Related papers: A microscopic, mechanical derivation for the adiab…
A sequence of exact relations is found which connect one- and many-particle time-dependent distribution functions of low-density gas with their derivatives in respect to mean density. It is shown that, at least in the context of spatially…
In this paper, we consider the dynamics of a tagged point particle in a gas of moving hard-spheres that are non-interacting among each other. This model is known as the ideal Rayleigh gas. We add to this model the possibility of…
We show that the van der Waals-like phase separation instability of a driven granular gas at zero gravity, previously investigated in two-dimensional settings, persists in three dimensions. We consider a monodisperse granular gas driven by…
We study a two-dimensional granular gas of inelastic spheres subject to multiplicative driving proportional to a power $|v(\vec{x})|^{\delta}$ of the local particle velocity $v(\vec{x})$. The steady state properties of the model are…
A new kinetic approach is developed and a quasi-practical gas is defined to which the new approach can be applied. One of the advantages of this new approach over the standard one is direct calculability in terms of today's computational…
The viscous inhomogeneities of a relativistic plasma determine a further class of entropic modes whose amplitude must be sufficiently small since curvature perturbations are observed to be predominantly adiabatic and Gaussian over large…
A variational model for epitaxially-strained thin films on rigid substrates is derived both by {\Gamma}-convergence from a transition-layer setting, and by relaxation from a sharp-interface description available in the literature for…
We present a new variational principle for linking models of beams and deformable solids, providing also its mathematical analysis. Despite the apparent differences between the two types of governing equations, it will be shown that the…
As a simple model for piezoelectricity we consider a gas of infinitely many non-interacting electrons subject to a slowly time-dependent periodic potential. We show that in the adiabatic limit the macroscopic current is determined by the…
Prolongating our previous paper on the Einstein relation, we study the motion of a particle diffusing in a random reversible environment when subject to a small external forcing. In order to describe the long time behavior of the particle,…
The equation of state for an ideal gas is simple, which is $P=nk_{\rm B}T$. In the case of imperfect gases where mutual interactions among the constituents are important, pressure $P$ can be expressed as the series expansion of density $n$…
A generalized entropy arising in the context of superstatistics is obtained for an ideal gas. The curvature scalar associated to the thermodynamic space generated by this modified entropy is calculated using two formalisms of the geometric…
We develop an adiabatic theory for generators of contracting evolution on Banach spaces. This provides a uniform framework for a host of adiabatic theorems ranging from unitary quantum evolutions through quantum evolutions of open systems…
We present the exact adiabatic theory for the dynamics of the inhomogeneous density distribution of a classical fluid. Erroneous particle number fluctuations of dynamical density functional theory are absent, both for canonical and grand…
The steady state of a vibrated granular gas confined by a movable piston on the top is discussed. Particular attention is given to the hydrodynamic boundary conditions to be used when solving the inelastic Navier-Stokes equations. The…
New exact solutions emerge by replacing the dust source of the Lem\^aitre-Tolman-Bondi metrics with a viscous fluid satisfying the monatomic gas equation of state. The solutions have a consistent thermodynamical interpretation. The most…
Non-stationary Euler flows of gases are studied. The system of differential equations describing such flows can be represented by means of 2-forms on zero-jet space and we get some exact solutions by means of such a representation.…
We consider a dynamical system subjected to weak but adiabatically slow fluctuations of external origin. Based on the ``adiabatic following'' approximation we carry out an expansion in \alpha/|\mu|, where \alpha is the strength of…
One-dimensional ideal diatomic gas is simulated through possible types of motion of a molecule. Energy of each type of its motion is calculated from theory and numerical method. Calculation of kinetic energy of an atom in…
In this paper a one-dimensional model of two infinite gases separated by a movable heavy piston is considered. The non-linear Langevin equation for the motion of the piston is derived from first principles for the case when the…