混合物状态方程的计算

多介质流体动力学过程的数值模拟往往涉及混合物状态方程的计算. 做图法和Newton 法是混合物状态方程计算常采用的方法, 前者虽直观精度却差, 后者计算效率高却只具有局部收敛性, 当解与其初始猜测值相差较远时Newton法不一定能够获得收敛解. 为此, 本文给出一种具有大范围收敛性的嵌入算法(imbedding method)求解混合物状态方程, 其基本思想是通过引入嵌入参数, 将待解的混合物状态方程和易解的混合物状态方程线性组合, 构成嵌入方程组, 当嵌入参数从0连续地变化到1 时, 嵌入方程组的解由易解的混合物状态方程的解连续地变化为待解的混合物状态方程的解. 嵌入方程组可由Newton法迭代求解, 也可转化为以嵌入参数为自变量的常微分方程组, 从而易于由成熟的计算方法如梯形法等进行求解. 进一步利用热力学基本关系, Maxwell形式的微分方程描述了压力和温度随嵌入参数的演化速率与应变速率和组分质量分数演化速率的关系. 对铅锡混合物热力学量的计算表明了本文算法的有效性.     

Abelian Extensions of the Group of Diffeomorphisms of a Torus

In this Letter we construct Abelian extensions of the group of diffecomorphisms of a torus. We consider the Jacobian map, which is a crossed homomorphism from the group of diffeomorphisms into a toroidal gauge group. A pull-back under this map of an invariant central 2-cocycle on a gauge group turns out to be an Abelian cocycle on the group of diffeomorphisms. In the case of a circle we get an interpretation of the Virasoro–Bott cocycle as a pull-back of the Heisenberg cocycle. We also give an Abelian generalization of the Virasoro–Bott cocycle to the case of a manifold with a volume form.     

A series of irreducible unitary representations of a group of diffeomorphisms of the half-line

We present a family of unitary representations of a group of diffeomorphisms of a finite-dimensional real Euclidean space using a family of quasi-invariant measures. In the one-dimensional case, for a special kind of group diffeomorphisms of the halfline, we prove the irreducibility of the representations thus obtained.     

Effects of noise on detection of amplitude increments of sinusoidal vibration of the skin.

Vibrotactile thresholds for detecting a 300-Hz signal in the presence of both a 300-Hz sinusoidal pedestal and a background noise were measured as a function of the amplitudes of the pedestal and noise. Threshold increased monotonically as a function of the amplitude of the noise, but was a nonmonotonic function of the amplitude of the sinusoidal pedestal. Negative masking, in which the pedestal facilitated detection of the test stimulus, was observed in the absence of background noise and in the presence of subthreshold background noise when the pedestal was near or below threshold. Negative masking disappeared when the experiment was conducted in the presence of moderately intense to intense background noise. The results are consistent with a peripheral high-energy threshold for taction.     

Improvement of accuracy of interferometric measurement of wedge angle of plates

A method is proposed for improving the accuracy of measuring the wedge angle of transparent plates using a lateral-shear holographic interferometer. Consecutive processing of a pair of interferograms with doubled number of interference fringes leads to reduction of the observational error by a factor of two compared to traditional interferometric methods. Data on the experimental validation of the method are presented.     

Application of the method of smooth perturbations to the solution of problems of optical tomography of strongly scattering objects containing absorbing macroinhomogeneities

Monochromatic small-angle Fraunhofer diffraction from a spiral is studied as a function of its stretching. A simple relation between locations of the principal maxima and geometrical parameters of a spiral is obtained. Diffraction from a spiral is analyzed theoretically in the linear approximation of the boundaries of the profile of a periodic unit. An analytical expression for the light intensity at any point of a screen is derived, and analytical relations between locations of the principal maxima and geometrical parameters of a spiral, which are identical to the relations established experimentally, are obtained. The possibility for utilizing the results obtained in the development of systems of automatic control of the main geometrical parameters of spiral objects in the process of their production is demonstrated by the example of the analysis of diffraction patterns from a standard metallic screw and a twisted capron fiber.     

Approximation of equations of motion of particle in circular accelerator

It is shown that the equations of motion of a particle in a circular accelerator with general azimuthally periodic guiding magnetic field are substantially simplified if a large number of field periods is assumed. The simplified equations permit a clear picture of the influence of the magnetic field parameters on the dynamics of the accelerated particle to be obtained easily.     

Analysis of the stability of states of semiconductor superlattice in the presence of tilted magnetic field

A method to calculate the spectrum of the Lyapunov exponents for a periodic semiconductor nanostructure (superlattice) described in the framework of a semiclassical approach is proposed. The analysis of the stability of a stationary state in such a system is performed for autonomous dynamics and in the presence of a tilted magnetic field. The method of the Lyapunov exponents is used to study the effect of the tilted magnetic field on the stability of the stationary state and the characteristics of subterahertz oscillation regimes.     

Characteristics of the process of reorientation of bipolar drops of a nematic with rigidly fixed poles

The director configuration in a bipolar drop of a nematic with rigidly fixed poles is calculated as a function of the electric field directed perpendicular to the symmetry axis of the drop. It is shown that the reorientation of the drop is a dual process: a threshold process in the region where the initial director orientation is orthogonal to the electric field, and a nonthreshold process elsewhere in the drop. A relation for determining the critical field is obtained. Experimental investigations of the characteristics of scattered light for a film of polymer-encapsulated liquid crystals confirm the computational results. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 9, 696–700 (10 May 1998)     

On scattering of electromagnetic radiation by inhomogeneities of the velocity of motion of the medium

Analysis of the scattering of a plane monochromatic electromagnetic wave by an inhomogeneity of the velocity of motion of the medium is carried out. The inhomogeneity corresponds to the rotation of a finite portion of the medium with a constant angular velocity under the conditions of spatial homogeneity of the permittivity and the permeability. The case of oblique incidence of the wave is studied. The scattering cross sections for an inhomogeneity having the shape of a cylinder or a sphere of different dimensions are found for different angles of incidence of radiation.     

Observation of the condensation of a gas of interacting grains

We consider an ensemble of grains that interact through a dipole-dipole interaction. A granular gas is formed by the vertical motion of a piston at the bottom boundary of the system. The interaction between the grains is controlled by an horizontally applied magnetic field. When the speed of the piston is decreased, we observe a transition from a low density to a high density phase. When the interaction between grains is weak, the transition is continuous. It is discontinuous for stronger interaction. The phase diagram displays strong similarities with the ones observed for usual equilibrium phase transitions.     

Formation of a sequence of ultrashort signals in a collision of pulses consisting of a small number of oscillations of the light field in nonlinear optical media

Collisions of pulses consisting of a small number of oscillations and propagating in a nonlinear optical medium unidirectionally but with different group velocities because of a difference in the spectral composition are considered. It is shown that, at intensities of radiation ensuring the superbroadening of its spectrum, the interaction of two pulses can result in the formation of a quasi-discrete spectral supercontinuum whose temporal structure is described by a sequence of ultrashort signals with a nearly rectangular shape.     

Mixture of outgoing and incoming electromagnetic radiation. Change of mass of the source of radiation

In a previous paper the author, using a method of successive approximations, verified by means of the Einstein-Maxwell equations of general relativity the well-known result that outgoing electromagnetic radiation from a source conveys energy, so that the source loses gravitational mass corresponding to this energy. The purpose of this work is to show a similar result for the general case of any mixture of outgoing and incoming radiation.This work is included in a thesis submitted by the author (1964) to the University of London for the degree of Ph.D.     

Observation of a collective mode of an array of transmon qubits

Arrays of transmon qubits coupled to a λ/2 superconducting coplanar waveguide resonator have been studied by microwave spectroscopy. The emergence of a collective mode has been discovered for a cluster of N > 5 qubits, whose coupling constant to the electromagnetic field in the resonator is √N times greater compared to a single qubit. In addition, the emergence of collective multiphoton transitions exciting higher levels of a qubit cluster has been demonstrated and the interaction of an individual qubit with such a cluster has been investigated.     

Development of techniques of nondestructive testing of thermal properties of fuel elements with dense fuel

The results of the development of the techniques for determining the thermal resistance between a fuel and a fuel-element cladding and the fuel thermal conductivity, oriented to applications under conditions of a shielding box, are described. The schematic of the laboratory setup is presented, using which the operability of the techniques is shown on a fuel element prototype with dense fuel simulators.     

Relativistic scattering of electromagnetic radiation by inhomogeneities of the velocity of motion of the medium

Analysis of the relativistic scattering of electromagnetic radiation by inhomogeneities of the velocity of the motion of a medium is carried out. The characteristics of the scattering of a plane monochromatic wave by a rotating dielectric cylinder surrounded by an immobile medium with a refractive index the same as that of the cylinder are calculated. The differential scattering cross section is found. It is shown that the rotation of particles with actual parameters may yield a significant contribution to the scattering, of the same order of magnitude or larger than the contribution made by Rayleigh and Raman scattering.     

Investigation of the regimes of mixing of superconducting tunneling structures

The regimes of operation of a superconductor–insulator–superconductor tunnel junction based on three-layer structures Nb/AlOx/Nb and Nb/AlN/NbN as a harmonic mixer (for frequencies of the order of 600 and 20 GHz, respectively) and a frequency up-converter (in the frequency range from 0.1 to 5.0 GHz) have been investigated experimentally. The quasiparticle and Josephson mixing regimes have been compared. It has been shown that, in some practical applications, such as the use of the superconductor–insulator–superconductor junction as a cryogenic harmonic phase detector, the Josephson mixing regime is more preferable, because it can provide a higher signal and a greater signal-to-noise ratio as compared to the quasiparticle mixing regime. It has also been demonstrated that the Josephson mixing regime is promising for the use in signal multiplexing systems for superconducting detectors.     

Effect of delay of the thermocapillary response of a transparent liquid layer during laser heating of the absorbing substrate

The effect of delay in the thermocapillary response of a transparent liquid layer on an absorbing substrate during its heating by a laser beam is discovered. The response is an interference pattern formed on a screen placed in the beam cross section by the beam reflected from a thermocapillary dip. It is found that the delay time of the response of a thin (h < 1.8 mm) layer of a liquid in a viscosity range of 3–6 mPa s to a 20.9-mW exciting beam from a He-Ne laser (λ = 633 nm) is proportional to the squared layer thickness with a proportionality factor depending on the viscosity and thermal diffusivity of the liquid.