Related papers: Macroscale boundary conditions for a non-linear he…
Modeling distributions that depend on external control parameters is a common scenario in diverse applications like molecular simulations, where system properties like temperature affect molecular configurations. Despite the relevance of…
The thermodynamic approach to non-equilibrium dynamics describes the state of macroscopic systems by means of a collection of intensities or intensive variables. The latter are by definition the differentials of the entropy with respect to…
In this paper, we introduce a model for a buoyancy-driven, air-to-air heat exchanger. This model, derived from first principles, features a conservative boundary condition at inflow based on the compressible Bernoulli equation, and a…
We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…
Nanostructures with one-dimensional periodicity, such as multilayered structures, are currently in the focus of active research in the context of hyperbolic metamaterials and photonic topological structures. An efficient way to describe the…
In this paper, a new type of comparison theorem is presented for some initial-boundary value problems of second order nonlinear parabolic systems with nonlinear boundary conditions. This comparison theorem has an advantage over the…
Describing particle transport at the macroscopic or mesoscopic level in non-ideal environments poses fundamental theoretical challenges in domains ranging from inter and intra-cellular transport in biology to diffusion in porous media. Yet,…
Mathematical models of biological populations commonly use discrete structure classes to capture trait variation among individuals (e.g. age, size, phenotype, intracellular state). Upscaling these discrete models into continuum descriptions…
In this paper, we construct approximations of the microscopic solution of a nonlinear reaction--diffusion equation in a domain consisting of two bulk-domains, which are separated by a thin layer with a periodic heterogeneous structure. The…
We develop a three-timescale framework for modelling climate change and introduce a space-heterogeneous one-dimensional energy balance model. This model, addressing temperature fluctuations from rising carbon dioxide levels and the…
We derive boundary conditions and estimates based on the energy and entropy analysis of systems of the nonlinear shallow water equations in two spatial dimensions. It is shown that the energy method provides more details, but is fully…
We study systems containing electrons and nuclei. Based on the fact that the thermodynamic limit exists for systems with Dirichlet boundary conditions, we prove that the same limit is obtained if one imposes other boundary conditions such…
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…
Max-stable processes are natural models for spatial extremes because they provide suitable asymptotic approximations to the distribution of maxima of random fields. In the recent past, several parametric families of stationary max-stable…
A main challenge in numerical simulations of moving contact line problems is that the adherence, or no-slip boundary condition leads to a non-integrable stress singularity at the contact line. In this report we perform the first steps in…
Outer boundary conditions for strongly and symmetric hyperbolic formulations of 3D Einstein's field equations with a live gauge condition are discussed. The boundary conditions have the property that they ensure constraint propagation and…
Many physical systems are formulated on domains which are relatively large in some directions but relatively thin in other directions. We expect such systems to have emergent structures that vary slowly over the large dimensions. Common…
In previous work, we derived new energy and entropy stable open boundary conditions and implementation procedures for linear and nonlinear initial boundary value problems. These boundary procedures results in estimates bounded by external…
We present a new method for the numerical implementation of generating boundary conditions for a one dimensional Boussinesq system. This method is based on a reformulation of the equations and a resolution of the dispersive boundary layer…
Motivated by stochastic convection-diffusion problems we derive a posteriori error estimates for non-stationary non-linear convection-diffusion equations acting as a deterministic paradigm. The problem considered here neither fits into the…