Related papers: Local and Nonlocal Liquid Drop Models
In this paper the generalisation of previous author's formulation of fractional continuum mechanics to the case of anisotropic non-locality is presented. The considerations include the review of competitive formulations available in…
Motivated by Gamow's liquid drop model in the large mass regime, we consider an isoperimetric problem in which the standard perimeter $P(E)$ is replaced by $P(E)-\gamma P_\varepsilon(E)$, with $0<\gamma<1$ and $P_\varepsilon$ a nonlocal…
Consider the quasilinear diffusion problem \[\begin{cases}\mathbf{u}'+\Pi(t,x,\mathbf{u},\Sigma \mathbf{u})\mathbb{A}\mathbf{u}=\mathbf{f}(t,x,\mathbf{u},\Sigma \mathbf{u})&\text{ in }]0,T[\times\Omega,\\\mathbf{u}=\mathbf{0}&\text{ in…
In tiny metallic nanostructures, quantum confinement and nonlocal response change the collective plasmonic behavior with important consequences for e.g. field-enhancement and extinction cross sections. We report on our most recent…
This paper discusses the local linear smoothing to estimate the unknown first and second infinitesimal moments in second-order jump-diffusion model based on Gamma asymmetric kernels. Under the mild conditions, we obtain the weak consistency…
We recall the classical theory of capillarity, describing the shape of a liquid droplet in a container, and present a recent approach which aims at accounting for long-range particle interactions. This nonlocal setting recovers the…
In this paper we will consider the peridynamic equation of motion which is described by a second order in time partial integro-differential equation. This equation has recently received great attention in several fields of Engineering…
We compute support of formal cohomology modules in a serial of non-trivial cases. Applications are given. For example, we compute injective dimension of certain local cohomology modules in terms of dimension of their's support.
We derive the canonical structure and hamiltonian for arbitrary deformations of a higher-dimensional (quantum Hall) droplet of fermions with spin or color on a general phase space manifold. Gauge fields are introduced via a Kaluza-Klein…
A model for the fragmentation of a nucleus is developed. Parallels of the description of this process with other areas are shown which include Feynman's theory of the $\lambda$ transition in liquid Helium, Bose condensation, and Markov…
In this paper, we study the global existence of component-wise nonnegative solutions of the Gray-Scott model in $\Omega \subset \mathbb{R}^n$, $n \ge 1$, with a mixture of both local and nonlocal diffusion operators. We use semigroup theory…
Recently, several claims have been made that certain fundamental problems of distributed computing, including Leader Election and Distributed Consensus, begin to admit feasible and efficient solutions when the model of distributed…
Theoretical models for the liquid-vapor and metal-nonmetal transitions of alkali fluids are investigated. Mean-field models are considered first but shown to be inadequate. An alternate approach is then studied in which each statistical…
A classical model of fluid dynamics is considered which describes the shape evolution of a viscous liquid droplet on a homogeneous substrate. All equilibria are characterized and their stability is analyzed by a geometric reduction…
The dissipative properties of spatially nonlocal conductors are investigated in the context of quantum friction acting on an atom moving above a macroscopic body. The focus is on an extended version of the hydrodynamic model for the bulk…
Fractional diffusion has become a fundamental tool for the modeling of multiscale and heterogeneous phenomena. However, due to its nonlocal nature, its accurate numerical approximation is delicate. We survey our research program on the…
Nonlocality is important in realistic mathematical models of physical and biological systems when local models fail to capture the essential dynamics and interactions that occur over a range of distances. This review illustrates different…
This note is devoted to some nonlocal, nonlinear elliptic problems with an emphasis on the computation of the solution of such problems, reducing it in particular to a fixed point argument in R. Errors estimates and numerical experiments…
We present a variant of the recently developed quantum corrected model (QCM) for plasmonic nanoparticles [Nature Commun. 3, 825 (2012)] using non-local boundary conditions. The QCM accounts for electron tunneling in narrow gap regions of…
In this paper, we study some qualitative properties for an evolution problem that combines local and nonlocal diffusion operators acting in two different subdomains and, coupled in such a way that, the resulting evolution problem is the…