Solution of A. Einstein’s Problem on the Density of Matter in the Universe

Russian Physics Journal - On the basis of the special theory of relativity and a solution of the Schwarzschild equations of general relativity, a generalized equation of...     

Jeans instability analysis in the presence of heat in Eckart’s frame

It is shown that the coupling of heat with acceleration first proposed by Eckart would have an overwhelming effect in the growth of density mass fluctuations, even in non-relativistic fluids in the presence of a gravitational field. Gravitational effects would be negligible if the heat-acceleration relation is assumed to be valid for the hydrodynamic equations. A direct implication of this result is that recent alternative first order in the gradients theories must be taken into account while describing a special relativistic fluid.     

The effect of an aircraft’s boundary layer on propeller noise

This study concerns the influence of the boundary layer at an aircraft??s fuselage, simulated by an infinite hard cylinder, on propeller noise in the acoustic far field. Also studied is the effect of the boundary layer on noise as a function of the thickness and profile of the mean velocity of the boundary layer, the Mach number of the incident flow, and the rotation speed of the propeller. It is shown that the boundary layer at the fuselage can substantially modify propeller noise in the far field and should therefore be taken into account in calculating community noise.     

Comment on “Role of the velocity frame of reference in thermodiffusion in liquid mixtures” by M. Eslamian,C.G. Jiang and M.Z. Saghir

We analyze the material transport equations (MTE) derived by Eslamian and co-authors and address the criticism expressed regarding the approach formulated in our previous work. In doing so, we show that the MTE formulated by Eslamian and co-authors are valid only in closed stationary non-isothermal systems in combination with the restrictions on the Onsager coefficients formulated in our work which is criticized, and that for non-stationary systems the approach we took can be used.     

A.A. Ovchinnikov’s works on nonlinear dynamics and augmentations

This work is a tribute to fond memories of Aleksandr Anatol’evich Ovchinnikov, which touches upon only one of his multifaceted scientific activities, the dynamics of nonlinear systems, more specifically, its practical applications to the vibrational spectroscopy of polyatomic molecules and molecular crystals. A.A. Ovchinnikov was the first to predict and explain a number of peculiarities in the positions and intensity of lines in IR spectra. It was demonstrated that these peculiarities are associated with a substantial nonequilibrium in the population of vibrationally excited states: because of the nonlinearity of the interaction of atoms, the dynamic behavior of such systems may results in the localization of energy on certain vibrational modes. A.A. Ovchinnikov analyzed in detail possible cases and made predictions, which were confirmed experimentally 20 years later. Results of our recent studies are also briefly outlined, studies that cannot be considered a direct continuation of A.A. Ovchinnikov’s work, but which are nevertheless influenced by his ideas and by the results of our joint works.     

List of Ya.A. Smorodinsky’s publications

A list of Ya. Smorodinsky’s articles published in science journals is presented. The text was submitted by the author in English.     

A note on the integral formulation of Einstein’s equations induced on a braneworld

We revisit the integral formulation (or Greens function approach) of Einsteins equations in the context of braneworlds. The integral formulation has been proposed independently by several authors in the past, based on the assumption that it possible to give a reinterpretation of the local metric field in curved spacetimes as an integral expression involving sources and boundary conditions. This allows one to separate source-generated and source-free contributions to the metric field. As a consequence, an exact meaning to Machs Principle can be achieved in the sense that only source-generated (matter fields) contributions to the metric are allowed for; universes which do not obey this condition would be non-Machian. In this paper, we revisit this idea concentrating on a Randall–Sundrum-type model with a non-trivial cosmology on the brane. We argue that the role of the surface term (the source-free contribution) in the braneworld scenario may be quite subtler than in the 4D formulation. This may pose, for instance, an interesting issue to the cosmological constant problem.     

Relation of Poisson’s ratio on average with Young’s modulus. Auxetics on average

A linear relation between the Poisson’s ratio averaged along the transverse directions and Young’s modulus of the tensed cubic crystal is established. It is found that the coefficients of the linear relation in the dimensionless form depend on two dimensionless elastic parameters combined from three compliance coefficients. By virtue of this fact, the form of angular regions of the crystal orientation with negative Poisson’s ratio on average varies as the magnitude of one dimensionless coefficient and the sign of the other one. We find the critical value of the dimensionless parameter at which there is the topological change in the structure of the angular regions occurs is established.     

Using Lorentz’s theorem for studying the propagation wave packets in a nonlinear medium

We obtain integral relationships expressing the amplitude of wave-packet field on the output surface of a layer via the field amplitude on the input surface, the field on the side surface of the layer, and the integral of the nonlinear currents inside the layer at the previous times in the spectral and spatiotemporal forms. These relationships allow one to perform studies and develop numerical simulation algorithms of propagation and interaction of wave packets which have wide frequency and angular spectra, including calculations of excitation of evanescent waves in the case of sharp focusing or formation of supernarrow filaments. Using the obtained relationships, we propose an algorithm that employs a simple iteration of the first order and allows one to significantly speed up the calculations. The possibility of using the fast Fourier transform to develop algorithms for numerical simulation of the boundary-value problems of nonlinear optics is demonstrated.     

Symmetry Breaking in Laughlin’s State on a Cylinder

We investigate Laughlin’s fractional quantum Hall effect wave function on a cylinder. We show that it displays translational symmetry breaking in the axial direction for sufficiently thin cylinders. At filling factor 1/p, the period is p times the period of the filled lowest Landau level. The proof uses a connection with one-dimensional polymer systems and discrete renewal equations.     

Reply to a comment by S.N. Semenov and M.E. Schimpf on ‘Role of the velocity frame of reference in thermodiffusion in liquid mixtures’, Philosophical Magazine vol. 92, 705 (2012), by M. Eslamian,C.G. Jian and M.Z. Saghir.

A small angle X-ray scattering (SAXS) study of nanovoids in 99.988 and 99.995?at.% aluminium is presented. Absolute intensity calibration using a glassy carbon standard is used to extract the weak SAXS signature from nanovoids introduced by thermal quenching. SAXS analysis methods, including Guinier, Porod and Indirect Transform, are used to obtain values for the void–size, number distribution and volume fraction, as well as measures of the void-metal matrix interface structure in quenched aluminium samples. The SAXS analysis has identified a residual impurity effect on void formation and has been used to characterize trends in nanovoid size, number distribution and interface structure as a function of ageing time at elevated temperatures (artificial ageing). The work presented here, including identification of experimental tools that can be readily improved, demonstrates that SAXS studies are capable of providing precise characterization of nanovoid structure in aluminium. This level of information will be useful in developing phenomenological models of void nucleation and growth capable of linking atomic scale phenomena to macroscopic material properties.     

Solution of Maxwell’s equations on a de Sitter background

The Maxwell equations for the electromagnetic potential, supplemented by the Lorenz gauge condition, are decoupled and solved exactly in de Sitter space–time studied in static spherical coordinates. There is no source besides the background. One component of the vector field is expressed, in its radial part, through the solution of a fourth-order ordinary differential equation obeying given initial conditions. The other components of the vector field are then found by acting with lower-order differential operators on the solution of the fourth-order equation (while the transverse part is decoupled and solved exactly from the beginning). The whole four-vector potential is eventually expressed through hypergeometric functions and spherical harmonics. Its radial part is plotted for given choices of initial conditions. We have thus completely succeeded in solving the homogeneous vector wave equation for Maxwell theory in the Lorenz gauge when a de Sitter space–time is considered, which is relevant both for inflationary cosmology and gravitational wave theory. The decoupling technique and analytic formulae and plots are completely original. This is an important step towards solving exactly the tensor wave equation in de Sitter space–time, which has important applications to the theory of gravitational waves about curved backgrounds.     

Turbulent pressure fluctuations in a long cylinder’s boundary layer in the longitudinal flow around it

Frequency spectra of the turbulent pressure’s pulsations measurements have been performed in the low-noise wind tunnel on the extended cylinder’s surface during the longitudinal flow around it. The measurement results for frequency spectra caused by the integral contribution of all the pressure field’s modes as well as only the zero (ring) mode are presented. The obtained results are compared with other known experimental data. The longitudinal cross-spectra of the pressure field for the zero mode have been measured. With the help of Fourier transformation for the cross-spectra the analytical expressions for dimensional and dimensionless wavenumber-frequency spectrum of the zero mode have been obtained. The frequency-wave’s spectrum features considering large wavenumbers are discussed.     

Searching for a response: the intriguing mystery of Feynman’s theoretical reference amplifier

We analyze Feynman’s work on the response of an amplifier performed at Los Alamos and described in a technical report of 1946, as well as lectured on at the Cornell University in 1946–47 during his course on Mathematical Methods. The motivation for such a work was Feynman’s involvement in the Manhattan Project, for which the necessity emerged of feeding the output pulses of counters into amplifiers or several other circuits, with the risk of introducing distortion at each step. In order to deal with such a problem, Feynman designed a theoretical “reference amplifier”, thus enabling a characterization of the distortion by means of a benchmark relationship between phase and amplification for each frequency, and providing a standard tool for comparing the operation of real devices. A general theory was elaborated, from which he was able to deduce the basic features of an amplifier just from its response to a pulse or to a sine wave of definite frequency. Moreover, in order to apply such a theory to practical problems, a couple of remarkable examples were worked out, both for high-frequency cutoff amplifiers and for low-frequency ones. A special consideration deserves a mysteriously exceptional amplifier with best stability behavior introduced by Feynman, for which different physical interpretations are here envisaged. Feynman’s earlier work then later flowed in the Hughes lectures on Mathematical Methods in Physics and Engineering of 1970–71, where he also remarked on causality properties of an amplifier, that is on certain relations between frequency and phase shift that a real amplifier has to satisfy in order not to allow output signals to appear before input ones. Quite interestingly, dispersion relations to be satisfied by the response function were introduced.