Related papers: On a thermodynamic framework for developing bounda…
We consider the existence of bound and ground states for a family of nonlinear elliptic systems in $\mathbb{R}^N$, which involves equations with critical power nonlinearities and Hardy-type singular potentials. The equations are coupled by…
We study the dependence of entropy [per lattice site] of six-vertex model on boundary conditions. We start with lattices of finite size and then proceed to thermodynamic limit. We argue that the six-vertex model with periodic, anti-periodic…
We consider a free boundary problem of compressible-incompressible two-phase flows with phase transitions in general domains of $N$-dimensional Euclidean space (e.g. whole space; half-spaces; bounded domains; exterior domains). The…
Using a microscopic phase-space model of the membrane system, the boundary condition at a membrane is derived. According to the condition, the substance flow across the membrane is proportional to the difference of the substance…
We study the 6-vertex model with fixed boundary conditions. In the thermodynamical limit there is a formation of the limit shape. We collect most of the known results about the analytical properties of the free energy of the model as the…
We show the existence of weak solutions to the fluid-structure interaction problem of a largely deforming viscoelastic bulk solid with a viscous fluid governed by the incompressible Navier-Stokes equations. In contrast to previous works,…
In this paper we propose new boundary conditions at the hot walls with thermionic electron emission for two-temperature thermal arc models. In the derived boundary conditions the walls are assumed to be made from refractory metals and that…
We study the fundamental problem of two gas species in two dimensional velocity space whose molecules collide as hard circles in the presence of a flat boundary and with dependence on only one space dimension. The case of three-dimensional…
We develop a continuum theory to model low energy excitations of a generic four-band time reversal invariant electronic system with boundaries. We propose a variational energy functional for the wavefunctions which allows us derive natural…
Consider a homogenous fluid membrane, or vesicle, described by the Helfrich-Canham energy, quadratic in the mean curvature. When the membrane is axially symmetric, this energy can be viewed as an `action' describing the motion of a…
The classical van der Waals equation, applied to one or two mixing fluids, and the Helmholtz (free) energy function $A$ yield, for fixed temperature $T$, a curve in the plane $\mathbb{R}^2$ (one fluid) or a surface in 3-space $\mathbb{R}^3$…
Thermodynamics and dynamics of a classical two-dimensional system with dipole-like isotropic repulsive interactions are studied systematically using extensive molecular dynamics (MD) simulations supplemented by appropriate theoretical…
Surface-active agents (surfactants) release potential energy as they migrate from one of two adjacent fluids onto their fluid-fluid interface, a process that profoundly impacts the system's energy and entropy householding. The continuum…
Boundary conditions at the interface between the free-flow region and the adjacent porous medium is a key issue for physically consistent modeling and accurate numerical simulation of flow and transport processes in coupled systems due to…
We consider viscous, heat conducting mixtures of molecularly miscible chemical species forming a fluid in which the constituents can undergo chemical reactions. Assuming a common temperature for all components, we derive a closed system of…
Using contact geometry we give a new characterization of a simple but important class of thermodynamical systems which naturally satisfy the first law of thermodynamics (total energy preservation) and the second law (increase of entropy).…
We discuss the transition from a quantum to a classical domain for a model where a separation into environment and system is explicitely not given. Utilizing the coarse graining procedure for free quantum fields we also apply the projection…
We present a new method for studying equilibrium properties of interacting fluids in an arbitrary external field. The fluid is composed of monodisperse spherical particles with hard-core repulsion and additional interactions of arbitrary…
The implementation of boundary conditions is among the most challenging parts of modeling fluid flow through channels and complex media. Here, we show that the existing methods to deal with liquid-wall interactions using multicomponent…
A simple Lennard-Jones fluid confined in a slit nanopore with hard walls is studied on the basis of a multilayer structured model. Each layer is homogeneous and parallel to the walls of the pore. The Helmholtz energy of this system is…