Topological analysis of real space properties for the solid-state full-potential APW DFT method

For the solid-state density functional program Elk a module was developed that enables to interface the crystal orbitals data into the DGrid package. Within DGrid the real-space electronic properties, like the electron density and its gradient or Laplacian, kinetic energy density, electron localizability indicator, etc., are computed. The properties can be searched for critical points as well as for the interconnection lines between them. Additionally, the basins can be evaluated and the property integrals can be calculated. The results of topological analysis for fcc Al, MgB₂, CaTiO₃, and urea molecular crystal are discussed and compared with the experimental data. The role of certain computation parameters of (L)APW method is also analyzed.     

Solitary surface acoustic waves and bulk solitons in nanosecond and picosecond laser ultrasonics

Recent achievements of nonlinear acoustics concerning the realization of solitons and solitary waves in crystals and their surfaces attained by nanosecond and picosecond laser ultrasonics are discussed and compared. The corresponding pump-probe setups are described, which allow an all-optical contact-free excitation and detection of short strain pulses in the broad frequency range between 10 MHz and about 300 GHz. The formation of solitons in the propagating longitudinal strain pulses is investigated for nonlinear media with intrinsic lattice-based dispersion. The excitation of solitary surface acoustic waves is realized by a geometric film-based dispersion effect. Future developments and potential applications of nonlinear nanosecond and picosecond ultrasonics are discussed.     

A bundle modification strategy for convex minimization

We present a new bundle algorithm for minimizing convex not necessarily smooth functions. The novelty of our approach is based on a bundle modification strategy that we apply whenever the stability center is updated and which is aimed at substituting the points of the bundle by new points characterized by possibly better values of the objective function. Convergence of the algorithm is proved and numerical results are presented.     

Graphs of difference operators for p-ary sequences

For a given prime p and positive integer n, we consider the graph G _n of the difference operator acting on p-ary sequences of length n. We suggest new proofs of some results of V.I. Arnold on the graph G _n and the complexity of sequences and obtain new results for the length of a maximal cycle in the general case of p-ary sequences. We also provide estimates for the number of complicated sequences.      

CATALYTIC PROPERTIES OF NANOFIBROUS CARBON IN SELECTIVE OXIDATION OF HYDROGEN SULPHIDE

Nanofibrous carbonaceous materials （NFC） as a new class of materials having many applications, can catalyze the selective oxidation of H2S to sulfur. The correlation between NFC structure and its activity and selectivity in H2S oxidation was determined. It is demonstrated that selectivity can be improved if NFC with more ordered structure be synthesized and the portion of the original catalyst in carbon be reduced by increasing the carbon accumulated in the catalyst.     

On the Problem of Emergence of Classical Space—Time: The Quantum-Mechanical Approach

The Riemannian manifold structure of the classical (i.e., Einsteinian) space-time is derived from the structure of an abstract infinite-dimensional separable Hilbert space S. For this S is first realized as a Hilbert space H of functions of abstract parameters. The space H is associated with the space of states of a macroscopic test-particle in the universe. The spatial localization of state of the particle through its interaction with the environment is associated with the selection of a submanifold M of realization H. The submanifold M is then identified with the classical space (i.e., a space–like hypersurface in space-time). The mathematical formalism is developed which allows recovering of the usual Riemannian geometry on the classical space and, more generally, on space and time from the Hilbert structure on S. The specific functional realizations of S are capable of generating spacetimes of different geometry and topology. Variation of the length-type action functional on S is shown to produce both the equation of geodesics on M for macroscopic particles and the Schrödinger equation for microscopic particles.     

On the mechanism of the runaway of electrons in a gas: The upper branch of the paschen curve

Basing on the simulation results, it is shown that the Townsend mechanism of electron multiplication in a gas at sufficiently large interelectrode distances is valid at least up to such large values of E/p at which relativistic electrons are generated. Correspondingly, the runaway electron producing in a gas is determined not by the local criteria accepted presently, but by the ratio of interelectrode distance and the characteristic electron multiplication length. It is shown that the critical discharge voltage U, at which the runaway electrons appear in a given gas, is a function of the product of the interelectrode distance by the gas pressure. This function (U-pd dependence) defines not only well-known Paschen curve but also an additional branch, which describes the absence of a self-sustained discharge at a high voltages sufficiently rapidly supplied across the electrodes. Critical discharge voltage dependence for helium and xenon are presented.