Based on the Lax formalism, integrals of motion are constructed for the Sutherland hyperbolic systems of particles with internal degrees of freedom (su(n) spins) situated in an external field with the Morse potential characterized by the parameter τ2. It is shown that the corresponding infinite-dimensional algebra determining the hidden symmetry of the systems is not of the Yangian type.
Show AbstractThe basic properties of fractals and fractal objects are described. Papers devoted to diffraction on fractal lattices are surveyed. The optical Fourier transform is considered as a method for determining the fractal dimension of a diffraction lattice.
Show AbstractSolutions to the Dirac equations have been obtained for particles interacting with vector, axial-vector, and tensor condensates within the framework of the Standard Model Extension. Possible applications of these solutions for describing the neutrino behavior in dense matter and electromagnetic field are considered.
Show AbstractA new method previously proposed [1] for the encryption of information by means of chaotic mappings is studied in detail. Cryptanalysis by exhaustive key search and correlation analysis of the ciphers are performed. The predictability of the cipher values is estimated. A web application permitting users to exchange text messages encrypted by the new method is described.
Show AbstractA new expression for the pair distribution function of a multicomponent hard-sphere mixture is obtained using the method of accelerated convergence of the perturbation series and exactly known virial coefficients of the expansion in the powers of density. For binary and ternary mixtures, the calculation is in good agreement with the available data of experiments. For a one-component system, the found function transforms to an expression that describes the radial distribution function over the entire density range with the accuracy of the computer experiment.
Show AbstractThe quantum mechanics with a stationary non-Hermitian Hamiltonian and a complex evolution parameter, as well as its classical limit with nontrivial correlations have been studied. The corresponding dynamics is shown to be irreversible for the isothermal and adiabatic regimes of quantum and classical evolution. The possibility of a universal relationship between irreversibility and dynamical parity violation in the system has been established. The mechanism of gravity generation by the distribution of correlations in a free theory is demonstrated.
Show AbstractPossible ways of formalizing the concept of statistically homogeneous and isotropic curvature fluctuations in general relativity are considered. The straightforward way of constructing this concept, which is borrowed from statistical hydromechanics, is shown to lead to a physically degenerate result: the correlations between the fluctuations do not decrease with increasing distance between the points. It is emphasized that this result is a peculiar analogue of the Schur theorem.
Show AbstractThe results of the reprocessing of the experimental data on radio emission from extensive air showers (EAS) earlier obtained at the EAS facility (Moscow State University) are reported. The maximum depth distribution of showers is found from analysis of the width of the spatial distribution of radio emission. The average maximum depth is X$_{max}$ = 655 ± 8 g/cm$^2$ for the primary particle energy E$_0$ ∼ (3–4) × 10$^{17}$ eV. The normalized field strength at E$_0$ = 10$^{17}$ eV is 3.2 ± 0.6 and 2.8 ± 0.4 μV/(m MHz) at distances of 50 and 100 m from the axis, respectively. The accuracy of E$_0$ determination from the radio emission field strength at 50 m from the axis is about 20%.
Show AbstractA dynamical-statistical model is used to analyze the experimental angular distributions of fission fragments in the reactions $\alpha+{}^{238}$U, $^{237}$Np at $E_\alpha=(20\div100)$ MeV, as well as to determine the Am isotope fission probabilities and the shape isomer yields in the reactions $d+{}^{242,240}$Pu at $E_d=(20\div30)$ MeV. Manifestations of shell effects are found in the fission barrier structure up to the excitation energies of $(50\div60)$ MeV.
Show AbstractDiffraction gratings designed on the basis of the geometrical properties of 1D quasicrystalline structures are considered. It is shown that the diffraction peak position is highly stable against small perturbations of the grating profile when the periodic pattern of the alternating elements comprising the profile remains unchanged. The fractal character of the diffraction patterns is also preserved during perturbations, with the fractal geometry obeying the principle of the Golden ratio.
Show AbstractThe dispersion of permittivity and conductivity of crystals containing aqua complexes of different types ($\gamma$-HBO$_2$, Ca$_2$B$_6$O$_{11}\cdot{}$H$_2$O, La[B$_5$O$_8$](OH)$_2\cdot1.5$H$_2$O and TRB$_6$O$_9$(OH)$_3$ (TR - Tb, Tu)) is studied for the first time. The compounds were synthesized under hydrothermal conditions at T=270–280°C and P=70–100 atm. Depending on the contained aqua complex, the compounds display different temperature and frequency behavior of the electric properties. The measurements are carried out in the frequency range from $10^{-2}$ to 10$^6$ Hz and in the temperature range from −20 to 140°C.
Show AbstractThe angular dependences of nuclear resonant scattering are considerably different from respective X-ray reflectometry curves because of some special features of their detection and nuclear decay acceleration (speedup effect) in the conditions of coherent scattering. Model calculations show that the kinematic formula relating the intensity of the nuclear Bragg reflection maximum at different stages of annealing to the diffusion coefficient is inapplicable when the Bragg peak falls near the critical angle.
Show AbstractMelting of small copper clusters on a copper surface is simulated using the molecular dynamics method. The melting temperature of the (100) Cu surface is found to be lower than that of the bulk material. The melting temperature of clusters is shown to be a nonmonotonous function of their size.
Show AbstractThe enhanced seismic activity with periods in the range from 25 to 60 days observed in the Pamirs area is explained by the effect produced on the lithosphere by topographic planetary waves at the Siberian shelf.
Show AbstractThe detonation combustion of a supersonic flow of propane-air mixture, initiated by a pulsed discharge of a magnetoplasma compressor, is obtained in experiment. A backward wave of supersonic combustion propagating with a velocity of 450 m/s against the flow is observed.
Show AbstractCriteria for discrimination between the free and pinch modes of the expansion of pulsed high-current discharges in dense gases are determined on the basis of real experiments and literature data analysis.
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