259 research outputs found
Exchange of helicity in a knotted electromagnetic field
In this work we present for the first time an exact solution of Maxwell
equations in vacuum, having non trivial topology, in which there is an exchange
of helicity between the electric and magnetic part of such field. We calculate
the temporal evolution of the magnetic and electric helicities, and explain the
exchange of helicity making use of the Chern-Simon form. We also have found and
explained that, as time goes to infinity, both helicities reach the same value
and the exchange between the magnetic and electric part of the field stops.Comment: 9 pages, 6 fi
Density functional theory study of the nematic-isotropic transition in an hybrid cell
We have employed the Density Functional Theory formalism to investigate the
nematic-isotropic capillary transitions of a nematogen confined by walls that
favor antagonist orientations to the liquid crystal molecules (hybrid cell). We
analyse the behavior of the capillary transition as a function of the
fluid-substrate interactions and the pore width. In addition to the usual
capillary transition between isotropic-like to nematic-like states, we find
that this transition can be suppressed when one substrate is wet by the
isotropic phase and the other by the nematic phase. Under this condition the
system presents interface-like states which allow to continuously transform the
nematic-like phase to the isotropic-like phase without undergoing a phase
transition. Two different mechanisms for the disappearance of the capillary
transition are identified. When the director of the nematic-like state is
homogeneously planar-anchored with respect to the substrates, the capillary
transition ends up in a critical point. This scenario is analogous to the
observed in Ising models when confined in slit pores with opposing surface
fields which have critical wetting transitions. When the nematic-like state has
a linearly distorted director field, the capillary transition continuously
transforms in a transition between two nematic-like states.Comment: 31 pages, 10 figures, submitted to J. Chem. Phy
Plane shearing waves of arbitrary form: exact solutions of the Navier-Stokes equations
We present exact solutions of the incompressible Navier-Stokes equations in a
background linear shear flow. The method of construction is based on Kelvin's
investigations into linearized disturbances in an unbounded Couette flow. We
obtain explicit formulae for all three components of a Kelvin mode in terms of
elementary functions. We then prove that Kelvin modes with parallel (though
time-dependent) wave vectors can be superposed to construct the most general
plane transverse shearing wave. An explicit solution is given, with any
specified initial orientation, profile and polarization structure, with either
unbounded or shear-periodic boundary conditions.Comment: 6 pages, 2 figures; version published in the European Physical
Journal Plu
Rayleigh-Taylor instability and mushroom-pattern formation in a two-component Bose-Einstein condensate
The Rayleigh-Taylor instability at the interface in an immiscible
two-component Bose-Einstein condensate is investigated using the mean-field and
Bogoliubov theories. Rayleigh-Taylor fingers are found to grow from the
interface and mushroom patterns are formed. Quantized vortex rings and vortex
lines are then generated around the mushrooms. The Rayleigh-Taylor instability
and mushroom-pattern formation can be observed in a trapped system.Comment: 5 pages, 4 figure
Perturbative behaviour of a vortex in a trapped Bose-Einstein condensate
We derive a set of equations that describe the shape and behaviour of a
single perturbed vortex line in a Bose-Einstein condensate. Through the use of
a matched asymptotic expansion and a unique coordinate transform a relation for
a vortex's velocity, anywhere along the line, is found in terms of the
trapping, rotation, and distortion of the line at that location. This relation
is then used to find a set of differential equations that give the line's
specific shape and motion. This work corrects a previous similar derivation by
Anatoly A. Svidzinsky and Alexander L. Fetter [Phys. Rev. A \textbf{62}, 063617
(2000)], and enables a comparison with recent numerical results.Comment: 12 pages with 3 figure
Suppression of Kelvon-induced decay of quantized vortices in oblate Bose-Einstein Condensates
We study the Kelvin mode excitations on a vortex line in a three-dimensional
trapped Bose-Einstein condensate at finite temperature. Our stochastic
Gross-Pitaevskii simulations show that the activation of these modes can be
suppressed by tightening the confinement along the direction of the vortex
line, leading to a strong suppression in the vortex decay rate as the system
enters a regime of two-dimensional vortex dynamics. As the system approaches
the condensation transition temperature we find that the vortex decay rate is
strongly sensitive to dimensionality and temperature, observing a large
enhancement for quasi-two-dimensional traps. Three-dimensional simulations of
the recent vortex dipole decay experiment of Neely et al. [Phys. Rev. Lett.
104, 160401 (2010)] confirm two-dimensional vortex dynamics, and predict a
dipole lifetime consistent with experimental observations and suppression of
Kelvon-induced vortex decay in highly oblate condensates.Comment: 8 pages, 8 figure
A new chiral electro-optic effect: Sum-frequency generation from optically active liquids in the presence of a dc electric field
We report the observation of sum-frequency signals that depend linearly on an
applied electrostatic field and that change sign with the handedness of an
optically active solution. This recently predicted chiral electro-optic effect
exists in the electric-dipole approximation. The static electric field gives
rise to an electric-field-induced sum-frequency signal (an achiral third-order
process) that interferes with the chirality-specific sum-frequency at
second-order. The cross-terms linear in the electrostatic field constitute the
effect and may be used to determine the absolute sign of second- and
third-order nonlinear optical susceptibilities in isotropic media.Comment: Submitted to Physical Revie
Kelvin Wave Cascade and Decay of Superfluid Turbulence
Kelvin waves (kelvons)--the distortion waves on vortex lines--play a key part
in the relaxation of superfluid turbulence at low temperatures. We present a
weak-turbulence theory of kelvons. We show that non-trivial kinetics arises
only beyond the local-induction approximation and is governed by three-kelvon
collisions; corresponding kinetic equation is derived. On the basis of the
kinetic equation, we prove the existence of Kolmogorov cascade and find its
spectrum. The qualitative analysis is corroborated by numeric study of the
kinetic equation. The application of the results to the theory of superfluid
turbulence is discussed.Comment: 4 pages, RevTe
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
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