3,191 research outputs found
Remnants of dark matter clumps
What happened to the central cores of tidally destructed dark matter clumps
in the Galactic halo? We calculate the probability of surviving of the remnants
of dark matter clumps in the Galaxy by modelling the tidal destruction of the
small-scale clumps. It is demonstrated that a substantial fraction of clump
remnants may survive through the tidal destruction during the lifetime of the
Galaxy if the radius of a core is rather small. The resulting mass spectrum of
survived clumps is extended down to the mass of the core of the cosmologically
produced clumps with a minimal mass. Since the annihilation signal is dominated
by the dense part of the core, destruction of the outer part of the clump
affects the annihilation rate relatively weakly and the survived dense remnants
of tidally destructed clumps provide a large contribution to the annihilation
signal in the Galaxy. The uncertainties in minimal clump mass resulting from
the uncertainties in neutralino models are discussed.Comment: 13 pages, 6 figures, added reference
Quantum orbits of R-matrix type
Given a simple Lie algebra \gggg, we consider the orbits in \gggg^* which
are of R-matrix type, i.e., which possess a Poisson pencil generated by the
Kirillov-Kostant-Souriau bracket and the so-called R-matrix bracket. We call an
algebra quantizing the latter bracket a quantum orbit of R-matrix type. We
describe some orbits of this type explicitly and we construct a quantization of
the whole Poisson pencil on these orbits in a similar way. The notions of
q-deformed Lie brackets, braided coadjoint vector fields and tangent vector
fields are discussed as well.Comment: 18 pp., Late
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
Whitham systems and deformations
We consider the deformations of Whitham systems including the "dispersion
terms" and having the form of Dubrovin-Zhang deformations of Frobenius
manifolds. The procedure is connected with B.A. Dubrovin problem of
deformations of Frobenius manifolds corresponding to the Whitham systems of
integrable hierarchies. Under some non-degeneracy requirements we suggest a
general scheme of the deformation of the hyperbolic Whitham systems using the
initial non-linear system. The general form of the deformed Whitham system
coincides with the form of the "low-dispersion" asymptotic expansions used by
B.A. Dubrovin and Y. Zhang in the theory of deformations of Frobenius
manifolds.Comment: 27 pages, Late
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
Propagation of sound in a Bose Einstein condensate in an optical lattice
We study the propagation of sound waves in a Bose-Einstein condensate trapped
in a one-dimensional optical lattice. We find that the velocity of propagation
of sound wavepackets decreases with increasing optical lattice depth, as
predicted by the Bogoliubov theory. The strong interplay between nonlinearities
and the periodicity of the external potential raise new phenomena which are not
present in the uniform case. Shock waves, for instance, can propagate slower
than sound waves, due to the negative curvature of the dispersion relation.
Moreover, nonlinear corrections to the Bogoliubov theory appear to be important
even with very small density perturbations, inducing a saturation on the
amplitude of the sound signal
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 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 and calculated the
flux flow resistivity , and the nonlinear voltage-current
characteristics. The predicted dependence describes well our
experimental data on unirradiated and irradiated
bicrystals, from which the core size , and the intrinsic depairing
density on nanoscales of few GB dislocations were measured for the
first time. The observed temperature dependence of
indicates a significant order parameter suppression in current channels between
GB dislocation cores.Comment: 5 pages 5 figures. Phys. Rev. Lett. (accepted
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
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