Related papers: Absorbing boundaries in the conserved Manna model
In the present work the problem of distinguishing between essential and spurious (i.e., absorbable) constants contained in a metric tensor field in a Riemannian geometry is considered. The contribution of the study is the presentation of a…
The study of the limiting absorption principle for elliptic equations with periodic structures is very challenging when the dimension is greater than 1. The fundamental reason for the dimensional barrier is the mismatch between directional…
Marginally outer trapped surfaces (also referred to as apparent horizons) that are stable in 3-dimensional initial data sets obeying the dominant energy condition strictly are known to satisfy an area bound. The main purpose of this note is…
We consider a diffusion process on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ an energetic variational approach with both surface divergence and transport theorems to derive…
We prove an infrared bound for the transverse field Ising model. This bound is stronger than the previously known infrared bound for the model, and allows us to investigate mean-field behaviour. As an application we show that the critical…
We obtain sharp weighted estimates for solutions of the equation $\partial$ u = f in a lineally convex domain of finite type. Precisely we obtain estimates in the spaces L p ($\Omega$,$\delta$ $\gamma$), $\delta$ being the distance to the…
We introduce some notions of conditional mean dimension for a factor map between two topological dynamical systems and discuss their properties. With the help of these notions, we obtain an inequality to estimate the mean dimension of an…
We rederive the finite size scaling formula for the apparent critical temperature by using Mean Field Theory for the Ising Model above the upper critical dimension. We have also performed numerical simulations in five dimensions and our…
A conjecture of Manin predicts the asymptotic distribution of rational points of bounded height on Fano varieties. In this paper we use conic bundles to obtain correct lower bounds or a wide class of surfaces over number fields for which…
The boundary layer of a finite domain [a, b] covers mesoscopic lateral neighbourhoods, inside [a, b], of the endpoints a and b. The correct diagnostic of the integrand behaviour at a and b, based on its sampling inside the boundary layer,…
We demonstrate that absorbing phase transitions in one dimension may be induced by the dynamics of a single site. As an example we consider a one-dimensional model of diffusing particles, where a single site at the boundary evolves…
Absorbing-boundary-condition method and its applications to nuclear responses and breakup reactions are reported. The method facilitates calculations of the continuum states in the coordinate space of many degrees of freedom. Properties of…
Theoretical treatments of strong-field physics have long relied on the numerical solution of the time-dependent Schr\"odinger equation. The most effective such treatments utilize a discrete spatial representation---a grid. Since most…
The global existence and boundedness of solutions to volume-surface reaction diffusion systems with a mass control condition are investigated. Such systems arise typically in e.g. cell biology, ecology or fluid mechanics, when some…
We investigate the incompressible and compressible heat conducting boundary layer with applying the two-dimensional self-similar Ansatz. Analytic solutions can be found for the incompressible case which can be expressed with special…
We present the model of a diffusion-absorption process in a system which consists of two media separated by a thin partially permeable membrane. The kind of diffusion as well as the parameters of the process may be different in both media.…
Different approaches are presented to investigate diffusion from a point source in a slab delimited by two absorbing boundaries consisting of parallel infinite planes. These approaches enable to consider the effect of absorption at the…
The focus of this work is on the construction of a family of nonlinear absorbing boundary conditions for the Westervelt equation in one and two space dimensions. The principal ingredient used in the design of such conditions is…
We give a survey of computation of the conformal capacity of planar condensers, generalized capacity, and logarithmic capacity with emphasis on our recent work 2020-2025. We also discuss some applications of our method based on the boundary…
In this paper we propose and validate a multiscale model for the description of particle diffusion in presence of trapping boundaries. We start from a drift-diffusion equation in which the drift term describes the effect of bubble traps,…