Related papers: Rigorous Asymptotics For The Elecric Field In TM M…
Diffuse domain methods (DDMs) have garnered significant attention for approximating solutions to partial differential equations on complex geometries. These methods implicitly represent the geometry by replacing the sharp boundary interface…
Electromagnetic properties of periodic two-dimensional sub-wavelength structures consisting of closely-packed inclusions of materials with negative dielectric permittivity $\epsilon$ in a dielectric host with positive $\epsilon_h$ can be…
This paper studies the instability of two-dimensional magnetohydrodynamic (MHD) systems on a sphere using analytical methods. The underlying flow consists of a zonal differential rotation and a toroidal magnetic field is present. Semicircle…
The exchange-correlation potential experienced by an electron in the free space adjacent to a solid surface or to a low-dimensional system defines the fundamental image states and is generally important in surface- and nano-science. Here we…
A 2D nonlinear model for the electrical potential in the edge plasma in a tokamak generates a stiff problem due to the low resistivity in the direction parallel to the magnetic field lines. An asymptotic-preserving method based on a…
We study interacting electrons in a periodic potential and a uniform magnetic field ${\bf B}$ taking the spin-orbit interaction into account. We first establish a perturbation expansion for those electrons with respect to the Bloch states…
We consider quasi-two-dimensional gas of electrons in a typical Si-MOSFET, assuming repulsive contact interaction between electrons. Magnetisation and susceptibility are evaluated within the mean-field approach. Finite thickness of the…
In this paper we present a mathematical study of particle diffusion inside and outside a spherical biological cell that has been exposed on one side to a propagating planar diffusive front. The media inside and outside the spherical cell…
We consider asymptotic behavior of the following fourth order equation \[ \Delta^2 u= \rho \frac{e^{u}}{\int_\Om e^{u} dx} {in} \Om, u= \partial_\nu u=0 {on} \partial \Omega \] where $\Om$ is a smooth oriented bounded domain in $\R^4$.…
The electrical double layer at infinite flat solid surface was discussed with respect to the triple layer model. Charge density at the outer Helmholtz plane is assumed to be zero usually. However, the assumption causes the position of the…
The objective of our paper is to investigate fractional elliptic equations of the form $(-\Delta)^s u=\frac{\lambda }{(a-u)^2}$ within a bounded domain $\Omega$, subject to zero Dirichlet boundary conditions. Here, $s\in(0,1)$, $\lambda>0$,…
The $T^2$-scaling of resistivity with temperature is often viewed as a classic hallmark of a Fermi-liquid (FL) behavior in metals. However, if umklapp scattering is suppressed, this scaling is not universally guaranteed to occur. In this…
A multispecies, collisionless plasma is modeled by the Vlasov-Poisson system. Assuming that the electric field decays with sufficient rapidity as $t \to\infty$, we show that the velocity characteristics and spatial averages of the particle…
Transmembrane ion flow through channel proteins undergoing density fluctuations may cause lateral gradients of the electrical potential across the membrane giving rise to electrophoresis of charged channels. A model for the dynamics of the…
Electrons that are confined to a single Landau level in a two dimensional electron gas realize the effects of strong electron-electron repulsion in its purest form. The kinetic energy of individual electrons is completely quenched and all…
We study the infimum of the Ginzburg-Landau functional in the case of a vanishing external magnetic field in a two dimensional simply connected domain. We obtain an energy asymptotics which is valid when the Ginzburg-Landau parameter is…
We set up and study the hydrodynamic theory for inversion-symmetric active fluid and tethered membranes. For some choices of the activity parameter, such membranes are stable and described by linear hydrodynamic equations, which are exact…
We analyze open membranes immersed in a magnetic three-form field-strength $C$. While cylindrical membranes in the absence of $C$ behave like tensionless strings, when the $C$ flux is present the strings polarize into thin membrane ribbons,…
An asymptotic analysis is performed for thin anisotropic elastic plate clamped along its lateral side and also supported at a small area $\theta_{h}$ of one base with diameter of the same order as the plate thickness $h\ll1.$ A…
We discuss computational analysis of phononic thermal conduction in the suspended membrane geometry, in the experimentally commonly appearing case where heat can flow out radially in two dimensions from a central source. As we are mostly…