Consistent operator semigroups and their interpolation

Under a mild regularity condition we prove that the generator of the interpolation of two C0-semigroups is the interpolation of the two generators

H\"older estimates for parabolic operators on domains with rough boundary

We investigate linear parabolic, second-order boundary value problems with mixed boundary conditions on rough domains. Assuming only boundedness and ellipticity on the coefficient function and very mild conditions on the geometry of the domain, including a very weak compatibility condition between the Dirichlet boundary part and its complement, we prove H\"older continuity of the solution in space and time.Comment: 1 figur

Optimal Control of the Thermistor Problem in Three Spatial Dimensions

This paper is concerned with the state-constrained optimal control of the three-dimensional thermistor problem, a fully quasilinear coupled system of a parabolic and elliptic PDE with mixed boundary conditions. This system models the heating of a conducting material by means of direct current. Local existence, uniqueness and continuity for the state system are derived by employing maximal parabolic regularity in the fundamental theorem of Pr\"uss. Global solutions are addressed, which includes analysis of the linearized state system via maximal parabolic regularity, and existence of optimal controls is shown if the temperature gradient is under control. The adjoint system involving measures is investigated using a duality argument. These results allow to derive first-order necessary conditions for the optimal control problem in form of a qualified optimality system. The theoretical findings are illustrated by numerical results

Quantum Monte Carlo study of a positron in an electron gas

Quantum Monte Carlo calculations of the relaxation energy, pair-correlation function, and annihilating-pair momentum density are presented for a positron immersed in a homogeneous electron gas. We find smaller relaxation energies and contact pair-correlation functions in the important low-density regime than predicted by earlier studies. Our annihilating-pair momentum densities have almost zero weight above the Fermi momentum due to the cancellation of electron-electron and electron-positron correlation effects

Reversing a granular flow on a vibratory conveyor

Experimental results are presented on the transport properties of granular materials on a vibratory conveyor. For circular oscillations of the shaking trough a non-monotonous dependence of the transport velocity on the normalized acceleration is observed. Two maxima are separated by a regime, where the granular flow is much slower and, in a certain driving range, even reverses its direction. A similar behavior is found for a single solid body with a low coefficient of restitution, whereas an individual glass bead of 1 mm diameter is propagated in the same direction for all accelerations.Comment: 4 pages, 5 figures, submitted to Applied Physics Letter

Direct observation of twist mode in electroconvection in I52

I report on the direct observation of a uniform twist mode of the director field in electroconvection in I52. Recent theoretical work suggests that such a uniform twist mode of the director field is responsible for a number of secondary bifurcations in both electroconvection and thermal convection in nematics. I show here evidence that the proposed mechanisms are consistent with being the source of the previously reported SO2 state of electroconvection in I52. The same mechanisms also contribute to a tertiary Hopf bifurcation that I observe in electroconvection in I52. There are quantitative differences between the experiment and calculations that only include the twist mode. These differences suggest that a complete description must include effects described by the weak-electrolyte model of electroconvection

A Non-Equilibrium Defect-Unbinding Transition: Defect Trajectories and Loop Statistics

In a Ginzburg-Landau model for parametrically driven waves a transition between a state of ordered and one of disordered spatio-temporal defect chaos is found. To characterize the two different chaotic states and to get insight into the break-down of the order, the trajectories of the defects are tracked in detail. Since the defects are always created and annihilated in pairs the trajectories form loops in space time. The probability distribution functions for the size of the loops and the number of defects involved in them undergo a transition from exponential decay in the ordered regime to a power-law decay in the disordered regime. These power laws are also found in a simple lattice model of randomly created defect pairs that diffuse and annihilate upon collision.Comment: 4 pages 5 figure

Energetics of positron states trapped at vacancies in solids

We report a computational first-principles study of positron trapping at vacancy defects in metals and semiconductors. The main emphasis is on the energetics of the trapping process including the interplay between the positron state and the defect's ionic structure and on the ensuing annihilation characteristics of the trapped state. For vacancies in covalent semiconductors the ion relaxation is a crucial part of the positron trapping process enabling the localization of the positron state. However, positron trapping does not strongly affect the characteristic features of the electronic structure, e.g., the ionization levels change only moderately. Also in the case of metal vacancies the positron-induced ion relaxation has a noticeable effect on the calculated positron lifetime and momentum distribution of annihilating electron-positron pairs.Comment: Submitted to Physical Review B on 17 April 2007. Revised version submitted on 6 July 200

Vacancy complexes in nonequilibrium germanium-tin semiconductors

Understanding the nature and behavior of vacancy-like defects in epitaxial GeSn metastable alloys is crucial to elucidate the structural and optoelectronic properties of these emerging semiconductors. The formation of vacancies and their complexes is expected to be promoted by the relatively low substrate temperature required for the epitaxial growth of GeSn layers with Sn contents significantly above the equilibrium solubility of 1 at.%. These defects can impact both the microstructure and charge carrier lifetime. Herein, to identify the vacancy-related complexes and probe their evolution as a function of Sn content, depth-profiled pulsed low-energy positron annihilation lifetime spectroscopy and Doppler broadening spectroscopy were combined to investigate GeSn epitaxial layers with Sn content in the 6.5-13.0 at.% range. The samples were grown by chemical vapor deposition method at temperatures between 300 and 330 {\deg}C. Regardless of the Sn content, all GeSn samples showed the same depth-dependent increase in the positron annihilation line broadening parameters, which confirmed the presence of open volume defects. The measured average positron lifetimes were the highest (380-395 ps) in the region near the surface and monotonically decrease across the analyzed thickness, but remain above 350 ps. All GeSn layers exhibit lifetimes that are 85 to 110 ps higher than the Ge reference layers. Surprisingly, these lifetimes were found to decrease as Sn content increases in GeSn layers. These measurements indicate that divacancies are the dominant defect in the as-grown GeSn layers. However, their corresponding lifetime was found to be shorter than in epitaxial Ge thus suggesting that the presence of Sn may alter the structure of divacancies. Additionally, GeSn layers were found to also contain a small fraction of vacancy clusters, which become less important as Sn content increases