Related papers: Granular media equation with double-well external …
In this paper we are concerned with a initial boundary-value problem for a coupled system of two KdV equations, posed on the positive half line, under the effect of a localized damping term. The model arises when modeling the propagation of…
The stress response of a granular assembly subject to different changes of boundary conditions is studied experimentally in order to define the stress propagation characteristics. These results demonstrate that no simple and single…
The hydrodynamic stationary states of a granular fluid are addressed theoretically when subject to energy injection and a time-independent, but otherwise arbitrary external potential force. When the latter is not too symmetrical in a well…
This paper is concerned with analysis of electromagnetic wave scattering by an obstacle which is embedded in a two-layered lossy medium separated by an unbounded rough surface. Given a dipole point source, the direct problem is to determine…
A model has two main aims: predicting the behavior of a physical system and understanding its nature, that is how it works, at some desired level of abstraction. A promising recent approach to model building consists in deriving a…
Stochastic diffusion equations are crucial for modeling a range of physical phenomena influenced by uncertainties. We introduce the generalized finite difference method for solving these equations. Then, we examine its consistency,…
We study the "stiff pressure limit" of a nonlinear drift-diffusion equation, where the density is constrained to stay below the maximal value one. The challenge lies in the presence of a drift and the consequent lack of monotonicity in…
We develop a framework for stress response in two dimensional granular media, with and without friction, that respects vector force balance at the microscopic level. We introduce local gauge degrees of freedom that determine the response of…
We revisit the method of kinematical endpoints for particle mass determination, applied to the popular SUSY decay chain squark -> neutralino -> slepton -> LSP. We analyze the uniqueness of the solutions for the mass spectrum in terms of the…
We investigate positive steady states of an indefinite superlinear reaction-diffusion equation arising from population dynamics, coupled with a nonlinear boundary condition. Both the equation and the boundary condition depend upon a…
We consider nodal-based Lagrangian interpolations for the finite element approximation of the Maxwell eigenvalue problem. The first approach introduced is a standard Galerkin method on Powell-Sabin meshes, which has recently been shown to…
We derive and analyse well-posed boundary conditions for the linear shallow water wave equation. The analysis is based on the energy method and it identifies the number, location and form of the boundary conditions so that the initial…
When particles/molecules diffuse in systems that contain obstacles, the steady-state regime (during which the mean-square displacement scales linearly with time, $\left< r^2 \right> \sim t$) is preceded by a transient regime. It is common…
An asymptotic investigation of monochromatic electromagnetic fields in a layered periodic medium is carried out under the assumption that the wave frequency is close to the frequency of a stationary point of the dispersion surface. We find…
We prove a priori bounds for solutions of singular stochastic porous media equations with multiplicative noise in their natural $L^1$-based regularity class. We consider the first singular regime, i.e.~noise of space-time regularity…
The existence of solutions to Tolman-Openheimer-Volkoff equation with linear equation of state modeling relativistic cloud of interacting particles is proved for mass parameter below certain threshold. For the intermediate values of mass…
Understanding the structural evolution of granular systems is a long-standing problem. A recently proposed theory for such dynamics in two dimensions predicts that steady states of very dense systems satisfy detailed-balance. We analyse…
We study a kinetic mean-field equation for a system of particles with different sizes, in which particles are allowed to coagulate only if their sizes sum up to a prescribed time-dependent value. We prove well-posedness of this model, study…
The Langevin equation is a common tool to model diffusion at a single-particle level. In non-homogeneous environments, such as aqueous two-phase systems or biological condensates with different diffusion coefficients in different phases,…
The propagation of electromagnetic waves in general media is modeled by the time-dependent Maxwell's partial differential equations (PDEs), coupled with constitutive laws that describe the response of the media. In this work, we focus on…