Related papers: On some electroconvection models
We investigate the dynamics of a single deformable self-propelled particle which undergoes a spinning motion in a two-dimensional space. Equations of motion are derived from the symmetry argument for three kinds of variables. One is a…
The observed temperature dependence of electrical conduction in polymer electrolytes is usually fitted with two separated equations: an Arrhenius equation at low temperatures and Vogel-Tamman-Fulcher (VTF) at high temperatures. We report…
The spontaneous convective patterns induced by evaporation of a pure liquid layer are studied experimentally. A volatile liquid layer placed in a cylindrical container is left free to evaporate into air at rest under ambient conditions. The…
We discuss the electromagnetic properties of both a charged free particle, and a charged particle bounded by an harmonic potential, within collapse models. By choosing a particularly simple, yet physically relevant, collapse model, and…
Electrons bound to the surface of liquid helium are an emerging quantum computing platform, offering the potential for highly mobile spin qubits that can be manipulated using CMOS-fabricated devices. Here, as a step toward realizing this…
A moving boundary problem with two free boundaries modeling a two-dimensional idealized MEMS device with pull-in instability is discussed. We use a fixed point argument to show that the model possesses stationary solutions for small source…
We develop a characterization method of electroconvection structures in a planar nematic liquid crystal layer by a study of the electric current transport. Because the applied potential difference has a sinusoidal time dependence, we define…
The free motion of charged colloids within ionic solutions and in the vicinity of charged boundaries, is a phenomenon that occurs in various natural, biological and industrial settings. Here, we develop an electrohydrodynamic lubrication…
In this paper, we describe a mathematical model and a numerical simulation method for the condenser component of a novel two-phase thermosyphon cooling system for power electronics applications. The condenser consists of a set of…
In this paper we study analytically the viscous `sabra' shell model of energy turbulent cascade. We prove the global regularity of solutions and show that the shell model has finitely many asymptotic degrees of freedom, specifically: a…
We propose a very simple one dimensional analytically solvable model for understanding the problem of electronic relaxation of molecules in solution. This problem is modeled by a particle diffusing under the influence of parabolic potential…
A two PDEs-based model is developed for studies of a morphological and compositional evolution of a thermodynamically stable alloy surface in a strong electric field, assuming different and anisotropic diffusional mobilities of the two…
The problem of electromagnetic scattering by cylinders is an old problem that has been studied in many configurations. The present publication provides a theoretical study on a not yet investigated general case: the set of finite metallic…
We analyze a solenoidal motion in a vertically vibrated freely suspended thin smectic film. We demonstrate analytically that transverse oscillations of the film generate two-dimensional vortices in the plane of the film owing to…
Numerical simulations using the Monte Carlo method were performed to study the electrical conductivity of two-dimensional films filled with rodlike particles (rods). The main goal was to investigate the effect of rod alignment on the…
Continuum electrodynamics is an axiomatic formal theory based on the macroscopic Maxwell equations and the constitutive relations. We apply the formal theory to a thermodynamically closed system consisting of an antireflection coated block…
A theoretical model of electromigrative, diffusive and convectivetransport polymer-gel composites is presented. Bulk properties are derived from the standard electrokinetic model with an impenetrable charged sphere embedded in an…
This work studies the effects of a through-flow on two-dimensional electrohydrodynamic (EHD) flows of a dielectric liquid confined between two plane plates, as a model problem to further our understanding of the fluid mechanics in the…
The rapidly growing class of atomically thin and tunable van der Waals materials is intensely investigated both in the context of fundamental science and for new technologies. There is in this connection a widespread need for new ways to…
We study one-dimensional viscoelastic phase transitions modeled by a Ginzburg--Landau energy with a non-convex cubic stress-strain law. Extending the isothermal model, we couple the momentum equation to a heat equation for the temperature…