Vibration of double-graphene sheet-system is considered in this study. Graphene sheets are coupled by Pasternak elastic medium. Classic and Mindlin plate theories are utilized for modeling the coupled system. Upper sheet carries a moving mass. Governing equations are derived using energy method and Hamilton’s principle considering surface stress effects and nonlocal parameter.  Using Galerkin m...

An adaptive local mesh re nement algorithm originally developed for unsteady gas dynamics by Berger [12, 14] is extended to incompressible ow in porous media. Multilevel iteration and domain decomposition methods are introduced to accommodate the elliptic/parabolic aspects of the ow equations. The algorithm is applied to a two-phase polymer ooding model consisting of a system of nonlinear hyper...

A new fully-variational approach is studied for elliptic grid generation (EGG). It is based on a general algorithm developed in a companion paper [10] that involves using Newton’s method to linearize an appropriate equivalent first-order system, first-order system least squares (FOSLS) to formulate and discretize the Newton step, and algebraic multigrid (AMG) to solve the resulting matrix equat...

A new parallel discontinuous Galerkin solver, called ArcOn, is developed to describe the intermittent turbulent transport of filamentary blobs in the scrape-off layer (SOL) of fusion plasma. The model is comprised of an elliptic subsystem coupled to two convection-dominated reactiondiffusion-convection equations. Upwinding is used for a class of numerical fluxes developed to accommodate cross p...

Many equations can be expressed as a cubic nonlinear Schrödinger (NLS) equation with additional terms, such as the Davey-Stewartson (DS) system [1]. As it is the case for the NLS equation, the solutions of the DS system are invariant under the pseudo-conformal transformation. For the elliptic NLS, this invariance plays a key role in understanding the blow-up profile of solutions, whereas in the...

We study the classical model for chemotaxis, the so-called Keller-Segel model, which is a drift-diffusion equation for the cell density coupled with an elliptic equation describing the evolution of the chemoattractant. We investigate the case of small cell diffusivity and, in particular, the hyperbolic limit of the system as the diffusion coefficient goes to zero. Considering a model where the ...

Two phase flow problem in a porous medium is governed by a system of nonlinear equations. One is an elliptic equation for the pressure and the other is a parabolic equation for the concentration of one of the fluids. Since the pressure appears in the concentration only through its velocity field, we choose a mixed finite element to approximate the pressure equation and use the standard Galerkin...

This work establishes nonlinear orbital asymptotic stability of scalar radiative shock profiles, namely, traveling wave solutions to the simplified model system of radiating gas [8], consisting of a scalar conservation law coupled with an elliptic equation for the radiation flux. The method is based on the derivation of pointwise Green function bounds and description of the linearized solution ...

We study nonlinear time-asymptotic stability of small–amplitude planar Lax shocks in a model consisting of a system of multi–dimensional conservation laws coupled with an elliptic system. Such a model can be found in context of dynamics of a gas in presence of radiation. Our main result asserts that the standard uniform Evans stability condition implies nonlinear stability. The main analysis is...

We demonstrate that the symmetric elliptic polynomials $E_\lambda(x)$ originally discovered in study of generalized Noumi-Shiraishi functions are eigenfunctions Ruijsenaars-Schneider (eRS) Hamiltonians act on mother function variable $y_i$ (substitute Young-diagram $\lambda$). This means they dual eRS system. At same time, their orthogonal complements Schur scalar product, $P_R(x)$ reduction Ko...