The motion of a shock wave through a non-uniform one-dimensional medium in the case of arbitrary equation of state

The derivation of the equation of one-dimensional movement of a solitary shock wave is given. This derivation shows, that the differential equation of movement of a solitary plane shock wave in the channel with variable area, is exact, if simplifying assumptions, made during derivation, are realized. But these assumptions in plane geometry it is possible to realize only approximately; situation with spherical and cylindrical shock waves is opposite.Comment: 11 pages, 1 figure, 1 tabl

Multi-Component Gas-Dynamics and Turbulence

In the article, correct method for the kinetic Boltzmann equation asymptotic solution is formulated, the Hilbert method and the Enskog error are considered. The equations system of multi-component nonequilibrium gas-dynamics is derived, that corresponds to the first order in the approximate method for solution of the kinetic Boltzmann equation within the Struminskii approach. It is shown, that velocity distribution functions, received by the proposed method and by the Enskog method within the Enskog approach to solving of kinetic Boltzmann equation for gas mixture, are equivalent to first infinitesimal order terms, but, generally speaking, differ in the next order. An interpretation of turbulent gas flow is proposed, as stratified to components gas flow, which is described by the derived equations system of multi-component nonequilibrium gas-dynamics.Comment: revtex, 31 pages in English, after "\end{document}" of english part of tex-file original russian text is added; now we use more accurate definition of the temperature, Enskog mistake is considered in more detail

Real-Space Renormalization Group (RSRG) Approach to Quantum Spin Lattice Systems

The paper describes an explicit variational modification of the standard RSRG method and its application to quantum spin lattice systems. The modified approach is applied to exactly solvable ITF, XX and isotropic Heisenberg models. Better upper bounds for the systems' ground state energy are obtained as compared to the standard RSRG approach.Comment: http://www.mff.cuni.cz/veda/konference/wds/proc/proc-contents.php?year=2011#phy

Solution of the Schr\"odinger equation using exterior complex scaling and fast Fourier transform

The split-operator pseudo-spectral method based on the fast Fourier transform (SO-FFT) is a fast and accurate method for the numerical solution of the time-dependent Schr\"odinger-like equations (TDSE). As well as other grid-based approaches, SO-FFT encounters a problem of the unphysical reflection of the wave function from the grid boundaries. Exterior complex scaling (ECS) is an effective method widely applied for the suppression of the unphysical reflection. However, SO-FFT and ECS have not been used together heretofore because of the kinetic energy operator coordinate dependence that appears in ECS applying. We propose an approach for the combining the ECS with SO-FFT for the purpose of the solution of TDSE with outgoing-wave boundary conditions. Also, we propose an effective ECS-friendly FFT-based preconditioner for the solution of the stationary Schr\"odinger equation by means of the preconditioned conjugate gradients method.Comment: 20 pages, 7 figure

Is the Wannier threshold law for angular distribution in double photoionization of atoms true at practically attainable energies of ejected electrons?

We calculated ab initio the three-fold differential cross section of a double single-photon Helium photoionization at equal energy sharing, and obtained from one the Gaussian width parameter, describing the angular interelectron correlations, for the total electrons energies range E from 0.1 eV to 100 eV. The results are in excellent agreement with experimental data but indicate that the Wannier threshold law for angular distribition is not correct at energies attainable in modern experiments. It is shown that the Gaussian width parameter dependence on energy is much better described by the modified threshold law, obtained by Kazansky and Ostrovsky [J. Phys. B 26, 2231 (1993)]. Also, we explored the Gaussian width parameter for a double photoionization of the targets with the strongly asymmetrical initial state configuration: the atomic Hydrogen negative ion and the Helium in the 2s1S and 3s1S excited states. We found that the Gaussian width parameter dependence on the total ejected electrons energy for this targets has a maximum at low energies. We show also that the correlation parameter dependence on the interelectron angle for these targets is essentially non-Gaussian and has a number of peaks equal to a number of initial state radial nodes, that reveals the new abilities for the qualitative analysis of electron structure.Comment: 13 pages, 8 figure

Angular anisotropy of time delay in XUV/IR photoionization of H2+_2^+

We develop a novel technique for modeling of atomic and molecular ionization in superposition of XUV and IR fields with characteristics typical for attosecond streaking and RABBITT experiments. The method is based on solving the time-dependent Schr\"odinger equation in the coordinate frame expanding along with the photoelectron wave packet. The efficiency of the method is demonstrated by calculating angular anisotropy of photoemission time delay of the H$_2^+$ ion in a field configuration of recent RABBITT experiments.Comment: 18 pages, 8 figure

The p-H symmetry breaking in dissociative ionization of H2 due to the molecular ion interaction with the ejected electron

We propose a novel mechanism of electron localization and molecular symmetry breaking in dissociative photoionization of the H$_2$ molecule. The Coulomb field of the ejected electron can induce transition of the remaining H$_2^+$ ion from the gerade $^2\Sigma_g^1(1s\sigma_g)$ to the ungerade $^2\Sigma_u^1(2p\sigma_u)$ electronic state when the nuclei in a bound vibrational state are near the outer turning point. The superposition of this process with a direct transition to vibrational continuum should produce a non-gerade ionic state which results in observed asymmetry in the $p$-H ejection relative to the electron ejection direction at a small kinetic energy release.Comment: 5 pages, 5 figure

Time-dependent calculations of transfer ionization by fast proton-helium collision in one-dimensional kinematics

We analyze a transfer ionization (TI) reaction in the fast proton-helium collision $\rm H^+ + He \to H^0 + He^{2+} + e^-$ by solving a time-dependent Schr\"odinger equation (TDSE) under the classical projectile motion approximation in one-dimensional kinematics. In addition, we construct various time independent analogues of our model using lowest order perturbation theory in the form of the Born series. By comparing various aspects of the TDSE and the Born series calculations, we conclude that the recent discrepancies of experimental and theoretical data may be attributed to deficiency of the Born models used by other authors. We demonstrate that the correct Born series for TI should include the momentum space overlap between the double ionization amplitude and the wave function of the transferred electron.Comment: 10 pages, 6 figure

Time delay in XUV/IR photoionization of H2_2O

We solve the time-dependent Schr\"odinger equation describing a water molecule driven by a superposition of the XUV and IR pulses typical for a RABBITT experiment. This solution is obtained by a combination of the time-dependent coordinate scaling and the density functional theory with self-interaction correction. Results of this solution are used to determine the time delay in photoionization of the water and hydrogen molecules.Comment: 6 pages, 3 figures. arXiv admin note: text overlap with arXiv:1604.0493

A full proof of universal inequalities for the distribution function of the binomial law

We present a new form and a short full proof of explicit two-sided estimates for the distribution function F_{n,p}(x) of the binomial law from the paper published by D.Alfers and H.Dinges in 1984. These inequalities are universal (valid for all binomial distribution and all values of argument) and exact (namely, the upper bound for F_{n,p}(k) is the lower bound for F_{n,p}(k+1)). By means of such estimates it is possible to bound any quantile of the binomial law by 2 subsequent integers.Comment: 7 pages; to be published in "Teorija verojatnostei i ee primenenija" (in Rissian