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AbstractAbstract

[en] Complete text of publication follows: The lecture series 'Discrete Simulation of Fluid Dynamics (DSFD)' began in 1986 in Los Alamos thanks to Gary D. Doolen's initiative. Since then, this annual conference has allowed researchers to take stock of the progress being made in fluid mechanics simulation using kinetic methods on networks. The many topics covered in this lecture series include lattice Boltzmann schemes, particulate dissipative approaches, particle hydrodynamics, direct Monte Carlo methods, etc. The Scientific Committee of the International Conference DSFD proposed that Paris welcome its 23. edition in 2014. This choice stemmed from the international reputation of the city of Paris both scientifically and culturally. In addition, the discrete kinetic approach to fluid mechanics was born in the years 1970-1990 between the mechanics lab at the Universite Pierre et Marie Curie (Paris 6 University) and the physics lab of the Ecole Normale Superieure in Paris. The lattice Boltzmann approach also uses theoretical tools inspired by the Boltzmann kinetic framework, which is a theme of excellence of the French school of mathematics. Given the various physical areas covered by numerical methods exposed during DSFD conferences, one of the objectives of the 2014 edition, which took place at the Ecole Normale Superieure in Paris from 28 July to 1 August 2014, was to promote a multi-disciplinary approach by hosting conferences and lectures on highly theoretical subjects, such as those aimed at justifying the Boltzmann lattice algorithms, as well as on very applied topics and even industrial ones. At the fundamental level, conference-goers noted the Lattice Boltzmann models of high order, multi-speed models, boundary conditions, etc. Among the numerous applications which may be mentioned are optimization of the aerodynamic shape of a car, the problems of multiphase flow for the oil industry, colloidal suspensions, simulation of micro-fluidic devices, etc. Lattice Boltzmann methods (LBM) have developed in recent decades in all countries of the world. It is sufficient to be convinced to read the list of the 13 members of the International Scientific Committee of the conference DSFD 2014: Ilya Karlin (Chairman, Eidgenossische Technische Hochschule Zurich, Switzerland), Santosh Ansumali (Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore, India), Bruce Boghosian (Boston, USA and American University of Armenia, Yerevan), Jean-Pierre Boon (Universite Libre of Brussels), Bastien Chopard (University of Geneva, Switzerland), Paul Dellar (University of Oxford, United Kingdom), Jens Harting (Technical University, Eindhoven, Netherlands), Takaji Inamuro (Kyoto University, Japan), Paulo Cesar Philippi (Federal University of Santa Catarina, Brazil), Marisol Ripoll (Forschungszentrum Julich, Germany), Shan Xiaowen (Beijing Aero-Science and Technology Research Institute, China) Sauro Succi (National Research Council (CNR), Italy) and Alexander Wagner (North Dakota State University, USA). During the DSFD 2014 conference, we counted 155 participants, including 60 students or post-docs, with more than 30 nationalities from five continents. The conference was structured in 24 sessions, some specialized on granular materials, rarefied gases, transport of particles in fluid flows, compressible flows, turbulence, rheology, porous media, biophysics, and one of them entirely dedicated to industrial applications, particularly in industrial simulation software from the 'LaBS' project (Lattice Boltzmann Solver). The local organizing committee DSFD 2014 composed of Stephane Dellacherie (CEA, centre de Saclay, France and Ecole Polytechnique de Montreal, Canada), Francois Dubois (CNAM Paris and Universite Paris-Sud, France), Stephan Fauve (Ecole Normale Superieure, Paris, France), Renee Gatignol (Universite Pierre et Marie Curie, Paris, France) and Dominique d'Humieres (CNRS and Ecole Normale Superieure, Paris, France) was responsible for contacts with the Journal of Statistical Physics for publishing a thematic issue. This issue entitled 'Discrete Simulation of Fluid Dynamics' brings together 14 selected contributions proposed by the Local Organizing Committee and validated by the International Scientific Committee. Each contribution has led to a review process by two referees

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Available from doi: http://dx.doi.org/10.1007/s10955-015-1407-6; Country of input: France

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Journal of Statistical Physics; ISSN 0022-4715; ; v. 161; p. 1325-1326

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AbstractAbstract

[en] Nonlocal pseudopotentials which describe the effective interaction between

^{3}He quasiparticles, and between these quasiparticles and the background^{4}He liquid, are obtained as a function of concentration and pressure by generalizing the Aldrich--Pines pseudopotentials for pure^{3}He and^{4}He to dilute mixtures. The hierarchy of physical effects which determine these pseudopotentials is established. Interaction-induced short-range correlations are the dominant physical feature; next in order of importance is the greater zero point motion associated with the replacement of a^{4}He atom by a^{3}He atom, while spin-duced ''Pauli principle'' correlations play a significantly smaller, albeit still important role. We find a consistent trend in the change of the effective direct quasiparticle interactions with increasing concentration, and show how the Aldrich-Pines pseudopotentials for pure^{3}He quasiparticles represent a natural extension of our results for dilute mixtures. Our calculated nonlocal pseudopotential for^{3}He quasiparticles is qualitatively similar to that proposed by Bardeen, Baym, and Pines; it changes sign at somewhat lower momentum transfers than the BBP result, varies little with concentration, and provides a physical basis for understanding the BBP result. The effective interaction between quasiparticles of parallel spin, here determined for the first time, is essentially repulsive in the very dilute limit; as the concentration increases, it becomes increasingly attractive at low momentum transfers, and resembles closely that between antiparallel spin quasiparticles at 5% concentration. The concentration-dependent transport properties calculated from these pseudopotentials (which involve only one phenomenological parameter) are in good agreement with experiment at saturated vapor pressure (SVP), 10 atm, and 20 atmRecord Type

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Journal of Statistical Physics; ISSN 0022-4715; ; v. 38(1); p. 273-434

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AbstractAbstract

[en] The Oguchi approximation is shown to give an upper bound on the magnetization for spin-1/2 Ising models with arbitrary ferromagnetic pair couplings. The resulting bound on the critical temperature is shown to better couplings. The resulting bound on the critical temperature is shown to better than the mean field bound. For ferromagnetic spin-1/2 models where the three-body approximation predicts a unique magnetization, this too is shown to give a magnetization bound and an even better bound on the critical temperature

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Journal of Statistical Physics; ISSN 0022-4715; ; v. 38(2); p. 519-572

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AbstractAbstract

[en] A new thermodynamic analysis is given for the equilibrium between a liquid cluster and the surrounding supersaturated gas phase in a finite constant volume. It is shown that for constant total density and intermediate volume this equilibrium is stable, although it is unstable for very large volume. We show that observation of the critical cluster size l* then yields information on the surface free energy of the liquid cluster. THe accuracy of previous approximate prescriptions for obtaining the free energy of physical cluster is investigated. As an application, the theory is used to analyze Monte Carlo simulations of the two-dimensional lattice gas model at low temperatures. We obtain cluster surface area, diffusivity, and free energy for clusters with 26 < or =l< or =500. It is found that the capillarity approximation is inaccurate for l< or =100, but the free energy of small clusters is higher than the result of classical nucleation theory, in contrast to what one expects from Tolman-like corrections. We interpret these results, deriving low-temperature series expansions for very small clusters, thus showing that the capillarity approximation both underestimates the surface energy and overestimates the surface entropy of very small clusters. Finally, we use our results to give a speculative explanation of recent nucleation experiments. The dependence of the cluster diffusivity on cluster size is tentatively explained in terms of a crossover between two mechanisms yielding different power laws

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Journal of Statistical Physics; ISSN 0022-4715; ; v. 22(3); p. 363-396

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Tomozawa, Yukio

SLAC National Accelerator Laboratory, Menlo Park, CA (United States); University of Michigan, Ann Arbor, MI (United States). Funding organisation: US Atomic Energy Commission (AEC) (United States)

SLAC National Accelerator Laboratory, Menlo Park, CA (United States); University of Michigan, Ann Arbor, MI (United States). Funding organisation: US Atomic Energy Commission (AEC) (United States)

AbstractAbstract

[en] The Gram-Charlier series of type A is discussed here in terms ofdeviants which are related to moments in a way similar to the way Hermite polynomials are related to the powers. Distribution functions are also expressed in terms of the mode and moments (cumulants or deviants), which are useful expansions when the distributions are approximately normal. It is shown that such expansions as well as the Gram-Charlier series are valid asymptotically for discrete distributions defined on the semiinfinite interval [0, ∞].

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SLAC-PUB--1233; OSTIID--1442839; AC02-76SF00515; Available from https://www.osti.gov/servlets/purl/1442839; DOE Accepted Manuscript full text, or the publishers Best Available Version will be available free of charge after the embargo period; DOE-OR--23177-4356' arXiv:1802.00266

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Journal of Statistical Physics; ISSN 0022-4715; ; v. 11(3); p. 195-205

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AbstractAbstract

[en] The role of functional equations to describe the exact local structure of highly bifurcated attractors of x/sub n/+1=lambdaf (X/sub n/) independent of a specific f is formally developed. A hierarchy of universal functions g/sub tau/(X) exists, each descriptive of the same local structure but at levels of a cluster of 2/sup tau/ points. The hierarchy obeys g/sub tau-1/(X) =-αg/sub tau/(g/sub tau/(X/α)), with g =lim/sub tauarrow-rightinfinity/g/sub tau/ existing and obeying g (X) =-αg (g (X/α)), an equation whose solution determines both g and α. For r asymptotic g/sub tau/approx.g-delta/sup -tau/h where delta>1 and h are determined as the associated eigenvalue and eigenvector of the operator L: L[psi]=-α[psi (g (X/α))+g' (g (X/α)) psi (-X/α)] We conjecture that L possesses a unique eigenvalue in excess of 1, and show that this delta is the lambda-convergence rate. The form (*) is then continued to all lambda rather than just discrete lambda/sub tau/ and bifurcation values Λ/sub tau/ and dynamics at such lambda is determined. These results hold for the high bifurcations of any fundamental cycle. We proceed to analyze the approach to the asymptotic regime and show, granted L's spectral conjecture, the stability of the g/sub tau/ limit of highly iterated lambdaf's, thus establishing our theory in a local sense. We show in the course of this that highly iterated lambdaf's are conjugate to g/sub tau/'s, thereby providing some elementary approximation schemes for obtaining lambda/sub tau/ for a chosen f

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Journal of Statistical Physics; ISSN 0022-4715; ; v. 21(6); p. 669-706

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AbstractAbstract

[en] WE establish the FKG correlation inequality for the Euclidean scalar Yukawa

_{2}quantum field model and, when the Fermi mass is zero, for pseudoscalar Yukawa_{2}. To do so we approximate the quantum field model by a lattice spin system and show that the FKG inequality for this system follows from a positivity condition on the fundamental solution of the Euclidean Dirac equation with external field. We prove this positivity condition by applying the Vekua--Bers theory of generalized analytic functionsPrimary Subject

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Journal of Statistical Physics; ISSN 0022-4715; ; v. 22(2); p. 123-192

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AbstractAbstract

[en] We discuss the simple, randomly driven system dx/dt =-μx-yx

^{3}+f(t), where f(t) is a Gaussian random function or stirring force with < f(t)f(t')> =F delta(t-t'). We show how to obtain approximately the coefficients of the expansion of the equal-time Green's function as power series in (1/R)/sup n/, where R is the internal Reynolds number (Fγ)/sup 1/2//μ, by using a new expansion for the path integral representation of the generating functional for the correlation functions. Exploiting the fact that the action for the randomly driven system is related to that of a quantum mechanical anharmonic oscillator with Hamiltonian p^{2}/2+m^{2}x^{2}/2+νx^{4}+lambdax^{6}/2, we evaluate the path integral on a lattice by assuming that the lambdax^{6}term dominates the action. This gives an expansion of the lattice theory Green's functions as power series in 1/(lambdaa)/sup 1/3/, where a is the lattice spacing. Using Pade approximants to extrapolate to a=0, we obtain the desired large-Reynolds-number expansion of the two-point functionPrimary Subject

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Journal of Statistical Physics; ISSN 0022-4715; ; v. 22(6); p. 647-660

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[en] The far-from-equilibrium statistical dynamics of classical particle systems is formulated in terms of self-consistently determined phase-space density response, fluctuation, and vertex functions. Collective and single-particle effects are treated on an equal footing. Two approximations are discussed, one of which reduces to the Vlasov equation direct interaction approximation of Orszag and Kraichnan when terms that are explicitly due to particles are removed

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Journal of Statistical Physics; ISSN 0022-4715; ; v. 20(4); p. 415-447

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[en] A resolution of the ''ellipsoid paradox in thermodynamics'' is proposed based on elementary geometrical optics

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Journal of Statistical Physics; ISSN 0022-4715; ; v. 28(3); p. 603-612

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