Second-harmonic generation of Bogoliubov excitations in a two-component Bose-Einstein condensate

A second-harmonic generation (SHG) is predicted for the Bogoliubov excitations in a two-component Bose-Einstein condensate. It is shown that, because the linear dispersion curve of the excitations displays two branches, the phase-matching condition for the SHG can be fulfilled if the wave vectors and frequencies of fundamental and second-harmonic waves are selected suitably from different branches. The nonlinearly coupled envelope equations for the SHG are derived by using a method of multiple scales. The explicit solutions of these envelope equations are provided and the conversion efficiency of the SHG is also discussed.

Optimization and comparison of single- and dual-pump fiber-optical parametric amplifiers with dispersion fluctuations

Solutions for fiber-optical parametric amplifiers (FOPAs) with dispersion fluctuations are derived using matrix operators. On the basis of the propagation matrix product and the hybrid genetic algorithm, we have optimized and compared single- and dual-pump FOPAs with zero-dispersion-wavelength variations. The simulations prove that the design of FOPAs involves multimodal function optimization problems. The numerical results show that dual-pump FOPAs are highly sensitive to dispersion fluctuations whereas dispersion variations have less impact on the gain of single-pump FOPAs. To increase signal gain and reduce ripple, dual-pump FOPAs, instead of single-pump FOPAs, have to be carefully optimized with a suitable multisegment fiber structure rather than a one-segment fiber structure. The different combinations of multisegment fibers can provide highly different gain properties. The increase in gain is at the cost of the ripple.

Transient and nonlinear analysis of slow-light pulse propagation in an optical fiber via stimulated Brillouin scattering

We investigate slow-light pulse propagation in an optical fiber via transient stimulated Brillouin scattering. Space-time evolution of a generating slow-light pulse is numerically calculated by solving three-wave coupled-mode equations between a pump beam, an acoustic wave, and a counterpropagating signal pulse. Our mathematical treatments are applicable to both narrowband and broadband pump cases. We show that the time delay of 85% pulse width can be obtained for a signal pulse of the order of subnanosecond pulse width by using a broadband pump, while the signal pulse is broadened only by 40% of the input signal pulse. The physical origin of the pulse broadening and distortion is explained in terms of the temporal decay of the induced acoustic field. (C) 2009 Optical Society of America

Statistical distribution of wave-surface elevation for second-order random directional ocean waves in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, a statistical distribution of the wave-surface elevation is derived by using the characteristic function expansion method. It is found that the distribution, after normalization of the wave-surface elevation, depends only on two parameters. One parameter describes the small mean bias of the surface produced by the second-order wave-wave interactions. Another one is approximately proportional to the skewness of the distribution. Both of these two parameters can be determined by the water depth and the wave-number spectrum of ocean waves. As an illustrative example, we consider a fully developed wind-generated sea and the parameters are calculated for various wind speeds and water depths by using Donelan and Pierson spectrum. It is also found that, for deep water, the dimensionless distribution reduces to the third-order Gram-Charlier series obtained by Longuet-Higgins [J. Fluid Mech. 17 (1963) 459]. The newly proposed distribution is compared with the data of Bitner [Appl. Ocean Res. 2 (1980) 63], Gaussian distribution and the fourth-order Gram-Charlier series, and found our distribution gives a more reasonable fit to the data. (C) 2002 Elsevier Science B.V. All rights reserved.

Nonlinear MHD stability of aluminium reduction cells

An industrial electrolysis cell used to produce primary aluminium is sensitive to waves at the interface of liquid aluminium and electrolyte. The interface waves are similar to stratified sea layers [1], but the penetrating electric current and the associated magnetic field are intricately involved in the oscillation process, and the observed wave frequencies are shifted from the purely hydrodynamic ones [2]. The interface stability problem is of great practical importance because the electrolytic aluminium production is a major electrical energy consumer, and it is related to environmental pollution rate. The stability analysis was started in [3] and a short summary of the main developments is given in [2]. Important aspects of the multiple mode interaction have been introduced in [4], and a widely used linear friction law first applied in [5]. In [6] a systematic perturbation expansion is developed for the fluid dynamics and electric current problems permitting reduction of the three-dimensional problem to a two dimensional one. The procedure is more generally known as “shallow water approximation” which can be extended for the case of weakly non-linear and dispersive waves. The Boussinesq formulation permits to generalise the problem for non-unidirectionally propagating waves accounting for side walls and for a two fluid layer interface [1]. Attempts to extend the electrolytic cell wave modelling to the weakly nonlinear case have started in [7] where the basic equations are derived, including the nonlinearity and linear dispersion terms. An alternative approach for the nonlinear numerical simulation for an electrolysis cell wave evolution is attempted in [8 and references there], yet, omitting the dispersion terms and without a proper account for the dissipation, the model can predict unstable waves growth only. The present paper contains a generalisation of the previous non linear wave equations [7] by accounting for the turbulent horizontal circulation flows in the two fluid layers. The inclusion of the turbulence model is essential in order to explain the small amplitude self-sustained oscillations of the liquid metal surface observed in real cells, known as “MHD noise”. The fluid dynamic model is coupled to the extended electromagnetic simulation including not only the fluid layers, but the whole bus bar circuit and the ferromagnetic effects [9].

Parametric instabilities and localization of nonlinearly coupled electromagnetic modes in astrophysical dusty plasmas

The nonlinear coupling between the Alfven-Rao (AR) and dust-Alfven (DA) modes in a uniform magnetized dusty plasma is considered. For this purpose, multi- fluid equations (composed of the continuity and momentum equations), the laws of Faraday and Ampere and the quasi-neutrality condition are adopted to derive a set of equations, which show how the fields of the modes are nonlinearly coupled. The equations are then used to investigate decay and modulational instabilities in magnetized dusty plasmas. Stationary nonlinear solutions of the coupled AR and DA equations are presented. The relevance of the investigation to nonlinear phenomena (instabilities and localized structures) in interstellar molecular clouds is also discussed.

Realistic many electron coupled channel calculations in heavy ion scattering

The time dependent Dirac equation which describes a heavy ion-atom collision system is solved via a set of coupled channel equations with energy eigenvalues and matrix elements which are given by a selfconsistent field many electron calculation. After a brief discussion of the theoretical approximations and the connection of the many particle with the one particle interpretation we discuss first results for the systems F{^8+} - Ne and F{^6+} - Ne. The resulting P(b) curves for the creation of a Ne K-hole are in good agreement with the experimental results.

Many electron coupled channel calculations for the system F{^8+} - Ne

To describe the time dependence of an atomic collision system the Dirac equation usually is rewritten in a coupled channel equation. We first discuss part of the approximation used in this approach and the connection of the many particle with the one particle interpretation. The coupled channel equations are solved for the system F{^8+} - Ne using static selfconsistent many electron Dirac-Fock-Slater wavefunctions as basis. The resulting P(b) curves for the creation of a Ne K-hole are in reasonable agreement with the experimental results.

Strongly damped wave problems: Bootstrapping and regularity of solutions

The aim of the article is to present a unified approach to the existence, uniqueness and regularity of solutions to problems belonging to a class of second order in time semilinear partial differential equations in Banach spaces. Our results are applied next to a number of examples appearing in literature, which fall into the class of strongly damped semilinear wave equations. The present work essentially extends the results on the existence and regularity of solutions to such problems. Previously, these problems have been considered mostly within the Hilbert space setting and with the main part operators being selfadjoint. In this article we present a more general approach, involving sectorial operators in reflexive Banach spaces. (C) 2008 Elsevier Inc. All rights reserved.

Localization in splitting of matter waves

In this paper we present an analysis of how matter waves, guided as propagating modes in potential structures, are split under adiabatic conditions. The description is formulated in terms of localized states obtained through a unitary transformation acting on the mode functions. The mathematical framework results in coupled propagation equations that are decoupled in the asymptotic regions as well before as after the split. The resulting states have the advantage of describing propagation in situations, for instance matter-wave interferometers, where local perturbations make the transverse modes of the guiding potential unsuitable as a basis. The different regimes of validity of adiabatic propagation schemes based on localized versus delocalized basis states are also outlined. Nontrivial dynamics for superposition states propagating through split potential structures is investigated through numerical simulations. For superposition states the influence of longitudinal wave-packet extension on the localization is investigated and shown to be accurately described in quantitative terms using the adiabatic formulations presented here.

BOUSSINESQ-TYPE SYSTEM OF EQUATIONS IN THE BENARD-MARANGONI SYSTEM

A system of coupled evolution equations for the bulk velocity and the surface displacement is found to govern the long-wavelength perturbations in a Benard-Marangoni system. This system of equations, involving nonlinearity, dispersion, and dissipation, is a generalization of the usual Boussinesq system.

A MODEL OF THE DEUTERON BASED ON A BREIT TYPE EQUATION

A relativistic treatment of the deuteron and its observables based on a two-body Dirac (Breit) equation, with phenomenological interactions, associated to one-boson exchanges with cutoff masses, is presented. The 16-component wave function for the deuteron (J(pi) = 1+) solution contains four independent radial functions which obey a system of four coupled differential equations of first order. This radial system is numerically integrated, from infinity to the origin, by fixing the value of the deuteron binding energy and using appropriate boundary conditions at infinity. Specific examples of mixtures containing scalar, pseudoscalar and vector like terms are discussed in some detail and several observables of the deuteron are calculated. Our treatment differs from more conventional ones in that nonrelativistic reductions of the order c-2 are not used.

DISSIPATIVE BOUSSINESQ SYSTEM OF EQUATIONS IN THE BENARD-MARANGONI PHENOMENON

By using the long-wavelength approximation, a system of coupled evolution equations for the bulk velocity and the surface perturbations of a Benard-Marangoni system is obtained. It includes nonlinearity, dispersion, and dissipation, and it can be interpreted as a dissipative generalization of the usual Boussinesq system of equations. As a particular case, a strictly dissipative version of the Boussinesq system is obtained.

Comment on Wave functions for a Duffin-Kemmer-Petiau particle in a time-dependent potential [J. Math. Phys. 48, 073515 (2007)]

It is shown that the paper Wave functions for a Duffin-Kemmer-Petiau particle in a time-dependent potential by Merad and Bensaid [J. Math. Phys. 48, 073515 (2007)] is not correct in using inadvertently a non-Hermitian Hamiltonian in a formalism that does require Hermitian Hamiltonians.

Modulational instability analysis of surface-waves in the Bénard-Marangoni phenomenon

By using the long-wave approximation, a system of coupled evolutions equations for the bulk velocity and the surface perturbations of a Bénard-Marangoni system is obtained. It includes nonlinearity, dispersion and dissipation, and it is interpreted as a dissipative generalization of the usual Boussinesq system of equations. Then, by considering that the Marangoni number is near the critical value M = -12, we show that the modulation of the Boussinesq waves is described by a perturbed Nonlinear Schrödinger Equation, and we study the conditions under which a Benjamin-Feir instability could eventually set in. The results give sufficient conditions for stability, but are inconclusive about the existence or not of a Benjamin-Feir instability in the long-wave limit. © 1995.