Calculation of displacement function of crystal atoms in the presence of temperature gradient

The thermal conductivity equation is solved with allowance for experimental conditions. An expression for the displacement function is derived. A method for calculating the displacement functions for different axes of symmetry of a crystal is proposed.     

Stages of transformation of block elements

The property to have various representations is investigated for the block elements describing the solutions of boundary-value problems for sets of partial differential equations in the regions with a boundary. These representations have various destinations. One of the representations, which is called packed, is convenient for constructing solutions in block structures on the basis of solutions in separate blocks. Another representation, which is called unpacked, is convenient for a detailed investigation of the properties of solutions in an individual block of the block structure.     

混合物物态方程的计算

 在采用体积相加原理计算混合物物态方程的基础上,建立了一种物理模型确定混合物温度。根据混合物中各组分温度和压强平衡条件,采用压强-密度迭代方法计算给出混合物物态方程,编制了两种组分的混合物物态方程计算程序。为检验建立的温度模型的合理性及程序的有效性,分析了不同密度、温度状态的氢（H2）和钨（W）组成的混合物状态参量,计算了以下情形及其组合情形的混合物物态方程：H₂和W以不同质量比混合;质量比固定,单组分状态不同;温度区间和密度区间不同。研究表明:实际应用中在建立的混合物温度模型基础上确定的混合物物态方程是合理的。     

On the Equation of State of Coulomb Systems

A quantum statistical expression is given for the pressure of multi-component plasmas which is correct up to the second cluster coefficient. The Montroll-Ward formula for the pressure is evaluated for any degree of degeneration. As an example the thermodynamic stability of an electronhole plasma is discussed.     

Analysis of Calculation of the Critical Temperature of Metals

General considerations on the form of the real equation of state make it possible to assume that the ratio of the melting temperature to the critical temperature is constant for each group of elements. This assumption is verified for two groups of elements, the critical temperatures of which are measured. It is shown that, for certain groups of elements, the critical temperatures of which are calculated instead of being measured, this assumption is also valid. The critical temperatures of certain elements are calculated or refined.     

Distribution of energy of solutions of the wave equation on singular spaces of constant curvature and on a homogeneous tree

In the paper, the Cauchy problem for the wave equation on singular spaces of constant curvature and on an infinite homogeneous tree is studied. Two singular spaces are considered: the first one consists of a three-dimensional Euclidean space to which a ray is glued, and the other is formed by two three-dimensional Euclidean spaces joined by a segment. The solution of the Cauchy problem for the wave equation on these objects is described and the behavior of the energy of a wave as time tends to infinity is studied.The Cauchy problem for the wave equation on an infinite homogeneous tree is also considered, where the matching conditions for the Laplace operator at the vertices are chosen in the form generalizing the Kirchhoff conditions. The spectrum of such an operator is found, and the solution of the Cauchy problem for the wave equation is described. The behavior of wave energy as time tends to infinity is also studied.     

On calculation of volume fractions of competing phases

A method for calculating the volume fractions of phases in a system with several simultaneously growing phases is proposed. A solution of the problem is obtained for two-and three-dimensional spaces. The approximation of independent phases is considered, in which expressions for volume fractions have the simplest form. The high accuracy of this approximation is demonstrated.     

Modeling of Optical Waveguides and Devices by Combination of the Method of Lines and Finite Differences of Second Order Accuracy

Based on generalized transmission line equations a novel impedance/admittance transformation algorithm with finite differences is proposed and substantiated. The algorithm is of second order accuracy. It is combined with the Method of Lines. The algorithm is suitable for eigenmode calculations and for the analysis of optical waveguides and devices including anisotropic materials. The proposed algorithm is verified by numerical results for rib waveguide and azimuthally inhomogeneous fibres.     

Calculation of spectra of solids: Conduction electron susceptibility of Gd,Tb and Dy

The Gilat-Raubenheimer method simplified to tetrahedron division is used to calculate the real and imaginary part of the dynamical response function for electrons. A frequency expansion for the real part is discussed. The Lindhard function is calculated as a test for numerical accuracy. The conduction electron susceptibility is calculated for Gd, Tb and Dy using the RAPW energy bands by Keeton and Louks.     

Evolution of a microstructure of materials under irradiation

The evolution of a microstructure of metals (or alloys) under irradiation resulting in swelling of the material is considered for the case with the formation of Frenkel pairs. A closed system of equations describing the evolution of the microstructure of the material exposed to irradiation is obtained, and relationships for the swelling rate are derived. It is shown that the swelling rate varies linearly with time for a stationary source of point defects (the number of Frenkel pairs per lattice site). An expression for the swelling rate is deduced for a radiation source operating in a more realistic pulsed mode.     

The equation of state of solids

An equation of state for solids, in reduced variables, is obtained within the context of a system-independent formulation of the thermodynamics of high pressures. This formulation is valid for materials obeying a linear relationship between shock and particle velocities. An adequate set of scaling factors for pressure, compression, specific energy, and temperature, is first introduced. A modified Mie-Grüneisen equation, as well as many other thermodynamic relationships and coefficients, are then expressed in terms of reduced variables. Explicit expressions for the temperature along the Hugoniot, and for the equation of state, are obtained. It is also shown that when given in their reduced form, each of the two thermodynamic coefficients appearing in the equation of state can be considered as having the same constant value for many different materials. The possibility and convenience of using a “standard material” is discussed. Numerical results obtained using this reduced variables formalism are in good agreement with those computed or measured, by different authors, for various materials over a wide range of pressures. This is a good indication of the “universality” of the reduced equations obtained, and of the usefulness of the formalism.     

On the possibility of observation of the future for movement in the field of black holes of different types

It is shown for a spherically symmetric black hole of general type that it is impossible to observe the infinite future of the Universe external to the hole during the finite proper time interval of the free fall. Quantitative evaluations of the effect of time dilatation for circular orbits around the Kerr black hole are obtained and it is shown that the effect is essential for ultrarelativistic energies of the rotating particle.     

The intrinsic linearization of equilibria of nonholonomic systems

The linearization of equilibria of Hamiltonian systems is Hamiltonian; this has well-known and important implications for the spectrum. The analogous statement for nonholonomic systems is provided. It follows, for example, that the linearization of the ground state of a nonholonomic system is always Hamiltonian.     

Analysis of the Topology of the Kerr Metric

The equations of motion of a test particle are integrated for the field of a rotating Kerr black hole (BH) (in accordance with [1]). Due to the lack of analytical transformations for the Carter–Penrose diagrams (CPDs) for the Kerr metric, the topology of the Kerr BH is studied by analytical investigation of the equations of motion. Transformations for the CPDs for the Reisner–Nordström metric are analyzed. The problem of boundary conditions for the Reisner–Nordström topology is analyzed. A solution to this problem of boundary conditions is proposed. It is proved that, in the Reisner–Nordström topology, only one way to go to another universe is possible. For the Kerr topology, the possibility of the existence of an alternative transition to another universe that does not coincide with the universe for the ordinary transition is found. This alternative transition is performed through a surface with a zero radial coordinate (zero radius). Initial conditions for the falling particle are found that correspond to an alternative transition to another universe. The tidal forces acting on a falling body in the Kerr metric are estimated, and the possibility of the transition of the body to other universes without being destroyed by tidal forces is proved.     

耦合双原子Jaynes-Cummings模型的腔场谱H

研究了处于激发态的两原子与高Q腔场相互作用单光子过程的腔场谱,给出了初始光场为光子数态、相干态、压缩真空态时的腔场谱数值计算结果,分析了原子间偶极-偶极相互作用强度gα对腔场谱结构的影响.发现真空场Rabi峰,当gα较弱时为4峰,gα较强时为3峰结构;弱场数态(n＞0)时为5峰,强场时为3峰结构.相干态和压缩真空态时,谱结构与光子数分布有关,一般为复杂的多峰结构.结果表明,gα对峰位峰高都有影响,破坏了谱结构的对称性,但这种影响只在真空场和弱场时才较明显.     

The roles of extrinsic periodic information on the stability of stock price

The perturbation expansion for the nonlinear Schrödinger equation with a random potential that was developed in earlier works by some of us is extended to higher orders. As the order is increased a solution that is valid for longer time can be found. In particular it is found that Anderson localization persists in the fifth and sixth orders for times when perturbation theory is valid. The perturbation expansion is asymptotic and for the value of the nonlinearity parameter used, the fifth order is the optimal order of the perturbation theory. There are indications that for the sixth order perturbation theory may not be valid.     

Determination of the sign of the order parameter from MAS spectra of oriented molecules

The use of the intensities of the spinning sidebands in the magic-angle spinning spectra of oriented molecules is proposed for the determination of the signs of the order parameters. The method is demonstrated for benzene and chloroform oriented in nematic phases of liquid crystals. On the basis of the theoretical expressions derived for the various order sidebands, the applicability of the method for different experimental conditions is discussed.     

Regions of stability of high-power gyrotron oscillators

The problem of mode competition in a high-power gyrotron oscillator is considered. The regions of parameter space in which a preexisting large-amplitude mode is able to suppress competing satellites are determined for cases in which the coupling coefficients and cavity quality factors for the operating and satellite modes are different. In addition, the effect of beam quality on the regimes of stable single-mode operation is investigated. Generally speaking, the requirement of stable operation favors devices whose interaction length measured by the parameter μ is not too large. It is found that for μ near 10 the operation is relatively stable and μ near 17 is not     

On the correct writing of the law of conservation of amount of substance at the moving fluid-fluid interface

The reasons for the erroneous writing of the substance conservation law at the moving fluid-fluid interface, which is commonly encountered in related publications, are analyzed. A mathematical statement of this law that is valid for any curved surface that has a nonzero curvature in its equilibrium state is derived in terms of vector analysis. The new writing is independent of the coordinates and can be used for analysis of relaxation phenomena associated with nonlinear wave motions.     

The structure of anomalies for arbitrary dimension of the space-time

The construction of anomalies in Ward identities is investigated for arbitrary dimension of the space-time. If the internal symmetry group is semi-simple and compact we find that for even dimension of the space-time the anomalous term is unique and that no anomaly is constructible for odd dimension.