An embedding domain approach for a class of 2-d shape optimization problems: mathematical analysis

This contribution combines a shape optimization approach to free boundary value problems of Bernoulli type with an embedding domain technique. A theoretical framework is developed which allows to prove continuous dependence of the primal and dual variables in the resulting saddle point problems with respect to the domain. This ensures the existence of a solution of a related shape optimization problem in a sufficiently large class of admissible domains.     

Of Dogs and Fleas: The Dynamics of N Uncoupled Two-State Systems

The historical Ehrenfest model dating back to 1907 describes the process of equilibration together with fluctuations around the thermal equilibrium. This approach represents a special case in the dynamics of N uncoupled two-state systems. In this article we present a generalization of the original model by introducing an additional parameter p which denotes the probability of a single state change. Analytical solutions for the probability distribution of the system's state as well as the fluctuation distribution are derived. Interestingly, close inspection of the fluctuation distribution reveals an intrinsic time scale. Sampling the system's state at much slower rates yields the familiar macroscopic exponential distribution for equilibrium processes. For faster measurements a power law extends roughly over log₁₀ N orders of magnitude followed by an exponential tail. At some point, further increases of the sampling rate merely result in a shift of the fluctuation distribution towards higher values leaving plateau at small fluctuation sizes behind. Since the generic solution is rather unwieldy, we derive and discuss simple and intuitive analytical solutions in the limit of small p and large N. Furthermore, we relax the quantization of time by considering a complementary approach in continuous time. Finally we demonstrate that the fluctuation distributions resulting from the two different approaches bear identical characteristic features.     

A comparison between optically active CdZnSe/ZnSe and CdZnSe/ZnBeSe self-assembled quantum dots: effect of beryllium

The composition and size of optically active Cd_xZn_1−xSe/ZnSe quantum dots are estimated with a previously developed method. The results are then compared with those obtained for Cd_xZn_1−xSe/Zn_0.97Be_0.03Se QDs. We show that introducing Be into the barrier material enhances both Cd composition and quantum size effect of optically active quantum dots.     

Electron-level dynamics in the presence of impurities and the Ruijsenaars-Schneider model

The dynamic equations for the energy level of a finite system with impurities are shown to be equivalent to the rational Ruijsenaars-Schneider system. The action, which is simultaneously the generating function of the Bäcklund canonical transformation for this system, is calculated. Various variants of statistical averaging of the energy-level distribution are discussed.     

Carrier diffusion in InGaAs/GaAs quantum wells grown on vicinal GaAs(0 0 1) substrates

We have investigated the influence of vicinal GaAs substrates on the optical and electronic properties of InGaAs/GaAs quantum wells (QWs). A single In_0.10Ga_0.90As QW was grown by molecular-beam epitaxy on a vicinal GaAs(0 0 1) substrate with a miscut angle of 0° (nominal), 2°, 4° and 6° towards [1 1 0]. The carrier diffusion was obtained by a micro-photoluminescence scan technique that permits to observe the effective diffusion length characterized by the lateral spread of carriers in the QW followed by radiative recombination. The carrier diffusion length was obtained parallel (L_||) and perpendicular (L) to the atomic steps. The diffusion length decreases as the temperature increases up to 100 K. Above this temperature we found different behaviours that depend on the sample miscut angle.     

Composition of the Cobalt Sulfide Coating after Its Electrochemical Reduction

X-ray photoelectrom spectroscopy was used to study the composition of the initial and electrochemically reduced cobalt coating formed by the adsorption procedure involving treatment of a carbon glass electrode in a solution of Co(II) ammine complexes, hydrolytic washing in water, and conversion to sulfide in Na₂S solution.     

Exchange of stability and finite-dimensional dynamics in a bifurcation problem with marginally stable continuous spectrum

We consider solutions bifurcating from a spatially homogeneous equilibrium under the assumption that the associated linearization possesses continuous spectrum up to the imaginary axis, for all values of the bifurcation parameter, and that a real eigenvalue crosses the imaginary axis. For a model we investigate the nonlinear stability of the trivial solution with respect to spatially localized perturbations, prove the occurrence of a pitchfork bifurcation of equilibria and the nonlinear stability of the bifurcating equilibria, again with respect to spatially localized perturbations.