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1.
《Physics letters. A》2006,359(1):52-55
The Weibel instability is prompted by a temperature anisotropy within a plasma. We present an analytical model based on a non-relativistic two temperatures waterbag distribution function. The model is exactly solvable in terms of the stability condition, the growth rate for any wave vector and temperature parameters, the maximum growth rate and the wave number for which it is reached. 相似文献
2.
Saroj K Majumdar 《Pramana》1982,19(3):269-277
The nonlinear distribution function introduced by Allis has been used to investigate the stability of the solution of Vlasov-Poisson’s
equations. The ‘average’ Lagrangian is calculated on the basis of this distribution function, and the ‘average’ variational
principle of Witham is applied to discuss modulational stability. It is found that the distribution function of Allis exactly
gives rise to the Lighthill’s stability condition of non-linear waves. 相似文献
3.
P. H. Chavanis 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,53(4):487-501
Systems with long-range interactions can reach a Quasi
Stationary State (QSS) as a result of a violent collisionless
relaxation. If the system mixes well (ergodicity), the QSS can be
predicted by the statistical theory of Lynden-Bell (1967) based on
the Vlasov equation. When the initial condition takes only two
values, the Lynden-Bell distribution is similar to the Fermi-Dirac
statistics. Such distributions have recently been observed in
direct numerical simulations of the HMF model (Antoniazzi et al. 2006). In this paper, we determine the caloric curve
corresponding to the Lynden-Bell statistics in relation with the
HMF model and analyze the dynamical and thermodynamical stability
of spatially homogeneous solutions by using two general criteria
previously introduced in the literature. We express the critical
energy and the critical temperature as a function of a degeneracy
parameter fixed by the initial condition. Below these critical
values, the homogeneous Lynden-Bell distribution is not a maximum
entropy state but an unstable saddle point. Known stability
criteria corresponding to the Maxwellian distribution and the
water-bag distribution are recovered as particular limits of our
study. In addition, we find a critical point below which the
homogeneous Lynden-Bell distribution is always stable. We apply
these results to the situation considered in Antoniazzi et
al. For a given energy, we find a critical initial
magnetization above which the homogeneous Lynden-Bell distribution
ceases to be a maximum entropy state. For an energy U=0.69, this
transition occurs above an initial magnetization Mx=0.897. In
that case, the system should reach an inhomogeneous Lynden-Bell
distribution (most mixed) or an incompletely mixed state (possibly
fitted by a Tsallis distribution). Thus, our theoretical study
proves that the dynamics is different for small and large initial
magnetizations, in agreement with numerical results of Pluchino et
al. (2004). This new dynamical phase transition may reconcile the
two communities by showing that they study different regimes. 相似文献
4.
We study exact stationary properties of the one-dimensional Kardar-Parisi-Zhang (KPZ) equation by using the replica approach. The stationary state for the KPZ equation is realized by setting the initial condition the two-sided Brownian motion (BM) with respect to the space variable. Developing techniques for dealing with this initial condition in the replica analysis, we elucidate some exact nature of the height fluctuation for the KPZ equation. In particular, we obtain an explicit representation of the probability distribution of the height in terms of the Fredholm determinants. Furthermore from this expression, we also get the exact expression of the space-time two-point correlation function. 相似文献
5.
T. V. Dudnikova 《Russian Journal of Mathematical Physics》2008,15(4):460-472
We consider the dynamics of a harmonic crystal in the half-space with zero boundary condition. It is assumed that the initial
date is a random function with zero-mean, finite-mean energy density which also satisfies a mixing condition of Rosenblatt
or Ibragimov type. We study the distribution μ
t
of the solution at time t ∈ ℝ. The main result is the convergence of μ
t
as t → ∞ to a Gaussian measure which is time stationary with a covariance inherited from the initial measure (non-Gaussian in
general).
Supported partly by research grant of RFBR (06-01-00096). 相似文献
6.
We generalize the second law of thermodynamics in its maximum work formulation for a nonequilibrium initial distribution. It is found that in an isothermal process, the Boltzmann relative entropy (H-function) is not just a Lyapunov function but also tells us the maximum work that may be gained from a nonequilibrium initial state. The generalized second law also gives a fundamental relation between work and information. It is valid even for a small Hamiltonian system not in contact with a heat reservoir but with an effective temperature determined by the isentropic condition. Our relation can be tested in the Szilard engine, which will be realized in the laboratory. 相似文献
7.
V. P. Shkilev 《Journal of Experimental and Theoretical Physics》2010,110(1):162-169
A necessary condition is derived for the emergence of diffusion instability in media in which diffusion does not obey classical
Fick laws. The equations derived by Yadav and Horsthemke [Phys. Rev. E 74, 066118 (2006)] using the continuous-time random walk model are employed as equations simulating reaction—diffusion processes.
The waiting-time distribution function is represented by the sum of a finite number of exponents. It is shown that passage
to the diffusion limit in the time variable is an incorrect operation if it is used to analyze diffusion instability in media
with a distribution function that differs from the Poisson distribution function. 相似文献
8.
We study the nonequilibrium motion of an elastic string in a two dimensional pinning landscape using Langevin dynamics simulations. The relaxation of a line, initially flat, is characterized by a growing length L(t) separating the equilibrated short length scales from the flat long distance geometry that keeps a memory of the initial condition. We show that, in the long time limit, L(t) has a nonalgebraic growth with a universal distribution function. The distribution function of waiting times is also calculated, and related to the previous distribution. The barrier distribution is narrow enough to justify arguments based on scaling of the typical barrier. 相似文献
9.
Inertial effects in fluctuations of the work to sustain a system in a nonequilibrium steady state are discussed for a dragged
massive Brownian particle model using a path integral approach. We calculate the work distribution function in the laboratory
and comoving frames and prove the asymptotic fluctuation theorem for these works for any initial condition. Important and
observable differences between the work fluctuations in the two frames appear for finite times and are discussed concretely
for a nonequilibrium steady state initial condition. We also show that for finite times a time oscillatory behavior appears
in the work distribution function for masses larger than a nonzero critical value. 相似文献
10.
Chaoming Song 《Physica A》2010,389(21):4497-455
We introduce a “Hamiltonian”-like function, called the volume function, indispensable to describe the ensemble of jammed matter such as granular materials and emulsions from a geometrical point of view. The volume function represents the available volume of each particle in the jammed systems. At the microscopic level, we show that the volume function is the Voronoi volume associated to each particle and in turn we provide an analytical formula for the Voronoi volume in terms of the contact network, valid for any dimension. We then develop a statistical theory for the probability distribution of the volumes in 3d to calculate an average volume function coarse-grained at a mesoscopic level. The salient result is the discovery of a mesoscopic volume function inversely proportional to the coordination number. Our analysis is the first step toward the calculation of macroscopic observables and equations of state using the statistical mechanics of jammed matter, when supplemented by the condition of mechanical equilibrium of jamming that properly defines jammed matter at the ensemble level. 相似文献
11.
We obtain the solution to the problem of the skin effect in a metal with specular-diffusion boundary conditions for arbitrary
values of the anomaly parameter in the form of the Neumann series. For this purpose, we develop a method based on the idea
of representation of not only the boundary condition imposed on the field (as is conventionally done), but also the boundary
condition imposed on the distribution function, in the form of a source. The specular reflectance is an arbitrary function
of the angle of incidence of electrons on the metal surface. 相似文献
12.
Navinder Singh 《Journal of statistical physics》2008,131(3):405-414
We extend Tooru-Cohen analysis for nonequilibrium steady state (NSS) of a Brownian particle to nonequilibrium oscillatory
state (NOS) of Brownian particle by considering time dependent external drive protocol. We consider an unbounded charged Brownian
particle in the presence of oscillating electric field and prove work fluctuation theorem, which is valid for any initial
distribution and at all times. For harmonically bounded and constantly dragged Brownian particle considered by Tooru and Cohen,
work fluctuation theorem is valid for any initial condition (also NSS), but only in large time limit. We use Onsager-Machlup
Lagrangian with a constraint to obtain frequency dependent work distribution function, and describe entropy production rate
and properties of dissipation functions for the present system using Onsager-Machlup functional. 相似文献
13.
Bappa Saha Sutapa Mukherji 《The European Physical Journal B - Condensed Matter and Complex Systems》2015,88(6):146
We derive the distribution function of work performed by a harmonic force acting on a uniformly dragged Brownian particle subjected to a rotational torque. Following the Onsager and Machlup’s functional integral approach, we obtain the transition probability of finding the Brownian particle at a particular position at time t given that it started the journey from a specific location at an earlier time. The difference between the forward and the time-reversed form of the generalized Onsager-Machlup’s Lagrangian is identified as the rate of medium entropy production which further helps us develop the stochastic thermodynamics formalism for our model. The probability distribution for the work done by the harmonic trap is evaluated for an equilibrium initial condition. Although this distribution has a Gaussian form, it is found that the distribution does not satisfy the conventional work fluctuation theorem. 相似文献
14.
The one-dimensional totally asymmetric simple exclusion process (TASEP) is considered. We study the time evolution property
of a tagged particle in the TASEP with the step initial condition. Calculated is the multi-time joint distribution function
of its position. Using the relation of the dynamics of the TASEP to the Schur process, we show that the function is represented
as the Fredholm determinant. We also study the scaling limit. The universality of the largest eigenvalue in the random matrix
theory is realized in the limit. When the hopping rates of all particles are the same, it is found that the joint distribution
function converges to that of the Airy process after the time at which the particle begins to move. On the other hand, when
there are several particles with small hopping rate in front of a tagged particle, the limiting process changes at a certain
time from the Airy process to the process of the largest eigenvalue in the Hermitian multi-matrix model with external sources. 相似文献
15.
In its continuous version, the entropy functional measuring the information content of a given probability density may be plagued by a "measure" problem that results from improper weighting of phase space. This issue is addressed considering a generic collision process whereby a large number of particles or agents randomly and repeatedly interact in pairs, with prescribed conservation law(s). We find a sufficient condition under which the stationary single-particle distribution function maximizes an entropylike functional, that is free of the measure problem. This condition amounts to a factorization property of the Jacobian associated with the binary collision law, from which the proper weighting of phase space directly follows. 相似文献
16.
Yury M. Zinoviev 《Communications in Mathematical Physics》1995,174(1):1-27
A new inversion formula for the Laplace transformation of tempered distributions with supports in the closed positive semiaxis is obtained. The inverse Laplace transform of a tempered distribution is defined by means of a limit of a special distribution constructed from this distribution. The weak spectral condition on the Euclidean Green's functions implies that some of the limits needed for the inversion formula exist for any Euclidean Green's function with an even number of variables. We then prove that the initial Osterwalder-Schrader axioms [1] and the weak spectral condition are equivalent with the Wightman axioms.The research described in this publication was made possible in part by Grant No. 93-011-147 from the Russian Foundation for Basic Research 相似文献
17.
We consider single-humped symmetric one-dimensional maps generating fully developed chaotic iterations specified by the property that on the attractor the mapping is everywhere two to one. To calculate the probability distribution function, and in turn the Lyapunov exponent and the correlation function, a perturbation expansion is developed for the invariant measure. Besides deriving some general results, we treat several examples in detail and compare our theoretical results with recent numerical ones. Furthermore, a necessary condition is deduced for the probability distribution function to be symmetric and an effective functional iteration method for the measure is introduced for numerical purposes. 相似文献
18.
J. Xiao A. Zangwill M. D. Stiles 《The European Physical Journal B - Condensed Matter and Complex Systems》2007,59(4):415-427
We present a numerical algorithm to solve the Boltzmann
equation for the electron distribution function in magnetic multilayer
heterostructures with non-collinear magnetizations. The solution is
based on a scattering matrix formalism for layers that are
translationally invariant in plane so that properties only vary
perpendicular to the planes. Physical quantities like spin density,
spin current, and spin-transfer torque are calculated directly from
the distribution function. We illustrate our solution method with a
systematic study of the spin-transfer torque in a spin valve as a
function of its geometry. The results agree with a
hybrid circuit theory developed by Slonczewski for geometries typical
of those measured experimentally. 相似文献
19.
A classical gas at equilibrium satisfies the locality conditionif the correlations between local fluctuations at a pair of remote small regions diminish in the thermodynamic limit. The gas satisfies a strong locality conditionif the local fluctuations at any number of remote locations have no (pair, triple, quadruple....) correlations among them in the thermodynamic limit. We prove that locality is equivalent to a certain factorizability condition on the distribution function. The analogous quantum condition fails in the case of a freeBose gas. Next we prove that strong locality is equivalent to the total factorizability of the distribution function, and thus (given Liourilles theorem) to the Maxwell Boltzmann distribution for an ideal gas.Dedicated to Professor Max Jammer on the occasion of his eightieth birthday. April 13. 1995. 相似文献
20.
《Physics letters. A》1987,120(5):219-222
We analyze the evolution of distribution functions with a power-law decrease at large energies. We apply the temperature transform approach and show that these decays correspond to branch points of the transformed function. For the very hard particle (VHP) model we find that an initial condition with power-law decrease relaxes to an exponential one immediately for t > 0. For Maxwell models we study the displacement of the branch points and find that the power-law decrease is preserved as time elapses. 相似文献