3,027 research outputs found
Example of shock wave in unstaible medium: The focusing nonlinear Schrodinger equation
Dissipationless shock waves in modulational unstable one-dimensional medium
are investigated on the simplest example of integrable focusing nonlinear
Schr\''odinger (NS) equation. Our approach is based on the construction of
special exact solution of the Whitham-NS system, which ''partially saturates''
the modulational instability.Comment: 4 pages, LaTEX, version 2.09, submitted to Phys. Lett.
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
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
Detection of Quantum Noise from an Electrically-Driven Two-Level System
Quantum mechanics can strongly influence the noise properties of mesoscopic
devices. To probe this effect we have measured the current fluctuations at
high-frequency (5-90 GHz) using a superconductor-insulator-superconductor
tunnel junction as an on-chip spectrum analyser. By coupling this
frequency-resolved noise detector to a quantum device we can measure the
high-frequency, non-symmetrized noise as demonstrated for a Josephson junction.
The same scheme is used to detect the current fluctuations arising from
coherent charge oscillations in a two-level system, a superconducting charge
qubit. A narrow band peak is observed in the spectral noise density at the
frequency of the coherent charge oscillations.Comment: 16 pages, 4 figure
Phonon drag in ballistic quantum wires
The acoustic phonon-mediated drag-contribution to the drag current created in
the ballistic transport regime in a one-dimensional nanowire by phonons
generated by a current-carrying ballistic channel in a nearby nanowire is
calculated. The threshold of the phonon-mediated drag current with respect to
bias or gate voltage is predicted.Comment: 5 pages, 2 figure
Radiation Front Sweeping the Ambient Medium of Gamma-Ray Bursts
Gamma-ray bursts (GRBs) are emitted by relativistic ejecta from powerful
cosmic explosions. Their light curves suggest that the gamma-ray emission
occurs at early stages of the ejecta expansion, well before it decelerates in
the ambient medium. If so, the launched gamma-ray front must overtake the
ejecta and sweep the ambient medium outward. As a result a gap is opened
between the ejecta and the medium that surfs the radiation front ahead.
Effectively, the ejecta moves in a cavity until it reaches a radius
R_{gap}=10^{16}E_{54}^{1/2} cm where E is the isotropic energy of the GRB. At
R=R_{gap} the gap is closed, a blast wave forms and collects the medium swept
by radiation. Further development of the blast wave is strongly affected by the
leading radiation front: the front plays the role of a precursor where the
medium is loaded with e+- pairs and preaccelerated just ahead of the blast. It
impacts the emission from the blast at R < R_{load}=5R_{gap} (the early
afterglow). A spectacular observational effect results: GRB afterglows should
start in optical/UV and evolve fast (< min) to a normal X-ray afterglow. The
early optical emission observed in GRB 990123 may be explained in this way. The
impact of the front is especially strong if the ambient medium is a wind from a
massive progenitor of the GRB. In this case three phenomena are predicted: (1)
The ejecta decelerates at R<R_{load} producing a lot of soft radiation. (2) The
light curve of soft emission peaks at
t_{peak}=40(1+z)E_{54}^{1/2}(Gamma_{ej}/100)^{-2} s where Gamma_{ej} is the
Lorentz factor of the ejecta. Given measured redshift z and t_{peak}, one finds
Gamma_{ej}. (3) The GRB acquires a spectral break at 5 - 50 MeV because harder
photons are absorbed by radiation scattered in the wind.Comment: 20 pages, accepted to Ap
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