Development of a Simulation Model for Solid Objects Suspended in a Fluctuating Fluid

We introduce a new scheme for the future application of Real-coded Lattice Gas (RLG) to the numerical simulation of suspended solid objects in a fluctuating fluid environment. The reproduction of Brownian motion for a single solid object is verified through the Gaussian distribution of its displacements. The effectiveness of the solid–solid interaction model is also confirmed in an N-body simulation.     

Destruction of a solid film under the action of ultrashort laser pulse

Molecular-dynamics (MD) simulation of the destruction of a crystal film heated by a femtosecond laser pulse was carried out. Heating is assumed to be instantaneous, because there is no time for the material to be displaced during the pulse. Film destruction is caused by the interaction of unloading waves. It can be considered as a model of a more complex process of splitting out of a thin surface layer from a massive target in the case where the layer remains solid after heating. It was found that the crystal order is broken due to the stretching strains and to the strong anisotropy of residual stress, resulting in a bipartition of the layer separating from the target. The lattice stretching and the formation of anisotropic stresses are due to the expansion of a heated lattice.     

Explicit Formulas for Generalized Action–Angle Variables in a Neighborhood of an Isotropic Torus and Their Application

Different versions of the Darboux–Weinstein theorem guarantee the existence of action–angle-type variables and the harmonic-oscillator variables in a neighborhood of isotropic tori in the phase space. The procedure for constructing these variables is reduced to solving a rather complicated system of partial differential equations. We show that this system can be integrated in quadratures, which permits reducing the problem of constructing these variables to solving a system of quadratic equations. We discuss several applications of this purely geometric fact in problems of classical and quantum mechanics.     

Indeterminacy Criteria for the Stieltjes Matrix Moment Problem

In this paper, we obtain criteria for the indeterminacy of the Stieltjes matrix moment problem. We obtain explicit formulas for Stieltjes parameters and study the multiplicative structure of the resolvent matrix. In the indeterminate case, we study the analytic properties of the resolvent matrix of the moment problem. We describe the set of all matrix functions associated with the indeterminate Stieltjes moment problem in terms of linear fractional transformations over Stieltjes pairs.     

Polarization fluctuations in a dipolar medium in an electrostatic field

Radio Engineering and Electronics Institute, Academy of Sciences of the USSR. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 32, No. 9, pp. 1113–1124, September, 1989.     

Observation of nucleon clusters in the spontaneous decay of234U

The emission of Ne and Mg nuclei was detected in the spontaneous decay of²³⁴U with probabilities of, respectively, (3.9 ±1.0) × 10^?13 and (2.3 ±0.7) × 10^?13 relative toα-decay. The upper limits of this kind of decay for²³⁵U and²³⁶U have been established. Systematics of half-lives for cluster emission are found to be similar to the Geiger-Nuttall dependence forα-decay. Some evidence for the presence of hindrance to cluster emission from the odd-mass nuclei²³³U and²³⁵U is obtained.     

Iminobis(Methylenediphosphonic) acid

Conclusions When formamide was reacted with phosphorous acid and phosphorus trichloride, the formation of iminobis(methylenediphosphonic) acid was detected.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 4, pp. 865–868, April, 1987.The authors wish to express their graditude to Yu. P. Tsentalovich for helping with the NMR spectral analysis.     

The generation of three-dimensional internal waves and attendant boundary layers in a viscous continuously stratified fluid. Construction of an analytical solution

An analytical solution of a linearized problem of the emission of periodic internal waves by part of a plane which oscillates with a small amplitude in an arbitrary direction in a viscous exponentially stratified fluid is constructed. Solutions of the dispersion equation are given for all positions of the emitting surface (arbitrary, vertical, horizontal, and critical when one of the beam propagation directions is collinear with the emitting surface). The possibility of transition to the case of a uniform fluid, which is important for applications, is analyzed.     

FFT-based algorithms for the string matching with mismatches problem

The string matching with mismatches problem requires finding the Hamming distance between a pattern P of length m and every length m substring of text T with length n. Fischer and Paterson's FFT-based algorithm solves the problem without error in O(σnlogm), where σ is the size of the alphabet Σ [SIAM–AMS Proc. 7 (1973) 113–125]. However, this in the worst case reduces to O(nmlogm). Atallah, Chyzak and Dumas used the idea of randomly mapping the letters of the alphabet to complex roots of unity to estimate the score vector in time O(nlogm) [Algorithmica 29 (2001) 468–486]. We show that the algorithm's score variance can be substantially lowered by using a bijective mapping, and specifically to zero in the case of binary and ternary alphabets. This result is extended via alphabet remappings to deterministically solve the string matching with mismatches problem with a constant factor of 2 improvement over Fischer–Paterson's method.     

Generalized lattice model of liquid state and its relation to Ginzburg–Landau theory

Basic principles of the generalized lattice model of multicomponent condensed systems are formulated. Short-range parts of interatomic interactions are taken into account by means of the geometric constraints method. Long-range parts of the interactions are taken into account in mean field approximation. The expression for Helmholtz free energy is obtained. A system of integral equations for the equilibrium distributions of components is derived. The asymptotic properties of its solutions are investigated. Moment expansion of interatomic interactions and localization of integral terms in free energy is obtained. A Ginzburg–Landau-like functional of free energy is derived.