to an unpleasant disagreement which remains to be explained.
Wave transmission in nonlinear lattices
International Nuclear Information System (INIS)
Hennig, D.; Tsironis, G.P.
1999-01-01
The interplay of nonlinearity with lattice discreteness leads to phenomena and propagation properties quite distinct from those appearing in continuous nonlinear systems. For a large variety of condensed matter and optics applications the continuous wave approximation is not appropriate. In the present review we discuss wave transmission properties in one dimensional nonlinear lattices. Our paradigmatic equations are discrete nonlinear Schroedinger equations and their study is done through a dynamical systems approach. We focus on stationary wave properties and utilize well known results from the theory of dynamical systems to investigate various aspects of wave transmission and wave localization. We analyze in detail the more general dynamical system corresponding to the equation that interpolates between the non-integrable discrete nonlinear Schroedinger equation and the integrable Albowitz-Ladik equation. We utilize this analysis in a nonlinear Kronig-Penney model and investigate transmission and band modification properties. We discuss the modifications that are effected through an electric field and the nonlinear Wannier-Stark localization effects that are induced. Several applications are described, such as polarons in one dimensional lattices, semiconductor superlattices and one dimensional nonlinear photonic band gap systems. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)
Spin lattices of walking droplets
Saenz, Pedro; Pucci, Giuseppe; Goujon, Alexis; Dunkel, Jorn; Bush, John
2017-11-01
We present the results of an experimental investigation of the spontaneous emergence of collective behavior in spin lattice of droplets walking on a vibrating fluid bath. The bottom topography consists of relatively deep circular wells that encourage the walking droplets to follow circular trajectories centered at the lattice sites, in one direction or the other. Wave-mediated interactions between neighboring drops are enabled through a thin fluid layer between the wells. The sense of rotation of the walking droplets may thus become globally coupled. When the coupling is sufficiently strong, interactions with neighboring droplets may result in switches in spin that lead to preferred global arrangements, including correlated (all drops rotating in the same direction) or anti-correlated (neighboring drops rotating in opposite directions) states. Analogies with ferromagnetism and anti-ferromagnetism are drawn. Different spatial arrangements are presented in 1D and 2D lattices to illustrate the effects of topological frustration. This work was supported by the US National Science Foundation through Grants CMMI-1333242 and DMS-1614043.
Calculational methods for lattice cells
International Nuclear Information System (INIS)
Askew, J.R.
1980-01-01
At the current stage of development, direct simulation of all the processes involved in the reactor to the degree of accuracy required is not an economic proposition, and this is achieved by progressive synthesis of models for parts of the full space/angle/energy neutron behaviour. The split between reactor and lattice calculations is one such simplification. Most reactors are constructed of repetitions of similar geometric units, the fuel elements, having broadly similar properties. Thus the provision of detailed predictions of their behaviour is an important step towards overall modelling. We shall be dealing with these lattice methods in this series of lectures, but will refer back from time to time to their relationship with overall reactor calculation The lattice cell is itself composed of somewhat similar sub-units, the fuel pins, and will itself often rely upon a further break down of modelling. Construction of a good model depends upon the identification, on physical and mathematical grounds, of the most helpful division of the calculation at this level
High-throughput ab-initio dilute solute diffusion database.
Wu, Henry; Mayeshiba, Tam; Morgan, Dane
2016-07-19
We demonstrate automated generation of diffusion databases from high-throughput density functional theory (DFT) calculations. A total of more than 230 dilute solute diffusion systems in Mg, Al, Cu, Ni, Pd, and Pt host lattices have been determined using multi-frequency diffusion models. We apply a correction method for solute diffusion in alloys using experimental and simulated values of host self-diffusivity. We find good agreement with experimental solute diffusion data, obtaining a weighted activation barrier RMS error of 0.176 eV when excluding magnetic solutes in non-magnetic alloys. The compiled database is the largest collection of consistently calculated ab-initio solute diffusion data in the world.
International Nuclear Information System (INIS)
Habib, S.
1994-01-01
We consider a simple quantum system subjected to a classical random force. Under certain conditions it is shown that the noise-averaged Wigner function of the system follows an integro-differential stochastic Liouville equation. In the simple case of polynomial noise-couplings this equation reduces to a generalized Fokker-Planck form. With nonlinear noise injection new ''quantum diffusion'' terms rise that have no counterpart in the classical case. Two special examples that are not of a Fokker-Planck form are discussed: the first with a localized noise source and the other with a spatially modulated noise source
Hereditary Diffuse Gastric Cancer
... Hereditary Diffuse Gastric Cancer Request Permissions Hereditary Diffuse Gastric Cancer Approved by the Cancer.Net Editorial Board , 10/2017 What is hereditary diffuse gastric cancer? Hereditary diffuse gastric cancer (HDGC) is a rare ...
Stochastic lattice model of synaptic membrane protein domains.
Li, Yiwei; Kahraman, Osman; Haselwandter, Christoph A
2017-05-01
Neurotransmitter receptor molecules, concentrated in synaptic membrane domains along with scaffolds and other kinds of proteins, are crucial for signal transmission across chemical synapses. In common with other membrane protein domains, synaptic domains are characterized by low protein copy numbers and protein crowding, with rapid stochastic turnover of individual molecules. We study here in detail a stochastic lattice model of the receptor-scaffold reaction-diffusion dynamics at synaptic domains that was found previously to capture, at the mean-field level, the self-assembly, stability, and characteristic size of synaptic domains observed in experiments. We show that our stochastic lattice model yields quantitative agreement with mean-field models of nonlinear diffusion in crowded membranes. Through a combination of analytic and numerical solutions of the master equation governing the reaction dynamics at synaptic domains, together with kinetic Monte Carlo simulations, we find substantial discrepancies between mean-field and stochastic models for the reaction dynamics at synaptic domains. Based on the reaction and diffusion properties of synaptic receptors and scaffolds suggested by previous experiments and mean-field calculations, we show that the stochastic reaction-diffusion dynamics of synaptic receptors and scaffolds provide a simple physical mechanism for collective fluctuations in synaptic domains, the molecular turnover observed at synaptic domains, key features of the observed single-molecule trajectories, and spatial heterogeneity in the effective rates at which receptors and scaffolds are recycled at the cell membrane. Our work sheds light on the physical mechanisms and principles linking the collective properties of membrane protein domains to the stochastic dynamics that rule their molecular components.
Lin, J. Q.; Liu, X.; Blackburn, E.; Wakimoto, S.; Ding, H.; Islam, Z.; Sinha, S. K.
2018-05-01
The nanometer scale lattice deformation brought about by the dopants in the high temperature superconducting cuprate La2 -xSrx CuO4 (x =0.08 ) was investigated by measuring the associated x-ray diffuse scattering around multiple Bragg peaks. A characteristic diffuse scattering pattern was observed, which can be well described by continuum elastic theory. With the fitted dipole force parameters, the acoustic-type lattice deformation pattern was reconstructed and found to be of similar size to lattice thermal vibration at 7 K. Our results address the long-term concern of dopant introduced local lattice inhomogeneity, and show that the associated nanometer scale lattice deformation is marginal and cannot, alone, be responsible for the patched variation in the spectral gaps observed with scanning tunneling microscopy in the cuprates.
Topological magnon bands in ferromagnetic star lattice
International Nuclear Information System (INIS)
Owerre, S A
2017-01-01
The experimental observation of topological magnon bands and thermal Hall effect in a kagomé lattice ferromagnet Cu(1–3, bdc) has inspired the search for topological magnon effects in various insulating ferromagnets that lack an inversion center allowing a Dzyaloshinskii–Moriya (DM) spin–orbit interaction. The star lattice (also known as the decorated honeycomb lattice) ferromagnet is an ideal candidate for this purpose because it is a variant of the kagomé lattice with additional links that connect the up-pointing and down-pointing triangles. This gives rise to twice the unit cell of the kagomé lattice, and hence more interesting topological magnon effects. In particular, the triangular bridges on the star lattice can be coupled either ferromagnetically or antiferromagnetically which is not possible on the kagomé lattice ferromagnets. Here, we study DM-induced topological magnon bands, chiral edge modes, and thermal magnon Hall effect on the star lattice ferromagnet in different parameter regimes. The star lattice can also be visualized as the parent material from which topological magnon bands can be realized for the kagomé and honeycomb lattices in some limiting cases. (paper)
Topological magnon bands in ferromagnetic star lattice.
Owerre, S A
2017-05-10
The experimental observation of topological magnon bands and thermal Hall effect in a kagomé lattice ferromagnet Cu(1-3, bdc) has inspired the search for topological magnon effects in various insulating ferromagnets that lack an inversion center allowing a Dzyaloshinskii-Moriya (DM) spin-orbit interaction. The star lattice (also known as the decorated honeycomb lattice) ferromagnet is an ideal candidate for this purpose because it is a variant of the kagomé lattice with additional links that connect the up-pointing and down-pointing triangles. This gives rise to twice the unit cell of the kagomé lattice, and hence more interesting topological magnon effects. In particular, the triangular bridges on the star lattice can be coupled either ferromagnetically or antiferromagnetically which is not possible on the kagomé lattice ferromagnets. Here, we study DM-induced topological magnon bands, chiral edge modes, and thermal magnon Hall effect on the star lattice ferromagnet in different parameter regimes. The star lattice can also be visualized as the parent material from which topological magnon bands can be realized for the kagomé and honeycomb lattices in some limiting cases.
Group theoretic reduction of Laplacian dynamical problems on fractal lattices
International Nuclear Information System (INIS)
Schwalm, W.A.; Schwalm, M.K.; Giona, M.
1997-01-01
Discrete forms of the Schroedinger equation, the diffusion equation, the linearized Landau-Ginzburg equation, and discrete models for vibrations and spin dynamics belong to a class of Laplacian-based finite difference models. Real-space renormalization of such models on finitely ramified regular fractals is known to give exact recursion relations. It is shown that these recursions commute with Lie groups representing continuous symmetries of the discrete models. Each such symmetry reduces the order of the renormalization recursions by one, resulting in a system of recursions with one fewer variable. Group trajectories are obtained from inverse images of fixed and invariant sets of the recursions. A subset of the Laplacian finite difference models can be mapped by change of boundary conditions and time dependence to a diffusion problem with closed boundaries. In such cases conservation of mass simplifies the group flow and obtaining the groups becomes easier. To illustrate this, the renormalization recursions for Green functions on four standard examples are decoupled. The examples are (1) the linear chain, (2) an anisotropic version of Dhar close-quote s 3-simplex, similar to a model dealt with by Hood and Southern, (3) the fourfold coordinated Sierpiacute nski lattice of Rammal and of Domany et al., and (4) a form of the Vicsek lattice. Prospects for applying the group theoretic method to more general dynamical systems are discussed. copyright 1997 The American Physical Society
Lattice dynamics and lattice thermal conductivity of thorium dicarbide
Energy Technology Data Exchange (ETDEWEB)
Liao, Zongmeng [Institute of Theoretical Physics and Department of Physics, East China Normal University, Shanghai 200241 (China); Huai, Ping, E-mail: huaiping@sinap.ac.cn [Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800 (China); Qiu, Wujie [Institute of Theoretical Physics and Department of Physics, East China Normal University, Shanghai 200241 (China); State Key Laboratory of High Performance Ceramics and Superfine Microstructure, Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai 200050 (China); Ke, Xuezhi, E-mail: xzke@phy.ecnu.edu.cn [Institute of Theoretical Physics and Department of Physics, East China Normal University, Shanghai 200241 (China); Zhang, Wenqing [State Key Laboratory of High Performance Ceramics and Superfine Microstructure, Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai 200050 (China); Zhu, Zhiyuan [Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 201800 (China)
2014-11-15
The elastic and thermodynamic properties of ThC{sub 2} with a monoclinic symmetry have been studied by means of density functional theory and direct force-constant method. The calculated properties including the thermal expansion, the heat capacity and the elastic constants are in a good agreement with experiment. Our results show that the vibrational property of the C{sub 2} dimer in ThC{sub 2} is similar to that of a free standing C{sub 2} dimer. This indicates that the C{sub 2} dimer in ThC{sub 2} is not strongly bonded to Th atoms. The lattice thermal conductivity for ThC{sub 2} was calculated by means of the Debye–Callaway model. As a comparison, the conductivity of ThC was also calculated. Our results show that the ThC and ThC{sub 2} contributions of the lattice thermal conductivity to the total conductivity are 29% and 17%, respectively.
Surface diffusion studies by optical diffraction techniques
International Nuclear Information System (INIS)
Xiao, X.D.
1992-11-01
The newly developed optical techniques have been combined with either second harmonic (SH) diffraction or linear diffraction off a monolayer adsorbate grating for surface diffusion measurement. Anisotropy of surface diffusion of CO on Ni(l10) was used as a demonstration for the second harmonic dim reaction method. The linear diffraction method, which possesses a much higher sensitivity than the SH diffraction method, was employed to study the effect of adsorbate-adsorbate interaction on CO diffusion on Ni(l10) surface. Results showed that only the short range direct CO-CO orbital overlapping interaction influences CO diffusion but not the long range dipole-dipole and CO-NI-CO interactions. Effects of impurities and defects on surface diffusion were further explored by using linear diffraction method on CO/Ni(110) system. It was found that a few percent S impurity can alter the CO diffusion barrier height to a much higher value through changing the Ni(110) surface. The point defects of Ni(l10) surface seem to speed up CO diffusion significantly. A mechanism with long jumps over multiple lattice distance initiated by CO filled vacancy is proposed to explain the observed defect effect
Nucleon deformation from lattice QCD
International Nuclear Information System (INIS)
Tsapalis, A.
2008-01-01
The issue of nucleon and Delta(1232) deformation is discussed through the evaluation of the N to Delta electromagnetic transition and Delta electromagnetic form factors in Lattice QCD. The momentum dependence of the form factors is studied using 2+1 staggered dynamical flavors at pion masses as low as 350 MeV and compared to results obtained in the Wilson quenched and two-flavor dynamical theory at similar pion masses. The measurement of small non-zero quadrupole amplitudes, in agreement to recent experiments, establishes the existence of deformation in the N and Delta states. (author)
Nucleon Structure from Lattice QCD
International Nuclear Information System (INIS)
Zanotti, J. M.
2011-01-01
Lattice simulations of hadronic structure are now reaching a level where they are able to not only complement, but also provide guidance to current and forthcoming experimental programmes.By considering new simulations at low quark masses and on large volumes, we review the recent progress that has been made in this area by the QCDSF/UKQCD collaboration. In particular, results obtained close to the physical point for several quantities, including electromagnetic form factors and moments of parton distribution functions, show some indication of approaching their phenomenological values.
GLAD: a generic lattice debugger
International Nuclear Information System (INIS)
Lee, M.J.
1992-01-01
Today, numerous simulation and analysis codes exist for the design, commission, and operation of accelerator beam lines. There is a need to develop a common user interface and database link to run these codes interactively. This paper will describe a proposed system, GLAD (Generic LAttice Debugger), to fulfill this need. Specifically, GLAD can be used to find errors in beam lines during commissioning, control beam parameters during operation, and design beam line optics and error correction systems for the next generation of linear accelerators and storage rings. (author)
Lattice dynamics of ionic crystals
International Nuclear Information System (INIS)
Mahan, G.D.
1990-01-01
The theory of lattice dynamics for ionic and rare-gas crystals is derived in the harmonic approximation. We start from a Hamiltonian and average over electron coordinates in order to obtain an effective interaction between ion displacements. We assume that electronic excitations are localized on a single ion, which limits the theory to ionic crystals. The deformation-dipole model and the indirect-ionic-interaction model are derived. These two contributions are closely linked, and together provide an accurate description of short-range forces
Rojas Bocanegra, Alberto
2004-01-01
Objetivo: Determinar la prevalencia de degeneración periférica de retina Lattice y su relación con estados refractivos y rupturas retinales. Metodología: Estudio de corte transversal con exploración de asociación, mediante análisis de casos y controles. Se examinaron 680 ojos en el Instituto de Investigaciones Optométricas e Instituto de Córnea. El estado refractivo se determinó mediante técnica estática y el estado retinal mediante oftalmoscopia indirecta con indentación escleral. Resultados...
Lattice degeneration of the retina.
Byer, N E
1979-01-01
Lattice degeneration of the retina is the most important of all clinically distinct entities that effect the peripheral fundus and are related to retinal detachment. The purpose of this review is to survey the extensive literature, to evaluate the many diverse opinions on this subject, and to correlate and summarize all the known facts regarding this disease entity. The disease is fully defined and described, both clinically and histologically. Some aspects of the disease are still poorly understood, and some remain controversial, especially in the area of management. For this reason, the indications for treatment are discussed under eight subsections, with a view toward providing practical guidelines for recommendations in management.
The lattice dynamics of imidazole
International Nuclear Information System (INIS)
Link, K.H.
1983-05-01
The lattice dynamics of imidazole have been investigated. To this end dispersion curves have been determined at 10 K by inelastic coherent neutron scattering. RAMAN measurements have been done to investigate identical gamma - point modes. The combination of extinction rules for RAMAN - and neutron scattering leads to the symmetry assignment of identical gamma - point modes. The experiment yields a force constant of the streching vibration of the hydrogen bond of 0.33 mdyn/A. A force model has been developed to describe the intermolecular atom - atom Interactions in imidazole. (orig./BHO)
Working Group Report: Lattice Field Theory
Energy Technology Data Exchange (ETDEWEB)
Blum, T.; et al.,
2013-10-22
This is the report of the Computing Frontier working group on Lattice Field Theory prepared for the proceedings of the 2013 Community Summer Study ("Snowmass"). We present the future computing needs and plans of the U.S. lattice gauge theory community and argue that continued support of the U.S. (and worldwide) lattice-QCD effort is essential to fully capitalize on the enormous investment in the high-energy physics experimental program. We first summarize the dramatic progress of numerical lattice-QCD simulations in the past decade, with some emphasis on calculations carried out under the auspices of the U.S. Lattice-QCD Collaboration, and describe a broad program of lattice-QCD calculations that will be relevant for future experiments at the intensity and energy frontiers. We then present details of the computational hardware and software resources needed to undertake these calculations.
Further localization studies of Co atoms diffused into silicon
International Nuclear Information System (INIS)
Dezsi, I.; Feher, S.; Forgacs, G.; Horvath, D.; Kotai, E.; Manuaba, A.; Mezey, G.; Molnar, B.; Nagy, D.L.; Zsoldos, E.
1982-01-01
57 Co atoms diffused at 1270 K for 1 h into single crystals of Si have a single Moessbauer line at (-0.059 +- 0.001) mm/s. Channelling studies show that 77% of the Co atoms occupy some substitutional sites. It is found that Co forms epitaxial CoSi 2 clusters in the Si lattice. (orig.)
Further localization studies of Co atoms diffused into silicon
International Nuclear Information System (INIS)
Dezsi, I.; Feher, S.; Forgacs, Gy.; Horvath, D.; Kotai, E.; Manuaba, A.; Mezey, G.; Molnar, B.; Nagy, D.L.; Zsoldos, E.
1981-01-01
57 Co atoms diffused at 1270 K for 1 hour into single crystals of Si have a single Moessbauer line at -0.059+-0.001 mm/s. Channelling studies show 77 per cent of the Co atoms to occupy substitutional sites. It is found that Co forms epitaxial CoSi 2 clusters in the Si lattice. (author)
Deposition on disordered substrates with precursor layer diffusion
Filipe, J. A. N.; Rodgers, G. J.; Tavassoli, Z.
1998-09-01
Recently we introduced a one-dimensional accelerated random sequential adsorption process as a model for chemisorption with precursor layer diffusion. In this paper we consider this deposition process on disordered or impure substrates. The problem is solved exactly on both the lattice and continuum and for various impurity distributions. The results are compared with those from the standard random sequential adsorption model.
International Nuclear Information System (INIS)
Fischer, E.A.
1981-01-01
Basic problems of the definition and calculation of the perpendicular cell diffusion coefficient in slab lattices of fast critical assemblies are discussed in terms of an integral transport formalism. Numerical estimates of correction terms are given which are usually neglected. In addition, a detailed derivation of an equation for the diffusion-coefficient in a cylindrical low-density channel is given
International Nuclear Information System (INIS)
Richter, W.
1976-01-01
α-rhombohedral boron is the simplest boron modification, with only 12 atoms per unit cell. The boron atoms are arranged in B 12 icosahedra, which are centered at the lattice points of a primitive rhombohedral lattice. The icosahedra are slightly deformed, as the five-fold symmetry of the ideal icosahedron is incompatible with any crystal structure. The lattice dynamics of α-boron are discussed in terms of the model developed by Weber and Thorpe. (Auth.)
Experimental generation of optical coherence lattices
Energy Technology Data Exchange (ETDEWEB)
Chen, Yahong; Cai, Yangjian, E-mail: serpo@dal.ca, E-mail: yangjiancai@suda.edu.cn [College of Physics, Optoelectronics and Energy and Collaborative Innovation Center of Suzhou Nano Science and Technology, Soochow University, Suzhou 215006 (China); Key Lab of Advanced Optical Manufacturing Technologies of Jiangsu Province and Key Lab of Modern Optical Technologies of Education Ministry of China, Soochow University, Suzhou 215006 (China); Ponomarenko, Sergey A., E-mail: serpo@dal.ca, E-mail: yangjiancai@suda.edu.cn [Department of Electrical and Computer Engineering, Dalhousie University, Halifax, Nova Scotia B3J 2X4 (Canada)
2016-08-08
We report experimental generation and measurement of recently introduced optical coherence lattices. The presented optical coherence lattice realization technique hinges on a superposition of mutually uncorrelated partially coherent Schell-model beams with tailored coherence properties. We show theoretically that information can be encoded into and, in principle, recovered from the lattice degree of coherence. Our results can find applications to image transmission and optical encryption.
Introduction to Vortex Lattice Theory
Directory of Open Access Journals (Sweden)
Santiago Pinzón
2015-10-01
Full Text Available Panel methods have been widely used in industry and are well established since the 1970s for aerodynamic analysis and computation. The Vortex Lattice Panel Method presented in this study comes across a sophisticated method that provides a quick solution time, allows rapid changes in geometry and suits well for aerodynamic analysis. The aerospace industry is highly competitive in design efficiency, and perhaps one of the most important factors on airplane design and engineering today is multidisciplinary optimization. Any cost reduction method in the design cycle of a product becomes vital in the success of its outcome. The subsequent sections of this article will further explain in depth the theory behind the vortex lattice method, and the reason behind its selection as the method for aerodynamic analysis during preliminary design work and computation within the aerospace industry. This article is analytic in nature, and its main objective is to present a mathematical summary of this widely used computational method in aerodynamics.
Coherent lattice vibrations in superconductors
International Nuclear Information System (INIS)
Kadin, Alan M.
2008-01-01
A recent analysis has shown that the pair wavefunction within the BCS theory may be represented in real-space as a spherical electronic orbital (on the scale of the coherence length ξ 0 ) coupled to a standing-wave lattice vibration with wavevector 2k F and a near-resonant phonon frequency. The present paper extends this picture to a coherent pattern of phonon standing-waves on the macroscopic scale, with electrons forming Bloch waves and an energy gap much like those in the classic band theory of crystals. These parallel planes form a diffractive waveguide permitting electron waves to traveling parallel to the planes, corresponding to lossless supercurrent. A similar picture may be extended to unconventional superconductors such as the cuprates, with an array of standing spin waves rather than phonons. Such coherent lattice vibrations should be universal indicators of the superconducting state, and should be observable below T c using X-ray and neutron diffraction techniques. Further implications of this picture are discussed
Lattice dynamics in solid oxygen
International Nuclear Information System (INIS)
Kobashi, K.; Klein, M.L.; Chandrasekharan, V.
1979-01-01
Lattice dynamical calculations for the bulk α, β, and γ phases of solid O 2 and for the monolayer α and β phases have been made in the harmonic approximation. In the α and β phases, atom-atom 6-12 potentials are employed. In the γ phase, effective potentials are used between molecular centers and only the translational lattice vibrations are calculated. It is found that Laufer and Leroi's potential parameters give two k=O frequencies at 42.7 and 43.6 cm -1 in the bulk α-O 2 , and at 40.7 cm -1 for the degenerate k=0 modes in the β phase. The observed Raman lines for α-O 2 at 43 and 79 cm -1 , which are both known to exhibit isotope shifts, are thus tentatively assigned to an accidentally degenerate line and a two-phonon band, respectively, In view of the possible contribution from anharmonic effects, the agreement of the calculation with experiment (48-51 cm -1 ) in β-O 2 may be better than it seems. For the bulk γ-O 2 , a discrepancy is observed between the calculated elastic constants and those derived from Brillouin scattering experiments. This discrepancy may be due to the neglect of translation-rotation coupling. In the monolayer O 2 , Raman active modes at 28.3 and 40.6 cm -1 for the α phase, and 31.9 cm -1 for the β phase are predicted
Polarization response of RHIC electron lens lattices
International Nuclear Information System (INIS)
Ranjbar, V. H.; Méot, F.; Bai, M.; Abell, D. T.; Meiser, D.
2016-01-01
Depolarization response for a system of two orthogonal snakes at irrational tunes is studied in depth using lattice independent spin integration. Particularly, we consider the effect of overlapping spin resonances in this system, to understand the impact of phase, tune, relative location and threshold strengths of the spin resonances. Furthermore, these results are benchmarked and compared to two dimensional direct tracking results for the RHIC e-lens lattice and the standard lattice. We then consider the effect of longitudinal motion via chromatic scans using direct six dimensional lattice tracking.
Advancements in simulations of lattice quantum chromodynamics
International Nuclear Information System (INIS)
Lippert, T.
2008-01-01
An introduction to lattice QCD with emphasis on advanced fermion formulations and their simulation is given. In particular, overlap fermions will be presented, a quite novel fermionic discretization scheme that is able to exactly preserve chiral symmetry on the lattice. I will discuss efficiencies of state-of-the-art algorithms on highly scalable supercomputers and I will show that, due to many algorithmic improvements, overlap simulations will soon become feasible for realistic physical lattice sizes. Finally I am going to sketch the status of some current large scale lattice QCD simulations. (author)
On diffeomorphism invariance for lattice theories
International Nuclear Information System (INIS)
Corichi, A.; Zapata, J.
1997-01-01
We consider the role of the diffeomorphism constraint in the quantization of lattice formulations of diffeomorphism invariant theories of connections. It has been argued that in working with abstract lattices one automatically takes care of the diffeomorphism constraint in the quantum theory. We use two systems in order to show that imposing the diffeomorphism constraint is imperative to obtain a physically acceptable quantum theory. First, we consider 2+1 gravity where an exact lattice formulation is available. Next, general theories of connections for compact gauge groups are treated, where the quantum theories are known - for both the continuum and the lattice - and can be compared. (orig.)
Elastic lattice in an incommensurate background
International Nuclear Information System (INIS)
Dickman, R.; Chudnovsky, E.M.
1995-01-01
We study a harmonic triangular lattice, which relaxes in the presence of an incommensurate short-wavelength potential. Monte Carlo simulations reveal that the elastic lattice exhibits only short-ranged translational correlations, despite the absence of defects in either lattice. Extended orientational order, however, persists in the presence of the background. Translational correlation lengths exhibit approximate power-law dependence upon cooling rate and background strength. Our results may be relevant to Wigner crystals, atomic monolayers on crystals surfaces, and flux-line and magnetic bubble lattices
Polarization response of RHIC electron lens lattices
Directory of Open Access Journals (Sweden)
V. H. Ranjbar
2016-10-01
Full Text Available Depolarization response for a system of two orthogonal snakes at irrational tunes is studied in depth using lattice independent spin integration. In particular we consider the effect of overlapping spin resonances in this system, to understand the impact of phase, tune, relative location and threshold strengths of the spin resonances. These results are benchmarked and compared to two dimensional direct tracking results for the RHIC e-lens lattice and the standard lattice. Finally we consider the effect of longitudinal motion via chromatic scans using direct six dimensional lattice tracking.
Internal space decimation for lattice gauge theories
International Nuclear Information System (INIS)
Flyvbjerg, H.
1984-01-01
By a systematic decimation of internal space lattice gauge theories with continuous symmetry groups are mapped into effective lattice gauge theories with finite symmetry groups. The decimation of internal space makes a larger lattice tractable with the same computational resources. In this sense the method is an alternative to Wilson's and Symanzik's programs of improved actions. As an illustrative test of the method U(1) is decimated to Z(N) and the results compared with Monte Carlo data for Z(4)- and Z(5)-invariant lattice gauge theories. The result of decimating SU(3) to its 1080-element crystal-group-like subgroup is given and discussed. (orig.)
Transmission Electron Microscope Measures Lattice Parameters
Pike, William T.
1996-01-01
Convergent-beam microdiffraction (CBM) in thermionic-emission transmission electron microscope (TEM) is technique for measuring lattice parameters of nanometer-sized specimens of crystalline materials. Lattice parameters determined by use of CBM accurate to within few parts in thousand. Technique developed especially for use in quantifying lattice parameters, and thus strains, in epitaxial mismatched-crystal-lattice multilayer structures in multiple-quantum-well and other advanced semiconductor electronic devices. Ability to determine strains in indivdual layers contributes to understanding of novel electronic behaviors of devices.
Testing the holographic principle using lattice simulations
Directory of Open Access Journals (Sweden)
Jha Raghav G.
2018-01-01
Full Text Available The lattice studies of maximally supersymmetric Yang-Mills (MSYM theory at strong coupling and large N is important for verifying gauge/gravity duality. Due to the progress made in the last decade, based on ideas from topological twisting and orbifolding, it is now possible to study these theories on the lattice while preserving an exact supersymmetry on the lattice. We present some results from the lattice studies of two-dimensional MSYM which is related to Type II supergravity. Our results agree with the thermodynamics of different black hole phases on the gravity side and the phase transition (Gregory–Laflamme between them.
Stochastic flows, reaction-diffusion processes, and morphogenesis
International Nuclear Information System (INIS)
Kozak, J.J.; Hatlee, M.D.; Musho, M.K.; Politowicz, P.A.; Walsh, C.A.
1983-01-01
Recently, an exact procedure has been introduced [C. A. Walsh and J. J. Kozak, Phys. Rev. Lett.. 47: 1500 (1981)] for calculating the expected walk length for a walker undergoing random displacements on a finite or infinite (periodic) d-dimensional lattice with traps (reactive sites). The method (which is based on a classification of the symmetry of the sites surrounding the central deep trap and a coding of the fate of the random walker as it encounters a site of given symmetry) is applied here to several problems in lattice statistics for each of which exact results are presented. First, we assess the importance of lattice geometry in influencing the efficiency of reaction-diffusion processs in simple and multiple trap systems by reporting values of for square (cubic) versus hexagonal lattices in d = 2,3. We then show how the method may be applied to variable-step (distance-dependent) walks for a single walker on a given lattice and also demonstrate the calculation of the expected walk length for the case of multiple walkers. Finally, we make contact with recent discussions of ''mixing'' by showing that the degree of chaos associated with flows in certain lattice-systems can be calibrated by monitoring the lattice walks induced by the Poincare map of a certain parabolic function
Beijeren, H. van; Kehr, K.W.
1986-01-01
The correlation factor, defined as the ratio between the tracer diffusion coefficient in lattice gases and the diffusion coefficient for a corresponding uncorrelated random walk, is known to assume a very simple form under certain conditions. A simple derivation of this is given with the aid of
Fine structure at the diffusion welded interface of Fe3Al/Q235 ...
Indian Academy of Sciences (India)
Unknown
iron lattice sites (Fair and Wood 1994). 3.2 TEM morphology at the diffusion joint of. Fe3Al/Q235. For the welding of dissimilar materials, the element diffusion and phase formed at the interface of dissimilar. Table 1. Chemical composition and thermophysical properties of Fe3Al intermetallic compound. Chemical composition ...
Energy Technology Data Exchange (ETDEWEB)
Sathiyanarayanan, Rajesh, E-mail: rajessat@in.ibm.com, E-mail: rajesh.sathiyanarayanan@gmail.com; Pandey, R. K.; Murali, K. V. R. M. [IBM Semiconductor Research and Development Center, Bangalore 560045 (India)
2015-01-21
Using first-principles simulations, we have computed incorporation energies and diffusion barriers of ammonia, the nitrogen molecule and atomic nitrogen in monoclinic hafnia (m-HfO{sub 2}). Our calculations show that ammonia is likely to dissociate into an NH{sub 2} molecular unit, whereas the nitrogen molecule remains as a molecule either in the interstitial space or at an oxygen lattice site. The lowest energy pathway for the diffusion of atomic nitrogen interstitials consists of the hopping of the nitrogen interstitial between neighboring three-coordinated lattice oxygen atoms that share a single Hf atom, and the barrier for such hops is determined by a switching mechanism. The substitutional nitrogen atom shows a preference for diffusion through the doubly positive oxygen vacancy-mediated mechanism. Furthermore, we have investigated the impact of nitrogen atoms on the diffusion barriers of oxygen and hydrogen interstitials in m-HfO{sub 2}. Our results show that nitrogen incorporation has a significant impact on the barriers for oxygen and hydrogen diffusion: nitrogen atoms attract oxygen and hydrogen interstitials diffusing in the vicinity, thereby slowing down (reducing) their diffusion (diffusion length)
Hadron physics from lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Schaefer, Andreas [Regensburg Univ. (Germany). Inst. for Theoretical Physics
2016-11-01
Particle physics experiments at modern high luminosity particle accelerators achieve orders of magnitude higher count rates than what was possible ten or twenty years ago. This extremely large statistics allows to draw far reaching conclusions even from minute signals, provided that these signals are well understood by theory. This is, however, ever more difficult to achieve. Presently, technical and scientific progress in general and experimental progress in particle physics in particular, shows typically an exponential growth rate. For example, data acquisition and analysis are, among many other factor, driven by the development of ever more efficient computers and thus by Moore's law. Theory has to keep up with this development by also achieving an exponential increase in precision, which is only possible using powerful computers. This is true for both types of calculations, analytic ones as, e.g., in quantum field perturbation theory, and purely numerical ones as in Lattice QCD. As stated above such calculations are absolutely indispensable to make best use of the extremely costly large particle physics experiments. Thus, it is economically reasonable to invest a certain percentage of the cost of accelerators and experiments in related theory efforts. The basic ideas behind Lattice QCD simulations are the following: Because quarks and gluons can never be observed individually but are always ''confined'' into colorless hadrons, like the proton, all quark-gluon states can be expressed in two different systems of basis states, namely in a quark-gluon basis and the basis of hadron states. The proton, e.g., is an eigenstate of the latter, a specific quark-gluon configuration is part of the former. In the quark-gluon basis a physical hadron, like a proton, is given by an extremely complicated multi-particle wave function containing all effects of quantum fluctuations. This state is so complicated that it is basically impossible to model it
Diffusion archeology for diffusion progression history reconstruction.
Sefer, Emre; Kingsford, Carl
2016-11-01
Diffusion through graphs can be used to model many real-world processes, such as the spread of diseases, social network memes, computer viruses, or water contaminants. Often, a real-world diffusion cannot be directly observed while it is occurring - perhaps it is not noticed until some time has passed, continuous monitoring is too costly, or privacy concerns limit data access. This leads to the need to reconstruct how the present state of the diffusion came to be from partial diffusion data. Here, we tackle the problem of reconstructing a diffusion history from one or more snapshots of the diffusion state. This ability can be invaluable to learn when certain computer nodes are infected or which people are the initial disease spreaders to control future diffusions. We formulate this problem over discrete-time SEIRS-type diffusion models in terms of maximum likelihood. We design methods that are based on submodularity and a novel prize-collecting dominating-set vertex cover (PCDSVC) relaxation that can identify likely diffusion steps with some provable performance guarantees. Our methods are the first to be able to reconstruct complete diffusion histories accurately in real and simulated situations. As a special case, they can also identify the initial spreaders better than the existing methods for that problem. Our results for both meme and contaminant diffusion show that the partial diffusion data problem can be overcome with proper modeling and methods, and that hidden temporal characteristics of diffusion can be predicted from limited data.
Lattices for laymen: a non-specialist's introduction to lattice gauge theory
International Nuclear Information System (INIS)
Callaway, D.J.E.
1985-01-01
The review on lattice gauge theory is based upon a series of lectures given to the Materials Science and Technology Division at Argonne National Laboratory. Firstly the structure of gauge theories in the continuum is discussed. Then the lattice formulation of these theories is presented, including quantum electrodynamics and non-abelian lattice gauge theories. (U.K.)
Trace diffusion of different nuclear reactions products in polycrystalline tantalum
International Nuclear Information System (INIS)
Beyer, G.J.; Fromm, W.D.; Novgorodov, A.F.
1976-07-01
Measurements of the lattice diffusion coefficients for carrier free isotopes of Hf, Lu, Yb, Tm, Tb, Gd, Eu, Ba, Cs, Y, Sr, Rb and As in polycrystalline tantalum were made over the temperature range 1700 Fsub(As)>Fsub(lanthanides)>Fsub(Sr)>Fsub(Ba)>Fsub(Hf)>Fsub(Rb)>Fsub(Cs). The data indicate, that the Arrhenius relation was obeyed over the entire temperature range. Within the lanthanide-group no differences in the diffusion velocities could be detected, this fact points to a diffusion mechanism of Me 3+ -ions of lanthanides, Me 2+ -ions of earth alkaline elements and Me + -ions of alkaline elements. (author)
Self diffusion of sodium ion in sodium chloride
International Nuclear Information System (INIS)
Haridasan, T.M.; Lawrence, N.
1985-09-01
The problem of cation self diffusion in NaCl for a single vacancy mechanism is attempted using a reaction coordinate approach employing the phonons in the system. The vacancy is given an active role by estimating the displacements of its nearest neighbour Cl - ions in the environment of the vacancy through the lattice Green's functions and the t matrix formalism. The jump frequency, the isotope effect and diffusion coefficients estimated by this approach agree well with the experimentally deduced values. These results support the experimental conclusion of about 30% of vacancy pairs in the cation diffusion in NaCl. (author)
Pion structure from lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Javadi Motaghi, Narjes
2015-05-12
In this thesis we use lattice QCD to compute the second Mellin moments of pion generalized parton distributions and pion electromagnetic form factors. For our calculations we are able to analyze a large set of gauge configurations with 2 dynamical flavours using non-perturbatively the improved Wilson-Sheikholeslami-Wohlert fermionic action pion masses ranging down to 151 MeV. By employing improved smearing we were able to suppress excited state contamination. However, our data in the physical quark mass limit show that some excited state contamination remains. We show the non-zero sink momentum is optimal for the computation of the electromagnetic form factors and generalized form factors at finite momenta.
Computer programs for lattice calculations
International Nuclear Information System (INIS)
Keil, E.; Reich, K.H.
1984-01-01
The aim of the workshop was to find out whether some standardisation could be achieved for future work in this field. A certain amount of useful information was unearthed, and desirable features of a ''standard'' program emerged. Progress is not expected to be breathtaking, although participants (practically from all interested US, Canadian and European accelerator laboratories) agreed that the mathematics of the existing programs is more or less the same. Apart from the NIH (not invented here) effect, there is a - to quite some extent understandable - tendency to stay with a program one knows and to add to it if unavoidable rather than to start using a new one. Users of the well supported program TRANSPORT (designed for beam line calculations) would prefer to have it fully extended for lattice calculations (to some extent already possible now), while SYNCH users wish to see that program provided with a user-friendly input, rather than spending time and effort for mastering a new program
Monte Carlo lattice program KIM
International Nuclear Information System (INIS)
Cupini, E.; De Matteis, A.; Simonini, R.
1980-01-01
The Monte Carlo program KIM solves the steady-state linear neutron transport equation for a fixed-source problem or, by successive fixed-source runs, for the eigenvalue problem, in a two-dimensional thermal reactor lattice. Fluxes and reaction rates are the main quantities computed by the program, from which power distribution and few-group averaged cross sections are derived. The simulation ranges from 10 MeV to zero and includes anisotropic and inelastic scattering in the fast energy region, the epithermal Doppler broadening of the resonances of some nuclides, and the thermalization phenomenon by taking into account the thermal velocity distribution of some molecules. Besides the well known combinatorial geometry, the program allows complex configurations to be represented by a discrete set of points, an approach greatly improving calculation speed
Particle states of lattice QCD
Energy Technology Data Exchange (ETDEWEB)
Kapoyannis, A.S.; Panagiotou, A.D. [University of Athens, Nuclear and Particle Physics Section, Faculty of Physics, Athens (Greece)
2017-11-15
We determine the degeneracy factor and the average particle mass of particles that produce the lattice QCD pressure and specific entropy at zero baryon chemical potential. The number of states of the gluons and the quarks are found to converge above T = 230 MeV to almost constant values, close to the number of states of an ideal quark-gluon phase, while their assigned masses retain high values. The number of states and the average mass of a system containing quarks in interaction with gluons are found to decrease steeply with increase of temperature between T ∝ 150 and 160 MeV, a region contained within the region of the chiral transition. The minimum value of the number of states within this temperature interval indicates that the states are of hadronic nature. (orig.)
Fermion determinants in lattice QCD
International Nuclear Information System (INIS)
Johnson, Christopher Andrew
2001-01-01
The main topic of this thesis concerns efficient algorithms for the calculation of determinants of the kind of matrix typically encountered in lattice QCD. In particular an efficient method for calculating the fermion determinant is described. Such a calculation is useful to illustrate the effects of light dynamical (virtual) quarks. The methods employed in this thesis are stochastic methods, based on the Lanczos algorithm, which is used for the solution of large, sparse matrix problems via a partial tridiagonalisation of the matrix. Here an implementation is explored which requires less exhaustive treatment of the matrix than previous Lanczos methods. This technique exploits the analogy between the Lanczos tridiagonalisation algorithm and Gaussian quadrature in order to calculate the fermion determinant. A technique for determining a number of the eigenvalues of the matrix is also presented. A demonstration is then given of how one can improve upon this estimate considerably using variance reduction techniques, reducing the variance by a factor of order 100 with a further, equal amount of work. The variance reduction method is a two-stage process, involving a Chebyshev approximation to the quantity in question and then the subtraction of traceless operators. The method is applied to the fermion determinant for non-perturbatively improved Wilson fermions on a 16 3 x 32 lattice. It is also applicable to a wider class of matrix operators. Finally we discuss how dynamical quark effects may be simulated in a Monte Carlo process with an effective partitioning of low and high eigenmodes. This may be done via selective updating of a trial configuration which highlights the physically relevant effects of light quark modes. (author)
An Application of Linear Algebra over Lattices
Directory of Open Access Journals (Sweden)
M. Hosseinyazdi
2008-03-01
Full Text Available In this paper, first we consider L n as a semimodule over a complete bounded distributive lattice L. Then we define the basic concepts of module theory for L n. After that, we proved many similar theorems in linear algebra for the space L n. An application of linear algebra over lattices for solving linear systems, was given
An Application of Linear Algebra over Lattices
M. Hosseinyazdi
2008-01-01
In this paper, first we consider L n as a semimodule over a complete bounded distributive lattice L. Then we define the basic concepts of module theory for L n. After that, we proved many similar theorems in linear algebra for the space L n. An application of linear algebra over lattices for solving linear systems, was given
Compact lattice QED with Wilson fermions
International Nuclear Information System (INIS)
Hoferichter, A.
1994-08-01
We study the phase structure and the chiral limit of 4d compact lattice QED with Wilson fermions (both dynamical and quenched). We use the standard Wilson gauge action and also a modified one suppressing lattice artifacts. Different techniques and observables to locate the chiral limit are discussed. (orig.)
Chimera states in Gaussian coupled map lattices
Li, Xiao-Wen; Bi, Ran; Sun, Yue-Xiang; Zhang, Shuo; Song, Qian-Qian
2018-04-01
We study chimera states in one-dimensional and two-dimensional Gaussian coupled map lattices through simulations and experiments. Similar to the case of global coupling oscillators, individual lattices can be regarded as being controlled by a common mean field. A space-dependent order parameter is derived from a self-consistency condition in order to represent the collective state.
Dark Solitons in FPU Lattice Chain
Wang, Deng-Long; Yang, Ru-Shu; Yang, You-Tian
2007-11-01
Based on multiple scales method, we study the nonlinear properties of a new Fermi-Pasta-Ulam lattice model analytically. It is found that the lattice chain exhibits a novel nonlinear elementary excitation, i.e. a dark soliton. Moreover, the modulation depth of dark soliton is increasing as the anharmonic parameter increases.
Dark Solitons in FPU Lattice Chain
International Nuclear Information System (INIS)
Wang Denglong; Yang Youtian; Yang Rushu
2007-01-01
Based on multiple scales method, we study the nonlinear properties of a new Fermi-Pasta-Ulam lattice model analytically. It is found that the lattice chain exhibits a novel nonlinear elementary excitation, i.e. a dark soliton. Moreover, the modulation depth of dark soliton is increasing as the anharmonic parameter increases.
Lattice-Valued Possibilistic Entropy Measure
Czech Academy of Sciences Publication Activity Database
Kramosil, Ivan
2008-01-01
Roč. 16, č. 6 (2008), s. 829-846 ISSN 0218-4885 R&D Projects: GA AV ČR IAA100300503 Institutional research plan: CEZ:AV0Z10300504 Keywords : complete lattice * lattice-valued possibilistic distribution * entropy measure * product of possibilistic distribution Subject RIV: BA - General Mathematics Impact factor: 1.000, year: 2008
Unorthodox lattice fermion derivatives and their shortcomings
International Nuclear Information System (INIS)
Bodwin, G.T.; Kovacs, E.V.
1987-01-01
We discuss the DWY (Lagrangian), Quinn-Weinstein, and Rebbi proposals for incorporating fermions into lattice gauge theory and analyze them in the context of weak coupling perturbation theory. We find that none of these proposals leads to a completely satisfactory lattice transcription of fully-interacting gauge theory
Gauge field theories on a || lattice
International Nuclear Information System (INIS)
Burkardt, Matthias
1999-01-01
In these notes, the transverse || lattice approach is presented as a means to control the k + →0 divergences in light-front QCD. Technical difficulties of both the canonical compact formulation as well as the non-compact formulation of the || lattice motivate the color-dielectric formulation, where the link fields are linearized
Selective nanoscale growth of lattice mismatched materials
Lee, Seung-Chang; Brueck, Steven R. J.
2017-06-20
Exemplary embodiments provide materials and methods of forming high-quality semiconductor devices using lattice-mismatched materials. In one embodiment, a composite film including one or more substantially-single-particle-thick nanoparticle layers can be deposited over a substrate as a nanoscale selective growth mask for epitaxially growing lattice-mismatched materials over the substrate.
Spectral Gaps in Graphene Antidot Lattices
DEFF Research Database (Denmark)
Barbaroux, Jean-Marie; Cornean, Decebal Horia; Stockmeyer, Edgardo
2017-01-01
We consider the gap creation problem in an antidot graphene lattice, i.e. a sheet of graphene with periodically distributed obstacles. We prove several spectral results concerning the size of the gap and its dependence on different natural parameters related to the antidot lattice....
Layer features of the lattice gas model for self-organized criticality
International Nuclear Information System (INIS)
Pesheva, N.C.; Brankov, J.G.
1995-06-01
A layer-by-layer description of the asymmetric lattice gas model for 1/f-noise suggested by Jensen [Phys. Rev. Lett. 64, 3103 (1990)] is presented. The power spectra of the lattice layers in the direction perpendicular to the particle flux is studied in order to understand how the white noise at the input boundary evolves, on the average, into 1/f-noise for the system. The effects of high boundary drive and uniform driving force on the power spectrum of the total number of diffusing particles are considered. In the case of nearest-neighbor particle interactions, high statistics simulation results show that the power spectra of single lattice layers are characterized by different β x exponents such that β x → 1.9 as one approaches the outer boundary. (author). 10 refs, 6 figs
Classically exact surface diffusion constants at arbitrary temperature
International Nuclear Information System (INIS)
Voter, A.F.; Cohen, J.M.
1989-01-01
An expression is presented for computing the classical diffusion constant of a point defect (e.g., an adatom) in an infinite lattice of binding sites at arbitrary temperature. The transition state theory diffusion constant is simply multiplied by a dynamical correction factor that is computed from short-time classical trajectories initiated at the site boundaries. The time scale limitations of direct molecular dynamics are thus avoided in the low- and middle-temperature regimes. The expression results from taking the time derivative of the particle mean-square displacement in the lattice-discretized coordinate system. Applications are presented for surface diffusion on fcc(100) and fcc(111) Lennard-Jones crystal faces
Diffuse scattering in metallic tin polymorphs
International Nuclear Information System (INIS)
Wehinger, Björn; Bosak, Alexeï; Piccolboni, Giuseppe; Krisch, Michael; Refson, Keith; Chernyshov, Dmitry; Ivanov, Alexandre; Rumiantsev, Alexander
2014-01-01
The lattice dynamics of the metallic tin β and γ polymorphs has been studied by a combination of diffuse scattering, inelastic x-ray scattering and density functional perturbation theory. The non-symmorphic space group of the β -tin structure results in unusual asymmetry of thermal diffuse scattering. Strong resemblance of the diffuse scattering intensity distribution in β and γ-tin were observed, reflecting the structural relationship between the two phases and revealing the qualitative similarity of the underlying electronic potential. The strong influence of the electron subsystem on inter-ionic interactions creates anomalies in the phonon dispersion relations. All observed features are described in great detail by the density functional perturbation theory for both β - and γ-tin at arbitrary momentum transfers. The combined approach delivers thus a complete picture of the lattice dynamics in harmonic description. (paper)
Cold collisions in dissipative optical lattices
International Nuclear Information System (INIS)
Piilo, J; Suominen, K-A
2005-01-01
The invention of laser cooling methods for neutral atoms allows optical and magnetic trapping of cold atomic clouds in the temperature regime below 1 mK. In the past, light-assisted cold collisions between laser cooled atoms have been widely studied in magneto-optical atom traps (MOTs). We describe here theoretical studies of dynamical interactions, specifically cold collisions, between atoms trapped in near-resonant, dissipative optical lattices. The extension of collision studies to the regime of optical lattices introduces several complicating factors. For the lattice studies, one has to account for the internal substates of atoms, position-dependent matter-light coupling, and position-dependent couplings between the atoms, in addition to the spontaneous decay of electronically excited atomic states. The developed one-dimensional quantum-mechanical model combines atomic cooling and collision dynamics in a single framework. The model is based on Monte Carlo wavefunction simulations and is applied when the lattice-creating lasers have frequencies both below (red-detuned lattice) and above (blue-detuned lattice) the atomic resonance frequency. It turns out that the radiative heating mechanism affects the dynamics of atomic cloud in a red-detuned lattice in a way that is not directly expected from the MOT studies. The optical lattice and position-dependent light-matter coupling introduces selectivity of collision partners. The atoms which are most mobile and energetic are strongly favoured to participate in collisions, and are more often ejected from the lattice, than the slow ones in the laser parameter region selected for study. Consequently, the atoms remaining in the lattice have a smaller average kinetic energy per atom than in the case of non-interacting atoms. For blue-detuned lattices, we study how optical shielding emerges as a natural part of the lattice and look for ways to optimize the effect. We find that the cooling and shielding dynamics do not mix
Quantum transport in d -dimensional lattices
International Nuclear Information System (INIS)
Manzano, Daniel; Chuang, Chern; Cao, Jianshu
2016-01-01
We show that both fermionic and bosonic uniform d -dimensional lattices can be reduced to a set of independent one-dimensional chains. This reduction leads to the expression for ballistic energy fluxes in uniform fermionic and bosonic lattices. By the use of the Jordan–Wigner transformation we can extend our analysis to spin lattices, proving the coexistence of both ballistic and non-ballistic subspaces in any dimension and for any system size. We then relate the nature of transport to the number of excitations in the homogeneous spin lattice, indicating that a single excitation always propagates ballistically and that the non-ballistic behaviour of uniform spin lattices is a consequence of the interaction between different excitations. (paper)
A lattice approach to spinorial quantum gravity
Renteln, Paul; Smolin, Lee
1989-01-01
A new lattice regularization of quantum general relativity based on Ashtekar's reformulation of Hamiltonian general relativity is presented. In this form, quantum states of the gravitational field are represented within the physical Hilbert space of a Kogut-Susskind lattice gauge theory. The gauge field of the theory is a complexified SU(2) connection which is the gravitational connection for left-handed spinor fields. The physical states of the gravitational field are those which are annihilated by additional constraints which correspond to the four constraints of general relativity. Lattice versions of these constraints are constructed. Those corresponding to the three-dimensional diffeomorphism generators move states associated with Wilson loops around on the lattice. The lattice Hamiltonian constraint has a simple form, and a correspondingly simple interpretation: it is an operator which cuts and joins Wilson loops at points of intersection.
Design of the SPEAR 3 magnet lattice
International Nuclear Information System (INIS)
Corbett, J.; Limborg, C.; Nosochkov, Y.; Safranek, J.
1998-01-01
The SPEAR 3 Upgrade Project seeks to replace the present 160 nm-rad FODO lattice with an 18 nm-rad double bend achromat (DBA) lattice. The new lattice must conform to the layout of the SPEAR racetrack tunnel and service the existing photon beamlines. Working within these constraints, the authors designed a lattice with 18 achromatic cells and 3 GeV beam energy. This paper reports on design of the main DBA cells, design of the matching cells leading into the 6.5 m racetrack straights, and simulation of the dynamic aperture. The new lattice has gradient dipoles, conventional quadrupoles, and provides horizontal dynamic aperture to ± 20 mm with conservative magnetic multipole errors
Light Hadron Spectroscopy on course lattices with
Lee, F
1999-01-01
The masses and dispersions of light hadrons are calculated in lattice QCD using an O(a sup 2) tadpole-improved gluon action and an O(a sup 2) tadpole-improved next-nearest-neighbor fermion action originally proposed by Hamber and Wu. Two lattices of constant volume with lattice spacings of approximately 0.40 fm and 0.24 fm are considered. The results reveal some scaling violations at the coarser lattice spacing on the order of 5%. At the finer lattice spacing, the nucleon to rho mass ratio reproduces state-of-the-art results using unimproved actions. Good dispersion and rotational invariance up to momenta of pa approx = 1 are also found. The relative merit of alternative choices for improvement operators is assessed through close comparisons with other plaquette-based tadpole-improved actions.
Supersymmetry on a space-time lattice
Energy Technology Data Exchange (ETDEWEB)
Kaestner, Tobias
2008-10-28
In this thesis the WZ model in one and two dimensions has been thoroughly investigated. With the help of the Nicolai map it was possible to construct supersymmetrically improved lattice actions that preserve one of several supersymmetries. For the WZ model in one dimension SLAC fermions were utilized for the first time leading to a near-perfect elimination of lattice artifacts. In addition the lattice superpotential does not get modified which in two dimensions becomes important when further (discrete) symmetries of the continuum action are considered. For Wilson fermions two new improvements have been suggested and were shown to yield far better results than standard Wilson fermions concerning lattice artifacts. In the one-dimensional theory Ward Identities were studied.However, supersymmetry violations due to broken supersymmetry could only be detected at coarse lattices and very strong couplings. For the two-dimensional models a detailed analysis of supersymmetric improvement terms was given, both for Wilson and SLAC fermions. (orig.)
Lattices for the TRIUMF KAON factory
International Nuclear Information System (INIS)
Servranckx, R.V.; Craddock, M.K.
1989-09-01
Separated-function racetrack lattices have been developed for the KAON Factory accelerators that have more flexibility than the old circular lattices. The arcs of the large rings have a regular FODO structure with a superimposed six-fold symmetric modulation of the betafunction in order to raise γ t to infinity. Straight sections with zero dispersion are provided for rf cavities and fast injection and extraction, and with controlled dispersion for H - injection and slow extraction. For the small rings, sixfold symmetric circular lattices with high γ t are retained. In the Accumulator lattice, a straight section with double waist and controlled η function allows for H - injection and phase-space painting. The ion-optical properties of the lattices and the results from tracking studies are discussed
Ising antiferromagnet on the Archimedean lattices
Yu, Unjong
2015-06-01
Geometric frustration effects were studied systematically with the Ising antiferromagnet on the 11 Archimedean lattices using the Monte Carlo methods. The Wang-Landau algorithm for static properties (specific heat and residual entropy) and the Metropolis algorithm for a freezing order parameter were adopted. The exact residual entropy was also found. Based on the degree of frustration and dynamic properties, ground states of them were determined. The Shastry-Sutherland lattice and the trellis lattice are weakly frustrated and have two- and one-dimensional long-range-ordered ground states, respectively. The bounce, maple-leaf, and star lattices have the spin ice phase. The spin liquid phase appears in the triangular and kagome lattices.
Synthesizing lattice structures in phase space
International Nuclear Information System (INIS)
Guo, Lingzhen; Marthaler, Michael
2016-01-01
In one dimensional systems, it is possible to create periodic structures in phase space through driving, which is called phase space crystals (Guo et al 2013 Phys. Rev. Lett. 111 205303). This is possible even if for particles trapped in a potential without periodicity. In this paper we discuss ultracold atoms in a driven optical lattice, which is a realization of such a phase space crystals. The corresponding lattice structure in phase space is complex and contains rich physics. A phase space lattice differs fundamentally from a lattice in real space, because its coordinate system, i.e., phase space, has a noncommutative geometry, which naturally provides an artificial gauge (magnetic) field. We study the behavior of the quasienergy band structure and investigate the dissipative dynamics. Synthesizing lattice structures in phase space provides a new platform to simulate the condensed matter phenomena and study the intriguing phenomena of driven systems far away from equilibrium. (paper)
Supersymmetry on a space-time lattice
International Nuclear Information System (INIS)
Kaestner, Tobias
2008-01-01
In this thesis the WZ model in one and two dimensions has been thoroughly investigated. With the help of the Nicolai map it was possible to construct supersymmetrically improved lattice actions that preserve one of several supersymmetries. For the WZ model in one dimension SLAC fermions were utilized for the first time leading to a near-perfect elimination of lattice artifacts. In addition the lattice superpotential does not get modified which in two dimensions becomes important when further (discrete) symmetries of the continuum action are considered. For Wilson fermions two new improvements have been suggested and were shown to yield far better results than standard Wilson fermions concerning lattice artifacts. In the one-dimensional theory Ward Identities were studied.However, supersymmetry violations due to broken supersymmetry could only be detected at coarse lattices and very strong couplings. For the two-dimensional models a detailed analysis of supersymmetric improvement terms was given, both for Wilson and SLAC fermions. (orig.)
Lattice gravity near the continuum limit
International Nuclear Information System (INIS)
Feinberg, G.; Friedberg, R.; Lee, T.D.; Ren, H.C.
1984-01-01
We prove that the lattice gravity always approaches the usual continuum limit when the link length l -> 0, provided that certain general boundary conditions are satisfied. This result holds for any lattice, regular or irregular. Furthermore, for a given lattice, the deviation from its continuum limit can be expressed as a power series in l 2 . General formulas for such a perturbative calculation are given, together with a number of illustrative examples, including the graviton propagator. The lattice gravity satisfies all the invariance properties of Einstein's theory of general relativity. In addition, it is symmetric under a new class of transformations that are absent in the usual continuum theory. The possibility that the lattice theory (with a nonzero l) may be more fundamental is discussed. (orig.)
Synthetic magnetic fluxes on the honeycomb lattice
Energy Technology Data Exchange (ETDEWEB)
Gorecka, Agnieszka [Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 (Singapore); Gremaud, Benoit [Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 (Singapore); Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542 (Singapore); Laboratoire Kastler Brossel, Ecole Normale Superieure, CNRS, UPMC, 4 Place Jussieu, FR-75005 Paris (France); Miniatura, Christian [Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 (Singapore); Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542 (Singapore); Institut Non Lineaire de Nice, UMR 6618, UNS, CNRS, 1361 Route des Lucioles, FR-06560 Valbonne (France); Institute of Advanced Studies, Nanyang Technological university, 60 Nanyang View, Singapore 639673 (Singapore)
2011-08-15
We devise experimental schemes that are able to mimic uniform and staggered magnetic fluxes acting on ultracold two-electron atoms, such as ytterbium atoms, propagating in a honeycomb lattice. The atoms are first trapped into two independent state-selective triangular lattices and then further exposed to a suitable configuration of resonant Raman laser beams. These beams induce hops between the two triangular lattices and make atoms move in a honeycomb lattice. Atoms traveling around each unit cell of this honeycomb lattice pick up a nonzero phase. In the uniform case, the artificial magnetic flux sustained by each cell can reach about two flux quanta, thereby realizing a cold-atom analog of the Harper model with its notorious Hofstadter's butterfly structure. Different condensed-matter phenomena such as the relativistic integer and fractional quantum Hall effects, as observed in graphene samples, could be targeted with this scheme.
Excess Entropy and Diffusivity
Indian Academy of Sciences (India)
First page Back Continue Last page Graphics. Excess Entropy and Diffusivity. Excess entropy scaling of diffusivity (Rosenfeld,1977). Analogous relationships also exist for viscosity and thermal conductivity.
Interstructure Lattices and Types of Peano Arithmetic
Abdul-Quader, Athar
The collection of elementary substructures of a model of PA forms a lattice, and is referred to as the substructure lattice of the model. In this thesis, we study substructure and interstructure lattices of models of PA. We apply techniques used in studying these lattices to other problems in the model theory of PA. In Chapter 2, we study a problem that had its origin in Simpson ([Sim74]), who used arithmetic forcing to show that every countable model of PA has an expansion to PA* that is pointwise definable. Enayat ([Ena88]) later showed that there are 2N0 models with the property that every expansion to PA* is pointwise definable. In this Chapter, we use techniques involved in representations of lattices to show that there is a model of PA with this property which contains an infinite descending chain of elementary cuts. In Chapter 3, we study the question of when subsets can be coded in elementary end extensions with prescribed interstructure lattices. This problem originated in Gaifman [Gai76], who showed that every model of PA has a conservative, minimal elementary end extension. That is, every model of PA has a minimal elementary end extension which codes only definable sets. Kossak and Paris [KP92] showed that if a model is countable and a subset X can be coded in any elementary end extension, then it can be coded in a minimal extension. Schmerl ([Sch14] and [Sch15]) extended this work by considering which collections of sets can be the sets coded in a minimal elementary end extension. In this Chapter, we extend this work to other lattices. We study two questions: given a countable model M, which sets can be coded in an elementary end extension such that the interstructure lattice is some prescribed finite distributive lattice; and, given an arbitrary model M, which sets can be coded in an elementary end extension whose interstructure lattice is a finite Boolean algebra?
Deterministic Diffusion in Delayed Coupled Maps
International Nuclear Information System (INIS)
Sozanski, M.
2005-01-01
Coupled Map Lattices (CML) are discrete time and discrete space dynamical systems used for modeling phenomena arising in nonlinear systems with many degrees of freedom. In this work, the dynamical and statistical properties of a modified version of the CML with global coupling are considered. The main modification of the model is the extension of the coupling over a set of local map states corresponding to different time iterations. The model with both stochastic and chaotic one-dimensional local maps is studied. Deterministic diffusion in the CML under variation of a control parameter is analyzed for unimodal maps. As a main result, simple relations between statistical and dynamical measures are found for the model and the cases where substituting nonlinear lattices with simpler processes is possible are presented. (author)
Bidirectional Fano Algorithm for Lattice Coded MIMO Channels
Al-Quwaiee, Hessa
2013-01-01
channel model. Channel codes based on lattices are preferred due to three facts: lattice codes have simple structure, the code can achieve the limits of the channel, and they can be decoded efficiently using lattice decoders which can be considered
Numerical simulation of direct methanol fuel cells using lattice Boltzmann method
Energy Technology Data Exchange (ETDEWEB)
Delavar, Mojtaba Aghajani; Farhadi, Mousa; Sedighi, Kurosh [Faculty of Mechanical Engineering, Babol University of Technology, Babol, P.O. Box 484 (Iran)
2010-09-15
In this study Lattice Boltzmann Method (LBM) as an alternative of conventional computational fluid dynamics method is used to simulate Direct Methanol Fuel Cell (DMFC). A two dimensional lattice Boltzmann model with 9 velocities, D2Q9, is used to solve the problem. The computational domain includes all seven parts of DMFC: anode channel, catalyst and diffusion layers, membrane and cathode channel, catalyst and diffusion layers. The model has been used to predict the flow pattern and concentration fields of different species in both clear and porous channels to investigate cell performance. The results have been compared well with results in literature for flow in porous and clear channels and cell polarization curves of the DMFC at different flow speeds and feed methanol concentrations. (author)
Lattice Three-Species Models of the Spatial Spread of Rabies among FOXES
Benyoussef, A.; Boccara, N.; Chakib, H.; Ez-Zahraouy, H.
Lattice models describing the spatial spread of rabies among foxes are studied. In these models, the fox population is divided into three-species: susceptible (S), infected or incubating (I), and infectious or rabid (R). They are based on the fact that susceptible and incubating foxes are territorial while rabid foxes have lost their sense of direction and move erratically. Two different models are investigated: a one-dimensional coupled-map lattice model, and a two-dimensional automata network model. Both models take into account the short-range character of the infection process and the diffusive motion of rabid foxes. Numerical simulations show how the spatial distribution of rabies, and the speed of propagation of the epizootic front depend upon the carrying capacity of the environment and diffusion of rabid foxes out of their territory.
The accuracy of the diffusion theory component of removal-diffusion theory
International Nuclear Information System (INIS)
Donnelly, I.J.
1976-03-01
The neutron fluxes in five neutron shields consisting of water, concrete, graphite, iron and an iron-water lattice respectively, have been calculated using P 1 theory, diffusion theory with the usual transport correction for anisotropic scattering (DT), and diffusion theory with a diagonal transport correction (DDT). The calculations have been repeated using transport theory for the flux above 0.5 MeV and the diffusion theories for lower energies. Comparisons with transport theory calculations reveal the accuracy of each diffusion theory when it is used for flux evaluation at all energies, and also its accuracy when used for flux evaluation below 0.5 MeV given the correct flux above 0.5 MeV. It is concluded that the diffusion component of removal-diffusion theory has adequate accuracy unless the high energy diffusion entering the shield is significantly larger than the removal flux. In general, P 1 and DT are more accurate than DDT and give similar fluxes except for shields having a large hydrogen content, in which case DT is better. Therefore it is recommended that DT be used in preference to P 1 theory or DDT. (author)
Network formation determined by the diffusion process of random walkers
International Nuclear Information System (INIS)
Ikeda, Nobutoshi
2008-01-01
We studied the diffusion process of random walkers in networks formed by their traces. This model considers the rise and fall of links determined by the frequency of transports of random walkers. In order to examine the relation between the formed network and the diffusion process, a situation in which multiple random walkers start from the same vertex is investigated. The difference in diffusion rate of random walkers according to the difference in dimension of the initial lattice is very important for determining the time evolution of the networks. For example, complete subgraphs can be formed on a one-dimensional lattice while a graph with a power-law vertex degree distribution is formed on a two-dimensional lattice. We derived some formulae for predicting network changes for the 1D case, such as the time evolution of the size of nearly complete subgraphs and conditions for their collapse. The networks formed on the 2D lattice are characterized by the existence of clusters of highly connected vertices and their life time. As the life time of such clusters tends to be small, the exponent of the power-law distribution changes from γ ≅ 1-2 to γ ≅ 3
Manipulation and quantification of microtubule lattice integrity
Directory of Open Access Journals (Sweden)
Taylor A. Reid
2017-08-01
Full Text Available Microtubules are structural polymers that participate in a wide range of cellular functions. The addition and loss of tubulin subunits allows the microtubule to grow and shorten, as well as to develop and repair defects and gaps in its cylindrical lattice. These lattice defects act to modulate the interactions of microtubules with molecular motors and other microtubule-associated proteins. Therefore, tools to control and measure microtubule lattice structure will be invaluable for developing a quantitative understanding of how the structural state of the microtubule lattice may regulate its interactions with other proteins. In this work, we manipulated the lattice integrity of in vitro microtubules to create pools of microtubules with common nucleotide states, but with variations in structural states. We then developed a series of novel semi-automated analysis tools for both fluorescence and electron microscopy experiments to quantify the type and severity of alterations in microtubule lattice integrity. These techniques will enable new investigations that explore the role of microtubule lattice structure in interactions with microtubule-associated proteins.
Commensurability effects in holographic homogeneous lattices
International Nuclear Information System (INIS)
Andrade, Tomas; Krikun, Alexander
2016-01-01
An interesting application of the gauge/gravity duality to condensed matter physics is the description of a lattice via breaking translational invariance on the gravity side. By making use of global symmetries, it is possible to do so without scarifying homogeneity of the pertinent bulk solutions, which we thus term as “homogeneous holographic lattices.' Due to their technical simplicity, these configurations have received a great deal of attention in the last few years and have been shown to correctly describe momentum relaxation and hence (finite) DC conductivities. However, it is not clear whether they are able to capture other lattice effects which are of interest in condensed matter. In this paper we investigate this question focusing our attention on the phenomenon of commensurability, which arises when the lattice scale is tuned to be equal to (an integer multiple of) another momentum scale in the system. We do so by studying the formation of spatially modulated phases in various models of homogeneous holographic lattices. Our results indicate that the onset of the instability is controlled by the near horizon geometry, which for insulating solutions does carry information about the lattice. However, we observe no sharp connection between the characteristic momentum of the broken phase and the lattice pitch, which calls into question the applicability of these models to the physics of commensurability.
Lattice-Based Revocable Certificateless Signature
Directory of Open Access Journals (Sweden)
Ying-Hao Hung
2017-10-01
Full Text Available Certificateless signatures (CLS are noticeable because they may resolve the key escrow problem in ID-based signatures and break away the management problem regarding certificate in conventional signatures. However, the security of the mostly previous CLS schemes relies on the difficulty of solving discrete logarithm or large integer factorization problems. These two problems would be solved by quantum computers in the future so that the signature schemes based on them will also become insecure. For post-quantum cryptography, lattice-based cryptography is significant due to its efficiency and security. However, no study on addressing the revocation problem in the existing lattice-based CLS schemes is presented. In this paper, we focus on the revocation issue and present the first revocable CLS (RCLS scheme over lattices. Based on the short integer solution (SIS assumption over lattices, the proposed lattice-based RCLS scheme is shown to be existential unforgeability against adaptive chosen message attacks. By performance analysis and comparisons, the proposed lattice-based RCLS scheme is better than the previously proposed lattice-based CLS scheme, in terms of private key size, signature length and the revocation mechanism.
Status and future of lattice gauge theory
International Nuclear Information System (INIS)
Hoek, J.
1989-07-01
The current status of lattice Quantum Chromo Dynamics (QCD) calculations, the computer requirements to obtain physical results and the direction computing is taking are described. First of all, there is a lot of evidence that QCD is the correct theory of strong interactions. Since it is an asymptotically free theory we can use perturbation theory to solve it in the regime of very hard collisions. However even in the case of very hard parton collisions the end-results of the collisions are bound states of quarks and perturbation theory is not sufficient to calculate these final stages. The way to solve the theory in this regime was opened by Wilson. He contemplated replacing the space-time continuum by a discrete lattice, with a lattice spacing a. Continuum physics is then recovered in the limit where the correlation length of the theory, say ξ. is large with respect to the lattice spacing. This will be true if the lattice spacing becomes very small, which for asymptotically free theories also implies that the coupling g becomes small. The lattice approach to QCD is in many respects analogous to the use of finite element methods to solve classical field theories. These finite element methods are easy to apply in 2-dimensional simulations but are computationally demanding in the 3-dimensional case. Therefore it is not unexpected that the 4-dimensional simulations needed for lattice gauge theories have led to an explosion in demand for computing power by theorists. (author)
3D Metallic Lattices for Accelerator Applications
Shapiro, Michael A; Sirigiri, Jagadishwar R; Temkin, Richard J
2005-01-01
We present the results of research on 3D metallic lattices operating at microwave frequencies for application in (1) accelerator structures with higher order mode suppression, (2) Smith-Purcell radiation beam diagnostics, and (3) polaritonic materials for laser acceleration. Electromagnetic waves in a 3D simple cubic lattice formed by metal wires are calculated using HFSS. The bulk modes in the lattice are determined using single cell calculations with different phase advances in all three directions. The Brillouin diagram for the bulk modes is presented and indicates the absence of band gaps in simple lattices except the band below the cutoff. Lattices with thin wires as well as with thick wires have been analyzed. The Brillouin diagram also indicates the presence of low frequency 3D plasmon mode as well as the two degenerate photon modes analogous to those in a 2D lattice. Surface modes for a semi-infinite cubic lattice are modeled as a stack of cells with different phase advances in the two directions alon...
Diffusion of N adatoms on the Fe(100) surface
DEFF Research Database (Denmark)
Pedersen, M. Ø.; Österlund, L.; Mortensen, Jens Jørgen
2000-01-01
The diffusion of individual N adatoms on Fe(100) has been studied using scanning tunneling microscopy and ab initio density functional theory (DFT) calculations. The measured diffusion barrier for isolated N adatoms is E-d = (0.92 +/- 0.04) eV, with a prefactor of nu(0) = 4.3 x 10(12) s(-1), which...... is in quantitative agreement with the DFT calculations. Thr; diffusion is strongly coupled to lattice distortions. and. as a consequence, the presence of other N adatoms introduces an anisotropy in the diffusion. Based on experimentally determined values of the diffusion barriers and adsorbate......-adsorbate: interactions, the potential energy surface experienced by a N adatom is determined....
Effects of differential mobility on biased diffusion of two species
International Nuclear Information System (INIS)
Hipolito, R S; Zia, R K P; Schmittmann, B
2003-01-01
Using simulations and a simple mean-field theory, we investigate jamming transitions in a two-species lattice gas under non-equilibrium steady-state conditions. The two types of particles diffuse with different mobilities on a square lattice, subject to an excluded volume constraint and biased in opposite directions. Varying filling fraction, differential mobility and drive, we map out the phase diagram, identifying first order and continuous transitions between a free-flowing disordered and a spatially inhomogeneous jammed phase. Ordered structures are observed to drift, with a characteristic velocity, in the direction of the more mobile species
Quantum Monte Carlo studies in Hamiltonian lattice gauge theory
International Nuclear Information System (INIS)
Hamer, C.J.; Samaras, M.; Bursill, R.J.
2000-01-01
Full text: The application of Monte Carlo methods to the 'Hamiltonian' formulation of lattice gauge theory has been somewhat neglected, and lags at least ten years behind the classical Monte Carlo simulations of Euclidean lattice gauge theory. We have applied a Green's Function Monte Carlo algorithm to lattice Yang-Mills theories in the Hamiltonian formulation, combined with a 'forward-walking' technique to estimate expectation values and correlation functions. In this approach, one represents the wave function in configuration space by a discrete ensemble of random walkers, and application of the time development operator is simulated by a diffusion and branching process. The approach has been used to estimate the ground-state energy and Wilson loop values in the U(1) theory in (2+1)D, and the SU(3) Yang-Mills theory in (3+1)D. The finite-size scaling behaviour has been explored, and agrees with the predictions of effective Lagrangian theory, and weak-coupling expansions. Crude estimates of the string tension are derived, which agree with previous results at intermediate couplings; but more accurate results for larger loops will be required to establish scaling behaviour at weak couplings. A drawback to this method is that it is necessary to introduce a 'trial' or 'guiding wave function' to guide the walkers towards the most probable regions of configuration space, in order to achieve convergence and accuracy. The 'forward-walking' estimates should be independent of this guidance, but in fact for the SU(3) case they turn out to be sensitive to the choice of trial wave function. It would be preferable to use some sort of Metropolis algorithm instead to produce a correct distribution of walkers: this may point in the direction of a Path Integral Monte Carlo approach
Diffusion limited reactions in crystalline solids
International Nuclear Information System (INIS)
Fastenau, R.
1982-01-01
Diffusion limited reactions in crystal lattices are studied with diffusion and random walk theory. First the random walk on a crystal lattice is studied. These results are used in a formal study of diffusion limited reactions in which the following simplified traps are discussed: planes, cylinders, spheres, disks and rings. The traps are either present at the start of the process (annealing) or fed into the crystal at a constant rate (continuous production). For the study of trapping processes occurring in real crystals it was necessary to investigate the interaction of the reacting species on the atomic level. Using lattice relaxation calculations, several reactions were studied. These calculations result in a model for the potential energy of the crystal versus the separation of the reaction partners. This model is used in Monte Carlo simulations of the trapping process, which are made at a high trap density, since the extrapolation to the low density regime can be made using the formal part of this work. The following reactions were studied: the trapping of interstitial helium atoms by vacancies, self interstitial vacancy recombination, the trapping of vacancies by immobile, helium filled, vacancies and the capture of self interstitials and vacancies by dislocations. A part of these results is used in two models for the low temperature nucleation and growth of bubbles due to helium bombardment. The models described give the right bubble density versus helium dose, but differ widely in the fraction of helium present in the bubbles found. A mechanism of blistering based on a percolation effect is also discussed. (Auth.)
Magnetic nanoparticles in fluid environment: combining molecular dynamics and Lattice-Boltzmann
Energy Technology Data Exchange (ETDEWEB)
Melenev, Petr, E-mail: melenev@icmm.ru [Ural Federal University, 4, Turgeneva str., 620000 Ekaterinburg (Russian Federation); Institute of Continuous Media Mechanics, 1, Koroleva str., 614013 Perm (Russian Federation)
2017-06-01
Hydrodynamic interactions between magnetic nanoparticles suspended in the Newtonian liquid are accounted for using a combination of the lattice Boltzmann method and molecular dynamics simulations. Nanoparticle is modelled by the system of molecular dynamics material points (which form structure resembles raspberry) coupled to the lattice Boltzmann fluid. The hydrodynamic coupling between the colloids is studied by simulations of the thermo-induced rotational diffusion of two raspberry objects. It was found that for the considered range of model parameters the approaching of the raspberries leads to slight retard of the relaxation process. The presence of the weak magnetic dipolar interaction between the objects leads to modest decrease of the relaxation time and the extent of the acceleration of the diffusion is intensified along with magnetic forces. - Highlights: • The combination of molecular dynamics and lattice Boltzmann method is utilized for the reveal of the role of hydrodynamic interaction in rotational dynamics of colloid particles. • The verification of the model parameters is done based on the comparison with the results of Langevin dynamics. • For the task of free rotational diffusion of the pair of colloid particles the influence of the hydrodynamic interactions on the relaxation time is examined in the case of nonmagnetic particles and at the presence of weak dipolar interaction.
Lattice solitons in Bose-Einstein condensates
International Nuclear Information System (INIS)
Efremidis, Nikolaos K.; Christodoulides, Demetrios N.
2003-01-01
We systematically study the properties of lattice solitons in Bose-Einstein condensates with either attractive or repulsive atom interactions. This is done, by exactly solving the mean-field Gross-Pitaevskii equation in the presence of a periodic potential. We find new families of lattice soliton solutions that are characterized by the position of the energy eigenvalue within the associated band structure. These include lattice solitons in condensates with either attractive or repulsive atom interactions that exist in finite or semi-infinite gaps, as well as nonlinear modes that exhibit atomic population cutoffs
Supersymmetric quiver gauge theories on the lattice
International Nuclear Information System (INIS)
Joseph, Anosh
2013-12-01
In this paper we detail the lattice constructions of several classes of supersymmetric quiver gauge theories in two and three Euclidean spacetime dimensions possessing exact supersymmetry at finite lattice spacing. Such constructions are obtained through the methods of topological twisting and geometric discretization of Euclidean Yang-Mills theories with eight and sixteen supercharges in two and three dimensions. We detail the lattice constructions of two-dimensional quiver gauge theories possessing four and eight supercharges and three-dimensional quiver gauge theories possessing eight supercharges.
Construction of Capacity Achieving Lattice Gaussian Codes
Alghamdi, Wael
2016-04-01
We propose a new approach to proving results regarding channel coding schemes based on construction-A lattices for the Additive White Gaussian Noise (AWGN) channel that yields new characterizations of the code construction parameters, i.e., the primes and dimensions of the codes, as functions of the block-length. The approach we take introduces an averaging argument that explicitly involves the considered parameters. This averaging argument is applied to a generalized Loeliger ensemble [1] to provide a more practical proof of the existence of AWGN-good lattices, and to characterize suitable parameters for the lattice Gaussian coding scheme proposed by Ling and Belfiore [3].
Dynamical Regge calculus as lattice gravity
International Nuclear Information System (INIS)
Hagura, Hiroyuki
2001-01-01
We propose a hybrid approach to lattice quantum gravity by combining simultaneously the dynamical triangulation with the Regge calculus, called the dynamical Regge calculus (DRC). In this approach lattice diffeomorphism is realized as an exact symmetry by some hybrid (k, l) moves on the simplicial lattice. Numerical study of 3D pure gravity shows that an entropy of the DRC is not exponetially bounded if we adopt the uniform measure Π i dl i . On the other hand, using the scale-invariant measure Π i dl i /l i , we can calculate observables and observe a large hysteresis between two phases that indicates the first-order nature of the phase transition
Calculating luminosity for a coupled Tevatron lattice
International Nuclear Information System (INIS)
Holt, J.A.; Martens, M.A.; Michelotti, L.; Goderre, G.
1995-05-01
The traditional formula for calculating luminosity assumes an uncoupled lattice and makes use of one-degree-of-freedom lattice functions, β H and β v , for relating transverse beam widths to emittances. Strong coupling requires changing this approach. It is simplest to employ directly the linear normal form coordinates of the one turn map. An equilibrium distribution in phase space is expressed as a function of the Jacobian's eigenvectors and beam size parameters or emittances. Using the equilibrium distributions an expression for the luminosity was derived and applied to the Tevatron lattice, which was coupled due to a quadrupole roll
Optical lattice on an atom chip
DEFF Research Database (Denmark)
Gallego, D.; Hofferberth, S.; Schumm, Thorsten
2009-01-01
Optical dipole traps and atom chips are two very powerful tools for the quantum manipulation of neutral atoms. We demonstrate that both methods can be combined by creating an optical lattice potential on an atom chip. A red-detuned laser beam is retroreflected using the atom chip surface as a high......-quality mirror, generating a vertical array of purely optical oblate traps. We transfer thermal atoms from the chip into the lattice and observe cooling into the two-dimensional regime. Using a chip-generated Bose-Einstein condensate, we demonstrate coherent Bloch oscillations in the lattice....
Continuum gauge fields from lattice gauge fields
International Nuclear Information System (INIS)
Goeckeler, M.; Kronfeld, A.S.; Schierholz, G.; Wiese, U.J.
1993-01-01
On the lattice some of the salient features of pure gauge theories and of gauge theories with fermions in complex representations of the gauge group seem to be lost. These features can be recovered by considering part of the theory in the continuum. The prerequisite for that is the construction of continuum gauge fields from lattice gauge fields. Such a construction, which is gauge covariant and complies with geometrical constructions of the topological charge on the lattice, is given in this paper. The procedure is explicitly carried out in the U(1) theory in two dimensions, where it leads to simple results. (orig.)
International Nuclear Information System (INIS)
Jansen, K.; Michael, C.; Urbach, C.
2008-04-01
We study the flavour singlet pseudoscalar mesons from first principles using lattice QCD. With N f =2 flavours of light quark, this is the so-called η 2 meson and we discuss the phenomenological status of this. Using maximally twisted-mass lattice QCD, we extract the mass of the η 2 meson at two values of the lattice spacing for lighter quarks than previously discussed in the literature. We are able to estimate the mass value in the limit of light quarks with their physical masses. (orig.)
Racetrack lattices for the TRIUMF KAON factory
International Nuclear Information System (INIS)
Servranckx, R.V.; Craddock, M.K.
1989-05-01
Separated-function racetrack lattices have been developed for the KAON Factory accelerators that have more flexibility than the old circular lattices. The arcs of the large rings have a regular FODO structure with a superimposed six-fold symmetric modulation of the betafunction in order to raise γ t to infinity. In the small rings, γ t is kept high enough by choosing a sufficiently large phase advance in the arcs. Straight sections with zero dispersion are provided for rf cavities and fast injection and extraction, and with controlled dispersion for H - injection and slow extraction. The ion-optical properties of the lattices and the results from tracking studies are discussed
More on random-lattice fermions
International Nuclear Information System (INIS)
Kieu, T.D.; Institute for Advanced Study, Princeton, NJ; Markham, J.F.; Paranavitane, C.B.
1995-01-01
The lattice fermion determinants, in a given background gauge field, are evaluated for two different kinds of random lattices and compared to those of naive and wilson fermions in the continuum limit. While the fermion doubling is confirmed on one kind of lattices, there is positive evidence that it may be absent for the other, at least for vector interactions in two dimensions. Combined with previous studies, arbitrary randomness by itself is shown to be not a sufficient condition to remove the fermion doublers. 8 refs., 3 figs
Vortex-Peierls States in Optical Lattices
International Nuclear Information System (INIS)
Burkov, A.A.; Demler, Eugene
2006-01-01
We show that vortices, induced in cold atom superfluids in optical lattices, may order in a novel vortex-Peierls ground state. In such a state vortices do not form a simple lattice but arrange themselves in clusters, within which the vortices are partially delocalized, tunneling between classically degenerate configurations. We demonstrate that this exotic quantum many-body state is selected by an order-from-disorder mechanism for a special combination of the vortex filling and lattice geometry that has a macroscopic number of classically degenerate ground states
Lattice-Like Total Perfect Codes
Directory of Open Access Journals (Sweden)
Araujo Carlos
2014-02-01
Full Text Available A contribution is made to the classification of lattice-like total perfect codes in integer lattices Λn via pairs (G, Φ formed by abelian groups G and homomorphisms Φ: Zn → G. A conjecture is posed that the cited contribution covers all possible cases. A related conjecture on the unfinished work on open problems on lattice-like perfect dominating sets in Λn with induced components that are parallel paths of length > 1 is posed as well.
Electronic properties of graphene antidot lattices
DEFF Research Database (Denmark)
Fürst, Joachim Alexander; Pedersen, Jesper Goor; Flindt, C.
2009-01-01
Graphene antidot lattices constitute a novel class of nano-engineered graphene devices with controllable electronic and optical properties. An antidot lattice consists of a periodic array of holes that causes a band gap to open up around the Fermi level, turning graphene from a semimetal...... into a semiconductor. We calculate the electronic band structure of graphene antidot lattices using three numerical approaches with different levels of computational complexity, efficiency and accuracy. Fast finite-element solutions of the Dirac equation capture qualitative features of the band structure, while full...
How to Share a Lattice Trapdoor
DEFF Research Database (Denmark)
Bendlin, Rikke; Peikert, Chris; Krehbiel, Sara
2013-01-01
We develop secure threshold protocols for two important operations in lattice cryptography, namely, generating a hard lattice Λ together with a "strong" trapdoor, and sampling from a discrete Gaussian distribution over a desired coset of Λ using the trapdoor. These are the central operations...... delegation, which is used in lattice-based hierarchical IBE schemes. Our work therefore directly transfers all these systems to the threshold setting. Our protocols provide information-theoretic (i.e., statistical) security against adaptive corruptions in the UC framework, and they are robust against up to ℓ...
Group theory and lattice gauge fields
International Nuclear Information System (INIS)
Creutz, M.
1988-09-01
Lattice gauge theory, formulated in terms of invariant integrals over group elements on lattice bonds, benefits from many group theoretical notions. Gauge invariance provides an enormous symmetry and powerful constraints on expectation values. Strong coupling expansions require invariant integrals over polynomials in group elements, all of which can be evaluated by symmetry considerations. Numerical simulations involve random walks over the group. These walks automatically generate the invariant group measure, avoiding explicit parameterization. A recently proposed overrelaxation algorithm is particularly efficient at exploring the group manifold. These and other applications of group theory to lattice gauge fields are reviewed in this talk. 17 refs
Lattice Dynamics of Gallium Phosphide
International Nuclear Information System (INIS)
Yarnell, J.L.; Warren, J.L.; Wenzel, R.G.; Dean, P.J.
1968-01-01
Dispersion curves for phonons propagating in the [100], [110], and [111] directions in gallium phosphide have been measured using a triple-axis neutron diffraction spectrometer operating in the constant-Q mode. The sample was a pseudo-single crystal which was prepared by gluing together 36 single crystal plates of gallium phosphide 1 to 2.5 cm in diameter and ∼0.07 cm thick. The plates were grown epitaxially on substrates of gallium arsenide or gallium phosphide, and aligned individually by neutron diffraction. Rocking curves for eight reflections symmetrically distributed in the plane of the experiment had full widths at half maximum in the range 0.52° - 0.58° and were approximately Gaussian in shape. Gallium phosphide crystallizes in the zinc blende structure. A group theoretic analysis of the lattice dynamics of this structure and a shell model fit to the measured dispersion curves are presented. Various optical properties of gallium phosphide are discussed in terms of the phonon dispersion curves. In particular, the phonons which assist indirect electronic transitions are identified as those at the zone boundary in the [100] direction (symmetry point X) in agreement with theoretical and experimental indications that the extrema of the conduction and valence bands are at X and Γ (center of the zone), respectively. The LO branches lie above the TO branches throughout the Brillouin zone in contradiction to the predictions of Keyes and Mitra. The shell model fit indicates that the charge on the gallium atom is negative. (author)
Lattice dynamics of alpha uranium
International Nuclear Information System (INIS)
Crummett, W.P.
1978-01-01
Inelastic neutron scattering measurements of the phonon dispersion curves along the three-principal high-symmetry directions have been performed to investigate the lattice dynamics of α-U. The dispersion curves along the [0 zeta 0] and [00 zeta] directions are not too unusual. However, dips and depressions are observed in the [zeta 00] branches similar to those observed in high-T/sub c/ superconductors. Standard group theoretical techniques have been employed to discern the symmetry properties of the phonon branches and to block diagonalize the dynamical matrix of the various phenomenological models that have been applied to α-U. These phenomenological models include: a four neighbor Born-von Karman general tensor model, a twelve neighbor axially symmetric model, and a shell model. None of these models was able to satisfactorily fit the [zeta 00] data. However, a modified form of the shell model which included axially symmetric interactions to six neighbors was found to reproduce most of the dispersion curves well, including the [zeta 00] branches. A simple pseudopotential model was less successful. To obtain all real frequencies from this model it was necessary to include a Born-von Karman short range contribution. These measurements and calculations have implied that the bonding properties of α-U are particularly dependent upon the details of the electronic system
Essentially Entropic Lattice Boltzmann Model
Atif, Mohammad; Kolluru, Praveen Kumar; Thantanapally, Chakradhar; Ansumali, Santosh
2017-12-01
The entropic lattice Boltzmann model (ELBM), a discrete space-time kinetic theory for hydrodynamics, ensures nonlinear stability via the discrete time version of the second law of thermodynamics (the H theorem). Compliance with the H theorem is numerically enforced in this methodology and involves a search for the maximal discrete path length corresponding to the zero dissipation state by iteratively solving a nonlinear equation. We demonstrate that an exact solution for the path length can be obtained by assuming a natural criterion of negative entropy change, thereby reducing the problem to solving an inequality. This inequality is solved by creating a new framework for construction of Padé approximants via quadrature on appropriate convex function. This exact solution also resolves the issue of indeterminacy in case of nonexistence of the entropic involution step. Since our formulation is devoid of complex mathematical library functions, the computational cost is drastically reduced. To illustrate this, we have simulated a model setup of flow over the NACA-0012 airfoil at a Reynolds number of 2.88 ×106.
Infinitesimal diffeomorfisms on the lattice
CERN. Geneva
2015-01-01
The energy-momentum tensor and local translation Ward identities constitute the essential toolkit to probe the response of a QFT to an infinitesimal change of geometry. This is relevant in a number of contexts. For instance in order to get the thermodynamical equation of state, one wants to study the response of a Euclidean QFT in a finite box to a change in the size of the box. The lattice formulation of QFTs is a prime tool to study their dynamics beyond perturbation theory. However Poincaré invariance is explicitly broken, and is supposed to be recovered only in the continuum limit. Approximate local Ward identities for translations can be defined, by they require some care for two reasons: 1) the energy-momentum tensor needs to be properly defined through a renormalization procedure; 2) the action of infinitesimal local translations (i.e. infinitesimal diffeomorfisms) is ill-defined on local observables. In this talk I will review the issues related to the renormalization of the energy-momentum tensor ...
International Nuclear Information System (INIS)
Rees, J.; Wiedemann, H.
1976-01-01
A new low-beta configuration has been proposed for PEP which has a reduced β/sub y/* and is capable of delivering design luminosity with lower circulating beam currents that those required in the standard configuration described in the Conceptual Design Report of February, 1976. A feasibility study has been carried out and it is reported in PTM-65, September 8, 1976, by Lee, Morton and Wiedemann. The beam-stay-clear region is specified in PTM-66, September 3, 1976 by H. Wiedemann. The principal advantages of the new lattice are that the lower beam currents lead to lower higher-order-mode power and permit reduction of the total rf power required which in turn reduces both capital cost and operating cost. Its disadvantages stem primarily from the relatively high maximum beta values which occur in the interaction-region quadrupoles. These produce high chromaticities which require a generally stronger sextupole system for their compensation. The advantages outweigh the disadvantages and the new 11-cm-beta configuration has been adopted as the design configuration for energies of 15-GeV and lower. In the remainder of this report we shall discuss the implications of this new configuration for the various systems of PEP. 1 fig., 3 tabs
DEFF Research Database (Denmark)
Stassis, C.; Zaretsky, J.; Misemer, D. K.;
1983-01-01
A large single crystal of FCC Ca was grown and was used to study the lattice dynamics of this divalent metal by coherent inelastic neutron scattering. The phonon dispersion curves were measured, at room temperature, along the [ξ00], [ξξ0], [ξξξ], and [0ξ1] symmetry directions. The dispersion curves...... to the propagation of elastic waves. The frequencies of the T1[ξξ0] branch for ξ between approximately 0.5 and 0.8 are slightly above the velocity-of-sound line determined from the low-frequency measurements. Since a similar effect has been observed in FCC Yb, it is natural to assume that the anomalous dispersion...... bear a striking resemblance to those of FCC Yb, which is also a divalent metal with an electronic band structure similar to that of Ca. In particular, the shear moduli c44 and (c11-c 12)/2 differ by a factor of 3.4, which implies that FCC Ca (like FCC Yb) is very anisotropic with regard...
Neutron diffraction and lattice defects
International Nuclear Information System (INIS)
Hamaguchi, Yoshikazu
1974-01-01
Study on lattice defects by neutron diffraction technique is described. Wave length of neutron wave is longer than that of X-ray, and absorption cross-section is small. Number of defects observed by ESR is up to several defects, and the number studied with electron microscopes is more than 100. Information obtained by neutron diffraction concerns the number of defects between these two ranges. For practical analysis, several probable models are selected from the data of ESR or electron microscopes, and most probable one is determined by calculation. Then, defect concentration is obtained from scattering cross section. It is possible to measure elastic scattering exclusively by neutron diffraction. Minimum detectable concentration estimated is about 0.5% and 10 20 - 10 21 defects per unit volume. A chopper and a time of flight system are used as a measuring system. Cold neutrons are obtained from the neutron sources inserted into reactors. Examples of measurements by using similar equipments to PTNS-I system of Japan Atomic Energy Research Institute are presented. Interstitial concentration in the graphite irradiated by fast neutrons is shown. Defects in irradiated MgO were also investigated by measuring scattering cross section. Study of defects in Ge was made by measuring total cross section, and model analysis was performed in comparison with various models. (Kato, T.)
Halo Mitigation Using Nonlinear Lattices
Sonnad, Kiran G
2005-01-01
This work shows that halos in beams with space charge effects can be controlled by combining nonlinear focusing and collimation. The study relies on Particle-in-Cell (PIC) simulations for a one dimensional, continuous focusing model. The PIC simulation results show that nonlinear focusing leads to damping of the beam oscillations thereby reducing the mismatch. It is well established that reduced mismatch leads to reduced halo formation. However, the nonlinear damping is accompanied by emittance growth causing the beam to spread in phase space. As a result, inducing nonlinear damping alone cannot help mitigate the halo. To compensate for this expansion in phase space, the beam is collimated in the simulation and further evolution of the beam shows that the halo is not regenerated. The focusing model used in the PIC is analysed using the Lie Transform perturbation theory showing that by averaging over a lattice period, one can reuduce the focusing force to a form that is identical to that used in the PIC simula...
Lattice dynamics of α boron and of boron carbide
International Nuclear Information System (INIS)
Vast, N.
1999-01-01
The atomic structure and the lattice dynamics of α boron and of B 4 C boron carbide have been studied by Density Functional Theory (D.F.T.) and Density Functional Perturbation Theory (D.F.P.T.). The bulk moduli of the unit-cell and of the icosahedron have been investigated, and the equation of state at zero temperature has been determined. In α boron, Raman diffusion and infrared absorption have been studied under pressure, and the theoretical and experimental Grueneisen coefficients have been compared. In boron carbide, inspection of the theoretical and experimental vibrational spectra has led to the determination of the atomic structure of B 4 C. Finally, the effects of isotopic disorder have been modeled by an exact method beyond the mean-field approximation, and the effects onto the Raman lines has been investigated. The method has been applied to isotopic alloys of diamond and germanium. (author)
Traveling waves in lattice differential equations with distributed maturation delay
Directory of Open Access Journals (Sweden)
Hui-Ling Niu
2013-07-01
Full Text Available In this paper we derive a lattice model with infinite distributed delay to describe the growth of a single-species population in a 2D patchy environment with infinite number of patches connected locally by diffusion and global interaction. We consider the existence of traveling wave solutions when the birth rate is large enough that each patch can sustain a positive equilibrium. When the birth function is monotone, we prove that there exists a traveling wave solution connecting two equilibria with wave speed $c>c^*(\\theta$ by using the monotone iterative method and super and subsolution technique, where $\\theta\\in [0,2\\pi]$ is any fixed direction of propagation. When the birth function is non-monotone, we prove the existence of non-trivial traveling wave solutions by constructing two auxiliary systems satisfying quasi-monotonicity.
Thermal lattice Boltzmann simulation for multispecies fluid equilibration
International Nuclear Information System (INIS)
Vahala, Linda; Wah, Darren; Vahala, George; Carter, Jonathan; Pavlo, Pavol
2000-01-01
The equilibration rate for multispecies fluids is examined using thermal lattice Boltzmann simulations. Two-dimensional free-decay simulations are performed for effects of velocity shear layer turbulence on sharp temperature profiles. In particular, parameters are so chosen that the lighter species is turbulent while the heavier species is laminar--and so its vorticity layers would simply decay and diffuse in time. With species coupling, however, there is velocity equilibration followed by the final relaxation to one large co- and one large counter-rotating vortex. The temperature equilibration proceeds on a slower time scale and is in good agreement with the theoretical order of magnitude estimate of Morse [Phys. Fluids 6, 1420 (1963)]. (c) 2000 The American Physical Society
Thermal lattice Boltzmann simulation for multispecies fluid equilibration
Energy Technology Data Exchange (ETDEWEB)
Vahala, Linda [Department of Electrical and Computer Engineering, Old Dominion University, Norfolk, Virginia 23529 (United States); Wah, Darren [Department of Physics, William and Mary College, Williamsburg, Virginia 23187 (United States); Vahala, George [Department of Physics, William and Mary College, Williamsburg, Virginia 23187 (United States); Carter, Jonathan [NERSC, Lawrence Berkeley Laboratory, Berkeley, California 97320 (United States); Pavlo, Pavol [Institute of Plasma Physics, Czech Academy of Science, Praha 8, (Czech Republic)
2000-07-01
The equilibration rate for multispecies fluids is examined using thermal lattice Boltzmann simulations. Two-dimensional free-decay simulations are performed for effects of velocity shear layer turbulence on sharp temperature profiles. In particular, parameters are so chosen that the lighter species is turbulent while the heavier species is laminar--and so its vorticity layers would simply decay and diffuse in time. With species coupling, however, there is velocity equilibration followed by the final relaxation to one large co- and one large counter-rotating vortex. The temperature equilibration proceeds on a slower time scale and is in good agreement with the theoretical order of magnitude estimate of Morse [Phys. Fluids 6, 1420 (1963)]. (c) 2000 The American Physical Society.
Empirical constraints on the effects of radiation damage on helium diffusion in zircon
Anderson, Alyssa J.; Hodges, Kip V.; van Soest, Matthijs C.
2017-12-01
In this study, we empirically evaluate the impact of radiation damage on zircon (U-Th)/He closure temperatures for a suite of zircon crystals from the slowly cooled McClure Mountain syenite of south-central Colorado, USA. We present new zircon, titanite, and apatite conventional (U-Th)/He dates, zircon laser ablation (U-Th)/He and U-Pb dates, and zircon Raman spectra for crystals from the syenite. Titanite and apatite (U-Th)/He dates range from 447 to 523 Ma and 88.0 to 138.9 Ma, respectively, and display no clear correlation between (U-Th)/He date and effective uranium concentration. Conventional zircon (U-Th)/He dates range from 230.3 to 474 Ma, while laser ablation zircon (U-Th)/He dates show even greater dispersion, ranging from 5.31 to 520 Ma. Dates from both zircon (U-Th)/He datasets decrease with increasing alpha dose, indicating that most of the dispersion can be attributed to radiation damage. Alpha dose values for the dated zircon crystals range from effectively zero to 2.15 × 1019 α /g, spanning the complete damage spectrum. We use an independently constrained thermal model to empirically assign a closure temperature to each dated zircon grain. If we assume that this thermal model is robust, the zircon radiation damage accumulation and annealing model of Guenthner et al. (2013) does not accurately predict closure temperatures for many of the analyzed zircon crystals. Raman maps of the zircons dated by laser ablation document complex radiation damage zoning, sometimes revealing crystalline zones in grains with alpha dose values suggestive of amorphous material. Such zoning likely resulted in heterogeneous intra-crystalline helium diffusion and may help explain some of the discrepancies between our empirical findings and the Guenthner et al. (2013) model predictions. Because U-Th zoning is a common feature in zircon, radiation damage zoning is likely to be a concern for most ancient, slowly cooled zircon (U-Th)/He datasets. Whenever possible, multiple
High order spectral difference lattice Boltzmann method for incompressible hydrodynamics
Li, Weidong
2017-09-01
This work presents a lattice Boltzmann equation (LBE) based high order spectral difference method for incompressible flows. In the present method, the spectral difference (SD) method is adopted to discretize the convection and collision term of the LBE to obtain high order (≥3) accuracy. Because the SD scheme represents the solution as cell local polynomials and the solution polynomials have good tensor-product property, the present spectral difference lattice Boltzmann method (SD-LBM) can be implemented on arbitrary unstructured quadrilateral meshes for effective and efficient treatment of complex geometries. Thanks to only first oder PDEs involved in the LBE, no special techniques, such as hybridizable discontinuous Galerkin method (HDG), local discontinuous Galerkin method (LDG) and so on, are needed to discrete diffusion term, and thus, it simplifies the algorithm and implementation of the high order spectral difference method for simulating viscous flows. The proposed SD-LBM is validated with four incompressible flow benchmarks in two-dimensions: (a) the Poiseuille flow driven by a constant body force; (b) the lid-driven cavity flow without singularity at the two top corners-Burggraf flow; and (c) the unsteady Taylor-Green vortex flow; (d) the Blasius boundary-layer flow past a flat plate. Computational results are compared with analytical solutions of these cases and convergence studies of these cases are also given. The designed accuracy of the proposed SD-LBM is clearly verified.
Meretoja’s Syndrome: Lattice Corneal Dystrophy, Gelsolin Type
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I. Casal
2017-01-01
Full Text Available Lattice corneal dystrophy gelsolin type was first described in 1969 by Jouko Meretoja, a Finnish ophthalmologist. It is caused by an autosomal dominant mutation in gelsolin gene resulting in unstable protein fragments and amyloid deposition in various organs. The age of onset is usually after the third decade of life and typical diagnostic triad includes progressive bilateral facial paralysis, loose skin, and lattice corneal dystrophy. We report a case of a 53-year-old female patient referred to our Department of Ophthalmology by severe dry eye and incomplete eyelid closure. She had severe bilateral facial paresis, significant orbicularis, and perioral sagging as well as hypoesthesia of extremities and was diagnosed with Meretoja’s syndrome at the age of 50, confirmed by the presence of gelsolin mutation. At our observation she had bilateral diminished tear film break-up time and Schirmer test, diffuse keratitis, corneal opacification, and neovascularization in the left eye. She was treated with preservative-free lubricants and topical cyclosporine, associated with nocturnal complete occlusion of both eyes, and underwent placement of lacrimal punctal plugs. Ocular symptoms are the first to appear and our role as ophthalmologists is essential for the diagnosis, treatment, and monitoring of ocular alterations in these patients.
Lattice-polarity-driven epitaxy of hexagonal semiconductor nanowires
Wang, Ping
2015-12-22
Lattice-polarity-driven epitaxy of hexagonal semiconductor nanowires (NWs) is demonstrated on InN NWs. In-polarity InN NWs form typical hexagonal structure with pyramidal growth front, whereas N-polarity InN NWs slowly turn to the shape of hexagonal pyramid and then convert to an inverted pyramid growth, forming diagonal pyramids with flat surfaces and finally coalescence with each other. This contrary growth behavior driven by lattice-polarity is most likely due to the relatively lower growth rate of the (0001 ̅) plane, which results from the fact that the diffusion barriers of In and N adatoms on the (0001) plane (0.18 and 1.0 eV, respectively) are about two-fold larger in magnitude than those on the (0001 ̅) plane (0.07 and 0.52 eV), as calculated by first-principles density functional theory (DFT). The formation of diagonal pyramids for the N-polarity hexagonal NWs affords a novel way to locate quantum dot in the kink position, suggesting a new recipe for the fabrication of dot-based devices.
Diffusing diffusivity: Rotational diffusion in two and three dimensions
Jain, Rohit; Sebastian, K. L.
2017-06-01
We consider the problem of calculating the probability distribution function (pdf) of angular displacement for rotational diffusion in a crowded, rearranging medium. We use the diffusing diffusivity model and following our previous work on translational diffusion [R. Jain and K. L. Sebastian, J. Phys. Chem. B 120, 3988 (2016)], we show that the problem can be reduced to that of calculating the survival probability of a particle undergoing Brownian motion, in the presence of a sink. We use the approach to calculate the pdf for the rotational motion in two and three dimensions. We also propose new dimensionless, time dependent parameters, αr o t ,2 D and αr o t ,3 D, which can be used to analyze the experimental/simulation data to find the extent of deviation from the normal behavior, i.e., constant diffusivity, and obtain explicit analytical expressions for them, within our model.
International Nuclear Information System (INIS)
Tiwari, G.P.; Kale, G.B.; Patil, R.V.
1999-01-01
The article presents a brief survey of process of diffusion in solids. It is emphasised that the essence of diffusion is the mass transfer through the atomic jumps. To begin with formal equations for diffusion coefficient are presented. This is followed by discussions on mechanisms of diffusion. Except for solutes which form interstitial solid solution, diffusion in majority of cases is mediated through exchange of sites between an atom and its neighbouring vacancy. Various vacancy parameters such as activation volume, correlation factor, mass effect etc are discussed and their role in establishing the mode of diffusion is delineated. The contribution of dislocations and grain boundaries in diffusion process is brought out. The experimental determination of different types of diffusion coefficients are described. Finally, the pervasive nature of diffusion process in number of commercial processes is outlined to show the importance of diffusion studies in materials science and technology. (author)
Oxygen diffusion in high-Tc superconductors
International Nuclear Information System (INIS)
Rothman, S.J.; Routbort, J.L.
1992-07-01
The cuprate superconductors are fascinating not only because of their technical promise, but also because of their structures, especially the anisotropy of the crystal lattice. There are some structural similarities among these compounds, but also significant differences. Measurements of the oxygen tracer diffusion coefficients have been carried out as a function of temperature, oxygen partial pressure, crystal orientation, and doping in the La-Sr-Cu-0, Y-Ba-Cu-0, and Bi-Sr-Ca-Cu-0 systems. These measurements have revealed a variety of defect mechanisms operating in these compounds; the exact nature of the mechanism depends on the details of the structure
Ag diffusion in cubic silicon carbide
International Nuclear Information System (INIS)
Shrader, David; Khalil, Sarah M.; Gerczak, Tyler; Allen, Todd R.; Heim, Andrew J.; Szlufarska, Izabela; Morgan, Dane
2011-01-01
The diffusion of Ag impurities in bulk 3C-SiC is studied using ab initio methods based on density functional theory. This work is motivated by the desire to reduce transport of radioactive Ag isotopes through the SiC boundary layer in the Tristructural-Isotropic (TRISO) fuel pellet, which is a significant concern for the Very High Temperature Reactor (VHTR) nuclear reactor concept. The structure and stability of charged Ag and Ag-vacancy clusters in SiC are calculated. Relevant intrinsic SiC defect energies are also determined. The most stable state for the Ag impurity in SiC is found to be a Ag atom substituting on the Si sub-lattice and bound to a C vacancy. Bulk diffusion coefficients are estimated for different impurity states and values are all found to have very high activation energy. The impurity state with the lowest activation energy for diffusion is found to be the Ag interstitial, with an activation energy of approximately 7.9 eV. The high activation energies for Ag diffusion in bulk 3C-SiC cause Ag transport to be very slow in the bulk and suggests that observed Ag transport in this material is due to an alternative mechanism (e.g., grain boundary diffusion).
Diffusive epidemic process: theory and simulation
International Nuclear Information System (INIS)
Maia, Daniel Souza; Dickman, Ronald
2007-01-01
We study the continuous absorbing-state phase transition in the one-dimensional diffusive epidemic process via mean-field theory and Monte Carlo simulation. In this model, particles of two species (A and B) hop on a lattice and undergo reactions B → A and A+B → 2B; the total particle number is conserved. We formulate the model as a continuous-time Markov process described by a master equation. A phase transition between the (absorbing) B-free state and an active state is observed as the parameters (reaction and diffusion rates, and total particle density) are varied. Mean-field theory reveals a surprising, nonmonotonic dependence of the critical recovery rate on the diffusion rate of B particles. A computational realization of the process that is faithful to the transition rates defining the model is devised, allowing for direct comparison with theory. Using the quasi-stationary simulation method we determine the order parameter and the survival time in systems of up to 4000 sites. Due to strong finite-size effects, the results converge only for large system sizes. We find no evidence for a discontinuous transition. Our results are consistent with the existence of three distinct universality classes, depending on whether A particles diffusive more rapidly, less rapidly or at the same rate as B particles. We also perform quasi-stationary simulations of the triplet creation model, which yield results consistent with a discontinuous transition at high diffusion rates
Diffusion archeology for diffusion progression history reconstruction
Sefer, Emre; Kingsford, Carl
2015-01-01
Diffusion through graphs can be used to model many real-world processes, such as the spread of diseases, social network memes, computer viruses, or water contaminants. Often, a real-world diffusion cannot be directly observed while it is occurring — perhaps it is not noticed until some time has passed, continuous monitoring is too costly, or privacy concerns limit data access. This leads to the need to reconstruct how the present state of the diffusion came to be from partial d...
The Lattice-Valued Turing Machines and the Lattice-Valued Type 0 Grammars
Directory of Open Access Journals (Sweden)
Juan Tang
2014-01-01
Full Text Available Purpose. The purpose of this paper is to study a class of the natural languages called the lattice-valued phrase structure languages, which can be generated by the lattice-valued type 0 grammars and recognized by the lattice-valued Turing machines. Design/Methodology/Approach. From the characteristic of natural language, this paper puts forward a new concept of the l-valued Turing machine. It can be used to characterize recognition, natural language processing, and dynamic characteristics. Findings. The mechanisms of both the generation of grammars for the lattice-valued type 0 grammar and the dynamic transformation of the lattice-valued Turing machines were given. Originality/Value. This paper gives a new approach to study a class of natural languages by using lattice-valued logic theory.
Strange Baryon Physics in Full Lattice QCD
International Nuclear Information System (INIS)
Huey-Wen Lin
2007-01-01
Strange baryon spectra and form factors are key probes to study excited nuclear matter. The use of lattice QCD allows us to test the strength of the Standard Model by calculating strange baryon quantities from first principles