Related papers: Global energy minimizers for a diffusion-aggregati…
We consider a one-dimensional array of particles interacting via an infinite well potential. We explore the properties of energy spreading from an initial state where only a group of particles has non-zero velocities while others are…
We show that topological phases with fractional excitations can occur in two-dimensional ultracold dipolar gases on a particular class of optical lattices. Due to the dipolar interaction and lattice confinement, a quantum dimer model…
Transitions to absorbing states are of fundamental importance in non-equilibrium physics as well as ecology. In ecology, absorbing states correspond to the extinction of species. We here study the spatial population dynamics of three…
We consider finite discrete systems consisting of two different atomic types and investigate ground-state configurations for configurational energies featuring two-body short-ranged particle interactions. The atomic potentials favor some…
We give a variational formulation of classical statistical mechanics where the one-body density and the local entropy distribution constitute the trial fields. Using Levy's constrained search method it is shown that the grand potential is a…
We consider a hydrodynamic model of flocking-type with all-to-all interaction kernel in a periodic domain in one-space dimension with linear pressure term. The main result is the global existence of periodic entropy weak solutions, for…
We analyze the entropic equation of state for a many-particle interacting system in a scale-free network. The analysis is performed in terms of scaling functions which are of fundamental interest in the theory of critical phenomena and have…
This paper is concerned with a thermomechanical model describing phase separation phenomena in terms of the entropy balance and equilibrium equations for the microforces. The related system is highly nonlinear and admits singular potentials…
Statistical thermodynamics of small systems shows dramatic differences from normal systems. Parallel to the recently presented steady-state thermodynamic formalism for master equation and Fokker-Planck equation, we show that a…
We study an aggregation PDE with competing attractive and repulsive forces on a sphere of arbitrary dimension. In particular, we consider the limit of strongly localized repulsion with a constant attraction term. We prove convergence of…
We consider the minimization of an energy functional given by the sum of a density perimeter and a nonlocal interaction of Riesz type with exponent $\alpha$, under volume constraint, where the strength of the nonlocal interaction is…
This paper presents a nonequilibrium thermodynamic model for the relaxation of a local, isolated system in nonequilibrium using the principle of steepest entropy ascent (SEA), which can be expressed as a variational principle in…
We consider the energy landscape of a dissipative Klein-Gordon lattice with a $\phi^4$ on-site potential. Our analysis is based on suitable energy arguments, combined with a discrete version of the \L{}ojasiewicz inequality, in order to…
We study the infinite temperature dynamics of a prototypical one-dimensional system expected to exhibit many-body localization. Using numerically exact methods, we establish the dynamical phase diagram of this system based on the statistics…
We investigate the ground and low energy states of a one dimensional non local free energy functional describing at a mean field level a spin system with both ferromagnetic and antiferromagnetic interactions. In particular, the…
We investigate the formation of polycrystalline structures in a class of particle systems. The atomistic energy is modeled as a sum of particle energies that favor atoms being locally isometric to a reference lattice. The discrete frame…
Electro-energy-reaction-diffusion systems are thermodynamically consistent continuum models for reaction-diffusion processes that account for temperature and electrostatic effects in a way that total charge and energy are conserved. The…
For a system consisting of active soft spheres in three dimensions, we study the transition from a fluid where overlaps between particles can only occur for a short time after a collision to a state where clusters of overlapping particles…
In this paper the percolation of monomers on a square lattice is studied as the particles interact with either repulsive or attractive energies. By means of a finite-size scaling analysis, the critical exponents and the scaling collapsing…
We introduce a diffuse-interface Landau-de Gennes free energy for nematic liquid crystals (NLC) systems, with free boundaries, in three dimensions submerged in isotropic liquid, and a phase field is introduced to model the deformable…