We study the Landau-Lifshitz system associated with Maxwell equations in a bilayered ferromagnetic body when super-exchange and surface anisotropy interactions are present in the spacer in-between the layers. In the presence of these surface energies, the Neumann boundary condition becomes nonlinear. We prove, in three dimensions, the existence of global weak solutions to the Landau-Lifshitz-Ma...

We consider a gas of bosonic particles confined in box with Neumann boundary conditions. prove Bose-Einstein condensation the Gross-Pitaevskii regime, an optimal bound on condensate depletion. Our lower for ground state energy implies (via bracketing) Bose thermodynamic limit.

Hybrid computational aero-acoustic (CAA) solution schemes rely on the knowledge of a scattering function known as a Green’s function to propagate source fluctuations to the far-field. Presently, these schemes are restricted to relatively simple geometries. We present here a computational method for evaluating Green’s functions within more geometrically complex regions, as a means of extending t...

This paper deals with a finite element method involving Petrov-Galerkin method with quartic B-splines as basis functions and sextic B-splines as weight functions to solve a general sixth order boundary value problem with a particular case of boundary conditions. The basis functions are redefined into a new set of basis functions which vanish on the boundary where the Dirichlet and Neumann type ...