Formation of a bistructure of a solid in a computer experiment

Molecular-dynamics was used to investigate the structural changes occurring in a three-dimensional solid when the solid is transferred from an amorphous into a crystalline state. Crystal cells of a new type — pentadecahedrons with five square lateral faces and ten regular triangular faces at the vertices of a cell — were found for the first time in a computer experiment. It is shown that a bistructure consisting of crystal cells of different types, including cells with five-fold symmetry axes, are stable in the solid. Fiz. Tverd. Tela (St. Petersburg) 40, 1919–1924 (October 1998)     

Instability of a flat horizontal interface between a thin layer of a ferrofluid and a thin layer of a nonmagnetic liquid in the presence of a vertical magnetic field

An asymptotic analysis of the equations and boundary conditions of fluid dynamics is performed, and a nonlinear model is constructed for the onset of the development of Rosensweig instability in a thin horizontal ferrofluid layer at rest covered with a thin layer of a lighter nonmagnetic liquid. The surface of a nonmagnetized slab is the lower boundary of the ferrofluid, and the interface with a gas is the upper boundary of the nonmagnetic liquid. The pressure in the gas is constant. The instability being considered arises upon the application of a rather strong uniform vertical magnetic field. The proposed model involves five dimensionless parameters. The critical magnetization of the initial ferrofluid layer with a flat upper boundary and the threshold wave number are found. The effect of the governing parameters on the instability region and on the wavelength of the fastest growing mode is studied in the linear formulation of the problem.     

Determination of a response function of a thermocouple using a short acoustic pulse

This paper reports on an experimental technique to determine a response function of a thermocouple using a short acoustic pulse wave. A pulse of 10 ms is generated in a tube filled with 1 bar helium gas. The temperature is measured using the thermocouple. The reference temperature is deduced from the measured pressure on the basis of a laminar oscillating flow theory. The response function of the thermocouple is obtained as a function of frequency below 50 Hz through a comparison between the measured and reference temperatures.     

Behavior of a free surface of a magnetic fluid containing a magnetizable cylinder

The deformation of the free surface of a magnetic fluid containing a cylinder made of a magnetizable material subjected to a uniform applied magnetic field is analyzed. The statics and dynamics of a magnetic fluid free surface is studied theoretically and experimentally. A discontinuous (jump-like) change of the surface shape is shown to occur when the applied magnetic field gradually increases or decreases. If the applied magnetic field increases and then decreases, a hysteresis of the shape is observed.     

Design of a suspension of a training sulky

A design study based on a modelling approach was used to optimise the characteristics of a new concept of suspension for training sulkies. The numerical model of sulky including the suspension and, in a second stage, a mechanical model of driver, allowed the definition of technical specifications. They were used to manufacture a prototype of suspension mounted on a current production model of sulky. The prototype of suspension was then tested in the lab and in a racecourse in real conditions of use.The resulting vibration exposure was assessed from vibration measurements. It was slightly lower than the limit value enacted in the European Vibration directive (1.15 m s²), but drastically reduced in comparison with the exposure measured on the original sulky (2.56 m s²). The prototype and moreover the design procedure is currently in a transfer process towards sulky manufacturers.     

Inferring a Property of a Large System from a Small Number of Samples

Inferring the value of a property of a large stochastic system is a difficult task when the number of samples is insufficient to reliably estimate the probability distribution. The Bayesian estimator of the property of interest requires the knowledge of the prior distribution, and in many situations, it is not clear which prior should be used. Several estimators have been developed so far in which the proposed prior us individually tailored for each property of interest; such is the case, for example, for the entropy, the amount of mutual information, or the correlation between pairs of variables. In this paper, we propose a general framework to select priors that is valid for arbitrary properties. We first demonstrate that only certain aspects of the prior distribution actually affect the inference process. We then expand the sought prior as a linear combination of a one-dimensional family of indexed priors, each of which is obtained through a maximum entropy approach with constrained mean values of the property under study. In many cases of interest, only one or very few components of the expansion turn out to contribute to the Bayesian estimator, so it is often valid to only keep a single component. The relevant component is selected by the data, so no handcrafted priors are required. We test the performance of this approximation with a few paradigmatic examples and show that it performs well in comparison to the ad-hoc methods previously proposed in the literature. Our method highlights the connection between Bayesian inference and equilibrium statistical mechanics, since the most relevant component of the expansion can be argued to be that with the right temperature.     

Entropy of a needle in a haystack

In a quantum search algorithm, the initial state which is a linear superposition of all possible basis states is a separable state. At each iteration, the state becomes more and more entangled until eventually it disentangles and reverts to a separable state consisting of the marked state. It is therefore interesting to study how entanglement changes in a Grover search algorithm.     

Formation of a high-frequency subpulse upon propagation of a femtosecond pulse in a medium with a saturable potential

On the basis of computer simulation of propagation of femtosecond light pulses in terms of the one-dimensional nonstationary nonlinear Maxwell equations with a saturable restoring force, the possibility of formation of a sequence of subpulses with different carrier frequencies is shown. The formation of frequency-modulated pulses with an asymmetric distribution of spectral components with respect to the center of a local line is demonstrated. Appearance of such pulses indicates that a hysteretic dependence of the frequency of the corresponding local line on the amplitude of an external signal can be realized.     

Generation of a precursor of a pressure pulse in materials with a cluster structure

A study of the response of a heterogeneous material (stivlon) to a short pressure pulse reveals a qualitatively new effect: the onset of oscillatory precursors of the main pressure pulse when the concentration of a filler randomly distributed in a binder material exceeds a threshold value. The mechanism for the onset and propagation of these precursors is investigated on the basis of a cluster model. The results of a numerical simulation are compared with the experimental data. Zh. Tekh. Fiz. 67, 19–25 (November 1997)     

Solving a relativistic quasipotential equation for a superposition of a nonlocal separable and a local quasipotential

Within the relativistic quasipotential approach to quantum field theory, a method is developed for solving a finite-difference quasipotential equation for the case where a total quasipotential describing the interaction of two relativistic spinless particles of unequal masses is a superposition of a nonlocal separable and a local quasipotential. The cases are investigated where the local component of the total interaction—it is assumed to be known—either admits or does not admit the existence of bound states. This makes it possible to obtain an exact expression for the increment of the phase shift, to determine the conditions of the existence of bound states, and to give a generalization of the Levinson theorem.     

Propagation of a localized wavepacket in a metamaterial with a negative index of refraction

Propagation properties of electromagnetic waves in a medium with a negative index of refraction are investigated. A model of a physical signal that combines simultaneously qualities of both a spatially-localized beam and a wavepacket was used as the incident wave. Such a choice was necessary because of the strong frequency dispersion of metamaterials in the spectral region with a negative index of refraction. An approximate analytical solution was derived that describes the propagation dynamics of such a signal through a slab made of material showing simultaneously a negative dielectric permittivity and magnetic permeability. Presented at the XIIIth International Conference “Physics of Pulse Discharges in Condensed Media,” August 21–25, 2007, Nikolaev, Ukraine. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 75, No. 2, pp. 187–193, March–April, 2008.     

Diffraction of a Bose-Einstein condensate from a magnetic lattice on a microchip

We experimentally study the diffraction of a Bose-Einstein condensate from a magnetic lattice, realized by a set of 372 parallel gold conductors which are microfabricated on a silicon substrate. The conductors generate a periodic potential for the atoms with a lattice constant of 4 microm. After exposing the condensate to the lattice for several milliseconds we observe diffraction up to fifth order by standard time of flight imaging techniques. The experimental data can be quantitatively interpreted with a simple phase imprinting model. The demonstrated diffraction grating offers promising perspectives for the construction of an integrated atom interferometer.     

Application of a reflector with a nonuniform field in a mass-reflectron

The conditions under which the nonuniform compensating field of the reflector of the mass-reflectron can be generated with an acceptable accuracy at the symmetry axis of the reflector and extrapolated to the radial neighborhood of the axial line are determined. The plots that illustrate the distribution of the calculated nonuniform field of the reflector, the possibilities for implementation, and errors of focusing with respect to time of flight in the radial neighborhood are presented. Analytical expressions for the calculation of the time of flight of ions in the reflector in which the field distribution is described using a power series and analytical expressions for the calculation of the field distribution in the reflector in which the time of flight is determined using a power series are derived. A method for the analytical calculation of the compensating nonuniform field of the reflector based on the given dependence of the time of flight in the absence of such a field is proposed using a solution to the Abel integral equation. The solution to this equation yields analytical expressions for the calculation of the compensating field of the reflector in mass-reflectrons that contain the zero-field drift space and regions of acceleration (deceleration) of ions with a uniform field.     

Relaxation of a dislocation in a nanocrystallite

Experimental studies of dislocations in nanoparticles are just beginning. The corresponding theoretical models are still lacking. In this context, the author analyzes relaxation of a dislocation in a nanoparticle. Mechanistically, this process is considered to occur primarily via dislocation drift induced by the stress-related image forces. Elementary dislocation displacements include the formation of a kink at one of the sides of the dislocation line, its diffusion along this line, and annihilation at the opposite side. For this mechanism, the dependence of the time of dislocation disappearance on the nanoparticle size has been identified.     

Rigorous solution of a problem for a cylindrical cavity containing a ferrite

Conclusions Equation (6) relates the complex frequency for a TM_nmo mode in a cylindrical cavity to the geometrical parameters, ferrite parameters, and volume and position of the specimen.Formula (6) is a generalization of characteristic equations previously derived [3, 4], which are of great value.The dispersion equation of (6) is of interest in that it allows one to calculate the effects of the dielectric parameters on the cavity, which is of value if a large tuning range is needed.Numerical results are rather laborious to obtain, but some valuable conclusions can be drawn in a relatively simple fashion, as will be shown in a forthcoming paper.     

Validating a hypothesis of the form of a correlation function of a stationary random process

The problem of validating a statistical hypothesis stating that the correlation function of a stationary Gaussian random process possesses a specified form is considered for the case in which measurements of the process are performed at arbitrary moments of time. Anzhero-Sudzhen Division, Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 10–15, April, 1998.     

Spectrum of a particle on a polyhedron enclosing a synthetic magnetic monopole

We consider a single particle hopping on a tight binding lattice formed by the vertices of a regular polyhedron and discuss the effect of a magnetic monopole enclosed in the polyhedron. The presence of the monopole induces phases on the hopping terms, given by Peierls substitution. By requiring the flux through each face of a regular polyhedron to be the same, Dirac’s quantization condition is obtained in this discrete setting. For each regular polyhedron, we calculate the energy spectrum for an arbitrary value of the flux through a Dirac string coming in from one of the faces. We find that the energy levels are degenerate only when the flux through the Dirac string corresponds to a quantized monopole. We show that the degeneracies in the presence of the monopole can be classified using the double group of the symmetry of the polyhedron and label all energy levels with corresponding irreducible representations.     

Conductivity of a two-dimensional model of a structurally anisotropic composite with a system of scratches

The conductivity of a two-dimensional model of a structurally anisotropic composite, an isotropic matrix with nonconducting inclusions in the form of parallel scratches, is considered. The centers of the scratches are randomly distributed over the (x, y) plane. An approximate method is applied to derive an expression for the effective conductivity tensor, which satisfactorily describes of the electric conductivity of the model over a wide range of concentrations.