Related papers: A Two-dimensional eddy current model using thin in…
We consider the flow of a generalized Newtonian fluid through a thin porous medium of height $h_\varepsilon$ perforated with $\varepsilon$-periodically distributed solid cylinders of very small diameter $\varepsilon\delta_\varepsilon$,…
This paper is concerned with Darcy's law for an incompressible viscous fluid flowing in a porous medium. We establish the sharp $O(\sqrt{\e})$ convergence rate in a periodically perforated and bounded domain in $R^d$ for $d\ge 2$, where…
The diffusion of uni-directional magnetic fields by two dimensional turbulent flows in a weakly ionized gas is studied. The fields here are orthogonal to the plane of fluid motion. This simple model arises in the context of the decay of the…
Diffuse domain methods (DDMs) have gained significant attention for solving partial differential equations (PDEs) on complex geometries. These methods approximate the domain by replacing sharp boundaries with a diffuse layer of thickness…
In this study we investigate shallow turbidity density currents and underflows from mechanical point of view. We propose a simple hyperbolic model for such flows. On one hand, our model is based on very basic conservation principles. On the…
In this paper, we consider steady Euler flows in two-dimensional bounded annuli, as well as in exterior circular domains, in punctured disks and in the punctured plane. We always assume rigid wall boundary conditions. We prove that, if the…
A continuous sequence of infinitesimal unitary transformations is used to diagonalize the quantum sine-Gordon model for \beta^2\in(2\pi,\infty). This approach can be understood as an extension of perturbative scaling theory since it links…
Present models of the superconducting-to-normal transition in transition-edge sensors (TESs) do not describe the current distribution within a biased TES. This distribution is complicated by normal-metal features that are integral to TES…
By using topological current theory, we study the inner topological structure of disclinations during the melting of two-dimensional systems. From two-dimensional elasticity theory, it is found topological currents for topological defects…
Two-parametric eddy viscosity (TPEV) and other spectral characteristics of two-dimensional (2D) turbulence in the energy transfer sub-range are calculated from direct numerical simulation (DNS) with 512$^2$ resolution. The DNS-based TPEV is…
The subject of this paper is the rigorous derivation of lower dimensional models for a nonlinearly elastic thin-walled beam whose cross-section is given by a thin tubular neighbourhood of a smooth curve. Denoting by h and {\delta}_h,…
The infuence of the conduction-electron spin magnetization density, induced in a two-dimensional electron layer by a microwave electromagnetic field, on the rejection and transmission of the field is considered. Because of the induced…
We consider the inverse conductivity problem in a strictly convex domain whose boundary is not known. Usually the numerical reconstruction from the measured current and voltage data is done assuming the domain has a known fixed geometry.…
Using Monte Carlo simulation, we studied the electrical conductance of two-dimensional films. The films consisted of a poorly conductive host matrix and highly conductive rodlike fillers (rods). The rods were of various lengths, obeying a…
A new model is proposed for low $Rm$ MHD flows which remain turbulent even in the presence of a magnetic field. These flows minimize the Joule dissipation because of their tendency to become two-dimensional and, therefore to suppress all…
We analyse a numerical method for the coupled system of the eddy current equations in $\mathbb{R}^3$ with the Landau-Lifshitz-Gilbert equation in a bounded domain. The unbounded domain is discretised by means of…
The flow of an electrically conducting fluid in a thin disc under the action of an azimuthal Lorentz force is studied experimentally. At small forcing, the Lorentz force is balanced by either viscosity or inertia, yielding quasi-Keplerian…
In this paper we derive consistent shallow water equations for thin films of power law fluids down an incline. These models account for the streamwise diffusion of momentum which is important to describe accurately the full dynamic of the…
The geometric, kinetic, and total inductances and the attenuation constant are theoretically analyzed for a thin-film superconducting coplanar waveguide (CPW) resonator consisting of a current-carrying central conductor, adjacent slots, and…
A domain decomposition method is proposed based on carefully chosen impedance transmission operators for a hybrid formulation of the eddy current problem. Preliminary analysis and numerical results are provided in the spherical case showing…