Related papers: Classical gases with singular densities
We address the problem of the so-called ``granular gases'', i.e. gases of massive particles in rapid movement undergoing inelastic collisions. We introduce a class of models of driven granular gases for which the stationary state is the…
We study the motion of independent particles in a dynamical random environment on the integer lattice. The environment has a product distribution. For the multidimensional case, we characterize the class of spatially ergodic invariant…
We give two examples of spiral galaxies that show non-circular gas motions in the inner kiloparsecs, from SAURON integral field spectroscopy. We use harmonic decomposition of the velocity field of the ionized gas to study the underlying…
We study systematically stationary solutions to the coupled Vlasov and Poisson equations which have `self-similar' or scaling symmetry in phase space. In particular, we find analytically {\it all} spherically symmetric distribution…
In this paper, a system of one-dimensional gas dynamics equations is considered. This system is a particular case of Jacobi type systems and has a natural representation in terms of 2-forms on 0-jet space. We use this observation to find a…
We investigate the effect of repeated measurement for quantum dynamics of the suppressed systems which classical counterparts exhibit chaos. The essential feature of such systems is the quantum localization phenomena strongly limiting…
It is revealed that distribution functions of practical gases relate to singularities and such singularities can, with molecular motion, spread to the entire region of interest. It is also shown that even common continuous distribution…
In this paper we study a stellar dynamic model for the stars' rotational-dynamics, with a distribution of its own mass, rotating around its center with a higher density, like spiral galaxies happen, by means of a classical calculus of the…
The necessity and benefit of singular solutions in the study of physical systems is shown. By singular solutions we mean solutions that are not contained in the general solution of the system of equations that describes the dynamic system…
Two classes of topological spaces are introduced on which every probability Radon measure possesses a uniformly distributed sequence or a uniformly tight uniformly distributed sequence. It is shown that these classes are stable under…
A phenomenon of classical quantization is discussed. This is revealed in the class of pseudoclassical gauge systems with nonlinear nilpotent constraints containing some free parameters. Variation of parameters does not change local (gauge)…
Peculiar velocities are the motions of galaxies due to the gravitational influence of large-scale structure, and thus are an important cosmological probe of the underlying matter density field. In recent years the number of surveys designed…
We continue the study of random continued fraction expansions, generated by random application of the Gauss and the R\'enyi backward continued fraction maps. We show that this random dynamical system admits a unique absolutely continuous…
We consider the consequences of applying general relativity to the description of the dynamics of a galaxy, given the observed flattened rotation curves. The galaxy is modeled as a stationary axially symmetric pressure-free fluid. In spite…
A classical (non-quantum-mechanical) relativistic ideal gas in thermodynamic equilibrium in a uniformly accelerated frame of reference is studied using Gibbs's microcanonical and grand canonical formulations of statistical mechanics. Using…
A striking feature of our fundamentally indeterministic quantum universe is its quasiclassical realm -- the wide range of time place and scale in which the deterministic laws of classical physics hold. Our quasiclassical realmis an emergent…
We prove singularity of some distributions of random continued fractions that correspond to iterated function systems with overlap and a parabolic point. These arose while studying the conductance of Galton-Watson trees.
We give a new criterion for a classical gas with a repulsive pair potential to exhibit uniqueness of the infinite volume Gibbs measure and analyticity of the pressure. Our improvement on the bound for analyticity is by a factor $e^2$ over…
We study finitely additive extensions of the asymptotic density to all the subsets of natural numbers. Such measures are called density measures. We consider a class of density measures constructed from free ultrafilters on $\mathbb{N}$ and…
We formulate the conditions under which the dynamics of a continuously measured quantum system becomes indistinguishable from that of the corresponding classical system. In particular, we demonstrate that even in a classically chaotic…