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1.
Bartolomé Coll Joan Josep Ferrando Juan Antonio Sáez 《General Relativity and Gravitation》2017,49(5):66
Every evolution of a fluid is uniquely described by an energy tensor. But the converse is not true: an energy tensor may describe the evolution of different fluids. The problem of determining them is called here the inverse problem. This problem may admit unphysical or non-deterministic solutions. This paper is devoted to solve the inverse problem for perfect energy tensors in the class of perfect fluids evolving in local thermal equilibrium (l.t.e.). The starting point is a previous result (Coll and Ferrando in J Math Phys 30:2918–2922, 1989) showing that thermodynamic fluids evolving in l.t.e. admit a purely hydrodynamic characterization. This characterization allows solving this inverse problem in a very compact form. The paradigmatic case of perfect energy tensors representing the evolution of ideal gases is studied in detail and some applications and examples are outlined. 相似文献
2.
It is demonstrated that the kinetic equation of Davis's effective potential theory follows directly from the application of well-defined approximations to the three-body correlations involved in the second equation of the BBGKY hierarchy. The same, simple mathematical techniques involved in this demonstration are used to derive two other kinetic equations, one of which is a generalization to high densities of the Boltzmann equation. In order to facilitate its application to the calculation of the van Hove and other correlation functions, the kinetic equation of the effective potential theory is Fourier-Laplace transformed: explicit formulae are given for the matrix elements of all operators that occur in this equation. 相似文献
3.
We first consider the Boltzmann equation with a collision kernel such that all kinematically possible collisions are run at equal rates. This is the simplest Boltzmann equation having the compressible Euler equations as a scaling limit. For it we prove a stability result for theH-theorem which says that when the entropy production is small, the solution of the spatially homogeneous Boltzmann equation is necessarily close to equilibrium in the entropie sense, and therefore strongL
1 sense. We use this to prove that solutions to the spatially homogeneous Boltzmann equation converge to equilibrium in the entropie sense with a rate of convergence which is uniform in the initial condition for all initial conditions belonging to certain natural regularity classes. Every initial condition with finite entropy andp
th velocity moment for some p>2 belongs to such a class. We then extend these results by a simple monotonicity argument to the case where the collision rate is uniformly bounded below, which covers a wide class of slightly modified physical collision kernels. These results are the basis of a study of the relation between scaling limits of solutions of the Boltzmann equation and hydrodynamics which will be developed in subsequent papers; the program is described here.On leave from School of Mathematics, Georgia Institute of Technology, Atlanta, Georgia 30332.On leave from C.F.M.C. and Departamento de Matemática da Faculdade de Ciencias de Lisboa, 1700 Lisboa codex, Portugal. 相似文献
4.
We present an energy-conserving multiple-relaxation-time finite difference lattice Boltzmann model for compressible flows. The collision step is first calculated in the moment space and then mapped back to the velocity space. The moment space and corresponding transformation matrix are constructed according to the group representation theory. Equilibria of the nonconserved moments are chosen according to the need of recovering compressible Navier-Stokes equations through the Chapman-Enskog expansion. Numerical experiments showed that compressible flows with strong shocks can be well simulated by the present model. The new model works for both low and high speeds compressible flows. It contains more physical information and has better numerical stability and accuracy than its single-relaxation-time version. 相似文献
5.
信息熵、玻尔兹曼熵以及克劳修斯熵之间的关系--兼论玻尔兹曼熵和克劳修斯熵是否等价 总被引:6,自引:0,他引:6
论述了信息熵、玻尔兹曼熵以及克劳修斯熵之间的关系;由不涉及具体系统的方法从玻尔兹曼关系、信息熵推导出了克劳修斯熵的表达式;指出玻尔兹曼熵与克劳修斯熵不是等价关系,而是玻尔兹曼熵包含克劳修斯熵,信息熵又包含玻尔兹曼熵。 相似文献
6.
C. Brot 《Molecular physics》2013,111(5):1195-1201
The Kerr constant of anisometric non-polar molecules in solvents of spherical molecules is calculated using the model of an ellipsoidal cavity in an isotropic dielectric continuum. It is shown that the Kerr constants has the same form as for dilute gases: provided that effective polarizability elements α xx l * (optical) and α xx s * (static) replace the vacuum values α xx l and α xx s in Γ*, which then reads Γ* = 1/2[(α xx l * - α yy l *)(α xx s *) - α yy s *) + circular permutation]. Each effective polarizability element α xx * (either optical or static) is composed of two contributions, one pertaining to the anisometric solute itself and another arising from the anisotropic distortion of the polarization in the neighbouring continuum. These two contributions are of opposite signs, so that large variations of the magnitude of the Kerr effect are predicted, depending essentially upon the mean refractivity and permittivity of the solute compared with those of the solvent. 相似文献
7.
A new high frequency kinetic sum rule for classical simple fluids is obtained. It involves only the static pair- and triplet-correlation functions; its self part and the local limit depend only on the pair correlation function. 相似文献
8.
G. Kaniadakis 《The European Physical Journal A - Hadrons and Nuclei》2009,40(3):275-287
It is well known that the particular form of the two-particle correlation function, in the collisional integral of the classical Boltzmman equation, fixes univocally the entropy of the system, which turns out to be the Boltzmann-Gibbs-Shannon entropy. In the ordinary relativistic Boltzmann equation, some standard generalizations, with respect to its classical version, imposed by the special relativity, are customarily performed. The only ingredient of the equation, which tacitly remains in its original classical form, is the two-particle correlation function, and this fact imposes that also the relativistic kinetics is governed by the Boltzmann-Gibbs-Shannon entropy. Indeed the ordinary relativistic Boltzmann equation admits as stationary stable distribution, the exponential Juttner distribution. Here, we show that the special relativity laws and the maximum entropy principle suggest a relativistic generalization also of the two-particle correlation function and then of the entropy. The so obtained, fully relativistic Boltzmann equation, obeys the H-theorem and predicts a stationary stable distribution, presenting power law tails in the high-energy region. The ensued relativistic kinetic theory preserves the main features of the classical kinetics, which recovers in the c \( \rightarrow\) ∞ limit. 相似文献
9.
A Lattice Boltzmann Method for van der Waals fluids with variable temperature is described. Thermo-hydrodynamic equations are correctly reproduced at second order of a Chapman-Enskog expansion. The method is applied to study initial stages of phase separation of a fluid quenched by contact with colder walls. Thermal equilibration is favoured by pressure waves which propagate with the sound velocity. 相似文献
10.
A method is proposed to calculate the Boltzmann non equilibrium entropy as a Taylor series expansion in terms of the successive moments of the velocity distribution function. As a first application, the entropy of the BKW solution of the Boltzmann equation is calculated for both even and odd dimensions. The properties of the entropy of the Tjon Wu modeld=2) are studied and a quantitative condition is derived, showing that the McKean conjecture is incorrect. As a second application of the method, the entropy of one of the solutions of the very hard particle model for the Boltzmann equation is also derived. 相似文献
11.
Anthony J. C. Ladd W. Edward Alley Berni J. Alder 《Journal of statistical physics》1987,48(5-6):1147-1156
The long-time decay of the shear-stress autocorrelation function is shown to be quantitatively related to the decay of correlations between the orientation of bonds connecting colliding pairs of particles. Within computational uncertainties, we find that orientational correlations in high-density fluids decay as a stretched exponential in time, with an exponent that is independent of density. However, at low densities the decay is exponential. In two-dimensional systems the decay is exponential, even at high density. 相似文献
12.
13.
An expression for the mutual diffusion coefficient of a dense binary system of hard spheres, derived by using the Percus-Yevick approximation for the contact radial distribution function, together with Thorne's extension of the Enskog theory, is used to study the variation of the mutual diffusion coefficient with pressure, composition and ratio of the molecular diameters. Applications are made to real systems. 相似文献
14.
15.
Summary A rigorous deduction of the thermodynamic-equilibrium condition is provided for a homogeneous, uncharged and linear dielectric
fluid contained in an electrostatic field. Contrary to the previous ones, this deduction does not postulate the existence
of a mechanical stress tensor and of a body force density in the polarized fluid. Then, the equilibrium condition is employed
to obtain the mass density distribution of the fluid and to present a correct proof of the well-known formula for the attractive
force between the plates of a plane-parallel capacitor immersed in the fluid. 相似文献
16.
Byung C Eu 《Annals of Physics》1979,118(1):187-229
A kinetic theory of dense fluids is presented in this series of papers. The theory is based on a kinetic equation for subsystems which represents a subset of equations structurally invariant to the sizes of the subsystem that includes the Boltzmann equation as an element at the low density limit. There exists a H-function for the kinetic equation and the equilibrium solution is uniquely given by the canonical distribution functions for the subsystems comprising the entire system. The cluster expansion is discussed for the N-body collision operator appearing in the kinetic equation. The kinetic parts of transport coefficients are obtained by means of a moment method and their density expansions are formally obtained. The Chapman-Enskog method is discussed in the subsequent paper. 相似文献
17.
The velocity autocorrelation functions and memory functions of dense classical fluids may be directly obtained from the static radial distribution function g(r) in an approximate way. Following the Mori projection operator formalism, the memory functions may be related to the fluctuating force correlation. At low densities, these functions may be evaluated by following the trajectories of particle pairs in the interatomic potential. At higher densities, the force correlation functions can be evaluated approximately from particle pair trajectories via the potential of the mean force. The contributions to the memory function come mainly from particle pairs with rather specific and rather short interatomic distances. At higher temperatures, this specific distance is even shorter, hence the memory function decays quickly with time. At lower temperatures, a negative region of the memory function may develop. On the other hand, there is relatively little density dependence of the normalized memory function. The results for argon fluids at various densities and temperatures agree satisfactorily with the molecular dynamics and the Enskog values. The decrease of the diffusion coefficient with density is partly due to the nature of g(r) which reflects the stronger clustering of atoms at higher densities. 相似文献
18.
19.
William G. Hoover 《Journal of statistical physics》1986,42(3-4):587-600
We find exact solutions of the two-particle Boltzmann equation for hard disks and hard spheres diffusing isothermally in an external field. The corresponding transport coefficient, one-particle current divided by field strength, decreases as the field increases. This nonlinear dependence of the current on the field and the corresponding nonlinear dependence of the distribution function on the current are compared to the predictions of single-time information theory. Our exact steady-state distribution function, from Boltzmann's equation, is quite different from the approximate information-theory analog. The approximate theory badly underestimates the nonlinear decrease of entropy with current. The exact two-particle solutions we find here should prove useful in testing and improving theories of steady-state and transient distribution functions far from equilibrium. 相似文献
20.
H. Ted Davis 《Journal of statistical physics》1973,7(3):225-241
A new kinetic equation is developed which incorporates the desirable features of the Enskog, the Rice-Allnatt, and the Prigogine-Nicolis-Misguich kinetic theories of dense fluids. Advantages of the present theory over the latter three theories are (1) it yields the correct local equilibrium hydrodynamic equations, (2) unlike the Rice-Allnatt theory, it determines the singlet and doublet distribution functions from the same equation, and (3) unlike the Prigogine-Nicolis-Misguich theory, it predicts the kinetic and kinetic-potential transport coefficients. The kinetic equation is solved by the Chapman-Enskog method and the coefficients of shear viscosity, bulk viscosity, thermal conductivity, and self-diffusion are obtained. The predicted bulk viscosity and thermal conductivity coefficients are singular at the critical point, while the shear viscosity and self-diffusion coefficients are not. 相似文献