2,980 research outputs found
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
Dynamics of Macroscopic Tunneling in Elongated BEC
We investigate macroscopic tunneling from an elongated quasi 1-d trap,
forming a 'cigar shaped' BEC. Using recently developed formalism we get the
leading analytical approximation for the right hand side of the potential wall,
i.e. outside the trap, and a formalism based on Wigner functions, for the left
side of the potential wall, i.e. inside the BEC. We then present accomplished
results of numerical calculations, which show a 'blip' in the particle density
traveling with an asymptotic shock velocity, as resulted from previous works on
a dot-like trap, but with significant differences from the latter. Inside the
BEC a pattern of a traveling dispersive shock wave is revealed. In the
attractive case, we find trains of bright solitons frozen near the boundary.Comment: 6 pages, 15 figure
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
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
Effect of fluctuations on vortex lattice structural transitions in superconductors
The rhombic-to-square transition field for cubic and tetragonal
materials in fields along [001] is evaluated using the nonlocal London theory
with account of thermal vortex fluctuations. Unlike extended Ginzburg-Landau
models, our approach shows that the line and the upper critical
field do not cross due to strong fluctuations near
which suppress the square anisotropy induced by the nonlocality. In increasing
fields, this causes re-entrance of the rhombic structure in agreement with
recent neutron scattering data on borocarbides.Comment: 4 pages, 2 figure
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
Formation of Quantum Shock Waves by Merging and Splitting Bose-Einstein Condensates
The processes of merging and splitting dilute-gas Bose-Einstein condensates
are studied in the nonadiabatic, high-density regime. Rich dynamics are found.
Depending on the experimental parameters, uniform soliton trains containing
more than ten solitons or the formation of a high-density bulge as well as
quantum (or dispersive) shock waves are observed experimentally within merged
BECs. Our numerical simulations indicate the formation of many vortex rings. In
the case of splitting a BEC, the transition from sound-wave formation to
dispersive shock-wave formation is studied by use of increasingly stronger
splitting barriers. These experiments realize prototypical dispersive shock
situations.Comment: 10 pages, 8 figure
On the temperature dependence of ballistic Coulomb drag in nanowires
We have investigated within the theory of Fermi liquid dependence of Coulomb
drag current in a passive quantum wire on the applied voltage across an
active wire and on the temperature for any values of . We assume
that the bottoms of the 1D minibands in both wires almost coincide with the
Fermi level. We come to conclusions that 1) within a certain temperature
interval the drag current can be a descending function of the temperature ;
2) the experimentally observed temperature dependence of the drag
current can be interpreted within the framework of Fermi liquid theory; 3) at
relatively high applied voltages the drag current as a function of the applied
voltage saturates; 4) the screening of the electron potential by metallic gate
electrodes can be of importance.Comment: 7 pages, 1 figur
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