Related papers: A free boundary problem modeling electrostatic MEM…
The existence of weak solutions to the obstacle problem for a nonlocal semilinear fourth-order parabolic equation is shown, using its underlying gradient flow structure. The model governs the dynamics of a microelectromechanical system with…
The goal of this work is to study the electromagnetic scattering problem of time-domain Maxwell's equations in an unbounded structure. An exact transparent boundary condition is developed to reformulate the scattering problem into an…
Membranes are an important subject of study in physical chemistry and biology. They can be considered as material surfaces with a surface energy depending on the curvature tensor. Usually, mathematical models developed in the literature…
We study the electro-hydrodynamics of the Debye screening layer that arises in an aqueous binary solution near a planar insulating wall when applying a spatially modulated AC-voltage. Combining this with first order perturbation theory we…
The aim of this paper is to deal with multi-physics simulation of micro-electro-mechanical systems (MEMS) based on an advanced numerical methodology. MEMS are very small devices in which electric as well as mechanical and fluid phenomena…
Random lateral translocation of lipids and proteins is a universal process on membrane surfaces. Local aggregation or organization of lipids and proteins can be induced when this lateral random diffusion is mediated by the electrostatic…
We consider the electrostatic interaction between two rigid membranes, with different surface charge densities of opposite sign, across an aqueous solution without added salt. Exact solutions to the nonlinear Poisson-Boltzmann equation are…
In this paper, we present a cell motility model that takes into account the cell membrane effect. The model introduced is an incompressible Darcy free boundary problem. This model involves a nonlinear term in the boundary condition to model…
A dielectric elastomer whose edges are held fixed will buckle, given sufficient applied voltage, resulting in a nontrivial out-of-plane deformation. We study this situation numerically using a nonlinear elastic model which decouples two of…
This paper investigates the asymptotic behavior of the Helmholtz free energy of mixtures at small compressibility. We start from a general representation for the local free energy that is valid in stable subregions of the phase diagram. On…
We consider a semi-infinite spatially dispersive dielectric with unequal transverse and longitudinal susceptibilities. The effect of the boundary is characterized by arbitrary reflection coefficients for polarization waves in the material…
In this work, we consider a transmission problem describing a thermoelastic plate surrounding a membrane without any mechanical damping. The main results consist of the lack of exponential stability for this problem and the polynomial…
Although free electron models have been established in order to capture the essential physics of interfacial and bulk properties in metals, some issues still remain regarding the application of free electron models to thin metal films. One…
It is shown that conformal symmetry exists in force-free electrodynamics (FFE) in Minkowski spacetime, a foundational framework for describing magnetospheres around astronomical objects. In force-free magnetospheres, charges are constrained…
We investigate effects of quantum (zero-temperature) long wavelength fluctuations of free standing crystalline membranes, that are two-dimensional objects embedded into three-dimensional space. The fluctuations produce logarithmic…
We study the instability of a thin membrane (of zero bending rigidity) to out-of-plane deflections, when the membrane is immersed in an inviscid fluid flow and sheds a trailing vortex-sheet wake. We solve the nonlinear eigenvalue problem…
We introduce the concept of stationary metastable states (SMS's) in the presence of another more stable state. The stationary nature allows us to study SMS's by using a restricted partition function formalism as advocated by Penrose and…
The aim of this paper is to study a free boundary problem for a uniformly elliptic fully non-linear operator. Under certain assumptions we show that free and fixed boundaries meet tangentially at contact points.
In this paper, we perform a numerical analysis in frequency domain for various electromagnetic problems based on discrete exterior calculus (DEC) with an arbitrary 2-D triangular or 3-D tetrahedral mesh. We formulate the governing equations…
We provide a theoretical framework to describe the dynamics of a free-electron beam interacting with quantized bound systems in arbitrary electromagnetic environments. This expands the quantum optics toolbox to incorporate free-electron…