We consider the electromagnetic detection of hidden moving or oscillating conductive targets. The resulting mathematical problem involves computation of a Doppler shift for an electromagnetic wave reflecting from a moving interface. This entails solving Maxwell’s equations on a domain changing in time. We employ the method of mappings to transform the problem to one of computing solutions of a ...

The aim of this paper is to show the global existence of weak solutions for a moving boundary problem arising in the non-isothermal crystallization of polymers. The main features of our works are (i) the moving interface is shown to be of co-dimension one; (ii)finite Hölder continuous propagation speed yields an intrinsic estimate of finite co-dimension one Hausdorff measure of the moving inter...

Finite element approximations of positive weak solutions to a onephase unidimensional moving-boundary system with kinetic condition describing the penetration of a sharp-reaction interface in concrete are considered. A priori and a posteriori error estimates for the semi-discrete fields of active concentrations and for the position of the moving interface are obtained. The important feature of ...

We present a modified finite element method that is able to approximate interface problems with high accuracy. We consider interface problems, where the solution is continuous, its derivatives however may be discontinuous across interface curves within the domain. The proposed discretization is based on a local modification of the finite element basis which corresponds to a fitted finite elemen...

We use Brownian Dynamics (BD) simulations and continuum models to study the microstructures and mechanics in the colloidal film drying process. Colloidal suspensions are compressed between a planar moving interface and a stationary substrate. In the BD simulations, we develop a new Energy Minimization Potential-Free (EMPF) algorithm to enforce the hard-sphere potential in confined systems and t...

A novel algorithm for solving the classic Stefan problem is proposed in the paper. Instead of front tracking, we preset the moving interface locations and use these location coordinates as the grid points to find out the arrival time of moving interface respectively. Through this approach, the difficulty in mesh generation can be avoided completely. The simulation shows the numerical result is ...

Recent research developments in the area of spacetime metamaterial structures and systems have raised new questions as to how physics fundamental phenomena is altered presence modulation. In this context, we present a generalized comparative description phenomenon total internal reflection (TIR) at different dynamic interfaces. Such interfaces include, beyond classical corresponding boundaries ...

Phase-field models provide a way to model fluid interfaces as having finite thickness; the interface between two immiscible fluids is treated as a thin mixing layer across which physical properties vary steeply but continuously. One of the main challenges of this approach is in resolving the sharp gradients at the interface. In this paper, moving finite-element methods are used to simulate inte...

<p style='text-indent:20px;'>In this article, we develop a new mixed immersed finite element discretization for two-dimensional unsteady Stokes interface problems with unfitted meshes. The proposed IFE spaces use conforming linear elements one velocity component and non-conforming the other component. pressure is approximated by piecewise constant. Unisolvency, among fundamental propertie...

A diffuse interface method is used to simulate two-phase flows with moving contact lines in 3D. The specific numerical issue is the validation of the method regarding the dynamics of moving contact lines in 3D. In particular, we aim to use the method to extend previous (2D and/or creeping-flow) work on sheardriven motion of a droplet on a wall to the full 3D problem, accounting for inertial eff...