Related papers: Infinite volume limit for the dipole gas
We prove a lower bound for the free energy (per unit volume) of the two-dimensional Bose gas in the thermodynamic limit. We show that the free energy at density $\rho$ and inverse temperature $\beta$ differs from the one of the…
We provide an $N/V$-limit for the infinite particle, infinite volume stochastic dynamics associated with Gibbs states in continuous particle systems on $\mathbb R^d$, $d \ge 1$. Starting point is an $N$-particle stochastic dynamic with…
We consider an unbounded lattice and at each point of this lattice an anharmonic oscillator, that interacts with its first neighborhoods via a pair potential $V$ and is subjected to a restoring force of potential $U$. We assume that $U$ and…
This article deals with topological assumptions under which the minimal volume entropy of a closed manifold, and more generally of a finite simplicial complex, vanishes or is positive. In the first part of the article, we present…
We study the incompressible limit of the porous medium equation with a reaction term that is non-monotone with respect to the pressure variable. More specifically we consider reaction terms that are either bistable or monostable. We show…
We consider an analogous version of the diffusion-limited aggregation model defined on the hyperbolic plane. We prove that almost surely the aggregate viewed at time infinity will have a positive density.
We study the damped wave equation with a damping coefficient which is possibly singular and unbounded at infinity. In general, zero belongs to the spectrum of the corresponding generator, which prevents a uniform (exponential) decay for the…
We show that if an infinite measure preserving system is well approximated on most of the phase space by a system satisfying the local limit theorem, then the original system enjoys mixing with respect to global observables, that is, the…
Confinement of electrically charged test particles in the dilute plasma of monopoles and pointlike magnetic dipoles is studied. We calculate the tension of the string emerging between the infinitely separated test particles. The string…
We consider classical steady water waves with a free surface, a flat bottom and constant vorticity $\gamma$. In the adverse case $\gamma>0$ we prove that there is an absolute upper bound on the amplitude, independent of the physical…
The present paper regards the volume function of a doubly truncated hyperbolic tetrahedron. Starting from the previous results of J. Murakami, U. Yano and A. Ushijima, we have developed a unified approach to express the volume in different…
It is proved that the volume of spherical or hyperbolic simplices, when considered as a function of the dihedral angles, can be extended continuously to degenerated simplices.
We study the equilibrium statistical mechanics of classical two-dimensional Coulomb systems living on a pseudosphere (an infinite surface of constant negative curvature). The Coulomb potential created by one point charge exists and goes to…
We define a natural topology on the collection of (equivalence classes up to scaling of) locally finite measures on a homogeneous space and prove that in this topology, pushforwards of certain infinite volume orbits equidistribute in the…
A Bose gas in an external potential is studied by means of the semi-classical approximation. Analytical results are derived for the energy of an interacting Bose gas in a generic power-law trapping potential. An expression for the chemical…
In this survey article we will consider universal lower bounds on the volume of a Riemannian manifold, given in terms of the volume of lower dimensional objects (primarily the lengths of geodesics). By `universal' we mean without curvature…
Motivated by the buckling of glassy crusts formed on evaporating droplets of polymer and colloid solutions, we numerically model the deformation and buckling of spherical elastic caps controlled by varying the volume between the shell and…
There exists, in general, no unique definition of the size (volume, area, etc., depending on dimension) of a soliton. Here we demonstrate that the geometric volume (area etc.) of a soliton is singled out in the sense that it exactly…
We discover a new class of topological solitons. These solitons can exist in a space of infinite volume like, e.g., $\mathbb{R}^n$, but they cannot be placed in any finite volume, because the resulting formal solutions have infinite energy.…
The aim of this letter is to check the ultra-relativistic limit of a recent model proposed by Pennisi and Ruggeri [Ann. Phys. 377, 414 (2017)] for a relativistic gas with internal structure. Considering an Eulerian fluid we prove that there…