Related papers: Macroscale boundary conditions for a non-linear he…
We consider a one-dimensional exclusion dynamics in mild contact with boundary reservoirs. In the diffusive scale, the particles' density evolves as the solution of the heat equation with non-linear Robin boundary conditions. For…
In the field of corona discharges, the complex chemical mechanisms inside the ionization region have prompted the development of simplified models to replicate the macroscopic effects of ion generation, thereby reducing the computational…
In topology optimization of compliant mechanisms, the specific placement of boundary conditions strongly affects the resulting material distribution and performance of the design. At the same time, the most effective locations of the loads…
Considering the example of interacting Brownian particles we present a linear response derivation of the boundary condition for the corresponding hydrodynamic description (the diffusion equation). This requires us to identify a non-analytic…
A new two-layer model has been proposed to study microscale heat transfer associated with a developing flow boundary layer. As an example, a cold, microscale film of liquid impinging on an isothermal hot, horizontal surface has been…
We investigate limit models resulting from a dimensional analysis of quite general heterogeneous catalysis models with fast sorption (i.e.\ exchange of mass between the bulk phase and the catalytic surface of a reactor) and fast surface…
Spatially extended stationary and traveling states in the strongly nonlinear regime of convection in layers of binary fluid mixtures heated from below are described by a few-mode-model. It is derived from the proper hydrodynamic balance…
This paper uses linear magnetohydrodynamics to model resonant absorption in coronal plasma with a Cartesian coordinate system. We impose line-tied boundary conditions and tilt the background magnetic field to be oblique to the transition…
We study a nonlocal diffusion operator in a bounded smooth domain prescribing the flux through the boundary. This problem may be seen as a generalization of the usual Neumann problem for the heat equation. First, we prove existence,…
We propose methods that augment existing numerical schemes for the simulation of hyperbolic balance laws with Dirichlet boundary conditions to allow for the simulation of a broad class of differential algebraic conditions. Our approach is…
Thermal models have proven to be an useful and simple tool used to make theoretical predictions and data analysis in relativistic and ultra-relativistic heavy ion collisions. A new version of these models is presented here, incorporating a…
We study the macroscopic profiles of temperature and angular momentum in the stationary state of chains of rotors under a thermo-mechanical forcing applied at the boundaries. These profiles are solutions of a system of diffusive partial…
In this paper we consider ignition-temperature, first-order reaction model of thermo-diffusive combustion that describes dynamics of thick flames arising in a theory of combustion of hydrogen-oxygen and ethylene-oxygen mixtures. These…
Multifluid simulations of plasma sheaths are increasingly used to model a wide variety of problems in plasma physics ranging from global magnetospheric flows around celestial bodies to plasma-wall interactions in thrusters and fusion…
This research explores refined boundary conditions for a traction-free surface in a non-local micropolar half-space, combining non-local and micropolar elasticity effects to study Rayleigh wave propagation in an isotropic, homogeneous…
In this paper, we prove the existence and global boundedness from above for a solution to an integrodifferential model for nonisothermal multi-phase transitions under nonhomogeneous third type boundary conditions. The system couples a…
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…
Many mathematical models for biological phenomena, such as the spread of diseases, are based on reaction-diffusion equations for densities of interacting cell populations. We present a consistent derivation of reaction-diffusion equations…
In this work we briefly present a thermomechanical model that could serve as starting point for industrial applications. We address the non-linearity due to temperature dependence of material properties and heterogeneity due to presence of…
In this paper, we are concerned with a reaction diffusion system arising from a nuclear reactor model in bounded domains with nonlinear boundary conditions. We show the existence of a stationary solution and its ordered uniqueness. It is…