Nonlinear diffraction of light beams propagating in photorefractive media with embedded reflecting wire

The theory of nonlinear diffraction of intensive light beams propagating through photorefractive media is developed. Diffraction occurs on a reflecting wire embedded in the nonlinear medium at a relatively small angle with respect to the direction of the beam propagation. It is shown that this process is analogous to the generation of waves by a flow of a superfluid past an obstacle. The ""equation of state"" of such a superfluid is determined by the nonlinear properties of the medium. On the basis of this hydrodynamic analogy, the notion of the ""Mach number"" is introduced where the transverse component of the wave vector plays the role of the fluid velocity. It is found that the Mach cone separates two regions of the diffraction pattern: inside the Mach cone oblique dark solitons are generated and outside the Mach cone the region of ""optical ship waves"" (the wave pattern formed by a two-dimensional packet of linear waves) is situated. Analytical theory of the ""optical ship waves"" is developed and two-dimensional dark soliton solutions of the generalized two-dimensional nonlinear Schrodinger equation describing the light beam propagation are found. Stability of dark solitons with respect to their decay into vortices is studied and it is shown that they are stable for large enough values of the Mach number.

Many-Body Effects on the rho(xx) Ringlike Structures in Two-Subband Wells

The longitudinal resistivity rho(xx) of two-dimensional electron gases formed in wells with two subbands displays ringlike structures when plotted in a density-magnetic-field diagram, due to the crossings of spin-split Landau levels (LLs) from distinct subbands. Using spin density functional theory and linear response, we investigate the shape and spin polarization of these structures as a function of temperature and magnetic-field tilt angle. We find that (i) some of the rings ""break'' at sufficiently low temperatures due to a quantum Hall ferromagnetic phase transition, thus exhibiting a high degree of spin polarization (similar to 50%) within, consistent with the NMR data of Zhang et al. [Phys. Rev. Lett. 98, 246802 (2007)], and (ii) for increasing tilting angles the interplay between the anticrossings due to inter-LL couplings and the exchange-correlation effects leads to a collapse of the rings at some critical angle theta(c), in agreement with the data of Guo et al. [Phys. Rev. B 78, 233305 (2008)].

Control of the persistent currents in two interacting quantum rings through the Coulomb interaction and interring tunneling

The persistent current in two vertically coupled quantum rings containing few electrons is studied. We find that the Coulomb interaction between the rings in the absence of tunneling affects the persistent current in each ring and the ground-state configurations. Quantum tunneling between the rings alters significantly the ground state and the persistent current in the system.

Verification of a mixed high-order accurate DNS code for laminar turbulent transition by the method of manufactured solutions

This paper presents results on a verification test of a Direct Numerical Simulation code of mixed high-order of accuracy using the method of manufactured solutions (MMS). This test is based on the formulation of an analytical solution for the Navier-Stokes equations modified by the addition of a source term. The present numerical code was aimed at simulating the temporal evolution of instability waves in a plane Poiseuille flow. The governing equations were solved in a vorticity-velocity formulation for a two-dimensional incompressible flow. The code employed two different numerical schemes. One used mixed high-order compact and non-compact finite-differences from fourth-order to sixth-order of accuracy. The other scheme used spectral methods instead of finite-difference methods for the streamwise direction, which was periodic. In the present test, particular attention was paid to the boundary conditions of the physical problem of interest. Indeed, the verification procedure using MMS can be more demanding than the often used comparison with Linear Stability Theory. That is particularly because in the latter test no attention is paid to the nonlinear terms. For the present verification test, it was possible to manufacture an analytical solution that reproduced some aspects of an instability wave in a nonlinear stage. Although the results of the verification by MMS for this mixed-order numerical scheme had to be interpreted with care, the test was very useful as it gave confidence that the code was free of programming errors. Copyright (C) 2009 John Wiley & Sons, Ltd.

Numerical solution of the two-phase expansion of a metastable flashing liquid jet using the dispersion-controlled dissipative scheme

This paper presents a study of the stationary phenomenon of superheated or metastable liquid jets, flashing into a two-dimensional axisymmetric domain, while in the two-phase region. In general, the phenomenon starts off when a high-pressure, high-temperature liquid jet emerges from a small nozzle or orifice expanding into a low-pressure chamber, below its saturation pressure taken at the injection temperature. As the process evolves, crossing the saturation curve, one observes that the fluid remains in the liquid phase reaching a superheated condition. Then, the liquid undergoes an abrupt phase change by means of an oblique evaporation wave. Across this phase change the superheated liquid becomes a two-phase high-speed mixture in various directions, expanding to supersonic velocities. In order to reach the downstream pressure, the supersonic fluid continues to expand, crossing a complex bow shock wave. The balance equations that govern the phenomenon are mass conservation, momentum conservation, and energy conservation, plus an equation-of-state for the substance. A false-transient model is implemented using the shock capturing scheme: dispersion-controlled dissipative (DCD), which was used to calculate the flow conditions as the steady-state condition is reached. Numerical results with computational code DCD-2D vI have been analyzed. Copyright (C) 2009 John Wiley & Sons, Ltd.

On the lower bound on the exchange-correlation energy in two dimensions

We study the properties of the lower bound on the exchange-correlation energy in two dimensions. First we review the derivation of the bound and show how it can be written in a simple density-functional form. This form allows an explicit determination of the prefactor of the bound and testing its tightness. Next we focus on finite two-dimensional systems and examine how their distance from the bound depends on the system geometry. The results for the high-density limit suggest that a finite system that comes as close as possible to the ultimate bound on the exchange-correlation energy has circular geometry and a weak confining potential with a negative curvature. (c) 2009 Elsevier B.V. All rights reserved.

Two- and three-dimensional shape fabric analysis by the intercept method in grey levels

The count intercept is a robust method for the numerical analysis of fabrics Launeau and Robin (1996). It counts the number of intersections between a set of parallel scan lines and a mineral phase, which must be identified on a digital image. However, the method is only sensitive to boundaries and therefore supposes the user has some knowledge about their significance. The aim of this paper is to show that a proper grey level detection of boundaries along scan lines is sufficient to calculate the two-dimensional anisotropy of grain or crystal distributions without any particular image processing. Populations of grains and crystals usually display elliptical anisotropies in rocks. When confirmed by the intercept analysis, a combination of a minimum of 3 mean length intercept roses, taken on 3 more or less perpendicular sections, allows the calculation of 3-dimensional ellipsoids and the determination of their standard deviation with direction and intensity in 3 dimensions as well. The feasibility of this quick method is attested by numerous examples on theoretical objects deformed by active and passive deformation, on BSE images of synthetic magma flow, on drawing or direct analysis of thin section pictures of sandstones and on digital images of granites directly taken and measured in the field. (C) 2010 Elsevier B.V. All rights reserved.

Hidden vorticity in binary Bose-Einstein condensates

We consider a binary Bose-Einstein condensate (BEC) described by a system of two-dimensional (2D) Gross-Pitaevskii equations with the harmonic-oscillator trapping potential. The intraspecies interactions are attractive, while the interaction between the species may have either sign. The same model applies to the copropagation of bimodal beams in photonic-crystal fibers. We consider a family of trapped hidden-vorticity (HV) modes in the form of bound states of two components with opposite vorticities S(1,2) = +/- 1, the total angular momentum being zero. A challenging problem is the stability of the HV modes. By means of a linear-stability analysis and direct simulations, stability domains are identified in a relevant parameter plane. In direct simulations, stable HV modes feature robustness against large perturbations, while unstable ones split into fragments whose number is identical to the azimuthal index of the fastest growing perturbation eigenmode. Conditions allowing for the creation of the HV modes in the experiment are discussed too. For comparison, a similar but simpler problem is studied in an analytical form, viz., the modulational instability of an HV state in a one-dimensional (1D) system with periodic boundary conditions (this system models a counterflow in a binary BEC mixture loaded into a toroidal trap or a bimodal optical beam coupled into a cylindrical shell). We demonstrate that the stabilization of the 1D HV modes is impossible, which stresses the significance of the stabilization of the HV modes in the 2D setting.

Semiclassical scattering in two dimensions

The semiclassical limit of quantum mechanical scattering in two dimensions is developed and the Wentzel-Kramers-Brillouin and eikonal results for two-dimensional scattering is derived. No backward or forward glory scattering is present in two dimensions. Other phenomena, such as rainbows and orbiting, do occur. (C) 2008 American Association of Physics Teachers.

Magnetoresistance oscillations in multilayer systems: Triple quantum wells

Magnetoresistance of two-dimensional electron systems with several occupied subbands oscillates owing to periodic modulation of the probability of intersubband transitions by the quantizing magnetic field. In addition to previous investigations of these magnetointersubband (MIS) oscillations in two-subband systems, we report on both experimental and theoretical studies of such a phenomenon in three-subband systems realized in triple quantum wells. We show that the presence of more than two subbands leads to a qualitatively different MIS oscillation picture, described as a superposition of several oscillating contributions. Under a continuous microwave irradiation, the magnetoresistance of triple-well systems exhibits an interference of MIS oscillations and microwave-induced resistance oscillations. The theory explaining these phenomena is presented in the general form, valid for an arbitrary number of subbands. A comparison of theory and experiment allows us to extract temperature dependence of quantum lifetime of electrons and to confirm the applicability of the inelastic mechanism of microwave photoresistance for the description of magnetotransport in multilayer systems.

Artificial molecular quantum rings under magnetic field influence

The ground states of a few electrons confined in two vertically coupled quantum rings in the presence of an external magnetic field are studied systematically within the current spin-density functional theory. Electron-electron interactions combined with inter-ring tunneling affect the electronic structure and the persistent current. For small values of the external magnetic field, we recover the zero magnetic field molecular quantum ring ground state configurations. Increasing the magnetic field many angular momentum, spin, and isospin transitions are predicted to occur in the ground state. We show that these transitions follow certain rules, which are governed by the parity of the number of electrons, the single-particle picture, Hund's rules, and many-body effects. (C) 2009 American Institute of Physics. [doi:10.1063/1.3223360]

Directed Abelian algebras and their application to stochastic models

With each directed acyclic graph (this includes some D-dimensional lattices) one can associate some Abelian algebras that we call directed Abelian algebras (DAAs). On each site of the graph one attaches a generator of the algebra. These algebras depend on several parameters and are semisimple. Using any DAA, one can define a family of Hamiltonians which give the continuous time evolution of a stochastic process. The calculation of the spectra and ground-state wave functions (stationary state probability distributions) is an easy algebraic exercise. If one considers D-dimensional lattices and chooses Hamiltonians linear in the generators, in finite-size scaling the Hamiltonian spectrum is gapless with a critical dynamic exponent z=D. One possible application of the DAA is to sandpile models. In the paper we present this application, considering one- and two-dimensional lattices. In the one-dimensional case, when the DAA conserves the number of particles, the avalanches belong to the random walker universality class (critical exponent sigma(tau)=3/2). We study the local density of particles inside large avalanches, showing a depletion of particles at the source of the avalanche and an enrichment at its end. In two dimensions we did extensive Monte-Carlo simulations and found sigma(tau)=1.780 +/- 0.005.

Constraints on the infrared behavior of the ghost propagator in Yang-Mills theories

We present rigorous upper and lower bounds for the momentum-space ghost propagator G(p) of Yang-Mills theories in terms of the smallest nonzero eigenvalue (and of the corresponding eigenvector) of the Faddeev-Popov matrix. We apply our analysis to data from simulations of SU(2) lattice gauge theory in Landau gauge, using the largest lattice sizes to date. Our results suggest that, in three and in four space-time dimensions, the Landau gauge ghost propagator is not enhanced as compared to its tree-level behavior. This is also seen in plots and fits of the ghost dressing function. In the two-dimensional case, on the other hand, we find that G(p) diverges as p(-2-2 kappa) with kappa approximate to 0.15, in agreement with A. Maas, Phys. Rev. D 75, 116004 (2007). We note that our discussion is general, although we make an application only to pure gauge theory in Landau gauge. Our simulations have been performed on the IBM supercomputer at the University of Sao Paulo.

Constraints on the infrared behavior of the gluon propagator in Yang-Mills theories

We present rigorous upper and lower bounds for the zero-momentum gluon propagator D(0) of Yang-Mills theories in terms of the average value of the gluon field. This allows us to perform a controlled extrapolation of lattice data to infinite volume, showing that the infrared limit of the Landau-gauge gluon propagator in SU(2) gauge theory is finite and nonzero in three and in four space-time dimensions. In the two-dimensional case, we find D(0)=0, in agreement with Maas. We suggest an explanation for these results. We note that our discussion is general, although we apply our analysis only to pure gauge theory in the Landau gauge. Simulations have been performed on the IBM supercomputer at the University of Sao Paulo.

Free-fall in a uniform gravitational field in noncommutative quantum mechanics

We study the free-fall of a quantum particle in the context of noncommutative quantum mechanics (NCQM). Assuming noncommutativity of the canonical type between the coordinates of a two-dimensional configuration space, we consider a neutral particle trapped in a gravitational well and exactly solve the energy eigenvalue problem. By resorting to experimental data from the GRANIT experiment, in which the first energy levels of freely falling quantum ultracold neutrons were determined, we impose an upper-bound on the noncommutativity parameter. We also investigate the time of flight of a quantum particle moving in a uniform gravitational field in NCQM. This is related to the weak equivalence principle. As we consider stationary, energy eigenstates, i.e., delocalized states, the time of flight must be measured by a quantum clock, suitably coupled to the particle. By considering the clock as a small perturbation, we solve the (stationary) scattering problem associated and show that the time of flight is equal to the classical result, when the measurement is made far from the turning point. This result is interpreted as an extension of the equivalence principle to the realm of NCQM. (C) 2010 American Institute of Physics. [doi:10.1063/1.3466812]