129 research outputs found
Dynamics of stripe patterns in type-I superconductors subject to a rotating field
The evolution of stripe patterns in type-I superconductors subject to a
rotating in-plane magnetic field is investigated magneto-optically. The
experimental results reveal a very rich and interesting behavior of the
patterns. For small rotation angles, a small parallel displacement of the main
part of the stripes and a co-rotation of their very ends is observed. For
larger angles, small sideward protrusions develop, which then generate a zigzag
instability, ultimately leading to a breaking of stripes into smaller segments.
The short segments then start to co-rotate with the applied field although they
lag behind by approximately . Very interestingly, if the rotation is
continued, also reconnection of segments into longer stripes takes place. These
observations demonstrate the importance of pinning in type-I superconductors.Comment: To appear in Phys. Rev.
State selection in the noisy stabilized Kuramoto-Sivashinsky equation
In this work, we study the 1D stabilized Kuramoto Sivashinsky equation with
additive uncorrelated stochastic noise. The Eckhaus stable band of the
deterministic equation collapses to a narrow region near the center of the
band. This is consistent with the behavior of the phase diffusion constants of
these states. Some connections to the phenomenon of state selection in driven
out of equilibrium systems are made.Comment: 8 pages, In version 3 we corrected minor/typo error
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
Reformulating the Schrodinger equation as a Shabat-Zakharov system
We reformulate the second-order Schrodinger equation as a set of two coupled
first order differential equations, a so-called "Shabat-Zakharov system",
(sometimes called a "Zakharov-Shabat" system). There is considerable
flexibility in this approach, and we emphasise the utility of introducing an
"auxiliary condition" or "gauge condition" that is used to cut down the degrees
of freedom. Using this formalism, we derive the explicit (but formal) general
solution to the Schrodinger equation. The general solution depends on three
arbitrarily chosen functions, and a path-ordered exponential matrix. If one
considers path ordering to be an "elementary" process, then this represents
complete quadrature, albeit formal, of the second-order linear ODE.Comment: 18 pages, plain LaTe
Thermodynamic Limit Of The Ginzburg-Landau Equations
We investigate the existence of a global semiflow for the complex
Ginzburg-Landau equation on the space of bounded functions in unbounded domain.
This semiflow is proven to exist in dimension 1 and 2 for any parameter values
of the standard cubic Ginzburg-Landau equation. In dimension 3 we need some
restrictions on the parameters but cover nevertheless some part of the
Benjamin-Feijer unstable domain.Comment: uuencoded dvi file (email: [email protected]
The Kundu--Eckhaus equation and its discretizations
In this article we show that the complex Burgers and the Kundu--Eckhaus
equations are related by a Miura transformation. We use this relation to
discretize the Kundu--Eckhaus equation.Comment: 10 page
Singular perturbation techniques in the gravitational self-force problem
Much of the progress in the gravitational self-force problem has involved the
use of singular perturbation techniques. Yet the formalism underlying these
techniques is not widely known. I remedy this situation by explicating the
foundations and geometrical structure of singular perturbation theory in
general relativity. Within that context, I sketch precise formulations of the
methods used in the self-force problem: dual expansions (including matched
asymptotic expansions), for which I identify precise matching conditions, one
of which is a weak condition arising only when multiple coordinate systems are
used; multiscale expansions, for which I provide a covariant formulation; and a
self-consistent expansion with a fixed worldline, for which I provide a precise
statement of the exact problem and its approximation. I then present a detailed
analysis of matched asymptotic expansions as they have been utilized in
calculating the self-force. Typically, the method has relied on a weak matching
condition, which I show cannot determine a unique equation of motion. I
formulate a refined condition that is sufficient to determine such an equation.
However, I conclude that the method yields significantly weaker results than do
alternative methods.Comment: 39 pages, 5 figures, final version to be published in Phys. Rev. D,
several typos corrected, added discussion of order-reductio
Parametric Forcing of Waves with Non-Monotonic Dispersion Relation: Domain Structures in Ferrofluids?
Surface waves on ferrofluids exposed to a dc-magnetic field exhibit a
non-monotonic dispersion relation. The effect of a parametric driving on such
waves is studied within suitable coupled Ginzburg-Landau equations. Due to the
non-monotonicity the neutral curve for the excitation of standing waves can
have up to three minima. The stability of the waves with respect to long-wave
perturbations is determined a phase-diffusion equation. It shows that the
band of stable wave numbers can split up into two or three sub-bands. The
resulting competition between the wave numbers corresponding to the respective
sub-bands leads quite naturally to patterns consisting of multiple domains of
standing waves which differ in their wave number. The coarsening dynamics of
such domain structures is addressed.Comment: 23 pages, 6 postscript figures, composed using RevTeX. Submitted to
PR
On the Cauchy Problem for the Korteweg-de Vries Equation with Steplike Finite-Gap Initial Data I. Schwartz-Type Perturbations
We solve the Cauchy problem for the Korteweg-de Vries equation with initial
conditions which are steplike Schwartz-type perturbations of finite-gap
potentials under the assumption that the respective spectral bands either
coincide or are disjoint.Comment: 29 page
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