Analytic model for a frictional shallow-water undular bore

We use the integrable Kaup-Boussinesq shallow water system, modified by a small viscous term, to model the formation of an undular bore with a steady profile. The description is made in terms of the corresponding integrable Whitham system, also appropriately modified by friction. This is derived in Riemann variables using a modified finite-gap integration technique for the AKNS scheme. The Whitham system is then reduced to a simple first-order differential equation which is integrated numerically to obtain an asymptotic profile of the undular bore, with the local oscillatory structure described by the periodic solution of the unperturbed Kaup-Boussinesq system. This solution of the Whitham equations is shown to be consistent with certain jump conditions following directly from conservation laws for the original system. A comparison is made with the recently studied dissipationless case for the same system, where the undular bore is unsteady.Comment: 24 page

Formation of shock waves in a Bose-Einstein condensate

We consider propagation of density wave packets in a Bose-Einstein condensate. We show that the shape of initially broad, laser-induced, density perturbation changes in the course of free time evolution so that a shock wave front finally forms. Our results are well beyond predictions of commonly used zero-amplitude approach, so they can be useful in extraction of a speed of sound from experimental data. We discuss a simple experimental setup for shock propagation and point out possible limitations of the mean-field approach for description of shock phenomena in a BEC.Comment: 8 pages & 6 figures, minor changes, more references, to appear in Phys. Rev.

The theory of optical dispersive shock waves in photorefractive media

The theory of optical dispersive shocks generated in propagation of light beams through photorefractive media is developed. Full one-dimensional analytical theory based on the Whitham modulation approach is given for the simplest case of sharp step-like initial discontinuity in a beam with one-dimensional strip-like geometry. This approach is confirmed by numerical simulations which are extended also to beams with cylindrical symmetry. The theory explains recent experiments where such dispersive shock waves have been observed.Comment: 26 page

On dissipationless shock waves in a discrete nonlinear Schr\"odinger equation

It is shown that the generalized discrete nonlinear Schr\"odinger equation can be reduced in a small amplitude approximation to the KdV, mKdV, KdV(2) or the fifth-order KdV equations, depending on values of the parameters. In dispersionless limit these equations lead to wave breaking phenomenon for general enough initial conditions, and, after taking into account small dispersion effects, result in formation of dissipationless shock waves. The Whitham theory of modulations of nonlinear waves is used for analytical description of such waves.Comment: 15 pages, 9 figure

A sol-gel method for growing superconducting MgB2 films

In this paper we report a new sol-gel method for the fabrication of MgB2 films. Polycrystalline MgB2 films were prepared by spin-coating a precursor solution of Mg(BH_4)_2 diethyl ether on (001)Al2O3 substrates followed with annealing in Mg vapor. In comparison with the MgB2 films grown by other techniques, our films show medium qualities including a superconducting transition temperature of Tc ~ 37 K, a critical current density of Jc(5 K, 0 T) ~ 5 {\times} 10^6 A cm^{-2}, and a critical field of H_{c2}(0) ~ 19 T. Such a sol-gel technique shows potential in the commercial fabrication of practically used MgB2 films as well as MgB2 wires and tapes.Comment: 8 pages, 5 figure

Differential-Algebraic Integrability Analysis of the Generalized Riemann Type and Korteweg-de Vries Hydrodynamical Equations

A differential-algebraic approach to studying the Lax type integrability of the generalized Riemann type hydrodynamic equations at N = 3; 4 is devised. The approach is also applied to studying the Lax type integrability of the well known Korteweg-de Vries dynamical system.Comment: 11 page

Transient heat generation in a quantum dot under a step-like pulse bias

We study the transient heat generation in a quantum dot system driven by a step-like or a square-shaped pulse bias. We find that a periodically oscillating heat generation arises after adding the sudden bias. One particularly surprising result is that there exists a heat absorption from the zero-temperature phonon subsystem. Thus the phonon population in non-equilibrium can be less than that of the equilibrium electron-phonon system. In addition, we also ascertain the optimal conditions for the operation of a quantum dot with the minimum heat generation.Comment: 6 pages, 4 figure

Influence of vortex-vortex interaction on critical currents across low-angle grain boundaries in YBa2Cu3O7-delta thin films

Low-angle grain boundaries with misorientation angles theta < 5 degrees in optimally doped thin films of YBCO are investigated by magnetooptical imaging. By using a numerical inversion scheme of Biot-Savart's law the critical current density across the grain boundary can be determined with a spatial resolution of about 5 micrometers. Detailed investigation of the spatially resolved flux density and current density data shows that the current density across the boundary varies with varying local flux density. Combining the corresponding flux and current pattern it is found that there exists a universal dependency of the grain boundary current on the local flux density. A change in the local flux density means a variation in the flux line-flux line distance. With this knowledge a model is developped that explains the flux-current relation by means of magnetic vortex-vortex interaction.Comment: 7 pages, 14 figure

Evidence of spin-density-wave order in RFeAsO from measurements of thermoelectric power

Data on the magneto-thermopower and specific heat of three compounds belonging to '1111' oxypnictides family are reported. One specimen (SmAsFeO0.8F0.2) is a superconductor with Tc = 53 K, while two others (SmAsFeO and NdAsFeO) are nonsuperconducting parent compounds. Our results confirm that spin density wave (SDW) order is present in SmAsFeO and NdAsFeO. In these two samples a strict connection between the thermoelectric power and electronic specific heat is found in the vicinity of SDW transition, what indicates that the chemical potential of charge carriers strongly depends on temperature in this region. Low temperature data suggest presence of significant contribution magnon-drag to the thermoelectric power.Comment: 14 pages, 5 figures; adjusted to referees' suggestions; to appear in Phys. Rev.

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 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 ``ship waves'' is situated. Analytical theory of ``ship waves'' is developed and two-dimensional dark soliton solutions of the equation describing the 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.Comment: 18 page