Edge-preserving Multiscale Image Decomposition based on Local Extrema

We propose a new model for detail that inherently captures oscillations, a key property that distinguishes textures from individual edges. Inspired by techniques in empirical data analysis and morphological image analysis, we use the local extrema of the input image to extract information about oscillations: We define detail as oscillations between local minima and maxima. Building on the key observation that the spatial scale of oscillations are characterized by the density of local extrema, we develop an algorithm for decomposing images into multiple scales of superposed oscillations. Current edge-preserving image decompositions assume image detail to be low contrast variation. Consequently they apply filters that extract features with increasing contrast as successive layers of detail. As a result, they are unable to distinguish between high-contrast, fine-scale features and edges of similar contrast that are to be preserved. We compare our results with existing edge-preserving image decomposition algorithms and demonstrate exciting applications that are made possible by our new notion of detail

The quasiparticle band gap in the topological insulator Bi2Te3

We present a theoretical study of dispersion of states which form the bulk band-gap edges in the three-dimensional topological insulator Bi2Te3. Within density functional theory, we analyze the effect of atomic positions varying within the error range of the available experimental data and approximation chosen for the exchange-correlation functional on the bulk band gap and k-space location of valence- and conduction-band extrema. For each set of the positions with different exchange-correlation functionals, we show how many-body corrections calculated within a one-shot GW approach affect the mentioned characteristics of electronic structure of Bi2Te3. We thus also illustrate to what degree the one-shot GW results are sensitive to the reference one-particle band structure in the case of bismuth telluride. We found that for this topological insulator the GW corrections enlarge the fundamental band gap and for certain atomic positions and reference band structure bring its value in close agreement with experiment.Comment: 12 pages, 6 figures, 5 table

Energy spectrum, density of states and optical transitions in strongly biased narrow-gap quantum wells

We study theoretically the effect of an electric field on the electron states and far-infrared optical properties in narrow-gap lead salt quantum wells. The electron states are described by a two-band Hamiltonian. An application of a strong electric field across the well allows the control of the energy gap between the two-dimensional (2D) states in a wide range. A sufficiently strong electric field transforms the narrow-gap quantum well to a nearly gapless 2D system, whose electron energy spectrum is described by linear dispersion relations \epsilon_{\sigma} (k) ~\pm (k-k_{\sigma}), where k_{\sigma} are the field-dependent 2D momenta corresponding to the minimum energy gaps for the states with spin numbers \sigma. Due to the field-induced shift of the 2D subband extrema away from k=0 the density of states has inverse-square-root divergencies at the edges. This property may result in a considerable increase of the magnitude of the optical absorption and in the efficiency of the electrooptical effect.Comment: Text 18 pages in Latex/Revtex format, 7 Postscript figure

Poisson's ratio in cubic materials

Expressions are given for the maximum and minimum values of Poisson's ratio $\nu$ for materials with cubic symmetry. Values less than -1 occur if and only if the maximum shear modulus is associated with the cube axis and is at least 25 times the value of the minimum shear modulus. Large values of $|\nu|$ occur in directions at which the Young's modulus is approximately equal to one half of its 111 value. Such directions, by their nature, are very close to 111. Application to data for cubic crystals indicates that certain Indium Thallium alloys simultaneously exhibit Poisson's ratio less than -1 and greater than +2.Comment: 20 pages, 6 figure