On Whitham theory for perturbed integrable equations

Whitham theory of modulations is developed for periodic waves described by nonlinear wave equations integrable by the inverse scattering transform method associated with $2\times2$ matrix or second order scalar spectral problems. The theory is illustrated by derivation of the Whitham equations for perturbed Korteweg-de Vries equation and nonlinear Schr\"odinger equation with linear damping.Comment: 17 pages, no figure

Synthetic Turbulence Modeling for Evaluation of Ultrasonic Cross-Correlation Flow Measurement

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI linkPerformance of an ultrasonic cross-correlation flow measurement instrument may be significantly affected by turbulence at the location of the ultrasonic sensors. In this paper, a new method of generating Synthetic Turbulence is presented, to provide an effective tool for creating a variety of turbulent fields, which can be used to model and analyze instrument performance under different flow conditions. In the proposed method, a turbulent field is presented as a Fourier time-series in each point in space. Turbulence structures are defined by a spatial distribution of phase functions for each harmonic. Principles of designing a phase function to achieve the desirable distribution of turbulence scales, and two-point correlations, are outlined by considering the example of Uniform Isotropic Turbulence. One application of this method, presented in this work, is the mathematical modeling of ultrasonic cross-correlation flow measurement. Results predicted by the proposed mathematical model show good agreement with experimental data

Refraction of dispersive shock waves

We study a dispersive counterpart of the classical gas dynamics problem of the interaction of a shock wave with a counter-propagating simple rarefaction wave often referred to as the shock wave refraction. The refraction of a one-dimensional dispersive shock wave (DSW) due to its head-on collision with the centred rarefaction wave (RW) is considered in the framework of defocusing nonlinear Schr\"odinger (NLS) equation. For the integrable cubic nonlinearity case we present a full asymptotic description of the DSW refraction by constructing appropriate exact solutions of the Whitham modulation equations in Riemann invariants. For the NLS equation with saturable nonlinearity, whose modulation system does not possess Riemann invariants, we take advantage of the recently developed method for the DSW description in non-integrable dispersive systems to obtain main physical parameters of the DSW refraction. The key features of the DSW-RW interaction predicted by our modulation theory analysis are confirmed by direct numerical solutions of the full dispersive problem.Comment: 45 pages, 23 figures, minor revisio

Formation of soliton trains in Bose-Einstein condensates as a nonlinear Fresnel diffraction of matter waves

The problem of generation of atomic soliton trains in elongated Bose-Einstein condensates is considered in framework of Whitham theory of modulations of nonlinear waves. Complete analytical solution is presented for the case when the initial density distribution has sharp enough boundaries. In this case the process of soliton train formation can be viewed as a nonlinear Fresnel diffraction of matter waves. Theoretical predictions are compared with results of numerical simulations of one- and three-dimensional Gross-Pitaevskii equation and with experimental data on formation of Bose-Einstein bright solitons in cigar-shaped traps.Comment: 8 pages, 3 figure

The Whitham Deformation of the Dijkgraaf-Vafa Theory

We discuss the Whitham deformation of the effective superpotential in the Dijkgraaf-Vafa (DV) theory. It amounts to discussing the Whitham deformation of an underlying (hyper)elliptic curve. Taking the elliptic case for simplicity we derive the Whitham equation for the period, which governs flowings of branch points on the Riemann surface. By studying the hodograph solution to the Whitham equation it is shown that the effective superpotential in the DV theory is realized by many different meromorphic differentials. Depending on which meromorphic differential to take, the effective superpotential undergoes different deformations. This aspect of the DV theory is discussed in detail by taking the N=1^* theory. We give a physical interpretation of the deformation parameters.Comment: 35pages, 1 figure; v2: one section added to give a physical interpretation of the deformation parameters, one reference added, minor corrections; v4: minor correction

Low-temperature heat capacity of fullerite C₆₀ doped with nitrogen

The heat capacity Cm of polycrystalline fullerite C₆₀ doped with nitrogen has been measured in the temperature interval 2–13 K. The contributions to the heat capacity from translational lattice vibrations (Debye contribution), orientational vibrations of the C₆₀ molecules (Einstein contribution), and from the motion of the N₂ molecules in the octahedral cavities of the C₆₀ lattice have been estimated. However, we could not find (beyond the experimental error limits) any indications of the first-order phase transformation that had been detected earlier in the dilatometric investigation of the orientational N₂–C₆₀ glass. A possible explanation of this fact is proposed

Tilt Grain-Boundary Effects in S- and D-Wave Superconductors

We calculate the s- and d-wave superconductor order parameter in the vicinity of a tilt grain boundary. We do this self-consistently within the Bogoliubov de Gennes equations, using a realistic microscopic model of the grain boundary. We present the first self-consistent calculations of supercurrent flows in such boundaries, obtaining the current-phase characteristics of grain boundaries in both s-wave and d-wave superconductors

Tailoring Anderson localization by disorder correlations in 1D speckle potentials

We study Anderson localization of single particles in continuous, correlated, one-dimensional disordered potentials. We show that tailored correlations can completely change the energy-dependence of the localization length. By considering two suitable models of disorder, we explicitly show that disorder correlations can lead to a nonmonotonic behavior of the localization length versus energy. Numerical calculations performed within the transfer-matrix approach and analytical calculations performed within the phase formalism up to order three show excellent agreement and demonstrate the effect. We finally show how the nonmonotonic behavior of the localization length with energy can be observed using expanding ultracold-atom gases

Relativistic Laser-Matter Interaction and Relativistic Laboratory Astrophysics

The paper is devoted to the prospects of using the laser radiation interaction with plasmas in the laboratory relativistic astrophysics context. We discuss the dimensionless parameters characterizing the processes in the laser and astrophysical plasmas and emphasize a similarity between the laser and astrophysical plasmas in the ultrarelativistic energy limit. In particular, we address basic mechanisms of the charged particle acceleration, the collisionless shock wave and magnetic reconnection and vortex dynamics properties relevant to the problem of ultrarelativistic particle acceleration.Comment: 58 pages, 19 figure