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

Magnetic cloaking by a paramagnet/superconductor cylindrical tube in the critical state

Cloaking of static magnetic fields by a finite thickness type-II superconductor tube being in the full critical state and surrounded by a coaxial paramagnet shell is studied. On the basis of exact solutions to the Maxwell equations, it is shown that, additionally to previous studies assuming the Meissner state of the superconductor constituent, perfect cloaking is still realizable at fields higher than the field of full flux penetration into the superconductor and for arbitrary geometrical parameters of both constituents. It is also proven that simultaneously the structure is fully undetectable under the cloaking conditions. Differently from the case of the Meissner state the cloaking properties in the application relevant critical state are realized, however, only at a certain field magnitude.Comment: 5 pages, 4 figures; to be published in Applied Physics Letters. arXiv admin note: substantial text overlap with arXiv:1401.356

Giant molecular clouds as regions of particle acceleration

One of the most interesting results of investigations carried out on the satellites SAS-II and COS-B is the discovery of unidentified discrete gamma sources. Possibly a considerable part of them may well be giant molecular clouds. Gamma emission from clouds is caused by the processes with participation of cosmic rays. The estimation of the cosmic ray density in clouds has shown that for the energy E approx. = I GeV their density can 10 to 1000 times exceed the one in intercloud space. We have made an attempt to determine the mechanism which could lead to the increase in the cosmic ray density in clouds

Whitham method for Benjamin-Ono-Burgers equation and dispersive shocks in internal waves in deep fluid

The Whitham modulation equations for the parameters of a periodic solution are derived using the generalized Lagrangian approach for the case of damped Benjamin-Ono equation. The structure of the dispersive shock in internal wave in deep water is considered by this method.Comment: 8 pages, 4 figure

Acoustoelectric current and pumping in a ballistic quantum point contact

The acoustoelectric current induced by a surface acoustic wave (SAW) in a ballistic quantum point contact is considered using a quantum approach. We find that the current is of the "pumping" type and is not related to drag, i.e. to the momentum transfer from the wave to the electron gas. At gate voltages corresponding to the plateaus of the quantized conductance the current is small. It is peaked at the conductance step voltages. The peak current oscillates and decays with increasing SAW wavenumber for short wavelengths. These results contradict previous calculations, based on the classical Boltzmann equation.Comment: 4 pages, 1 figur

Acoustoelectric effect in a finite-length ballistic quantum channel

The dc current induced by a coherent surface acoustic wave (SAW) of wave vector q in a ballistic channel of length L is calculated. The current contains two contributions, even and odd in q. The even current exists only in a asymmetric channel, when the electron reflection coefficients r_1 and r_2 at both channel ends are different. The direction of the even current does not depend on the direction of the SAW propagation, but is reversed upon interchanging r_1 and r_2. The direction of the odd current is correlated with the direction of the SAW propagation, but is insensitive to the interchange of r_1 and r_2. It is shown that both contributions to the current are non zero only when the electron reflection coefficients at the channel ends are energy dependent. The current exhibits geometric oscillations as function of qL. These oscillations are the hallmark of the coherence of the SAW and are completely washed out when the current is induced by a flux of non-coherent phonons. The results are compared with those obtained previously by different methods and under different assumptions.Comment: 7 pages, 2 figure

Coulomb drag between ballistic one-dimensional electron systems

The presence of pronounced electronic correlations in one-dimensional systems strongly enhances Coulomb coupling and is expected to result in distinctive features in the Coulomb drag between them that are absent in the drag between two-dimensional systems. We review recent Fermi and Luttinger liquid theories of Coulomb drag between ballistic one-dimensional electron systems, and give a brief summary of the experimental work reported so far on one-dimensional drag. Both the Fermi liquid (FL) and the Luttinger liquid (LL) theory predict a maximum of the drag resistance R_D when the one-dimensional subbands of the two quantum wires are aligned and the Fermi wave vector k_F is small, and also an exponential decay of R_D with increasing inter-wire separation, both features confirmed by experimental observations. A crucial difference between the two theoretical models emerges in the temperature dependence of the drag effect. Whereas the FL theory predicts a linear temperature dependence, the LL theory promises a rich and varied dependence on temperature depending on the relative magnitudes of the energy and length scales of the systems. At higher temperatures, the drag should show a power-law dependence on temperature, R_D \~ T^x, experimentally confirmed in a narrow temperature range, where x is determined by the Luttinger liquid parameters. The spin degree of freedom plays an important role in the LL theory in predicting the features of the drag effect and is crucial for the interpretation of experimental results.Comment: 25 pages, 14 figures, to appear in Semiconductor Science and Technolog