Stable periodic waves in coupled Kuramoto-Sivashinsky-Korteweg-de Vries equations

Periodic waves are investigated in a system composed of a Kuramoto-Sivashinsky-Korteweg-de Vries (KS-KdV) equation linearly coupled to an extra linear dissipative one. The model describes, e.g., a two-layer liquid film flowing down an inclined plane. It has been recently shown that the system supports stable solitary pulses. We demonstrate that a perturbation analysis, based on the balance equation for the net field momentum, predicts the existence of stable cnoidal waves (CnWs) in the same system. It is found that the mean value u(0) of the wave field u in the main subsystem, but not the mean value of the extra field, affects the stability of the periodic waves. Three different areas can be distinguished inside the stability region in the parameter plane (L, u(0)), where L is the wave's period. In these areas, stable are, respectively, CnWs with positive velocity, constant solutions, and CnWs with negative velocity. Multistability, i.e., the coexistence of several attractors, including the waves with several maxima per period, appears at large value of L. The analytical predictions are completely confirmed by direct simulations. Stable waves are also found numerically in the limit of vanishing dispersion, when the KS-KdV equation goes over into the KS one.

Metric-scalar gravity with torsion and the measurability of the non-minimal coupling

The measurability of the non-minimal coupling is discussed by considering the correction to the Newtonian static potential in the semiclassical approach. The coefficient of the gravitational Darwin term (GDT) gets redefined by the non-minimal torsion scalar couplings. Based on a similar analysis of the GDT in the effective field theory approach to non-minimal scalar, we conclude that for reasonable values of the couplings the correction is very small.

Effects of time-periodic linear coupling on two-component Bose-Einstein condensates in two dimensions

We examine two-component Gross-Pitaevskii equations with nonlinear and linear couplings, assuming self-attraction in one species and self-repulsion in the other, while the nonlinear inter-species coupling is also repulsive. For initial states with the condensate placed in the self-attractive component, a sufficiently strong linear coupling switches the collapse into decay (in the free space). Setting the linear-coupling coefficient to be time-periodic (alternating between positive and negative values, with zero mean value) can make localized states quasi-stable for the parameter ranges considered herein, but they slowly decay. The 2D states can then be completely stabilized by a weak trapping potential. In the case of the high-frequency modulation of the coupling constant, averaged equations are derived, which demonstrate good agreement with numerical solutions of the full equations. (C) 2007 Elsevier B.V. All rights reserved.

Mean-field equations for cigar- and disc-shaped Bose and Fermi superfluids

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

One-loop superstring amplitude from integrals on pure spinors space

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Notes on the overall coefficient of the two-loop superstring amplitude using pure spinor

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Non-Z(2) symmetric braneworlds in scalar tensorial gravity

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

A spin Hamiltonian for non-relativistic electrons and their interaction with an external field

We investigate the spin of the electron in a non-relativistic context by using the Galilean covariant Pauli-Dirac equation. From a non-relativistic Lagrangian density, we find an appropriate Dirac-like Hamiltonian in the momentum representation, which includes the spin operator in the Galilean covariant framework. Within this formalism, we show that the total angular momentum appears as a constant of motion. Additionally, we propose a non-minimal coupling that describes the Galilean interaction between an electron and the electromagnetic field. Thereby, we obtain, in a natural way, the Hamiltonian including all the essential interaction terms for the electron in a general vector field.

Evolution of spherical non-uniform perturbations in the universe

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

LIMITS on THE COUPLING CONSTANT of HIGHER-DERIVATIVE ELECTROMAGNETISM

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Numerical simulation of Ginzburg-Landau-Langevin equations

This work is concerned with non-equilibrium phenomena, with focus on the numerical simulation of the relaxation of non-conserved order parameters described by stochastic kinetic equations known as Ginzburg-Landau-Langevin (GLL) equations. We propose methods for solving numerically these type of equations, with additive and multiplicative noises. Illustrative applications of the methods are presented for different GLL equations, with emphasis on equations incorporating memory effects.

Signatures of primordial non-Gaussianities in the matter power-spectrum and bispectrum: the time-RG approach

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Effect of a frictional force on the Fermi-Ulam model

The dynamical properties of a classical particle bouncing between two rigid walls, in the presence of a drag force, are studied for the case where one wall is fixed and the other one moves periodically in time. The system is described in terms of a two-dimensional nonlinear map obtained by solution of the relevant differential equations. It is shown that the structure of the KAM curves and the chaotic sea is destroyed as the drag force is introduced. At high energy, the velocity of the particle decreases linearly with increasing iteration number, but with a small superimposed sinusoidal modulation. If the motion passes near enough to a fixed point, the particle approaches it exponentially as the iteration number evolves, with a speed of approach that depends on the strength of the drag force. For a simplified version of the model it is shown that, at low energies corresponding to the region of the chaotic sea in the non-dissipative model, the particle wanders in a chaotic transient that depends on the strength of the drag coefficient. However, the KAM islands survive in the presence of dissipation. It is confirmed that the fixed points and periodic orbits go over smoothly into the orbits of the well-known (non-dissipative) Fermi-Ulam model as the drag force goes to zero.

SPH simulations of clumps formation by dissipative collision of molecular clouds - I. Non magnetic case

Computer experiments of interstellar cloud collisions were performed with a new smoothed-particle-hydrodynamics (SPH) code. The SPH quantities were calculated by using spatially adaptive smoothing lengths and the SPH fluid equations of motion were solved by means of a hierarchical multiple time-scale leapfrog. Such a combination of methods allows the code to deal with a large range of hydrodynamic quantities. A careful treatment of gas cooling by H, H(2), CO and H II, as well as a heating mechanism by cosmic rays and by H(2) production on grains surface, were also included in the code. The gas model reproduces approximately the typical environment of dark molecular clouds. The experiments were performed by impinging two dynamically identical spherical clouds onto each other with a relative velocity of 10 km s(-1) but with a different impact parameter for each case. Each object has an initial density profile obeying an r(-1)-law with a cutoff radius of 10 pc and with an initial temperature of 20 K. As a main result, cloud-cloud collision triggers fragmentation but in expense of a large amount of energy dissipated, which occurred in the head-on case only. Off-center collision did not allow remnants to fragment along the considered time (similar to 6 Myr). However, it dissipated a considerable amount of orbital energy. Structures as small as 0.1 pc, with densities of similar to 10(4) cm(-3), were observed in the more energetic collision.

On saturation control of a non-ideal vibrating portal frame foundation type shear-building

In this paper, we examine the nonlinear control method based on the saturation phenomenon and of systems coupled with quadratic nonlinear ties applied to a shear-building portal plane frame foundation that supports an unbalanced direct cut-rent with limited power supply (non-ideal system). We analyze the equations of motion by using the method of averaging and numerical simulation. The interaction of the non-ideal structure with the saturation controller may lead to the occurrence of interesting phenomena during the forward passage through the several resonance states of the systems. Special attention is focused on passage through resonance when the non-ideal excitation frequency is near the portal frame natural frequency and when the non-ideal system frequency is approximately twice the controller frequency (two-to-one internal resonance).