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We investigate stationary nonequilibrium states of systems of particles moving according to Hamiltonian dynamics with specified potentials. The systems are driven away from equilibrium by Maxwell demon ``reflection rules'' at the walls.…
We study relaxation towards a stationary out of equilibrium state by analizing a one-dimensional stochastic process followed by a particle accelerated by an external field and propagating through a thermal bath. The effect of collisions is…
A system with equation and dynamic boundary condition of Cahn-Hilliard type is considered. This system comes from a derivation performed in Liu-Wu (Arch. Ration. Mech. Anal. 233 (2019), 167--247) via an energetic variational approach.…
We study the degenerate linear Boltzmann equation inside a bounded domain with a generalized diffuse reflection at the boundary and variable temperature, including the Maxwell boundary conditions with the wall Maxwellian or heavy-tailed…
We study the full Navier--Stokes--Fourier system governing the motion of a general viscous, heat-conducting, and compressible fluid subject to stochastic perturbation. The system is supplemented with non-homogeneous Neumann boundary…
Stochastic boundary conditions for interactions with a particle reservoir are discussed in many-particle systems. We introduce the boundary conditions with the injection rate and the momentum distribution of particles coming from a particle…
We study the equilibrating effects of the boundary and intermolecular collision in the kinetic theory for rarefied gases. We consider the Maxwell-type boundary condition, which has weaker equilibrating effect than the commonly studied…
We consider the one dimensional boundary driven harmonic model and its continuous version, both introduced in \cite{FGK}. By combining duality and integrability the authors of \cite{FG} obtained the invariant measures in a combinatorial…
We consider macroscopic systems in weak contact with boundary reservoirs and under the action of external fields. We present an explicit formula for the Hamiltonian of such systems, from which we deduce the equation of motions, the action…
The lattice Boltzmann method (LBM) has shown its promising capability in simulating microscale gas flows. However, the suitable boundary condition is still one of the critical issues for the LBM to model microgaseous flows involving curved…
We review some models of granular materials fluidized by means of external forces such as: random homogeneous forcing with damping, vibrating plates, flow in an inclined channel and flow in a double well potential. All these systems show…
In this paper, the boundary flex control problem of non stationary equation governing the coupled mass and heat flow of a viscous incompressible fluid in a generalized Boussinesq approximation by assuming that viscosity and heat…
We consider the numerical integration of Langevin equations for particles in a channel, in the presence of boundary conditions fixing the concentration values at the ends. This kind of boundary condition appears for instance when…
We present a new energy-stable open boundary condition, and an associated numerical algorithm, for simulating incompressible flows with outflow/open boundaries. This open boundary condition ensures the energy stability of the system, even…
While Macroscopic Fluctuation Theory (MFT) has been highly successful in analyzing non-equilibrium steady states, its application to non-steady-state processes remains limited. In this study, we apply MFT to the relaxation process of…
We investigate the dynamics of a one-dimensional asymmetric exclusion process with Langmuir kinetics and a fluctuating wall. At the left boundary, particles are injected onto the lattice; from there, the particles hop to the right. Along…
We investigate the speed of approach to Maxwellian equilibrium for a collisionless gas enclosed in a vessel whose wall are kept at a uniform, constant temperature, assuming diffuse reflection of gas molecules on the vessel wall. We…
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…
We present a generalized form of open boundary conditions, and an associated numerical algorithm, for simulating incompressible flows involving open or outflow boundaries. The generalized form represents a family of open boundary…
This article discusses the modeling of perturbed potential temperature in an atmospheric boundary layer. We adopt a convection-diffusion model with specified initial and boundary conditions that resulted from simplifying the linearized…