Evolution of initial discontinuities in the Riemann problem for the Kaup-Boussinesq equation with positive dispersion

We consider the space-time evolution of initial discontinuities of depth and flow velocity for an integrable version of the shallow water Boussinesq system introduced by Kaup. We focus on a specific version of this "Kaup-Boussinesq model" for which a flat water surface is modulationally stable, we speak below of "positive dispersion" model. This model also appears as an approximation to the equations governing the dynamics of polarisation waves in two-component Bose-Einstein condensates. We describe its periodic solutions and the corresponding Whitham modulation equations. The self-similar, one-phase wave structures are composed of different building blocks which are studied in detail. This makes it possible to establish a classification of all the possible wave configurations evolving from initial discontinuities. The analytic results are confirmed by numerical simulations

Effective fluid transport properties of deformable rocks

Modern reservoir monitoring technologies often make use of diffusion waves in order to estimate the hydraulic conductivity and diffusivity of reservoir rocks. However, most theoretical descriptions for these effective uid transport properties assume that the host rock is elastically rigid. Inhomogeneous poroelastic continua described by Biot's equations of dynamic or quasi-static poroelasticity provide an adequate framework to study the dependence of uid transport properties on the elastic properties of the host rock. Analysis of diffusion wave elds in randomly inhomogeneous poroelastic structures provides new insight into how uctuations of the compressible constituents of the rock affect the effective diffusivity. Using the method of statistical smoothing we derive an effective wave number of the coherent diffusion wave eld. This wave number yields expressions for the effective conductivity and diffusivity of a deformable and inhomogeneous porous medium. These uid transport properties are frequency-dependent. Comparison of the hydraulic conductivity derived here with that estimated from unsteady ow through porous media based on Darcy's law shows that they are identical in the limits of low and high frequencies

Flux flow of Abrikosov-Josephson vortices along grain boundaries in high-temperature superconductors

We show that low-angle grain boundaries (GB) in high-temperature superconductors exhibit intermediate Abrikosov vortices with Josephson cores, whose length $l$ along GB is smaller that the London penetration depth, but larger than the coherence length. We found an exact solution for a periodic vortex structure moving along GB in a magnetic field $H$ and calculated the flux flow resistivity $R_F(H)$, and the nonlinear voltage-current characteristics. The predicted $R_F(H)$ dependence describes well our experimental data on $7^{\circ}$ unirradiated and irradiated $YBa_2Cu_3O_7$ bicrystals, from which the core size $l(T)$, and the intrinsic depairing density $J_b(T)$ on nanoscales of few GB dislocations were measured for the first time. The observed temperature dependence of $J_b(T)=J_{b0}(1-T/T_c)^2$ indicates a significant order parameter suppression in current channels between GB dislocation cores.Comment: 5 pages 5 figures. Phys. Rev. Lett. (accepted

Quantum line bundles on noncommutative sphere

Noncommutative (NC) sphere is introduced as a quotient of the enveloping algebra of the Lie algebra su(2). Using the Cayley-Hamilton identities we introduce projective modules which are analogues of line bundles on the usual sphere (we call them quantum line bundles) and define a multiplicative structure in their family. Also, we compute a pairing between certain quantum line bundles and finite dimensional representations of the NC sphere in the spirit of the NC index theorem. A new approach to constructing the differential calculus on a NC sphere is suggested. The approach makes use of the projective modules in question and gives rise to a NC de Rham complex being a deformation of the classical one.Comment: LaTeX file, 15 pp, no figures. Some clarifying remarks are added at the beginning of section 2 and into section

Experimental Realization of an Exact Solution to the Vlasov Equations for an Expanding Plasma

We study the expansion of ultracold neutral plasmas in the regime in which inelastic collisions are negligible. The plasma expands due to the thermal pressure of the electrons, and for an initial spherically symmetric Gaussian density profle, the expansion is self-similar. Measurements of the plasma size and ion kinetic energy using fluorescence imaging and spectroscopy show that the expansion follows an analytic solution of the Vlasov equations for an adiabatically expanding plasma.Comment: 4 pages, 4 figure

Cross-over frequencies of seismic attenuation in fractured porous rocks

We analyze compressional wave attenuation in fluid saturated porous material with porous inclusions having different compressibilities and very different spatial scales in comparison with the background. Such a medium exhibits significant attenuation due to wave-induced fluid flow across the interface between inclusion and background. For the representative element containing two layers (one of them representing inclusion), we show that overall wave attenuation is governed by the superposition of two coupled fluid-diffusion processes. Associated with two characteristic spatial scales, we compute two cross-over frequencies that separate three different frequency regimes. At low frequencies inverse quality factor scales with the first power of frequency ?, while at high frequencies the attenuation is proportional to ?12. In the intermediate range of frequencies inverse quality factor scales with ?12. These characteristic frequency regimes can be observed in all theoretical models of wave-induced attenuation, but complete physical explanation is still missing. The potential application of this model is in estimation of the background permeability as well as inclusion scale (thickness) by identifying these frequencies from attenuation measurements

Solitonic asymptotics for the Korteweg-de Vries equation in the small dispersion limit

We study the small dispersion limit for the Korteweg-de Vries (KdV) equation $u_t+6uu_x+\epsilon^{2}u_{xxx}=0$ in a critical scaling regime where $x$ approaches the trailing edge of the region where the KdV solution shows oscillatory behavior. Using the Riemann-Hilbert approach, we obtain an asymptotic expansion for the KdV solution in a double scaling limit, which shows that the oscillations degenerate to sharp pulses near the trailing edge. Locally those pulses resemble soliton solutions of the KdV equation.Comment: 25 pages, 4 figure

Kinetic modelling and molecular dynamics simulation of ultracold neutral plasmas including ionic correlations

A kinetic approach for the evolution of ultracold neutral plasmas including interionic correlations and the treatment of ionization/excitation and recombination/deexcitation by rate equations is described in detail. To assess the reliability of the approximations inherent in the kinetic model, we have developed a hybrid molecular dynamics method. Comparison of the results reveals that the kinetic model describes the atomic and ionic observables of the ultracold plasma surprisingly well, confirming our earlier findings concerning the role of ion-ion correlations [Phys. Rev. A {\bf 68}, 010703]. In addition, the molecular dynamics approach allows one to study the relaxation of the ionic plasma component towards thermodynamical equilibrium

Giant Oscillations of Acoustoelectric Current in a Quantum Channel

A theory of d.c. electric current induced in a quantum channel by a propagating surface acoustic wave (acoustoelectric current) is worked out. The first observation of the acoustoelectric current in such a situation was reported by J. M. Shilton et al., Journ. Phys. C (to be published). The authors observed a very specific behavior of the acoustoelectric current in a quasi-one-dimensional channel defined in a GaAs-AlGaAs heterostructure by a split-gate depletion -- giant oscillations as a function of the gate voltage. Such a behavior was qualitatively explained by an interplay between the energy-momentum conservation law for the electrons in the upper transverse mode with a finite temperature splitting of the Fermi level. In the present paper, a more detailed theory is developed, and important limiting cases are considered.Comment: 7 pages, 2 Postscript figures, RevTeX 3.