Determining the lattice parameter and the single-electron model potential of the compound CdS by means of the soft x-ray absorption spectra

The method of determining the structure parameters of multiatomic systems, using the spectra of soft x rays (XANES) proposed earlier, is extended to the case of nonmetallic crystal bodies. This method is used to determine the lattice parameter and the empirical muffin-tin potential from the positions of maxima of single-electron origin in the sulfur K spectrum in the compound CdS. Fiz. Tverd. Tela (St. Petersburg) 40, 2168–2171 (December 1998)     

A variational method from the variance of energy

A variational method is studied based on the minimum of energy variance. The method is tested on exactly soluble problems in quantum mechanics, and is shown to be a useful tool whenever the properties of states are more relevant than the eigenvalues. In quantum field theory the method provides a consistent second-order extension to the Gaussian effective potential. PACS. 03.65.-w, 11.10.-z, 05.30.-d Received: 28 June 2005, Published online: 13 September 2005     

Morphological thermodynamics for hard bodies from a controlled expansion

ABSTRACT

The morphometric approach is a powerful ansatz for decomposing the chemical potential for a complex solute into purely geometrical terms. This method has proven accuracy in hard spheres, presenting an alternative to comparatively expensive (classical) density functional theory approaches. Despite this, fundamental questions remain over why it is accurate and how one might include higher-order terms to improve accuracy. We derive the morphometric approach as the exact resummation of terms in the virial series, providing further justification of the approach. The resulting theory is less accurate than previous morphometric theories, but provides fundamental insights into the inclusion of higher-order terms and to extensions to mixtures of convex bodies of arbitrary shape.     

Coisotropic quasi-periodic motions for a constrained system of rigid bodies

Abstract

We consider a constrained system of four rigid bodies located in axisymmetric potential and gyroscopic force fields and interacting by means of angular velocities. We describe an integrable case (not in Liouville sence!) when 12-dimensional phase space of the above system is fibered by the coisotropic invariant tori, the majority of which carry quasi-periodic motions with 7 independent frequences.     

Solution of the three-dimensional problem of wave diffraction by an ensemble of objects

The pattern equations method is extended to solving three-dimensional problems of wave diffraction by an ensemble of bodies. The method is based on the reduction of the initial problem to a system of N (N is the number of scatterers in the ensemble) integro-operator equations of the second kind for the scattering patterns of scatterers. With the use of the series expansions of the scattering patterns in angular spherical harmonics, the problem is reduced to an algebraic system of equations in the expansion coefficients. An explicit (asymptotic) solution to the problems is obtained in the case when the scattering bodies are separated by sufficiently long distances. It is shown that the method can be used to model the characteristics of wave scattering by complex-shaped bodies.     

Solving Simultaneously Dirac and Ricatti Equations

Abstract

We analyse the behaviour of the Dirac equation in d = 1 + 1 with Lorentz scalar potential. As the system is known to provide a physical realization of supersymmetric quantum mechanics, we take advantage of the factorization method in order to enlarge the restricted class of solvable problems. To be precise, it suffices to integrate a Ricatti equation to construct one-parameter families of solvable potentials. To illustrate the procedure in a simple but relevant context, we resort to a model which has proved useful in showing the phenomenon of fermion number fractionalization.     

Quantum creation of the universe with a minimum scalar-field energy

The quantum creation of a closed Friedmann universe is studied on the basis of a Wheeler-DeWitt equation with two arguments — a scale factor and a scalar-field potential. In the quasiclassical approximation the wave function of the universe (WF) starts to evolve at a zero scalar field. A near-Planckian energy density of the field arises as a result of tunneling through a potential barrier. In our opinion, this variant of the scenario most closely resembles creation ex nihilo. The only parameter controlling quantum evolution is the mass of a quantum of the scalar field. In the paper by Khalatnikov and Schiller [JETP Lett. 57,1 (1993)], tunneling through the classically inaccessible region of the superpotential U(a,φ) is calculated by the instanton method. However, this method requires that the potential U(a,φ) satisfy special conditions in the space (a,φ). For this reason, in the present paper the tunneling calculation is performed by the method of characteristics for the quasiclassical approximation of the Wheeler-DeWitt equation under the barrier. The WKB theory, which has been well-developed for one-dimensional problems, is employed along each characteristic. It is shown that the corresponding turning points are also points where U(a, φ)=0. The total barrier penetrability is obtained by averaging over a bundle of characteristics. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 5, 305–308 (10 September 1996)     

Inductance in a system of doubly connected, ideally diamagnetic bodies

General relations for the inductances of a system of doubly connected, ideally diamagnetic bodies with currents circulating through them are found with consideration of the induced current densities in the individual bodies due to the influence of their mutual shielding. Zh. Tekh. Fiz. 68, 131 (September 1998)     

Calculations of the EPR g-tensor using unrestricted two- and four-component relativistic approaches within the HF and DFT frameworks

ABSTRACT

Approaches and programs for calculations of the EPR g-tensor in the framework of the two- and four-component methods are still very rare. There are three main reasons for this: the wider community's unawareness of the importance of second- and higher order spin–orbit effects on the g-tensor, the methodological problems associated with performing such calculations and the lack of understanding of these problems. This paper reports on the implementation of a method for calculation of the g-tensor in the framework of the relativistic unrestricted two- and four-component Hartree–Fock and density functional theory approaches based on the Kramers pair formalism. This implementation allows us to analyse problems which arise when the g-tensor is calculated via Kramers pairs in the unrestricted framework.     

The caustic approach to Rayleigh-waves and their interaction with surface irregularities

During the past 25 years the method of caustics has matured to the stage where it offers a highly potential tool for qualitative as well as quantitative solutions of engineering problems in many fields. In conjunction with high-speed recording techniques such as high-speed cinematography, the method of caustics serves as a means for visualizing the highly complex interaction processes that occur when elastic stress waves interact with material inhomogeneities or discontinuities such as inclusions, surface or embedded cracks and contacting surfaces during impact.In this contribution, the method of caustics is applied to a number of dynamic problems all of which are associated with the propagation and interaction of Rayleigh-waves:

• the pseudo-caustic of a Rayleigh-wave;

• Rayleigh-wave generation during dynamic impact of two elastic bodies;

• Rayleigh-wave interaction with a shallow embedded crack;

• Rayleigh-wave interaction with various configurations of sets of surface cracks.

Sequences of high-speed cinematographic recordings of the evolution of a dynamic process provide the raw data for data and image analysis for the determination of stress intensity factors, contact forces, load-time traces or other quantities of physical interest.The paper also discusses some of the advantages and disadvantages of the method of caustics over other methods currently used in photomechanics such as dynamic photoelasticity. Data reduction and analysis aspects will also be highlighted.     

General integrable problems of classical mechanics

Several classical problems of mechanics are shown to be integrable for the special systems of coupled rigid bodies, introduced in this work and calledC ^k -central configurations. It is proven that dynamics of an arbitraryC ^k -central configuration in a Newtonian gravitational field with an arbitrary quadratic potential is integrable in the Liouville sense and in the theta-functions of Riemann surfaces. Hidden symmetry of the inertial dynamics of these configurations is disclosed and reductions of the Lagrange equations to the Euler equations on Lie coalgebras are obtained. Reductions and integrable cases of a heavyC ^k -central configuration rotation around a fixed point are indicated. Separation of rotations of a space station type orbiting system, being aC ^k -central configuration of rigid bodies, is proven. This result leads to the possibility of the independent stabilization of rotations of the rigid bodies in such orbiting configurations.Supported by the Ministry of Colleges and Universities of Ontario and the Natural Sciences and Engineering Research Council of Canada     

Theory for the calculation of the force characteristics of an electromagnetic suspension of a superconducting body

A theory based on the method of secondary sources is developed for the calculation of the magnetic field and the force characteristics of electromagnetic suspension. This method leads to a system of Fredholm vector integral equations of the second kind in the density of the secondary sources, whose solution gives the surface currents in the superconducting bodies and then by a simple integration, the magnetic field and the force characteristics of the suspension. It is shown how the problem can be reformulated to apply it to the determination of the scalar secondary sources (magnetic charges), leading to integral equations of lower dimension. Examples are given for the calculation of scalar secondary sources for a superconducting half-space and a cylinder. Zh. Tekh. Fiz. 67, 3–9 (January 1997)     

Yukawa potentials in systems with partial periodic boundary conditions. I. Ewald sums for quasi-two-dimensional systems

Yukawa potentials are often used as effective potentials for systems such as colloids, plasmas, etc. When the Debye screening length is large, the Yukawa potential tends to the non-screened Coulomb potential; in this small screening limit, or Coulomb limit, the potential is long-ranged. As is well known in computer simulation, a simple truncation of the long-ranged potential and the minimum image convention are insufficient to obtain accurate numerical data on systems. The Ewald method for bulk systems, i.e. with periodic boundary conditions in all three directions of space, has already been derived for the Yukawa potential [Molec. Phys. 88, 1357 (1996); J. Chem. Phys. 113, 10459 (2000)], but for systems with partial periodic boundary conditions, the Ewald sums have only recently been obtained [J. Chem. Phys. 126, 056101 (2007)]. In this paper, we provide a closed derivation of the Ewald sums for Yukawa potentials in systems with periodic boundary conditions in only two directions and for any value of the Debye length. Special attention is paid to the Coulomb limit and its relation to the electroneutrality of systems.     

Numerical solutions of matrix Riccati equations for radiative transfer in a plane-parallel geometry

Abstract

In this paper, we conduct numerical experiments with matrix Riccati equations (MREs) which describe the reflection (R) and transmission (T) matrices of the specific intensities in a layer containing randomly distributed scattering particles. The theoretical formulation of MREs is discussed in our previous paper where we show that R and T for a thick layer can be efficiently computed by successively doubling R and T matrices for a thin layer (with small optical thickness τ_Δ). We can compute R(τ_Δ) and T(τ_Δ) very accurately using either a fourth-order Runge–Kutta scheme or the fourth-order iterative solution. The differences between these results and those computed by the eigenmode expansion technique (EMET) are very small (<0.1%). Although the MRE formulation cannot be extended to handle the inhomogeneous term (source term) in the differential equation, we show that the force term can be reformulated as an equivalent boundary condition which is consistent with MRE methods. MRE methods offer an alternative way of solving plane-parallel radiative transport problems. For large problems that do not fit into computer memory, the MRE method provides a significant reduction in computer memory and computational time.     

Analytical formulas for complex permittivity of periodic composites. Estimation of gain and loss enhancement in active and passive composites

ABSTRACT

The asymptotic homogenization method is applied to complex dielectric periodic composites. An equivalence to coupled dielectric problems with real coefficients is shown. This is similar to a piezoelectric problem: an out-plane mechanical displacement and an in-plane electric potential establishing a correspondence principle. Closed-form formulas for the complex dielectric effective tensor in the case of a square array of circular inclusions embedded in a matrix are given. These formulas are written in terms of a real and symmetric matrix which facilitates the implementation of the computational scheme. We also get similar formulas for multilayered complex dielectric composites. The real closed-form formulas are advantageous for estimating gain and loss enhancement properties of active and passive composites in certain volume fraction intervals. Numerical computations are performed and the results are compared with other approaches showing the usefulness of the obtained formulas. This may be of interest in the context of metamaterials.     

A Dynamical Mapping Method in Nonrelativistic Models of Quantum Field Theory

Abstract

Exact solutions of Heisenberg equations and two-particle eigenvalue problems for the nonrelativistic four-fermion interaction and N, Θ model are obtained in the framework of a dynamical mapping method. Equivalence of different dynamical mappings is shown.     

Analytic Equation of State of a Quasi One-Dimensional Model Lipid Monolayer

The equation of state of a quasi one-dimensional model lipid monolayer is obtained in analytic form. The method used is the Laplace transform approach leading to a homogeneous Fredholm integral equation. Two cases are studied. The first considers a purely short range repulsive potential, when we recover the results previously obtained by Gianotti et al. (J. Phys. A.: Math. Gen. 25:2889 (1992)). The second incorporates the long range attractive Kac potential, and the equation of state is calculated in the van der Waals limit. This extends the approach originally developed by Kac et al. (J. Math. Phys. 4:216 (1963)).     

Calculation of line width in channeling radiation by optical potential method

Abstract

The line width problem in channeling radiation is considered in terms of the optical potential method. It is shown that the plasmon excitations do not contribute to the line width.     

Vibrational resonances of non-rotating HCN in the excited electronic state

A multi reference internally contracted configuration interaction (MRCI) method is used to generate the potential energy function (PEF) of the excited electronic state of HCN molecule. The analytic representation of the PEF is employed to calculate complex eigenvalues (resonance positions and widths) by a discrete variable representation (DVR) of the Hamiltonian for the non-rotating (J =0) molecule. The computational method used is a variant of the filter-diagonalization technique based on a recursive polynomial expansion of the absorbing-boundary-conditions (ABC) Green operator. Reasonable agreement with existing experimental data is found. Received 27 July 1999 and Received in final form 18 October 1999