1,949 research outputs found
Effect of Multiple Scattering on the Critical Electric Field for Runaway Electrons in the Atmosphere
A simple method for taking into account the multiple Coulomb scattering in
construction of a separatrix (the line separating the regions of runaway and
decelerating electrons in an electric field) is described. The desired line is
obtained by solving a simple transcendental equation.Comment: 3 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
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
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
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
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
A Modified Field Infiltrometer Test for Clay Liners
Regulatory agencies are looking more frequently to in situ field hydraulic conductivity tests for the assessment of a liner\u27s compliance to a specified hydraulic conductivity. Most field tests have evaluated hydraulic conductivity by measuring the infiltration rate of the liner. The infiltration rate can be used to arrive at a hydraulic conductivity value if the hydraulic boundary conditions of the test can be identified or if the head loss at different depths can be measured. A test fill of a clay liner was evaluated for its saturated vertical hydraulic conductivity. This paper discusses the use of eight tensiometers to measure soil suction at four depths beneath a double ring infiltrometer. The hydraulic conductivity results using the tensiometer data displayed good consistency and agreed well with laboratory test results
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
Coulomb drag between ballistic one-dimensional electron systems
The presence of pronounced electronic correlations in one-dimensional systems
strongly enhances Coulomb coupling and is expected to result in distinctive
features in the Coulomb drag between them that are absent in the drag between
two-dimensional systems. We review recent Fermi and Luttinger liquid theories
of Coulomb drag between ballistic one-dimensional electron systems, and give a
brief summary of the experimental work reported so far on one-dimensional drag.
Both the Fermi liquid (FL) and the Luttinger liquid (LL) theory predict a
maximum of the drag resistance R_D when the one-dimensional subbands of the two
quantum wires are aligned and the Fermi wave vector k_F is small, and also an
exponential decay of R_D with increasing inter-wire separation, both features
confirmed by experimental observations. A crucial difference between the two
theoretical models emerges in the temperature dependence of the drag effect.
Whereas the FL theory predicts a linear temperature dependence, the LL theory
promises a rich and varied dependence on temperature depending on the relative
magnitudes of the energy and length scales of the systems. At higher
temperatures, the drag should show a power-law dependence on temperature, R_D
\~ T^x, experimentally confirmed in a narrow temperature range, where x is
determined by the Luttinger liquid parameters. The spin degree of freedom plays
an important role in the LL theory in predicting the features of the drag
effect and is crucial for the interpretation of experimental results.Comment: 25 pages, 14 figures, to appear in Semiconductor Science and
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