Saha’s ionization equation for highZ elements

Saha’s ionization equation has been solved for highZ elements with the aim of providing input for opacity calculations. Results are presented for two elements, tungsten and uranium. The ionization potentials have been evaluated using the simple Bohr’s formula with suitable effective charges for ions. The reliability of the free electron density, ion concentrations, etc., obtained from the Saha’s equation solutions has been checked by comparing theP _T andE _T computed from them with those given by the Thomas-Fermi-Dirac equation of state. The agreement between the two is good from temperatures above 0.2 keV.     

Thermal conduction in a homogeneous two-phase system

Assuming a regular geometry of dispersed phase (λ ₂) an integrated theory for the effective thermal conductivityλ _e of all kind of two-phase materials (including loose materials) is developed. The flux modification is carried out by considering the effective neighbouring interactions in the solution of Poisson’s equation. A comparison of calculatedλ _e values with the reported experimental results over a wide range of two-phase materials shows a good agreement.     

The spontaneous formation of inhomogeneity in a classical one-particle “gas”: An example in silico

A single classical isoergic particle was placed in a cube and allowed to propagate for 100 ns to 10 ms. The interaction of the particle with the inner wall of the cube was modeled as a linear combination of specular and random reflection, the extent of the combination being governed by a user-defined “roughness” parameter α. As a function of α, the particle’s relative pressure and density spontaneously took on an inhomogenous distribution.     

A simple derivation of the three magnon bound state equation

A simple derivation of the equation for determining the bound states of three magnons in the Heisenberg linear chain with longitudinal anisotropy is given. The present method utilizes nothing more than the Schrödinger equation and Faddeev’s three body equations, and avoids the introduction of the ideal spin wave Hilbert space.     

On the Material Invariant Formulation of Maxwell’s Displacement Current

Maxwell accounted for the apparent elastic behavior of the electromagnetic field by augmenting Ampere’s law with the so-called displacement current, in much the same way that he treated the viscoelasticity of gases. Maxwell’s original constitutive relations for both electrodynamics and fluid dynamics were not material invariant. In the theory of viscoelastic fluids, the situation was later corrected by Oldroyd, who introduced the upper-convective derivative. Assuming that the electromagnetic field should follow the general requirements for a material field, we show that if the upper convected derivative is used in place of the partial time derivative in the displacement current term, Maxwell’s electrodynamics becomes material invariant. Note, that the material invariance of Faraday’s law is automatically established if the Lorentz force is admitted as an integral part of the model. The new formulation ensures that the equation for conservation of charge is also material invariant in vacuo. The viscoelastic medium whose apparent manifestation are the known phenomena of electrodynamics is called here the metacontinuum.     

Quantum treatment of the Anderson-Hasegawa model in the presence of superexchange

We revisit the Anderson-Hasegawa double-exchange model and critically examine its exact solution when the core spins are treated quantum mechanically. We show that the quantum effects, in the presence of an additional superexchange interaction between the core spins, yield a term, the significance of which has been hitherto ignored. The importance of this term is further assessed by numerically exact computation for a four-spin system.     

Stochastic quantization method for spinning particles in a gravitational plane wave field

The exact and analytic Green functions for spinning relativistic particles in interaction with a gravitational plane wave field are obtained within the Stochastic Quantization Method of Parisi and Wu. We have separated the classical calculations from those related to the quantum fluctuations. The problem has been solved by using a perturbative treatment via the Langevin equation relying on phase and configuration spaces formulation.      

A general approach to association using cluster partition functions

A systematic and fundamental approach to associating mixtures is presented. It is shown how the thermodynamic functions may be computed starting from a partition function based on the cluster concept such as occurs in chemical theory. The theory provides a basis for and an extension of the existing chemical theory of (continuous) association. It is applicable to arbitrary association schemes. Analysis of separate cases is not necessary. The assumptions that were made to allow the development were chosen such as to make the principle of reactivity valid. It is this same principle that links various theories: the chemical theory of continuous association, the lattice fluid hydrogen bonding model, and first-order perturbation theory. The equivalence between these theories in appropriate limits is shown in a general and rigorous way. The theory is believed to provide a practical framework for engineering modeling work. Binary interaction parameters can be incorporated. The association scheme is accounted for by a set of generic equations, which should facilitate robust implementation in computer programs.     

Random matrix model for disordered conductors

We present a random matrix ensemble where real, positive semi-definite matrix elements, x, are log-normal distributed, exp[−log²(x)]. We show that the level density varies with energy, E, as 2/(1+E) for large E, in the unitary family, consistent with the expectation for disordered conductors. The two-level correlation function is studied for the unitary family and found to be largely of the universal form despite the fact that the level density has a non-compact support. The results are based on the method of orthogonal polynomials (the Stieltjes-Wigert polynomials here). An interesting random walk problem associated with the joint probability distribution of the ensuing ensemble is discussed and its connection with level dynamics is brought out. It is further proved that Dyson’s Coulomb gas analogy breaks down whenever the confining potential is given by a transcendental function for which there exist orthogonal polynomials.     

Relations between boundary values of physical quantities between layers in the complete model of the circumterrestrial space and Earth structure

It is shown that the analytical solution of the “atmospheric dynamo” problem in the overall volume of the complete model of the near-Earth space and Earth structure, as well as the boundary conditions for physical quantities between its layers determine unambiguously the electrodynamic state of the whole system.     

Extended Hydrodynamics from Enskog’s Equation for a Two-Dimensional System General Formalism

Balance equations are derived from Enskog’s kinetic equation for a two-dimensional system of hard disks using Grad’s moment expansion method. This set of equations constitute an extended hydrodynamics for moderately dense bi-dimensional fluids. The set of independent hydrodynamic fields in the present formulations are: density, velocity, temperature and also—following Grad’s original idea—the symmetric and traceless pressure tensor p _ij and the heat flux vector q ^k . An approximation scheme similar in spirit to one made by Grad in his original work is made. Once the hydrodynamics is derived it is used to discuss the nature of a simple one-dimensional heat conduction problem. It is shown that, not too far from equilibrium, the nonequilibrium pressure in this case only depends on the density, temperature and heat flux vector. PACS: 51.10.+y, 05.20.Jj, 44.10.+i, 05.70.Ln     

Properties of hard disc fluids by Baxter’s method

The radial distribution function and the equation of state for hard disc fluids have been calculated at various densities by solving Ornstein-Zernike equation using Baxter’s method.     

Soft mode dynamics of perovskite type crystals

The soft mode dynamics and related properties of perovskite, ABO₃-type crystals have been studied using the operator form of the model Hamiltonian proposed by Pytte. The correlations have been evaluated using the double time thermal Green’s function technique and Dyson’s equation. Without any decoupling, the higher order correlations, appearing in the dynamical equation, have been evaluated using the renormalized Hamiltonian. The dielectric properties are directly related to the optical soft mode. The phonon width and shift have been calculated for different structural phases. The analysis of the temperature dependence of microwave loss tangent and dielectric constant explains the experimental results.     

Realization of a unique time evolution unitary operator in Klein Gordon theory

The scattering theory for the Klein Gordon equation, with time-dependent potential and in a non-static space-time, is considered. Using the Klein Gordon equation formulated in the Hubert spaceL ²(R ³) and the Einstein’s relativistic equation in the spaceL ²(R ³, dx) and establishing the equivalence of the vacuum states of their linearized forms in the Hubert spaceL ²(R ³) with the help of unique symmetric symplectic operator, the time evolution unitary operatorU(t) has been fixed for the Klein Gordon equation, incorporating either the positive or negative frequencies, in the infinite dimensional Hubert spaceL ²(R ³).     

Pseudopotential study of lattice parameter and heat of formation for substitutional alloys

Ashcroft’s empty core pseudopotential is applied to the substitutional alloy (K-CS) to calculate the heat of formation and lattice parameter over the entire concentration range. At any concentration the defect crystal is considered to be equivalent to a perfect crystal with a modified lattice parameter and the potential parameter for the defect crystal is calculated by using some suitable interpolation formula. The calculated results agree well with the available experimental results.     

Bethe-Salpeter equation with the sine-Gordon interaction

An attempt is made to study the interaction Hamiltonian,H _int =Gψ ²(x)U(φ(x)) in the Bethe-Salpeter framework for the confined states of theψ particles interactingvia the exchange of theU field, whereU(φ) = cos (gφ). An approximate solution of the eigenvalue problem is obtained in the instantaneous approximation by projecting the Wick-rotated Bethe-Salpeter equation onto the surface of a four-dimensional sphere and employing Hecke’s theorem in the weak-binding limit. We find that the spectrum of energies for the confined states,E =2m+B (B is the binding energy), is characterized byE ∼n ⁶, wheren is the principal quantum number.     

Method of Green’s function of nonlinear vibration of corrugated shallow shells

Based on the dynamic equations of nonlinear large deflection of axisymmetric shallow shells of revolution, the nonlinear free vibration and forced vibration of a corrugated shallow shell under concentrated load acting at the center have been investigated. The nonlinear partial differential equations of shallow shell were reduced to the nonlinear integral-differential equations by using the method of Green’s function. To solve the integral-differential equations, the expansion method was used to obtain Green’s function. Then the integral-differential equations were reduced to the form with a degenerate core by expanding Green’s function as a series of characteristic function. Therefore, the integral-differential equations became nonlinear ordinary differential equations with regard to time. The amplitude-frequency relation, with respect to the natural frequency of the lowest order and the amplitude-frequency response under harmonic force, were obtained by considering single mode vibration. As a numerical example, nonlinear free and forced vibration phenomena of shallow spherical shells with sinusoidal corrugation were studied. The obtained solutions are available for reference to the design of corrugated shells.     

Focusing of an electromagnetic plane wave into a uniaxial crystal by a Wood lens

High frequency fields, refracted by a geometry containing a Wood lens placed at a certain distance from a planar uniaxial interface, are derived by using Maslov’s method. The geometrical optics approximation generally valid for high frequency fields fails in the vicinity of a caustic. Maslov’s method is a systematic procedure for predicting the field in the caustic region, combining the simplicity of the ray and the generality of the transform method. Numerical computations are made for the field pattern around the caustic by using Maslov’s method. The results are found to be in good agreement with those obtained using Kirchhoff’s approximation.      

Heat Transport in Harmonic Lattices

We work out the non-equilibrium steady state properties of a harmonic lattice which is connected to heat reservoirs at different temperatures. The heat reservoirs are themselves modeled as harmonic systems. Our approach is to write quantum Langevin equations for the system and solve these to obtain steady state properties such as currents and other second moments involving the position and momentum operators. The resulting expressions will be seen to be similar in form to results obtained for electronic transport using the non-equilibrium Green’s function formalism. As an application of the formalism we discuss heat conduction in a harmonic chain connected to self-consistent reservoirs. We obtain a temperature dependent thermal conductivity which, in the high-temperature classical limit, reproduces the exact result on this model obtained recently by Bonetto, Lebowitz and Lukkarinen.