195 research outputs found
A Kelvin-wave cascade on a vortex in superfluid He at a very low temperature
A study by computer simulation is reported of the behaviour of a quantized
vortex line at a very low temperature when there is continuous excitation of
low-frequency Kelvin waves. There is no dissipation except by phonon radiation
at a very high frequency. It is shown that non-linear coupling leads to a net
flow of energy to higher wavenumbers and to the development of a simple
spectrum of Kelvin waves that is insensitive to the strength and frequency of
the exciting drive. The results are likely to be relevant to the decay of
turbulence in superfluid He at very low temperatures
Localized induction equation and pseudospherical surfaces
We describe a close connection between the localized induction equation
hierarchy of integrable evolution equations on space curves, and surfaces of
constant negative Gauss curvature.Comment: 21 pages, AMSTeX file. To appear in Journal of Physics A:
Mathematical and Genera
The hodograph method applicability in the problem of long-scale nonlinear dynamics of a thin vortex filament near a flat boundary
Hamiltonian dynamics of a thin vortex filament in ideal incompressible fluid
near a flat fixed boundary is considered at the conditions that at any point of
the curve determining shape of the filament the angle between tangent vector
and the boundary plane is small, also the distance from a point on the curve to
the plane is small in comparison with the curvature radius. The dynamics is
shown to be effectively described by a nonlinear system of two
(1+1)-dimensional partial differential equations. The hodograph transformation
reduces that system to a single linear differential equation of the second
order with separable variables. Simple solutions of the linear equation are
investigated at real values of spectral parameter when the filament
projection on the boundary plane has shape of a two-branch spiral or a smoothed
angle, depending on the sign of .Comment: 9 pages, revtex4, 6 eps-figure
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
Stability of the selfsimilar dynamics of a vortex filament
In this paper we continue our investigation about selfsimilar solutions of
the vortex filament equation, also known as the binormal flow (BF) or the
localized induction equation (LIE). Our main result is the stability of the
selfsimilar dynamics of small pertubations of a given selfsimilar solution. The
proof relies on finding precise asymptotics in space and time for the tangent
and the normal vectors of the perturbations. A main ingredient in the proof is
the control of the evolution of weighted norms for a cubic 1-D Schr\"odinger
equation, connected to the binormal flow by Hasimoto's transform.Comment: revised version, 36 page
Simulating (electro)hydrodynamic effects in colloidal dispersions: smoothed profile method
Previously, we have proposed a direct simulation scheme for colloidal
dispersions in a Newtonian solvent [Phys.Rev.E 71,036707 (2005)]. An improved
formulation called the ``Smoothed Profile (SP) method'' is presented here in
which simultaneous time-marching is used for the host fluid and colloids. The
SP method is a direct numerical simulation of particulate flows and provides a
coupling scheme between the continuum fluid dynamics and rigid-body dynamics
through utilization of a smoothed profile for the colloidal particles.
Moreover, the improved formulation includes an extension to incorporate
multi-component fluids, allowing systems such as charged colloids in
electrolyte solutions to be studied. The dynamics of the colloidal dispersions
are solved with the same computational cost as required for solving
non-particulate flows. Numerical results which assess the hydrodynamic
interactions of colloidal dispersions are presented to validate the SP method.
The SP method is not restricted to particular constitutive models of the host
fluids and can hence be applied to colloidal dispersions in complex fluids
Tunable tunneling: An application of stationary states of Bose-Einstein condensates in traps of finite depth
The fundamental question of how Bose-Einstein condensates tunnel into a
barrier is addressed. The cubic nonlinear Schrodinger equation with a finite
square well potential, which models a Bose-Einstein condensate in a
quasi-one-dimensional trap of finite depth, is solved for the complete set of
localized and partially localized stationary states, which the former evolve
into when the nonlinearity is increased. An immediate application of these
different solution types is tunable tunneling. Magnetically tunable Feshbach
resonances can change the scattering length of certain Bose-condensed atoms,
such as Rb, by several orders of magnitude, including the sign, and
thereby also change the mean field nonlinearity term of the equation and the
tunneling of the wavefunction. We find both linear-type localized solutions and
uniquely nonlinear partially localized solutions where the tails of the
wavefunction become nonzero at infinity when the nonlinearity increases. The
tunneling of the wavefunction into the non-classical regime and thus its
localization therefore becomes an external experimentally controllable
parameter.Comment: 11 pages, 5 figure
A Dissipative-Particle-Dynamics Model for Simulating Dynamics of Charged Colloid
A mesoscopic colloid model is developed in which a spherical colloid is
represented by many interacting sites on its surface. The hydrodynamic
interactions with thermal fluctuations are taken accounts in full using
Dissipative Particle Dynamics, and the electrostatic interactions are simulated
using Particle-Particle-Particle Mesh method. This new model is applied to
investigate the electrophoretic mobility of a charged colloid under an external
electric field, and the influence of salt concentration and colloid charge are
systematically studied. The simulation results show good agreement with
predictions from the electrokinetic theory.Comment: 17 pages, 8 figures, submitted to the proceedings of High Performance
Computing in Science & Engineering '1
Finite-gap Solutions of the Vortex Filament Equation: Isoperiodic Deformations
We study the topology of quasiperiodic solutions of the vortex filament
equation in a neighborhood of multiply covered circles. We construct these
solutions by means of a sequence of isoperiodic deformations, at each step of
which a real double point is "unpinched" to produce a new pair of branch points
and therefore a solution of higher genus. We prove that every step in this
process corresponds to a cabling operation on the previous curve, and we
provide a labelling scheme that matches the deformation data with the knot type
of the resulting filament.Comment: 33 pages, 5 figures; submitted to Journal of Nonlinear Scienc
The Viscous Nonlinear Dynamics of Twist and Writhe
Exploiting the "natural" frame of space curves, we formulate an intrinsic
dynamics of twisted elastic filaments in viscous fluids. A pair of coupled
nonlinear equations describing the temporal evolution of the filament's complex
curvature and twist density embodies the dynamic interplay of twist and writhe.
These are used to illustrate a novel nonlinear phenomenon: ``geometric
untwisting" of open filaments, whereby twisting strains relax through a
transient writhing instability without performing axial rotation. This may
explain certain experimentally observed motions of fibers of the bacterium B.
subtilis [N.H. Mendelson, et al., J. Bacteriol. 177, 7060 (1995)].Comment: 9 pages, 4 figure
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