Grenzbedingungen der Elektrodynamik für Medien mit räumlicher Dispersion und Übergangsschichten

Boundary Conditions of Electrodynamics for Media with Spatial Dispersion and for Transition Layers Starting from Maxwell's equations of macroscopic electrodynamics for spatially inhomogeneous anisotropic media with spatial dispersion the boundary conditions are derived with an essentially new method using generalized functions and expansions of the fields in terms of moments. We find a complete infinite system of boundary conditions, which can be reduced to finite systems by approximations. For the special cases of first order spatial dispersion and for transition layers we obtain boundary conditions in the first approximation, which improve and generalize the usual ones.     

The use of generalized sum rules in many-body theory (I). Microscopic description of nuclear rotation

Following a recent paper of Marumori et al. the idea of using sum rules expressing different single-particle transition operators in terms of higher powers of other operators is extended to the general case. With the help of these generalized sum rules a new microscopic method is developed to calculate energies and transition probabilities for nuclei within the rotational region. For simplicity we restrict ourselves to the single j-shell case with a quadrupole two-body interaction. The mass region where rotational phenomena may be expected is determined and is interpreted by a simple Hartree model. The calculated quadrupole moments and transition probabilities show excellent agreement with the exact calculations of Mulhall and ips.     

On a kinetic justification of the generalized nonequilibrium thermodynamics of multicomponent systems

The problem of the kinetic justification of the generalized thermodynamics of nonequilibrium processes using the method of moments for solving the kinetic equation for a multicomponent gas mixture is examined. Generalized expressions are obtained for the entropy density, entropy flux density, and entropy production as functions of an arbitrary number of state variables (moments of the distribution function). Different variants of writing the relations between fluxes and thermodynamic forces are considered, which correspond to the Onsager version for spatially homogeneous systems and, in a more general case, lead to the generalized thermodynamic forces of a complicated form, including derivatives of the fluxes with respect to time and spatial coordinates. Some consequences and new physical effects, following from the obtained equations, are analyzed. It is shown that a transition from results of the method of moments to expressions for the entropy production and the corresponding phenomenological relations of the generalized nonequilibrium thermodynamics is possible on the level of a linearized Barnett approximation of the Chapman–Enskog method.     

Powerlike decreasing solutions of the Boltzmann equation for a Maxwell gas

We study the homogeneous, isotropic, nonlinear Boltzmann equation for a Maxwellian interaction. We show that solutions decreasing like inverse powers of the energy are physically acceptable both in the linearized and the quadratic problem. Because all moments may not exist, we introduce a generalized generating function and a finite differential system for generalized Sonine moments is derived. These new solutions may lead to small relaxation rates and justify in most cases the linear approximation.     

The surface shear viscosity of a planar liquid-vapor interface I. Theory

In this paper we develop a theory for the calculation of the surface shear viscosity of a planar liquid-vapor interface. The theory is an extension of the generalized hydrodynamics formalism, originally developed for the calculation of linear transport coefficients in isotropic bulk fluids. We develop an expression for the surface shear viscosity in terms of the actual shear viscosity profile in the interfacial region. We derive an expression for this profile in terms of the first four moments of the autocorrelation function of the transverse parallel velocity (the component of velocity parallel to k, which is the projection of k on to the interface). Finally, we calculate these moments for a planar liquid-vapor interface.     

Polymers on disordered hierarchical lattices: A nonlinear combination of random variables

The problem of directed polymers on disordered hierarchical and hypercubic lattices is considered. For the hierarchical lattices the problem can be reduced to the study of the stable laws for combining random variables in a nonlinear way. We present the results of numerical simulations of two hierarchical lattices, finding evidence of a phase transition in one case. For a limiting case we extend the perturbation theory developed by Derrida and Griffiths to nonzero temperature and to higher order and use this approach to calculate thermal and geometrical properties (overlaps) of the model. In this limit we obtain an interpolation formula, allowing one to obtain the noninteger moments of the partition function from the integer moments. We obtain bounds for the transition temperature for hierarchical and hypercubic lattices, and some similarities between the problem on the two different types of lattice are discussed.     

A transition rate transformation method for solving advection–dispersion equation

Advection–dispersion equation is widely used to describe solute transport in hydrology. However, using conventional methods, e.g., finite difference method, to solve this equation may result in numerical dispersion and oscillation, especially when the advection velocity is large. This paper presents a novel transition rate transformation (TRT) method to simulate the advection–dispersion process. Advection–dispersion equation is invariant as the transition rate function is transformed under the condition that the first and second spatial moments of the transition rate are kept unchanged. According to this invariance, the TRT method constructs simple transition rate functions to solve the advection–dispersion equation. Our simulation shows that the results obtained by the TRT method agree well with analytical solutions. The freedom of the selection of transition rate functions may be very useful for the simulations of the advection–dispersion problems.     

Determination of Threshold Values of the Generalized Likelihood Ratio in the Problem of Detecting Partially Coherent Spatial Signals in the Case of Short Samples

In this paper, we solve the problem of detecting multidimensional Gaussian complex signals with an a priori unknown spatial covariance matrix against the background of spatially nonuniform Gaussian noise with unknown power in the case of a fixed false-alarm probability. For an arbitrary sample size, exact analytical expressions are obtained for the moments of a decision statistic represented in the form of a generalized likelihood ratio raised to power reciprocal of a positive integer. The series expansion of the probability density function of the decision statistic in terms of orthogonal Jacobi polynomials is obtained by the method of moments. We use numerical simulation to demonstrate the high accuracy of approximating the probability density and finding the threshold value of the decision statistic. The obtained results hold for the case of short samples whose sizes are comparable with the number of elements of a receiving antenna.     

Generalized effective-potential Landau theory for the two-dimensional extended Bose-Hubbard model

We analytically study the quantum phase diagrams of ultracold dipolar Bose gases in an optical square lattice at zero temperature by using the generalized effective-potential Landau theory (GEPLT). For a weak nearest-neighbor repulsion, our analytical results are better than the third-order strong-coupling expansion theory calculation. In contrast to a previous quantum Monte Carlo (QMC) simulation, we analytically calculate phase transition boundaries up to the third-order hopping, which are in excellent agreement with QMC simulations for second-order phase transition.     

A theoretical study of the effect of disorder of the transition dipole moments of molecules on the shape of optical bands of molecular aggregates

Aggregates with substitutional disorder, in which molecules of different types have different transition dipole moments, are considered. The relations between the absorption spectra of aggregates with disordered and nondisordered transition dipole moments are obtained for two limiting cases: (1) the case when there is no statistical correlation between the transition energies and transition dipole moments of the molecules and (2) the case of total correlation, when the transition energies and transition dipole moments are strictly related to each other. For aggregates that are characterized by substitutional disorder along with diagonal disorder, an effective method of calculation of the optical bands is developed. Numerical calculations of the absorption bands of aggregates consisting of molecules of two types are carried out at different values of the parameters.     

Generalized parton distributions from hadronic observables: non-zero skewness

We propose a physically motivated parameterization for the unpolarized generalized parton distributions, H and E, valid at both zero and non-zero values of the skewness variable, ζ. Our approach follows a previous detailed study of the ζ=0 case where H and E were determined using constraints from simultaneous fits of the experimental data on both the nucleon elastic form factors and the deep inelastic structure functions in the non-singlet sector. Additional constraints at ζ≠0 are provided by lattice calculations of the higher moments of generalized parton distributions. We illustrate a method for extracting generalized parton distributions from lattice moments based on a reconstruction using sets of orthogonal polynomials. The inclusion in our fit of data on Deeply Virtual Compton Scattering is also discussed. Our method provides a step towards an extraction of generalized distributions based on a global fit of the available data within the given set of constraints.     

Transition events fluctuations in jump markovian dynamics. A general approach to Šolc's problem

We introduce a new formalism for computing the moments of transition events for nonhomogeneous Markov jump processes. Our method is applied directly to the master equation and does not involve the use of diffusion approximation. The general theory is applied to produce exact expressions for means and dispersions. For time homogeneous Markov processes with a finite number of connected states we are able to prove that both means and dispersions asymptotically increase linearly in time.     

Generalized Poisson Hurdle Model for Count Data and Its Application in Ear Disease

For count data, though a zero-inflated model can work perfectly well with an excess of zeroes and the generalized Poisson model can tackle over- or under-dispersion, most models cannot simultaneously deal with both zero-inflated or zero-deflated data and over- or under-dispersion. Ear diseases are important in healthcare, and falls into this kind of count data. This paper introduces a generalized Poisson Hurdle model that work with count data of both too many/few zeroes and a sample variance not equal to the mean. To estimate parameters, we use the generalized method of moments. In addition, the asymptotic normality and efficiency of these estimators are established. Moreover, this model is applied to ear disease using data gained from the New South Wales Health Research Council in 1990. This model performs better than both the generalized Poisson model and the Hurdle model.     

Atomic-layer resolved magnetic and electronic structure analysis of ni thin film on a Cu(001) surface by diffraction spectroscopy

Up until now there has been no direct method for detecting the electronic and magnetic structure of each atomic layer at the surface, which is an essential analysis technique for nanotechnology. For this purpose, we have developed a new method, diffraction spectroscopy, based on the photon energy dependence of the angular distribution of Auger electron emission. We have applied this method to analyze the magnetic structure of a Ni ultrathin film on a Cu(001) surface around the spin reorientation transition. Atomic-layer resolved x-ray absorption and magnetic circular dichroism spectra were obtained. Surface and interior core-level shifts and magnetic moments are determined for each atomic layer individually.     

Relaxation of Collisional Magnetically Confined Plasmas to Mechanical Equilibria

The relaxation of magnetically confined plasmas in a toroidal geometry is analyzed. From the equations for the Hermitian moments, we show how the system relaxes towards the mechanical equilibrium. In the space of the parallel generalized frictions, after fast transients, the evolution of collisional magnetically confined plasmas is such that the projections of the evolution equations for the parallel generalized frictions and the shortest path on the Hermitian moments coincide. For spatially‐extended systems, a similar result is valid for the evolution of the thermodynamic mode (i.e., the mode with wave‐number k = 0 ). The expression for the affine connection of the space covered by the generalized frictions, close to mechanical equilibria, is also obtained. The knowledge of the components of the affine connection is a fundamental prerequisite for the construction of the (nonlinear) closure theory on transport processes (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The moment method for boundary layer problems in Brownian motion theory

We apply Grad's moment method, with Hermite moments and Marshak-type boundary conditions, to several boundary layer problems for the Klein-Kramers equation, the kinetic equation for noninteracting Brownian particles, and study its convergence properties as the number of moments is increased. The errors in various quantities of physical interest decrease asymptotically as inverse powers of this number; the exponent is roughly three times as large as in an earlier variational method, based on an expansion in the exact boundary layer eigenfunctions. For the case of a fully absorbing wall (the Milne problem) we obtain full agreement with the recent exact solution of Marshall and Watson; the relevant slip coefficient, the Milne length, is reproduced with an accuracy better than 10^–6. We also consider partially absorbing walls, with specular or diffuse reflection of nonabsorbed particles. In the latter case we allow for a temperature difference between the wall and the medium in which the particles move. There is noa priori reason why our method should work only for Brownian dynamics; one may hope to extend it to a broad class of linear transport equations. As a first test, we looked at the Milne problem for the BGK equation. In spite of the completely different analytic structure of the boundary layer eigenfunctions, the agreement with the exact solution is almost as good as for the Klein-Kramers equation.     

Random integral equation formulation of a generalized Langevin equation

In this paper, the generalized Langevin equation introduced by Kubo and Mori is formulated as a random integral equation. We consider (1) the existence and uniqueness of the solution, (2) moments of the solution process, (3) a comparison theorem for solution processes, and (4) the Cauchy polygonal approximation to the solution.     

Condensation of N interacting bosons: a hybrid approach to condensate fluctuations

We present a new method of calculating the distribution function and fluctuations for a Bose-Einstein condensate (BEC) of N interacting atoms. The present formulation combines our previous master equation and canonical ensemble quasiparticle techniques. It is applicable both for ideal and interacting Bogoliubov BEC and yields remarkable accuracy at all temperatures. For the interacting gas of 200 bosons in a box we plot the temperature dependence of the first four central moments of the condensate particle number and compare the results with the ideal gas. For the interacting mesoscopic BEC, as with the ideal gas, we find a smooth transition for the condensate particle number as we pass through the critical temperature.     

Emergence of Heavy-Tailed Distributions in a Random Multiplicative Model Driven by a Gaussian Stochastic Process

We consider a random multiplicative stochastic process with multipliers given by the exponential of a Brownian motion. The positive integer moments of the distribution function can be computed exactly, and can be represented as the grand partition function of an equivalent lattice gas with attractive 2-body interactions. The numerical results for the positive integer moments display a sharp transition at a critical value of the model parameters, which corresponds to a phase transition in the equivalent lattice gas model. The shape of the terminal distribution changes suddenly at the critical point to a heavy-tailed distribution. The transition can be related to the position of the complex zeros of the grand partition function of the lattice gas, in analogy with the Lee, Yang picture of phase transitions in statistical mechanics. We study the properties of the equivalent lattice gas in the thermodynamical limit, which corresponds to the continuous time limit of the random multiplicative model, and derive the asymptotics of the approach to the continuous time limit. The results can be generalized to a wider class of random multiplicative processes, driven by the exponential of a Gaussian stochastic process.     

Fine structure of X-ray magnetic circular dichroism for early 3<Emphasis Type="Italic">d</Emphasis> transition metals

We have performed a systematic study of the L_2,3 absorption fine structure along the 3d transition metals using X-ray magnetic circular dichroism. This is of importance since the decreased spin–orbit splitting for the early 3d transition metals results in stronger electron core–hole correlations, which lead to dramatic changes in the spectral intensities. For the Fe/V system we demonstrate that the fine structures can be modelled theoretically by means of fully relativistic ab initio calculations that also provide corresponding magnetic moments for vanadium. It turns out that in contrast to the late 3d elements Fe, Co, and Ni, the classical analysis by means of the integral sum rules yields erroneous results for the early 3d transition metals. PACS 78.70.Dm; 75.70.-i