489 research outputs found
Stratified shear flow instabilities at large Richardson numbers
Numerical simulations of stratified shear flow instabilities are performed in
two dimensions in the Boussinesq limit. The density variation length scale is
chosen to be four times smaller than the velocity variation length scale so
that Holmboe or Kelvin-Helmholtz unstable modes are present depending on the
choice of the global Richardson number Ri. Three different values of Ri were
examined Ri =0.2, 2, 20. The flows for the three examined values are all
unstable due to different modes namely: the Kelvin-Helmholtz mode for Ri=0.2,
the first Holmboe mode for Ri=2, and the second Holmboe mode for Ri=20 that has
been discovered recently and it is the first time that it is examined in the
non-linear stage. It is found that the amplitude of the velocity perturbation
of the second Holmboe mode at the non-linear stage is smaller but comparable to
first Holmboe mode. The increase of the potential energy however due to the
second Holmboe modes is greater than that of the first mode. The
Kelvin-Helmholtz mode is larger by two orders of magnitude in kinetic energy
than the Holmboe modes and about ten times larger in potential energy than the
Holmboe modes. The results in this paper suggest that although mixing is
suppressed at large Richardson numbers it is not negligible, and turbulent
mixing processes in strongly stratified environments can not be excluded.Comment: Submitted to Physics of Fluid
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.
Variational bound on energy dissipation in turbulent shear flow
We present numerical solutions to the extended Doering-Constantin variational
principle for upper bounds on the energy dissipation rate in plane Couette
flow, bridging the entire range from low to asymptotically high Reynolds
numbers. Our variational bound exhibits structure, namely a pronounced minimum
at intermediate Reynolds numbers, and recovers the Busse bound in the
asymptotic regime. The most notable feature is a bifurcation of the minimizing
wavenumbers, giving rise to simple scaling of the optimized variational
parameters, and of the upper bound, with the Reynolds number.Comment: 4 pages, RevTeX, 5 postscript figures are available as one .tar.gz
file from [email protected]
The Hyperbolic Heisenberg and Sigma Models in (1+1)-dimensions
Hyperbolic versions of the integrable (1+1)-dimensional Heisenberg
Ferromagnet and sigma models are discussed in the context of topological
solutions classifiable by an integer `winding number'. Some explicit solutions
are presented and the existence of certain classes of such winding solutions
examined.Comment: 13 pages, 1 figure, Latex, personal style file included tensind.sty,
Proof in section 3 altered, no changes to conclusion
A Riemann-Hilbert Problem for an Energy Dependent Schr\"odinger Operator
\We consider an inverse scattering problem for Schr\"odinger operators with
energy dependent potentials. The inverse problem is formulated as a
Riemann-Hilbert problem on a Riemann surface. A vanishing lemma is proved for
two distinct symmetry classes. As an application we prove global existence
theorems for the two distinct systems of partial differential equations
for suitably restricted,
complementary classes of initial data
Negaton and Positon Solutions of the KDV Equation
We give a systematic classification and a detailed discussion of the
structure, motion and scattering of the recently discovered negaton and positon
solutions of the Korteweg-de Vries equation. There are two distinct types of
negaton solutions which we label and , where is the
order of the Wronskian used in the derivation. For negatons, the number of
singularities and zeros is finite and they show very interesting time
dependence. The general motion is in the positive direction, except for
certain negatons which exhibit one oscillation around the origin. In contrast,
there is just one type of positon solution, which we label . For
positons, one gets a finite number of singularities for odd, but an
infinite number for even values of . The general motion of positons is in
the negative direction with periodic oscillations. Negatons and positons
retain their identities in a scattering process and their phase shifts are
discussed. We obtain a simple explanation of all phase shifts by generalizing
the notions of ``mass" and ``center of mass" to singular solutions. Finally, it
is shown that negaton and positon solutions of the KdV equation can be used to
obtain corresponding new solutions of the modified KdV equation.Comment: 20 pages plus 12 figures(available from authors on request),Latex
fil
Interaction of Nonlinear Schr\"odinger Solitons with an External Potential
Employing a particularly suitable higher order symplectic integration
algorithm, we integrate the 1- nonlinear Schr\"odinger equation numerically
for solitons moving in external potentials. In particular, we study the
scattering off an interface separating two regions of constant potential. We
find that the soliton can break up into two solitons, eventually accompanied by
radiation of non-solitary waves. Reflection coefficients and inelasticities are
computed as functions of the height of the potential step and of its steepness.Comment: 14 pages, uuencoded PS-file including 10 figure
Superposition in nonlinear wave and evolution equations
Real and bounded elliptic solutions suitable for applying the Khare-Sukhatme
superposition procedure are presented and used to generate superposition
solutions of the generalized modified Kadomtsev-Petviashvili equation (gmKPE)
and the nonlinear cubic-quintic Schroedinger equation (NLCQSE).Comment: submitted to International Journal of Theoretical Physics, 23 pages,
2 figures, style change
Tailoring optical nonlinearities via the Purcell effect
We predict that the effective nonlinear optical susceptibility can be
tailored using the Purcell effect. While this is a general physical principle
that applies to a wide variety of nonlinearities, we specifically investigate
the Kerr nonlinearity. We show theoretically that using the Purcell effect for
frequencies close to an atomic resonance can substantially influence the
resultant Kerr nonlinearity for light of all (even highly detuned) frequencies.
For example, in realistic physical systems, enhancement of the Kerr coefficient
by one to two orders of magnitude could be achieved
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