Local density of states of a finite-sized rectangular-lattice photonic crystal with separable profile of permittivity

A different approach in the calculation of two-dimensional local density of states has been presented for a two-dimensional finite rectangular-lattice photonic crystal with a separable profile of permittivity. Approximate staircase structures are already shown to be useful for their ability to reproduce actual properties of practical square lattice photonic crystals. Using the effective resonance approach in a Fabry–Perot resonator and transfer matrix method an analytical expression for calculating a two-dimensional local density of states can be derived for both polarisations in the structure. It is shown that for this geometry one can resolve the modes as a product of two separate functions each being a function of x- and y-coordinates. The results have been investigated for the two-dimensional local density of states in the ordered finite structure and in the disordered structure. The main advantage of this method in calculating the local density of states is its extremely efficient numerical evaluations. As an application we introduce a cavity-like defect in the vicinity of a waveguide-like defect and examine the variation of local density of states in the plane of the structure at band gap frequency.     

Calculation of short-range order in the method of cluster components

A scheme is proposed for calculating the short-range order in the method of cluster components for an n-component solid solution, taking into account an arbitrary number of spheres. The calculation of a single-, two-, and three-coordination spheres for a binary system and a calculation of a single sphere for a triple system are considered in detail. In the case of a binary system the possible type of property-composition dependence for a random distribution of the atoms in the case of one, two, and three coordination spheres are analyzed. The method is illustrated using a calculation of the concentration dependence of the elasticity constants of a KI_cBr_1-c solid solution.     

Analytic-numerical description of asymptotic solutions of a Cauchy problem in a neighborhood of singularities for a linearized system of shallow-water equations

S. Yu. Dobrokhotov, B. Tirozzi, S. Ya. Sekerzh-Zenkovich, A. I. Shafarevich, and their co-authors suggested new effective asymptotic formulas for solving a Cauchy problem with localized initial data for multidimensional linear hyperbolic equations with variable coefficients and, in particular, for a linearized system of shallow-water equations over an uneven bottom in their cycle of papers. The solutions are localized in a neighborhood of fronts on which focal points and self-intersection points (singular points) occur in the course of time, due to the variability of the coefficients. In the present paper, a numerical realization of asymptotic formulas in a neighborhood of singular points of fronts is presented in the case of the system of shallow-water equations, gluing problems for these formulas together with formulas for regular domains are discussed, and also a comparison of asymptotic solutions with solutions obtained by immediate numerical computations is carried out.     

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.     

Equations of Relativistic and Quantum Mechanics and Exact Solutions of Some Problems

Relativistic invariant equations are proposed for the action function and the wave function based on the invariance of the representation of the generalized momentum. The equations have solutions for any values of the interaction constant of a particle with a field, for example, in the problem of a hydrogen-like atom, when the atomic number of the nucleus Z > 137. Based on the parametric representation of the action, the expression for the canonical Lagrangian, the equations of motion and the expression for the force acting on the charge during motion in an external electromagnetic field are derived. The Dirac equation with the correct inclusion of the interaction for a particle in an external field is presented. In this form, the solutions of the equations are not limited by the value of the interaction constant. The solutions of the problem of charge motion in a constant electric field, problems for a particle in a potential well, and penetration of a particle through a potential barrier, as well as problem of a hydrogen atom are presented.     

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.     

Investigation of the Kernel of the Evolution Operator for One Class of Potentials

The convergence of the Schwinger–DeWitt expansion in quantum mechanics is investigated for a special class of potentials for which the squared derivative of a potential (e.g., the centrifugal potential, the modified Peschle–Teller potential, or the potential specified by the Weierstrass function) is represented as a polynomial in the powers of the potential itself. It has been established for which representatives of the class the expansion diverges and for which it converges (convergence may take place only at certain discrete values of the charge). For potentials singular at zero, the absence of singularities in the formula for the kernel has been demonstrated. A generalization of potentials with a converging expansion to a multidimensional case is proposed.     

New type of low temperature source of Ultra-cold neutrons and production of continous beams of UCN

We discuss a new type of source for Ultra-cold neutrons (UCN) in which the UCN are produced in a thin film on the walls of a cryogenic container. The UCN build up to a significant density inside the container, and the build-up time can be adjusted without effecting the UCN density. Applications to the production of intense, continous beams of UCN for scattering experiments are emphasized. The new source is well suited for installation inside the moderator of an intense neutron source.     

Investigation of Galilean invariance of multi-phase lattice Boltzmann methods

We examine the Galilean invariance of standard lattice Boltzmann methods for two-phase fluids. We show that the known Galilean invariant term that is cubic in the velocities, and is usually neglected, is a major source of Galilean invariance violations. We show that incorporating a correction term can improve the Galilean invariance of the method by up to two orders of magnitude for large velocities. We found that this is true in particular for methods in which the interactions are incorporated through a forcing term. Methods in which interactions are incorporated through a non-ideal pressure tensor only benefit for large velocities.     

Statistics of mesoscopic ensembles of bosons and fermions

Equilibrium distribution functions are obtained for boson and fermion ensembles with a limited number of particles. It is shown that the number-of-particle distribution functions in different quantum states are statistically dependent; this dependence disappears only for a large number of particles in the ensemble. The distributions are transformed into the Boltzmann distribution at a high temperature and into the Bose-Einstein and Fermi-Dirac distributions for a large number of particles in the ensemble.     

Modeling of the interrelation of mechanical and electrical parameters of the surface of solids

A mathematical model for the determination of physical constants in equations of state at the interface between a metal and an inert gas medium has been developed in terms of the surface physics and thermodynamics of nonequilibrium processes with due regard for internal stresses induced by a redistribution of conduction electrons. Physical characteristics of a surface layer, in particular, at the copper-inert gas medium interface and the silicon-inert gas medium interface, have been determined using experimental values of surface tensions and energies for contacting media.     

The effect of different combinations of boundary conditions on the average radiation efficiency of rectangular plates

The boundary conditions of a vibrating plate are known to have an influence on its sound radiation for frequencies below the critical frequency. To investigate this effect in a systematic way, the average radiation efficiency and radiated power are calculated for a rectangular plate set in an infinite baffle using a modal summation approach. Whereas analytical expressions exist for simply supported boundary conditions, a numerical approach is required for other cases. Nine combinations of boundary conditions are considered, consisting of simply supported, clamped and free edges on different plate edges. The structural vibration is approximated by using independent beam functions in orthogonal directions allowing simple approximate formulae for mode shapes and natural frequencies. This assumption is checked against a finite element model and shown to give reliable results. It is shown that a free plate has the lowest radiation efficiency and a clamped plate the highest for most frequencies between the fundamental panel natural frequency and the critical frequency. Other combinations of boundary condition give intermediate results according to the level of constraint introduced. The differences depend on frequency: excluding the extreme case of a fully free plate all the other boundary conditions give results within a range of 8 dB in the middle part of the short-circuiting region, decreasing towards the critical frequency. At low frequency the differences can be even greater, in some cases up to 20 dB. These conclusions are shown to hold for a range of plate thicknesses and dimensions.     

Processes of decay of Rydberg plasma

The lifetime of a molecule consisting of two Rydberg atoms with respect to electron release is determined from computer simulation of two classical electrons in the field of Coulomb centers. From this, the cross section of the Penning process of collision of two Rydberg atoms with electron release is obtained. The rate constant for ionization of Rydberg atoms is evaluated for the Rydberg plasma within the Thomson model. On the basis of these processes, the kinetics is analyzed for the decay of a Rydberg plasma. Comparison with experimental data shows that these decay processes are responsible for the first stage of the decay of a magnetized and nonmagnetized Rydberg plasma located in a magnetic superconducting trap, whereas other processes become important at a subsequent stage of the plasma evolution. This article was submitted by the authors in English.     

Predicting the eigenmodes of a cavity containing an array of circular pipes

An array of pipes inside a cavity, as found, for example, in a shell-and-tube heat exchanger, changes the eigenfrequencies of the cavity. It can be tedious to determine the shifted eigenfrequencies with a finite-element model. Based on previous work by Meyer and Neumann, Parker proposed a simple relationship for predicting the shifted eigenfrequencies. In this paper, results obtained from this relationship are compared with eigenfrequencies obtained from very accurate finite element simulations. From the results it can be concluded that Parker's relationship gives fairly good predictions of the eigenfrequencies for the first few modes in a cavity with pipes arranged in a rectangular configuration. The predictions are not so accurate for pipes arranged in a diamond configuration, and a modified version of the relationship is suggested for this configuration. If the number of pipes in the cavity is small, the simple relationship is no longer valid.     

Optimization of the calculations of the electronic structure of carbon nanotubes

A method is proposed for calculating the electronic structure and physical properties (in particular, Young’s modulus) of nanotubes, including single-walled carbon nanotubes. This method explicitly accounts for the periodic boundary conditions for the geometric structure of nanotubes and makes it possible to decrease considerably (by a factor of 10–10³) the time needed to calculate the electronic structure with minimum error. In essence, the proposed method consists in changing the geometry of the structure by partitioning nanotubes into sectors with the introduction of the appropriate boundary conditions. As a result, it becomes possible to reduce substantially the size of the unit cell of the nanotube in two dimensions, so that the number of atoms in a new unit cell of the modified nanotube is smaller than the number of atoms in the initial unit cell by a factor equal to an integral number. A decrease in the unit cell size and the corresponding decrease in the number of atoms provide a means for drastically reducing the computational time, which, in turn, substantially decreases with an increase in the degree of partition, especially for nanotubes with large diameters. The results of the calculations performed for carbon and non-carbon (boron nitride) nanotubes demonstrate that the electronic structures, densities of states, and Young’s moduli determined within the proposed approach differ insignificantly from those obtained by conventional computational methods.     

Model of ideal relaxation of thermoelastic stresses in the course of growth of single crystals

A simple dislocation model is proposed for relaxation of thermoelastic stresses generated during the growth of single crystals from a melt. This model does not require a solution of the kinetic equations for dislocations involved in relaxation and makes it possible to obtain the lower estimate of the dislocation density in the bulk of a grown crystal.     

The semi-classical hopping model of the electrical conductivity of semiconductors

A model of localized carriers moving in a hopping manner from one crystallographic point to a neighbouring one is the starting point for the model presented here for the electrical conductivity in semiconductors. An effort is made to link this hopping type of motion of carriers with their mean uniform motion in the crystal. With an assumed shape for the potential barrier for a single hop of a carrier, the model permits the calculation of the effective mass, the mobility of a carrier with energy E, the mean mobility of all carriers in the band, and the electrical conductivity as a function of temperature, T. The model is presented and exemplified by a one-dimensional system.     

Measurement of the viscosity-density product using multiple reflections of ultrasonic shear horizontal waves

We have developed an on-line computer-controlled sensor, based on ultrasound reflection measurements, to determine the product of the viscosity and density of a liquid or slurry for Newtonian fluids and the shear impedance of the liquid for non-Newtonian fluids. A 14 MHz shear wave transducer is bonded to one side of a 45-90 degrees fused silica wedge and the base is in contract with the liquid. Twenty-eight echoes were observed due to the multiple reflections of an ultrasonic shear horizontal (SH) wave within the wedge. The fast Fourier transform of each echo was obtained for a liquid and for water, which serves as the calibration fluid, and the reflection coefficient at the solid-liquid interface was obtained. Data were obtained for 11 sugar water solutions ranging in concentration from 10% to 66% by weight. The viscosity values are shown to be in good agreement with those obtained independently using a laboratory viscometer. The data acquisition time is 14s and this can be reduced by judicious selection of the echoes for determining the reflection coefficient. The measurement of the density results in a determination of the viscosity for Newtonian fluids or the shear wave velocity for non-Newtonian fluids. The sensor can be deployed for process control in a pipeline, with the base of the wedge as part of the pipeline wall, or immersed in a tank.     

Analysis of the Range of Applicability of Thermodynamic Calculations in the Engineering of Nitride Fuel Elements

The domains of applicability of thermodynamic calculations in the engineering of nitride fuel are analyzed. Characteristic values of the following parameters, which affect directly the concentration equilibration time, are estimated: nuclide production rate; characteristic times to local equilibrium in the considered temperature range; characteristic time needed for a stationary temperature profile to be established; characteristic time needed for a quasi-stationary concentration field to be established on a scale comparable to the size of a fuel pellet. It is demonstrated that equilibrium thermodynamic calculations are suitable for estimating the chemical and phase composition of fuel. However, a two-layer kinetic model should be developed in order to characterize the transport processes in condensed and gaseous phases. The process of diffusive transport needs to be taken into account in order to determine the composition in the hot region at the center of a fuel element.