Heiko Gimperlein

Ultracold Atoms in Optical Lattices with Random On-Site Interactions

We consider the physics of lattice bosons affected by disordered on-site interparticle interactions. Characteristic qualitative changes in the zero-temperature phase diagram are observed when compared to the case of randomness in the chemical potential. The Mott-insulating regions shrink and eventually vanish for any finite disorder strength beyond a sufficiently large filling factor. Furthermore, at low values of the chemical potential both the superfluid and Mott insulator are stable towards formation of a Bose glass leading to a possibly nontrivial tricritical point. We discuss feasible experimental realizations of our scenario in the context of ultracold atoms on optical lattices.

A priori error estimates for a time‐dependent boundary element method for the acoustic wave equation in a half‐space

We investigate a time-domain Galerkin boundary element method for the wave equation outside a Lipschitz obstacle in an absorbing half-space. A priori estimates are presented for both closed surfaces and screens, and we discuss the relevant properties of anisotropic Sobolev spaces and the boundary integral operators between them.

Adaptive time-domain boundary element methods and engineering applications

Parts of this work were funded by BMWi under the project SPERoN 2020, part II, Leiser StraB enverkehr, grant number 19 U 10016 F. H. G. acknowledges support by ERC Advanced Grant HARG 268105.

Adaptive FE–BE coupling for strongly nonlinear transmission problems with Coulomb friction

We analyze an adaptive finite element/boundary element procedure for scalar elastoplastic interface problems involving friction, where a nonlinear uniformly monotone operator such as the p-Laplacian is coupled to the linear Laplace equation on the exterior domain. The problem is reduced to a boundary/domain variational inequality, a discretized saddle point formulation of which is then solved using the Uzawa algorithm and adaptive mesh refinements based on a gradient recovery scheme. The Galerkin approximations are shown to converge to the unique solution of the variational problem in a suitable product of Lp- and L2-Sobolev spaces.

Stabilized mixed hp-BEM for frictional contact problems in linear elasticity

We analyze stabilized mixed hp-boundary element methods for frictional contact problems for the Lamé equation. The stabilization technique circumvents the discrete inf-sup condition for the mixed problem and thus allows us to use the same mesh and polynomial degree for the primal and dual variables. We prove a priori convergence rates in the case of Tresca friction, using Gauss-Legendre-Lagrange polynomials as test and trial functions for the Lagrange multiplier. Additionally, a residual based a posteriori error estimate for a more general class of discretizations is derived. It in particular applies to discretizations based on Bernstein polynomials for the discrete Lagrange multiplier, which we also analyze. The discretization and the a posteriori error estimate are extended to the case of Coulomb friction. Several numerical experiments underline our theoretical results, demonstrate the behavior of the method and its insensitivity to the scaling and perturbations of the stabilization term.

Analytic representation theory of Lie groups: general theory and analytic globalizations of Harish-Chandra modules

In this article a general framework for studying analytic representations of a real Lie group G is introduced. Fundamental topological properties of the representations are analyzed. A notion of temperedness for analytic representations is introduced, which indicates the existence of an action of a certain natural algebra A(G) of analytic functions of rapid decay. For reductive groups every Harish-Chandra module V is shown to admit a unique tempered analytic globalization, which is generated by V and A(G) and which embeds as the space of analytic vectors in all Banach globalizations of V.

Boundary elements with mesh refinements for the wave equation

The solution of the wave equation in a polyhedral domain in

A Deterministic Optimal Design Problem for the Heat Equation

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