Magnetotransport Properties and Subband Structure of the Two-Dimensional Electron Gas in the Inversion Layer of Hg1-xCdxTe Bicrystals

The electronic and magnetotransport properties of conduction electrons in the grain boundary interface of p-type Hg1-xCdxTe bicrystals are investigated. The results clearly demonstrate the existence of a two-dimensional degenerate n-type inversion layer in the vicinity of the grain boundary. The observed quantum oscillations of the magnetoresistivity result from a superposition of the Shubnikov-de Haas effect in several occupied electric subbands. The occupation of higher subbands is presumable depending on the total carrier density ns of the inversion layer. Electron densities, subband energies, and effective masses of these electric subbands in samples with different total densities are determined. The effective masses of lower subbands are markedly different from the band edge values of the bulk material, their values decrease with decreasing electron density and converging to the bulk values at lower densities. This agrees with predictions of the triangular potential well model and a pronounced nonparabolicity of the energy bands in Hg1-xCdxTe. At high magnetic fields (B > 10 T) it is experimentally verified that the Hall resistivity xy is quantized into integer multiplies of h/e2

Varieties of *-regular rings

Given a subdirectly irreducible *-regular ring R, we show that R is a homomorphic image of a regular *-subring of an ultraproduct of the (simple) eRe, e in the minimal ideal of R; moreover, R (with unit) is directly finite if all eRe are unit-regular. Finally, unit-regularity is shown for every member of the variety generated by artinian *-regular rings (endowed with unit and pseudo-inversion)

Unimodal wave trains and solitons in convex FPU chains

We consider atomic chains with nearest neighbour interactions and study periodic and homoclinic travelling waves which are called wave trains and solitons, respectively. Our main result is a new existence proof which relies on the constrained maximisation of the potential energy and exploits the invariance properties of an improvement operator. The approach is restricted to convex interaction potentials but refines the standard results as it provides the existence of travelling waves with unimodal and even profile functions. Moreover, we discuss the numerical approximation and complete localization of wave trains, and show that wave trains converge to solitons when the periodicity length tends to infinity.Comment: 27 pages, several figure

A fractal approach to the dark silicon problem: a comparison of 3D computer architectures -- standard slices versus fractal Menger sponge geometry

The dark silicon problem, which limits the power-growth of future computer generations, is interpreted as a heat energy transport problem when increasing the energy emitting surface area within a given volume. A comparison of two 3D-configuration models, namely a standard slicing and a fractal surface generation within the Menger sponge geometry is presented. It is shown, that for iteration orders $n>3$ the fractal model shows increasingly better thermal behavior. As a consequence cooling problems may be minimized by using a fractal architecture. Therefore the Menger sponge geometry is a good example for fractal architectures applicable not only in computer science, but also e.g. in chemistry when building chemical reactors, optimizing catalytic processes or in sensor construction technology building highly effective sensors for toxic gases or water analysis.Comment: 4 pages 2 figure

Covariant fractional extension of the modified Laplace-operator used in 3D-shape recovery

Extending the Liouville-Caputo definition of a fractional derivative to a nonlocal covariant generalization of arbitrary bound operators acting on multidimensional Riemannian spaces an appropriate approach for the 3D shape recovery of aperture afflicted 2D slide sequences is proposed. We demonstrate, that the step from a local to a nonlocal algorithm yields an order of magnitude in accuracy and by using the specific fractional approach an additional factor 2 in accuracy of the derived results.Comment: 5 pages, 3 figures, draft for proceedings IFAC FDA12 in Nanjing, Chin

Classification and Characterization of rationally elliptic manifolds in low dimensions

We give a characterization of closed, simply connected, rationally elliptic 6-manifolds in terms of their rational cohomology rings and a partial classification of their real cohomology rings. We classify rational, real and complex homotopy types of closed, simply connected, rationally elliptic 7-manifolds. We give partial results in dimensions 8 and 9.Comment: 23 pages; extended Section 2, revised Section 5 and several minor revision

On the origin of space

Within the framework of fractional calculus with variable order the evolution of space in the adiabatic limit is investigated. Based on the Caputo definition of a fractional derivative using the fractional quantum harmonic oscillator a model is presented, which describes space generation as a dynamic process, where the dimension $d$ of space evolves smoothly with time in the range 0 <= d(t) <=3, where the lower and upper boundaries of dimension are derived from first principles. It is demonstrated, that a minimum threshold for the space dimension is necessary to establish an interaction with external probe particles. A possible application in cosmology is suggested.Comment: 14 pages 3 figures, some clarifications adde