Differential cross section for Aharonov--Bohm effect with non standard boundary conditions

A basic analysis is provided for the differential cross section characterizing Aharonov--Bohm effect with non standard (non regular) boundary conditions imposed on a wave function at the potential barrier. If compared with the standard case two new features can occur: a violation of rotational symmetry and a more significant backward scattering.Comment: to appear in Europhys. Let

Stabilised hybrid discontinuous Galerkin methods for the Stokes problem with non-standard boundary conditions

In several studies it has been observed that, when using stabilised $\mathbb{P}_k^{}\times\mathbb{P}_k^{}$ elements for both velocity and pressure, the error for the pressure is smaller, or even of a higher order in some cases, than the one obtained when using inf-sup stable $\mathbb{P}_k^{}\times\mathbb{P}_{k-1}^{}$ (although no formal proof of either of these facts has been given). This increase in polynomial order requires the introduction of stabilising terms, since the finite element pairs used do not stability the inf-sup condition. With this motivation, we apply the stabilisation approach to the hybrid discontinuous Galerkin discretisation for the Stokes problem with non-standard boundary conditions

Spectral discretizations of the Darcy's equations with non standard boundary conditions

This paper is devoted to the approximation of anonstandard Darcy problem, which modelizes the flow in porous media, byspectral methods: the pressure is assigned on a part of the boundary.We propose two variational formulations, as well as three spectraldiscretizations. The second discretization improves the approximation of thedivergence-free condition, but the error estimate on the pressure is notoptimal, while the third one leads to optimal error estimate with adivergence-free discrete solution, which is important for someapplications. Next, their numerical analysis is performed in detailand we present some numerical experiments which confirm the interestof the third discretization

Strategies and obstacles in constructing realistic higher-dimensional models

We discuss several aspects of higher dimensional models that contain bulk gauge and fermion fields only. In particular we argue that non-standard boundary conditions involving charge-conjugate fermion fields offer attractive model building possibilities. We also discuss a no-go theorem for 5-dimensional models which severely limits their phenomenological relevance.Comment: 4 pages, 1 fugure; contribution to the SUSY06 proceeding

Stokes Equations and Elliptic Systems With Non Standard Boundary Conditions

8 pagesInternational audienceIn a three dimensional bounded possibly multiply-connected domain of class C 1,1 , we consider the stationary Stokes equations with nonstandard boundary conditions of the form u * n = g and curl u × n = h × n or u × n = g × n and π = π0 on the boundary Γ. We prove the existence and uniqueness of weak, strong and very weak solutions corresponding to each boundary condition in Lp theory. Our proofs are based on obtaining Inf −Sup conditions that play a fundamental role. And finally, we give two Helmholtz decompositions that consist of two kinds of boundary conditions such as u * n and u × n on Γ

Characterization of ellipsoids through an overdetermined boundary value problem of Monge-Ampère type

The study of the optimal constant in an Hessian-type Sobolev inequality leads to a fully nonlinear boundary value problem, overdetermined with non-standard boundary conditions. We show that all the solutions have ellipsoidal symmetry. In the proof we use the maximum principle applied to a suitable auxiliary function in conjunction with an entropy estimate from affine curvature flow