On the Γ\Gamma-limit for a non-uniformly bounded sequence of two phase metric functionals

In this study we consider the $\Gamma$-limit of a highly oscillatory Riemannian metric length functional as its period tends to 0. The metric coefficient takes values in either $\{1,\infty\}$ or $\{1,\beta \varepsilon^{-p}\}$ where $\beta,\varepsilon > 0$ and $p \in (0,\infty)$. We find that for a large class of metrics, in particular those metrics whose surface of discontinuity forms a differentiable manifold, the $\Gamma$-limit exists, as in the uniformly bounded case. However, when one attempts to determine the $\Gamma$-limit for the corresponding boundary value problem, the existence of the $\Gamma$-limit depends on the value of $p$. Specifically, we show that the power $p=1$ is critical in that the $\Gamma$-limit exists for $p < 1$, whereas it ceases to exist for $p \geq 1$. The results here have applications in both nonlinear optics and the effective description of a Hamiltonian particle in a discontinuous potential.Comment: 31 pages, 1 figure. Submitte

50 Jahre GWB: Ein Grund zum Feiern?

Vor 50 Jahren, am 3. Juli 1957, wurde das Gesetz gegen Wettbewerbsbeschränkungen vom Bundestag verabschiedet. Wie wurde das Gesetz zu Beginn beurteilt und welche Wandlungen hat es bis heute erfahren? Wie sehen die Beziehungen zur europäischen Wettbewerbspolitik aus? Welche Aufgaben müssen noch bewältigt werden? --

Using Ambients to Control Resources (long version)

Current software and hardware systems, being parallel and reconfigurable, raise new safety and reliability problems, and the resolution of these problems requires new methods. Numerous proposals attempt at reducing the threat of bugs and preventing several kinds of attacks. In this paper, we develop an extension of the calculus of Mobile Ambients, named Controlled Ambients, that is suited for expressing such issues, specifically Denial of Service attacks. We present a type system for Controlled Ambients, which makes static resource control possible in our setting

Super-localised wave function approximation of Bose-Einstein condensates

This paper presents a novel spatial discretisation method for the reliable and efficient simulation of Bose-Einstein condensates modelled by the Gross-Pitaevskii equation and the corresponding nonlinear eigenvector problem. The method combines the high-accuracy properties of numerical homogenisation methods with a novel super-localisation approach for the calculation of the basis functions. A rigorous numerical analysis demonstrates superconvergence of the approach compared to classical polynomial and multiscale finite element methods, even in low regularity regimes. Numerical tests reveal the method's competitiveness with spectral methods, particularly in capturing critical physical effects in extreme conditions, such as vortex lattice formation in fast-rotating potential traps. The method's potential is further highlighted through a dynamic simulation of a phase transition from Mott insulator to Bose-Einstein condensate, emphasising its capability for reliable exploration of physical phenomena

Mechanical losses in low loss materials studied by Cryogenic Resonant Acoustic spectroscopy of bulk materials (CRA spectroscopy)

Mechanical losses of crystalline silicon and calcium fluoride have been analyzed in the temperature range from 5 to 300 K by our novel mechanical spectroscopy method, cryogenic resonant acoustic spectroscopy of bulk materials (CRA spectrocopy). The focus lies on the interpretation of the measured data according to phonon-phonon interactions and defect induced losses in consideration of the excited mode shape.Comment: 4 pages, 4 figures, proceedings of the PHONONS 2007, submitted to Journal of Physics: Conference Serie