Convergence of partial-wave expansions for energies, scattering amplitudes and positron annihilation rates

We use many-body theory to find the asymptotic behaviour of second-order correlation corrections to the energies and positron annihilation rates in many- electron systems with respect to the angular momenta l of the single-particle orbitals included. The energy corrections decrease as 1/(l+1/2)4, in agreement with the result of Schwartz, whereas the positron annihilation rate has a slower 1/(l+1/2)2 convergence rate. We illustrate these results by numerical calculations of the energies of Ne and Kr and by examining results from extensive con?guration-interaction calculations of PsH binding and annihilation.

Partial Cooperative Equilibria: Existence and Characterization

We study the solution concepts of partial cooperative Cournot-Nash equilibria and partial cooperative Stackelberg equilibria. The partial cooperative Cournot-Nash equilibrium is axiomatically characterized by using notions of rationality, consistency and converse consistency with regard to reduced games. We also establish sufficient conditions for which partial cooperative Cournot-Nash equilibria and partial cooperative Stackelberg equilibria exist in supermodular games. Finally, we provide an application to strategic network formation where such solution concepts may be useful.

Robust face recognition with partial occlusion, illumination variation and limited training data by optimal feature selection

This study investigates face recognition with partial occlusion, illumination variation and their combination, assuming no prior information about the mismatch, and limited training data for each person. The authors extend their previous posterior union model (PUM) to give a new method capable of dealing with all these problems. PUM is an approach for selecting the optimal local image features for recognition to improve robustness to partial occlusion. The extension is in two stages. First, authors extend PUM from a probability-based formulation to a similarity-based formulation, so that it operates with as little as one single training sample to offer robustness to partial occlusion. Second, they extend this new formulation to make it robust to illumination variation, and to combined illumination variation and partial occlusion, by a novel combination of multicondition relighting and optimal feature selection. To evaluate the new methods, a number of databases with various simulated and realistic occlusion/illumination mismatches have been used. The results have demonstrated the improved robustness of the new methods.

Oblique amplitude modulation of dust-acoustic plasma waves

Theoretical and numerical studies are presented of the nonlinear amplitude modulation of dust-acoustic (DA) waves propagating in an unmagnetized three component, weakly-coupled, fully ionized plasma consisting of electrons, positive ions and charged dust particles, considering perturbations oblique to the carrier wave propagation direction. The stability analysis, based on a nonlinear Schrodinger-type equation (NLSE), shows that the wave may become unstable; the stability criteria depend on the angle theta between the modulation and propagation directions. Explicit expressions for the instability rate and threshold have been obtained in terms of the dispersion laws of the system. The possibility and conditions for the existence of different types of localized excitations have also been discussed.

Low-frequency electromagnetic waves in a Hall-magnetohydrodynamic plasma with charged dust macroparticles

A linear theory for intermediate-frequency [much smaller (larger) than the electron gyrofrequency (dust plasma and dust gyrofrequencies)], long wavelength (in comparison with the ion gyroradius and the electron skin depth) electromagnetic waves in a multicomponent, homogeneous electron-ion-dust magnetoplasma is presented. For this purpose, the generalized Hall-magnetohydrodynamic (GH-MHD) equations are derived for the case with immobile charged dust macroparticles. The GH-MHD equations in a quasineutral plasma consist of the ion continuity equation, the generalized ion momentum equation, and Faraday's law with the Hall term. The GH-MHD equations are Fourier transformed and combined to obtain a general dispersion relation. The latter is analyzed to understand the influence of immobile charged dust grains on various electromagnetic wave modes in a magnetized dusty plasma. (C) 2005 American Institute of Physics.

Ion-acoustic waves in a two-electron-temperatute plasma: oblique modulation and envelope excitations

Theoretical and numerical studies are carried out for the nonlinear amplitude modulation of ion-acoustic waves propagating in an unmagnetized, collisionless, three-component plasma composed of inertial positive ions moving in a background of two thermalized electron populations. Perturbations oblique to the carrier wave propagation direction have been considered. The stability analysis, based on a nonlinear Schrodinger-type equation, shows that the wave may become unstable; the stability criteria depend on the angle theta between the modulation and propagation directions. Different types of localized excitations (envelope solitary waves) are shown to exist in qualitative agreement with satellite observations in the magnetosphere.

Finite ion temperature effects on oblique modulational stability and envelope excitations of dust-ion acoustic waves

Theoretical and numerical investigations are carried out for the amplitude modulation of dust-ion acoustic waves (DIAW) propagating in an unmagnetized weakly coupled collisionless fully ionized plasma consisting of isothermal electrons, warm ions and charged dust grains. Modulation oblique (by an angle theta) to the carrier wave propagation direction is considered. The stability analysis, based on a nonlinear Schrodinger-type equation (NLSE), exhibits a sensitivity of the instability region to the modulation angle theta, the dust concentration and the ion temperature. It is found that the ion temperature may strongly modify the wave's stability profile, in qualitative agreement with previous results, obtained for an electron-ion plasma. The effect of the ion temperature on the formation of DIAW envelope excitations (envelope solitons) is also discussed.

Electron-acoustic plasma waves: Oblique modulation and envelope solitons

Theoretical and numerical studies are presented of the amplitude modulation of electron-acoustic waves (EAWs) propagating in space plasmas whose constituents are inertial cold electrons, Boltzmann distributed hot electrons, and stationary ions. Perturbations oblique to the carrier EAW propagation direction have been considered. The stability analysis, based on a nonlinear Schrodinger equation, reveals that the EAW may become unstable; the stability criteria depend on the angle theta between the modulation and propagation directions. Different types of localized EA excitations are shown to exist.

Linear and nonlinear properties of Rao-dust-Alfven waves in magnetized plasmas

The linear and nonlinear properties of the Rao-dust-magnetohydrodynamic (R-D-MHD) waves in a dusty magnetoplasma are studied. By employing the inertialess electron equation of motion, inertial ion equation of motion, Ampere's law, Faraday's law, and the continuity equation in a plasma with immobile charged dust grains, the linear and nonlinear propagation of two-dimensional R-D-MHD waves are investigated. In the linear regime, the existence of immobile dust grains produces the Rao cutoff frequency, which is proportional to the dust charge density and the ion gyrofrequency. On the other hand, the dynamics of amplitude modulated R-D-MHD waves is governed by the cubic nonlinear Schrodinger equation. The latter has been derived by using the reductive perturbation technique and the two-timescale analysis which accounts for the harmonic generation nonlinearity in plasmas. The stability of the modulated wave envelope against non-resonant perturbations is studied. Finally, the possibility of localized envelope excitations is discussed. (C) 2004 American Institute of Physics.

Nonlinear modulation of transverse dust lattice waves in complex plasma crystals

The occurrence of the modulational instability in transverse dust lattice waves propagating in a one-dimensional dusty plasma crystal is investigated. The amplitude modulation mechanism, which is related to the intrinsic nonlinearity of the sheath electric field, is shown to destabilize the carrier wave under certain conditions, possibly leading to the formation of localized envelope excitations. Explicit expressions for the instability growth rate and threshold are presented and discussed. (C) 2004 American Institute of Physics.

Nonlinear theory of solitary waves associated with longitudinal particle motion in lattices - Application to longitudinal grain oscillations in a dust crystal

The nonlinear aspects of longitudinal motion of interacting point masses in a lattice are revisited, with emphasis on the paradigm of charged dust grains in a dusty plasma (DP) crystal. Different types of localized excitations, predicted by nonlinear wave theories, are reviewed and conditions for their occurrence (and characteristics) in DP crystals are discussed. Making use of a general formulation, allowing for an arbitrary (e.g. the Debye electrostatic or else) analytic potential form phi(r) and arbitrarily long site-to-site range of interactions, it is shown that dust-crystals support nonlinear kink-shaped localized excitations propagating at velocities above the characteristic DP lattice sound speed v(0). Both compressive and rarefactive kink-type excitations are predicted, depending on the physical parameter values, which represent pulse- (shock-)like coherent structures for the dust grain relative displacement. Furthermore, the existence of breather-type localized oscillations, envelope-modulated wavepackets and shocks is established. The relation to previous results on atomic chains as well as to experimental results on strongly-coupled dust layers in gas discharge plasmas is discussed.