1,002 research outputs found
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
Free-energy transition in a gas of non-interacting nonlinear wave-particles
We investigate the dynamics of a gas of non-interacting particle-like soliton
waves, demonstrating that phase transitions originate from their collective
behavior. This is predicted by solving exactly the nonlinear equations and by
employing methods of the statistical mechanics of chaos. In particular, we show
that a suitable free energy undergoes a metamorphosis as the input excitation
is increased, thereby developing a first order phase transition whose
measurable manifestation is the formation of shock waves. This demonstrates
that even the simplest phase-space dynamics, involving independent (uncoupled)
degrees of freedom, can sustain critical phenomena.Comment: 4 pages, 3 figure
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