On the problem of non-equilibrium population of excitons

The non-linear response of the exciton system is considered and non-equilibrium exciton populations are calculated. It is shown that in the high frequency domain (ω > ω_c ≈ 10^-13 s^-1) the role and the influence of the external perturbation on the exciton population becomes unimportant.     

Statistical physics of shear flow: a non-equilibrium problem

Complex fluids are easily and reproducibly driven into non-equilibrium steady states by the action of shear flow. The statistics of the microstructure of non-equilibrium fluids is important to the material properties of every complex fluid that flows, e.g. axle grease on a rotating bearing; blood circulating in capillaries; molten plastic flowing into a mould; the non-equilibrium onion phase of amphiphiles used for drug delivery; the list is endless. Such states are as diverse and interesting as equilibrium states, but are not governed by the same statistics as equilibrium materials. I review some recently discovered principles governing the probabilities of various types of molecular re-arrangements taking place within a sheared fluid. As well as providing new foundations for the study of non-equilibrium matter, the principles are applied to some simple models of particles interacting under flow, showing that the theory exhibits physically convincing behaviour.     

Driven spin wave modes in XY ferromagnet: non-equilibrium phase transition

The dynamical responses of XY ferromagnet driven by linearly polarised propagating and standing magnetic field wave have been studied by Monte Carlo simulation in three dimensions. In the case of propagating magnetic field wave (with specified amplitude, frequency and the wavelength), the low temperature dynamical mode is a propagating spin wave and the system becomes structureless (or random) in the high temperature. A dynamical symmetry breaking phase transition is observed at a finite (non-zero) temperature. This symmetry breaking is confirmed by studying the statistical distribution of the angle of the spin vector. The dynamic non-equilibrium transition temperature was found to decrease as the amplitude of the propagating magnetic field wave increased. A comprehensive phase boundary is drawn in the plane formed by temperature and amplitude of propagating field wave. The phase boundary was observed to shrink (in the low temperature side) for longer wavelength of the propagating magnetic wave. In the case of standing magnetic field wave, the low temperature excitation is a standing spin wave which becomes structureless (or random) in the high temperature. Here also, like the case of propagating magnetic wave, a dynamical symmetry breaking non-equilibrium phase transition was observed. A comprehensive phase boundary was drawn. Unlike the case of propagating magnetic wave, the phase boundary does not show any systematic variation with the wavelength of the standing magnetic field wave. In the limit of vanishingly small amplitude of the field, the phase boundaries approach the recent Monte Carlo estimate of equilibrium transition temperature.     

一种全频散波方程的反问题

基于一种全频散波方程研究了对于谐波和波包的反问题。首先根据Mindlin理论建立了描述无耗散微结构线性固体中波传播模型一一一种全频散波方程,并讨论了其频散特性。然后基于该全频散波方程,提出了利用四种不同谐波的频率和相应波数确定波方程四个未知系数的反问题,并用严格的数学理论论证了此反问题。研究证明,通过测量同一种无耗散微结构线性固体中传播的四种不同谐波的频率和相应波数,在正常频散和反常频散情况下可唯一地确定波方程的未知系数,即材料的未知参数。     

Piston dispersive shock wave problem

The piston shock problem is a classical result of shock wave theory. In this work, the analogous dispersive shock wave (DSW) problem for a fluid described by the nonlinear Schr?dinger equation is analyzed. Asymptotic solutions are calculated for a piston (step potential) moving with uniform speed into a dispersive fluid at rest. In contrast to the classical case, there is a bifurcation of shock behavior where, for large enough piston velocities, the DSW develops a periodic wave train in its wake with vacuum points and a maximum density that remains fixed as the piston velocity is increased further. These results have application to Bose-Einstein condensates and nonlinear optics.     

The inverse problem based on a full dispersive wave equation

The inverse problem for harmonic waves and wave packets was studied based on a full dispersive wave equation.First,a full dispersive wave equation which describes wave propagation in nondissipative microstructured linear solids is established based on the Mindlin theory,and the dispersion characteristics are discussed.Second,based on the full dispersive wave equation,an inverse problem for determining the four unknown coefficients of wave equation is posed in terms of the frequencies and corresponding wave numbers of four different harmonic waves,and the inverse problem is demonstrated with rigorous mathematical theory. Research proves that the coefficients of wave equation related to material properties can be uniquely determined in cases of normal and anomalous dispersions by measuring the frequencies and corresponding wave numbers of four different harmonic waves which propagate in a nondissipative microstructured linear solids.     

Stability problem in nonlinear wave propagation

An explicit expression for the excitation spectrum of the stationary solutions of a nonlinear wave equation is obtained. It is found that all branches of many-valued solutions of a nonlinear wave equation between the (2K+1,2K+2) turning points (branch points in the complex plane of the nonlinearity parameter) are unstable. Some parts of branches between the (2K,2K+1) turning points are also unstable. The instability of the latter is related to the possibility that pairs of complex conjugate eigenvalues cross the real axis in the κ plane. Zh. éksp. Teor. Fiz. 114, 1487–1499 (October 1998) Published in English in the original Russian journal. Reproduced here with stylistic changes by the Translation Editor.     

The problem of surface wave propagation in a reduced Cosserat medium

This article continues a series of publications devoted to the study of waves in the framework of the asymmetric theory of elasticity, where the deformed state of the medium is characterized by independent vectors of translation and rotation. The problem of acoustic Rayleigh wave propagation in half space is considered within a model of the reduced Cosserat medium. A general analytic solution of this problem is obtained. The analysis of this solution is compared with the corresponding solution for a classical elastic medium and full linear Cosserat medium. It is shown that the Rayleigh wave is characterized by a range of forbidden frequencies, where this wave cannot propagate. The dispersion curve consists of two branches. One of them has a cut-off frequency and cut-off wavenumber.     

Using simulated Tianqin gravitational wave data and electromagnetic wave data to study the coincidence problem and Hubble tension problem

In this study, we used electromagnetic wave data (H0LiCOW, \begin{document}$ H(z) $\end{document}, SNe) and gravitational wave data (Tianqin) to constrain the interacting dark energy (IDE) model and investigate the Hubble tension and coincidence problems. By combining these four types of data (Tianqin+H0LiCOW+SNe+\begin{document}$ H(z) $\end{document}), we obtained the following parameter values with a confidence interval of \begin{document}$ 1\sigma $\end{document}: \begin{document}$ \Omega_m=0.36\pm0.18 $\end{document}, \begin{document}$ \omega_x=-1.29^{+0.61}_{-0.23} $\end{document}, \begin{document}$ \xi=3.15^{+0.36}_{-1.1} $\end{document}, and \begin{document}$H_0=70.04\pm $\end{document}\begin{document}$ 0.42~ {\rm kms}^{-1}{\rm Mpc}^{-1}$\end{document}. According to our results, the best value of \begin{document}$ H_0 $\end{document} shows that the Hubble tension problem can be alleviated to some extent. In addition, the center value of \begin{document}$ \xi+3\omega_x = -0.72^{+2.19}_{-1.19}(1\sigma) $\end{document} indicates that the coincidence problem is slightly alleviated. However, \begin{document}$ \xi+3\omega_x = 0 $\end{document} is still within the \begin{document}$ 1\sigma $\end{document} error range, which indicates that the ΛCDM model is still the model in best agreement with the observational data at present. Finally, we compared the constraint results of the electromagnetic and gravitational waves on the model parameters and found that the constraint effect of electromagnetic wave data on model parameters is better than that of simulated Tianqin gravitational wave data.     

Radar equations in the radio wave backscattering problem

We present a method for finding the relation between the singly scattered signal and the Fourier spectrum of dielectric permittivity fluctuations of a medium with regard to the scattering volume which is controlled by the antenna pattern and is not small. Using this method, we found a radar equation which relates the temporal Fourier spectrum of the scattered signal and the spatio-temporal spectrum of permittivity fluctuations. We also obtained a statistical radar equation to relate the statistically averaged spectral power of the scattered signal and the spectral density of permittivity fluctuations without the conventional assumption that the spatial correlation radius of irregularities is small compared with the Fresnel radius. Institute of Solar-Terrestrial Physics, Siberian Branch of the Russian Academy of Sciences, Irkutsk, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 43, No. 6, pp. 520–544, June, 2000.     

The effect of acoustic nonlinearity on nonlinear wave processes in solids: The inverse problem

The perturbation method is used to study nonlinear acoustic effects in solids that feature elastic, hysteresis, or inelastic nonlinearity. It is found that these media exhibit qualitatively different nonlinearity behavior laws, which facilitates classifying them based on the acoustic nonlinearity type.     

The influence of external noise on non-equilibrium phase transitions

The method of Ito stochastic differential equations is used to analyze the influence of external noise in non-equilibrium phase transitions. It is found that external noise deeply affects the behaviour of the system and gives rise to new phenomena not predicted by the deterministic analysis.     

The mean-field method in the problem of acoustic wave propagation in a turbulent atmosphere

We analyze the problem of acoustic-wave propagation in a turbulent atmosphere using the mean-field method. The equation for the sound pressure is written with accuracy up to terms that are linear with respect to the Mach number of the turbulent air flow. An expression for the attenuation constant of the mean field is obtained. For the turbulence model described by the von Kármán correlation function of fluctuations, the attenuation coefficient of the mean field is numerically studied in detail. It is shown that under typical conditions of the near-ground atmospheric layer, the predominant contribution to scattering of acoustic waves is given by the turbulent motion of the air masses. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 5, pp. 413–424, May 2008.     

The problem of the occurrence of neutrons of terrestrial origin during seismic wave travel

The results of experimental measurements of thermal neutrons in 1986–1997 in Pamir, which is one of the most seismoactive regions of the world, are studied. In this period, visible peaks in the thermal neutron flux near the Earth’s surface were found, especially in the periods near the upper and lower transits of the moon during a new moon or full moon, when the tidal gravitational wave reaches its maximum value. Additionally, about 500 earthquakes with m > 4 occurred in the same period of the operation of neutron counters. The time of seismic-wave travel across the given territory was known at a precision of less than 1 min (in some cases). Nevertheless, increases in neutron flux have never been observed during the travel of a seismic wave. Why is this? It appears that the mechanical effect on the Earth’s crust has the same impact with no respect to the cause of this effect; however, this was observed during experiments. This paper studies the reasons for this lack and the probable conditions that are favorable for an increase in terrestrial thermal neutron flux when a seismic wave travels across a territory.     

Approximate normalized wave functions for the finite-size Coulomb problem

Using perturbation methods developed previously for the finite-size energy shift, thes-state wave functions for a bound lepton in the Coulomb field of a nucleus with an arbitrary charge distribution are developed through order (Zα)². This technique allows a determination of the finite-size contribution to the normalization of the wave function up to order (Zα)², both for small separations of the lepton and nucleus and for the lepton outside the nucleus. General features of the wave function are discussea, including the transition of the Dirac problem to the (singular) point charge limit. A practical application is developed using these results.     

The shear viscosity of hard-sphere fluid via non-equilibrium molecular dynamics

The periodic boundary condition was generalized to maintain the stationary Couette flow. The shear viscosity and its shear-rate dependence were calculated from the temperature increase and the pressure tensor beyond the solid-fluid transition point.     

Solution of the Fokker-Planck equation for the shock wave problem

An eigenexpansion solution of the time-independent Brownian motion Fokker-Planck equation is given for a situation in which the external acceleration is a step function. The solution describes the heavy-species velocity distribution function in a binary mixture undergoing a shock wave, in the limit of high dilution of the heavy species and negligible width of the light-gas internal shock. The diffusion solution is part of the eigenexpansion. The coefficients of the series of eigenfunctions are obtained analytically with transcendentally small errors of order exp(–1/M), whereM 1 is the mass ratio. Comparison is made with results from a hypersonic approximation.