Related papers: Solvable stationary non equilibrium states
We prove that the statistical properties of random perturbations of a nonuniformly hyperbolic diffeomorphism are described by a finite number of stationary measures. We also give necessary and sufficient conditions for the stochastic…
Topological band theory has been studied for free fermions for decades, and one of the most profound physical results is the bulk-boundary correspondence. Recently a focus in topological physics is extending topological classification to…
We consider a multi component gas mixture with translational and internal energy degrees of freedom without chemical reactions assuming that the number of particles of each species remains constant. We will illustrate the derived model in…
The use of unitary invariant subspaces of a Hilbert space $\mathcal{H}$ is nowadays a recognized fact in the treatment of sampling problems. Indeed, shift-invariant subspaces of $L^2(\mathbb{R})$ and also periodic extensions of finite…
We investigate stochastic processes that generalize geometric Brownian motion, focusing on cases where the standard invariant measure, i.e. the solution of the stationary Fokker-Planck equation does not necessarily exist. We demonstrate…
In this paper, we introduce a new method for applying the implicit function theorem to find nontrivial solutions to overdetermined problems with a fixed boundary (given) and a free boundary (to be determined). The novelty of this method…
We study reaction-diffusion equations in cylinders with possibly nonlinear diffusion and possibly nonlinear Neumann boundary conditions. We provide a geometric Poincar\'e-type inequality and classification results for stable solutions, and…
We study the asymptotic diffusion processes with (generally nonlocal) open boundaries in one dimension which are exactly solvable by means of the recently developed recursion formula. We investigate the stationary states, which cannot be…
As model problem we consider the prototype for flow and transport of a concentration in porous media in an interior domain and couple it with a diffusion process in the corresponding unbounded exterior domain. To solve the problem we…
We investigate permutation-invariant continuous variable quantum states and their covariance matrices. We provide a complete characterization of the latter with respect to permutation-invariance, exchangeability and representing convex…
We investigate the existence of stationary fronts in a coupled system of two sine-Gordon equations with a smooth, "hat-like" spatial inhomogeneity. The spatial inhomogeneity corresponds to a spatially dependent scaling of the sine-Gordon…
Traditional finite element approaches are well-known to introduce spurious oscillations when applied to advection-dominated problems. We explore alleviation of this issue from the perspective of a generalized finite element formulation,…
Nonstationary and nonequilibrium processes are considered on the basis of an Enskog-Landau kinetic equation using a boundary conditions method. A nonstationary solution of this equation is found in the pair collision approximation. This…
The paper develops a hybrid method for solving a system of advection--diffusion equations in a bulk domain coupled to advection--diffusion equations on an embedded surface. A monotone nonlinear finite volume method for equations posed in…
We study spatially non-homogeneous kinetic models for vehicular traffic flow. Classical formulations, as for instance the BGK equation, lead to unconditionally unstable solutions in the congested regime of traffic. We address this issue by…
We investigate a Maxwell model of inelastic granular mixture under the influence of a stochastic driving and obtain its steady state properties in the context of classical kinetic theory. The model is studied analytically by computing the…
We review our recent results on the on-shell description of sine-Gordon model with integrable boundary conditions. We determined the spectrum of boundary states together with their reflection factors by closing the boundary bootstrap and…
We consider the boundary driven harmonic model, i.e. the Markov process associated to the open integrable XXX chain with non-compact spins. Using the factorial moments we characterize the stationary measure as a mixture of product measures.…
In [2] we introduced a method combining together an observability inequality and a spectral decomposition to get a logarithmic stability estimate for the inverse problem of determining both the potential and the damping coefficient in a…
An unsteady problem is considered for a space-fractional diffusion equation in a bounded domain. A first-order evolutionary equation containing a fractional power of an elliptic operator of second order is studied for general boundary…