Existence regions of regimes with anomalously high rates of plasma generation in grid plasma switch elements

Results are presented from a systematic investigation of the conditions under which anomalously high rates of plasma generation are observed in the anode region of a low-voltage Knudsen arc in grid plasma switch elements. The phenomenon develops over a wide range of currents and switched voltages under conditions for which the plasma density in the cathode-grid region is noticeably higher than the density in the anode region. and its onset is characterized by a pronounced pressure threshold of ∼2×10⁻² Torr. The results are analyzed from the standpoint of the possible mechanisms for anomalous plasma generation — collisional nonresonance diffusion of electrons in velocity space, leading to enrichment of the distribution function in fast particles, and the collapse of Langmuir waves in the gap at the high energies of the beam produced when the wires of the grid are bridged by the quenching pulse and and the current is blocked. Zh. Tekh. Fiz. 67, 15–21 (June 1997)     

Optical switching between bistable soliton states: a theoretical review

In this paper we summarize what is currently known about optical switching between bright bistable soliton states in one and higher dimensions. A guideline to selecting media with appropriate intensity-dependent refractive indices to support bistable solitary waves is presented. The stability criterion for robustness of the solitary waves is discussed. Finally, some methods and numerical examples of optical switching are presented.     

The solvable radical of Sylow factorizable groups

Let G be a finite group. A complete Sylow product of G is a product of Sylow subgroups of G, one for each prime divisor of |G|. We shall call G a Sylow factorizable group if it is equal to at least one of its complete Sylow products. We prove that if G is a Sylow factorizable group then the intersection of all complete Sylow products of G is equal to the solvable radical of G. We generalize the concepts and the result to Sylow products which involve an arbitrary subset of the prime divisors of |G|. Received: 26 January 2005     

Domain morphology in ultrathin ferromagnetic films with perpendicular magnetization

We determine the minimal domain structure for the equilibrium thickness of stripes as well as for the minimal energy of the domain configuration in ultrathin films of ferromagnetically coupled spins, where the easy direction of magnetization is perpendicular to the film. It is found that the equilibrium thickness of stripes and walls depend on the exchange energy. The normalized anisotropy, f, depends on interplay between the magnetic and anisotropy energies and is almost independent of the exchange energy inside the wall. The results are compared with the experimental data for thin Ag/Fe/Ag (0 0 1) films and a good coincidence is obtained between both results.     

The Chemical Potential

The definition of the fundamental quantity, the chemical potential, is badly confused in the literature: there are at least three distinct definitions in various books and papers. While they all give the same result in the thermodynamic limit, major differences between them can occur for finite systems, in anomalous cases even for finite systems as large as a cm³. We resolve the situation by arguing that the chemical potential defined as the symbol μ conventionally appearing in the grand canonical density operator is the uniquely correct definition valid for all finite systems, the grand canonical ensemble being the only one of the various ensembles usually discussed (microcanonical, canonical, Gibbs, grand canonical) that is appropriate for statistical thermodynamics, whenever the chemical potential is physically relevant. The zero–temperature limit of this μ was derived by Perdew et al. for finite systems involving electrons, generally allowing for electron–electron interactions; we extend this derivation and, for semiconductors, we also consider the zero–T limit taken after the thermodynamic limit. The enormous finite size corrections (in macroscopic samples, e.g. 1 cm³) for one rather common definition of the c.p., found recently by Shegelski within the standard effective mass model of an ideal intrinsic semiconductor, are discussed. Also, two very–small–system examples are given, including a quantum dot.     

Numerical treatment of an asset price model with non-stochastic uncertainty

In contrast to stochastic differential equation models used for the calculation of the term structure of interest rates, we develop an approach based on linear dynamical systems under non-stochastic uncertainty with perturbations. The uncertainty is described in terms of known feasible sets of varying parameters. Observations are used in order to estimate these parameters by minimizing the maximum of the absolute value of measurement errors, which leads to a linear or nonlinear semi-infinite programming problem. A regularized logarithmic barrier method for solving (ill-posed) convex semi-infinite programming problems is suggested. In this method a multi-step proximal regularization is coupled with an adaptive discretization strategy in the framework of an interior point approach. A special deleting rule permits one to use only a part of the constraints of the discretized problems. Convergence of the method and its stability with respect to data perturbations in the cone of convexC ¹-functions are studied. On the basis of the solutions of the semi-infinite programming problems a technical trading system for future contracts of the German DAX is suggested and developed. Supported by the Stiftung Rheinland/Pfalz für Innovation, No. 8312-386261/307.     

Stable hysteretic reflection of light at a nonlinear interface

We have observed a hysteretic (bistable) reflection of a Gaussian laser beam at the interface between glass and a liquid solution of polystyrene microspheres as nonlinear medium with both branches of the hysteretic curve being stable, in contrast to the results of previous experiments.