Mimic Simulations of Radio-Wave Propagation in a Randomly Irregular Ionosphere

We present the technique and results of mimic simulations of radio-wave propagation in a randomly irregular ionosphere with allowance for the Earth's sphericity and the background ionosphere. Based on consideration of the probability distributions of the angle of reception and of the corresponding amplitude, eikonal, and angle of radiation, obtained by the mimic modeling, we conclude that the most probable ray path is symmetric with respect to the region of its reflection from the ionosphere and that the mean reception angle and the corresponding mean radiation angle are equal. The simulations yield the statistical characteristics of a wave, such as the variances of the reception angle and the eikonal, as well as the correlation functions of the eikonal and the field. The simulation results concerning the variances of reception angles and eikonal are compared with the results of the first approximation of the perturbation theory. It is shown that the eikonal fluctuations in the irregularity-free space, caused by fluctuations of angles of the lower rays escaping from an ionospheric layer with random irregularities, should be taken into account.     

Phase transition at 204–250 K in the crystals of β-alanine: kinetically irreproduceable,or an artefact?

The crystals and the powder samples of β-alanine were studied in the wide temperature range by adiabatic calorimetry, differential scanning calorimetry, IR- and Raman spectroscopy and X-ray diffraction. No phase transitions could be observed. A small anomaly observed at about 256 K in the Cp(T) dependences measured for the samples re-crystallized from water was shown to be due to the presence of a small (about 0.14% of the total sample mass) amount of solvent inclusions. This anomaly was not observed in the solvent-free samples, either powders or single crystals.     

Random Motions at Finite Speed in Higher Dimensions

We present a general method of studying the transport process , t≥0, in the Euclidean space ℝ ^m , m≥2, based on the analysis of the integral transforms of its distributions. We show that the joint characteristic functions of are connected with each other by a convolution-type recurrent relation. This enables us to prove that the characteristic function (Fourier transform) of in any dimension m≥2 satisfies a convolution-type Volterra integral equation of second kind. We give its solution and obtain the characteristic function of in terms of the multiple convolutions of the kernel of the equation with itself. An explicit form of the Laplace transform of the characteristic function in any dimension is given. The complete solution of the problem of finding the initial conditions for the governing partial differential equations, is given. We also show that, under the standard Kac condition on the speed of the motion and on the intensity of the switching Poisson process, the transition density of the isotropic transport process converges to the transition density of the m-dimensional homogeneous Brownian motion with zero drift and diffusion coefficient depending on the dimension m. We give the conditional characteristic functions of the isotropic transport process in terms of the inverse Laplace transform of the powers of the Gauss hypergeometric function. Some important models of the isotropic transport processes in lower dimensions are considered and some known results are derived as the particular cases of our general model by means of the method developed.     

Monitoring environmental electromagnetic fields. 1. Remote-sensing methods

This paper discusses monitoring electromagnetic fields (natural and artificial) in the atmosphere. Methods are described for remote sensing of the atmosphere and surface in order to examine static and alternating electromagnetic-energy fluxes in the biosphere.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 69–79, December, 1991.     

A comparison of the results of a numerical simulation and an approximate calculation of the statistical characteristics of radio waves in a layer with random inhomogeneities of dielectric permittivity

We consider the formation algorithm for a random inhomogeneity field of dielectric permittivity of a medium that is used in simulations of the statistical characteristics of a wave that has propagated through a randomly inhomogeneous layer. We carry out a comparison of the statistical characteristics of a geometrical-optics wave, obtained via a numerical simulation, with the results of calculations of these characteristics by approximate formulae obtained using perturbation theory. It is pointed out that the applicability limits of the perturbation method, when solving geometrical-optics equations in a randomly inhomogeneous medium, depend on the formulation (one- or two-point) of the trajectory problem. It is shown that a calculation of the spatial correlation function of the field can be carried out using the perturbation method, even in the case of relatively strong fluctuations of dielectric permittivity. This is due to the fact that, in the region where this function differs markedly from zero, the correlation function of the eikonal obtained by the perturbation method is sufficiently accurate, and amplitude fluctuations are small.     

Physical principles of forecasting the characteristics of the ELF environmental electromagnetic background noise from the meteorological factors

Physical principles of forecasting the environmental electromagnetic background noise (EMBN) characteristics in the extra low frequency (ELF) range are suggested in the work based on an analysis of the meteorological conditions. Dependences of the spectral EMBN characteristics in the ELF range on the meteorological parameters such as the atmospheric pressure, ground wind velocity, temperature, and relative air humidity are obtained. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 89–94, September, 2008.     

Improvement of remainder term for the divisors problem

New bounds are obtained for the remainder term in the divisors problem.Translated from Matematicheskie Zametki, Vol. 6, No. 5, pp. 545–554, November, 1969.