相关论文: Asymptotics for Steady State Voltage Potentials in…

In quantum mechanics, asymptotic degeneracy is often considered in the context of a particle in a symmetric double-well potential, and is the phenomenon whereby pairs of energy levels come together to form doubly degenerate levels in…

We introduce a mechanism that can both hold and amplify electromagnetic waves by rapidly changing the permittivity of the medium during the wave travel from a positive to a dispersionless (i.e. non-Foster) negative value and then back…

We present a consistent theoretical approach for calculating effective nonlinear susceptibilities of metamaterials taking into account both frequency and spatial dispersion. Employing the discrete dipole model, we demonstrate that effects…

We show using computer simulations and mean field theory that a system of particles in two dimensions, when confined laterally by a pair of parallel hard walls within a quasi one dimensional channel, possesses several anomalous structural…

In this work, we consider the electromechanical density pulse as a coupled solitary waves represented by a longitudinal compression wave and an out-of-plane transversal wave (i.e., perpendicular to the membrane surface). We analyzed using,…

An ideal conductor electrode in contact with a semi-infinite two-dimensional two-component plasma in an external potential is considered. The model is mapped onto an integrable sine-Gordon theory with Dirichlet boundary conditions. The…

The purpose of this paper is to present the derivation and mathematical analysis of a new asymptotic model that describes the evolution of medium amplitude internal waves propagating between a flat rigid-lid and a highly variable…

We consider the Dirichlet Laplacian $A_q=-\Delta+q$ in a bounded domain $\Omega \subset \mathbb{R}^d$, $d \ge 3$, with real-valued perturbation $q \in L^{\max(2 , 3 d / 5)}(\Omega)$. We examine the stability issue in the inverse problem of…

Based on first-principles calculations, we systematically study the electronic, dielectric, and plasmonic properties of two-dimensional (2D) electride materials X$_2$N (X=Ca, Sr). We show that both Ca$_2$N and Sr$_2$N are stable down to…

We investigate a one-dimensional quantum system with a self-similar arrangement of delta-function potential barriers, exhibiting discrete scale invariance. The singular potential induces kinematically enforced symmetry breaking at $x=0$,…

In this paper, we study equations with nonlinearity in the form of a double-well potential, randomised by a velocity-switching (telegraph) stochastic process. If the speed parameters of the randomisation are small, then this dynamics has…

Imposing either Dirichlet or Neumann boundary conditions on the boundary of a smooth bounded domain $\Omega$, we study the perturbation incurred by the voltage potential when the conductivity is modified in a set of small measure. We…

In the context of elasticity theory, rigidity theorems allow to derive global properties of a deformation from local ones. This paper presents a new asymptotic version of rigidity, applicable to elastic bodies with sufficiently stiff…

In practice, physical membranes are exposed to a certain amount of external strain (tension or compression), due to the environment where they are placed. As a result, the behavior of the phonon modes of the membrane is modified. We show…

Hyperuniform point patterns are characterized by vanishing infinite wavelength density fluctuations and encompass all crystal structures, certain quasi-periodic systems, and special disordered point patterns. This article generalizes the…

From the perspective of physical properties, the cell membrane is an exotic two-dimensional material that has a dual nature: it exhibits characteristics of fluids, i.e., lipid molecules show lateral diffusion, while also demonstrating…

We couple the Leaky Membrane Model, which describes the diffusion and electromigration of ions in a homogenized porous medium of fixed background charge, with Butler-Volmer reaction kinetics for flat electrodes separated by such a medium in…

We present some non-topological static wall solutions in two-Higgs extensions of the standard model. They are classically stable in a large region of parameter space, compatible with perturbative unitarity and with present phenomenological…

In this article we extend B. Simon's construction and results for leading order eigenvalue asymptotics to $n$-dimensional Schr\"odinger operators with non-confining potentials given by: $H^\alpha_n=-\Delta +\prod\limits_{i=1}^n…

It is known that multidimensional complex potentials obeying $\mathcal{PT}$-symmetry may possess all real spectra and continuous families of solitons. Recently it was shown that for multi-dimensional systems these features can persist when…