1,754 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
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
Multiple hydrodynamical shocks induced by Raman effect in photonic crystal fibres
We theoretically predict the occurrence of multiple hydrodynamical-like shock
phenomena in the propagation of ultrashort intense pulses in a suitably
engineered photonic crystal fiber. The shocks are due to the Raman effect,
which acts as a nonlocal term favoring their generation in the focusing regime.
It is shown that the problem is mapped to shock formation in the presence of a
slope and a gravity-like potential. The signature of multiple shocks in XFROG
signals is unveiled
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 shock waves in a Bose-Einstein condensate
We consider propagation of density wave packets in a Bose-Einstein
condensate. We show that the shape of initially broad, laser-induced, density
perturbation changes in the course of free time evolution so that a shock wave
front finally forms. Our results are well beyond predictions of commonly used
zero-amplitude approach, so they can be useful in extraction of a speed of
sound from experimental data. We discuss a simple experimental setup for shock
propagation and point out possible limitations of the mean-field approach for
description of shock phenomena in a BEC.Comment: 8 pages & 6 figures, minor changes, more references, to appear in
Phys. Rev.
Orthogonality catastrophe and shock waves in a non-equilibrium Fermi gas
A semiclassical wave-packet propagating in a dissipationless Fermi gas
inevitably enters a "gradient catastrophe" regime, where an initially smooth
front develops large gradients and undergoes a dramatic shock wave phenomenon.
The non-linear effects in electronic transport are due to the curvature of the
electronic spectrum at the Fermi surface. They can be probed by a sudden
switching of a local potential. In equilibrium, this process produces a large
number of particle-hole pairs, a phenomenon closely related to the
Orthogonality Catastrophe. We study a generalization of this phenomenon to the
non-equilibrium regime and show how the Orthogonality Catastrophe cures the
Gradient Catastrophe, providing a dispersive regularization mechanism. We show
that a wave packet overturns and collapses into modulated oscillations with the
wave vector determined by the height of the initial wave. The oscillations
occupy a growing region extending forward with velocity proportional to the
initial height of the packet. We derive a fundamental equation for the
transition rates (MKP-equation) and solve it by means of the Whitham modulation
theory.Comment: 5 pages, 1 figure, revtex4, pr
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
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
Nonlocal feedback in ferromagnetic resonance
Ferromagnetic resonance in thin films is analyzed under the influence of
spatiotemporal feedback effects. The equation of motion for the magnetization
dynamics is nonlocal in both space and time and includes isotropic, anisotropic
and dipolar energy contributions as well as the conserved Gilbert- and the
non-conserved Bloch-damping. We derive an analytical expression for the
peak-to-peak linewidth. It consists of four separate parts originated by
Gilbert damping, Bloch-damping, a mixed Gilbert-Bloch component and a
contribution arising from retardation. In an intermediate frequency regime the
results are comparable with the commonly used Landau-Lifshitz-Gilbert theory
combined with two-magnon processes. Retardation effects together with Gilbert
damping lead to a linewidth the frequency dependence of which becomes strongly
nonlinear. The relevance and the applicability of our approach to ferromagnetic
resonance experiments is discussed.Comment: 22 pages, 9 figure
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