Damping of phase fluctuations in superfluid Bose gases

Using Popov's hydrodynamic approach we derive an effective Euclidean action for the long-wavelength phase fluctuations of superfluid Bose gases in D dimensions. We then use this action to calculate the damping of phase fluctuations at zero temperature as a function of D. For D >1 and wavevectors | k | << 2 mc (where m is the mass of the bosons and c is the sound velocity) we find that the damping in units of the phonon energy E_k = c | k | is to leading order gamma_k / E_k = A_D (k_0^D / 2 pi rho) (| k | / k_0)^{2 D -2}, where rho is the boson density and k_0 =2 mc is the inverse healing length. For D -> 1 the numerical coefficient A_D vanishes and the damping is proportional to an additional power of |k | /k_0; a self-consistent calculation yields in this case gamma_k / E_k = 1.32 (k_0 / 2 pi rho)^{1/2} |k | / k_0. In one dimension, we also calculate the entire spectral function of phase fluctuations.Comment: 6 pages, 4 figures, published versio

Stable two-dimensional solitary pulses in linearly coupled dissipative Kadomtsev-Petviashvili equations

A two-dimensional (2D) generalization of the stabilized Kuramoto - Sivashinsky (KS) system is presented. It is based on the Kadomtsev-Petviashvili (KP) equation including dissipation of the generic (Newell -- Whitehead -- Segel, NWS) type and gain. The system directly applies to the description of gravity-capillary waves on the surface of a liquid layer flowing down an inclined plane, with a surfactant diffusing along the layer's surface. Actually, the model is quite general, offering a simple way to stabilize nonlinear waves in media combining the weakly-2D dispersion of the KP type with gain and NWS dissipation. Parallel to this, another model is introduced, whose dissipative terms are isotropic, rather than of the NWS type. Both models include an additional linear equation of the advection-diffusion type, linearly coupled to the main KP-NWS equation. The extra equation provides for stability of the zero background in the system, opening a way to the existence of stable localized pulses. The consideration is focused on the case when the dispersive part of the system of the KP-I type, admitting the existence of 2D localized pulses. Treating the dissipation and gain as small perturbations and making use of the balance equation for the field momentum, we find that the equilibrium between the gain and losses may select two 2D solitons, from their continuous family existing in the conservative counterpart of the model (the latter family is found in an exact analytical form). The selected soliton with the larger amplitude is expected to be stable. Direct simulations completely corroborate the analytical predictions.Comment: a latex text file and 16 eps files with figures; Physical Review E, in pres

Patterns and Waves Generated by a Subcritical Instability in Systems with a Conservation Law under the Action of a Global Feedback Control

A global feedback control of a system that exhibits a subcritical monotonic instability at a non-zero wavenumber (short-wave, or Turing instability) in the presence of a zero mode is investigated using a Ginzburg-Landau equation coupled to an equation for the zero mode. The method based on a variational principle is applied for the derivation of a low-dimensional evolution model. In the framework of this model the investigation of the system’s dynamics and the linear and nonlinear stability analysis are carried out. The obtained results are compared with the results of direct numerical simulations of the original problem

On dynamic excitation of Marangoni instability in a liquid layer with insoluble surfactant on the deformable surface

This paper is a continuation of our previous work presented at the IMA-6, see [1]. We continue to analyze the parametric excitation of Marangoni instability by a periodic flux modulation in a liquid layer with insoluble surfactant. Contrary to the previous investigation here the upper free surface of the layer is deformable. The linear stability analysis for the disturbances with arbitrary wave numbers is performed. Three response modes of the system to an external periodic stimulation were found – synchronous, subharmonic, and quasi-periodic ones. Results for different Galileo and inverse capillary parameters are presented. It is shown that contrary to the situation with nondeformable interface, at small values of Galileo and inverse capillary parameters a new subharmonic instability region appears in the range of long waves

Influence of density stratification on stability of a two-layer binary-fluid system with a diffuse interface

A system of two layers separated by a diffuse interface which is created due to a phase separation in a binary liquid in the gravity field, is considered. The influence of the density stratification and the gravity on the stabilization of the solution is studied. The stability of two-layer base solutions with respect to long-wave disturbances in the framework of the linear stability analysis is investigated in the case of small density ratio and large Galileo number. It is found that the action of gravity can stabilize the equilibrium state

Fronts in subdiffusive FitzHugh–Nagumo systems

Front solutions of subdiffusive FitzHugh–Nagumo equations are studied for a piece-wise linear nonlinearity. Multiple solutions of the problem and the dependence of the propagation velocity on the parameters are discussed