632 research outputs found
Flux Ropes as Singularities of the Vector Potential
A flux rope is a domain of concentration of the magnetic field .
Insofar as outside such a domain is considered as vanishingly
small, a flux rope can be described as the core of a singularity of the outer
vector potential , whose topological invariant is the magnetic flux
through the rope. By 'topological' it is meant that
measures along any loop
surrounding the flux rope the same constant flux . The electric current
intensity is another invariant of the theory, but non-topological. We show
that, in this theoretical framework, the linear force-free field (LFFF)
Lundquist model and the non-linear (NLFFF) Gold-Hoyle model of a flux rope
exhibit stable solutions distributed over quantized strata of increasing
energies (an infinite number of strata in the first case, only one stratum in
the second case); each stratum is made of a continuous set of stable states.
The lowest LFFF stratum and the unique NLFFF stratum come numerically close one
to the other, and match with a reasonable accuracy the data collected by
spacecrafts travelling across magnetic clouds. The other LFFF strata do not
match these data at all. It is not possible at this stage to claim which model
fits better the magnetic cloud data. We also analyze in some detail the merging
of tubes belonging to the same stratum, with conservation of the magnetic
helicity, and the transition of a tube from one stratum to another one, which
does not conserve magnetic helicity.Comment: 24 pages, 1 figur
Imperfections in focal conic domains: the role of dislocations
It is usual to think of Focal Conic Domains (FCD) as perfect geometric
constructions in which the layers are folded into Dupin cyclides, about an
ellipse and a hyperbola that are conjugate. This ideal picture is often far
from reality. We have investigated in detail the FCDs in several materials
which have a transition from a smectic A (SmA) to a nematic phase. The ellipse
and the hyperbola are seldom perfect, and the FCD textures also suffer large
transformations (in shape or/and in nature) when approaching the transition to
the nematic phase, or appear imperfect on cooling from the nematic phase. We
interpret these imperfections as due to the interaction of FCDs with
dislocations. We analyze theoretically the general principles subtending the
interaction mechanisms between FCDs and finite Burgers vector dislocations,
namely the formation of kinks on disclinations, to which dislocations are
attached, and we present models relating to some experimental results. Whereas
the principles of the interactions are very general, their realizations can
differ widely in function of the boundary conditions.Comment: 19 pages, 18 figure
Model of hard spheroplatelets near a hard wall
A system of hard spheroplatelets near an impenetrable wall is studied in the
low-density Onsager approximation. Spheroplatelets have optimal shape between
rods and plates, and the direct transition from the isotropic to biaxial
nematic phase is present. A simple local approximation for the one-particle
distribution function is used. Analytical results for the surface tension and
the entropy contributions are derived. The density and the order-parameter
profiles near the wall are calculated. The preferred orientation of the short
molecule axes is perpendicular to the wall. Biaxiality close to the wall can
appear only if the phase is biaxial in the bulk.Comment: 11 pages, 9 figures, revised version published in PR
Disclinations, dislocations and continuous defects: a reappraisal
Disclinations, first observed in mesomorphic phases, are relevant to a number
of ill-ordered condensed matter media, with continuous symmetries or frustrated
order. They also appear in polycrystals at the edges of grain boundaries. They
are of limited interest in solid single crystals, where, owing to their large
elastic stresses, they mostly appear in close pairs of opposite signs. The
relaxation mechanisms associated with a disclination in its creation, motion,
change of shape, involve an interplay with continuous or quantized dislocations
and/or continuous disclinations. These are attached to the disclinations or are
akin to Nye's dislocation densities, well suited here. The notion of 'extended
Volterra process' takes these relaxation processes into account and covers
different situations where this interplay takes place. These concepts are
illustrated by applications in amorphous solids, mesomorphic phases and
frustrated media in their curved habit space. The powerful topological theory
of line defects only considers defects stable against relaxation processes
compatible with the structure considered. It can be seen as a simplified case
of the approach considered here, well suited for media of high plasticity
or/and complex structures. Topological stability cannot guarantee energetic
stability and sometimes cannot distinguish finer details of structure of
defects.Comment: 72 pages, 36 figure
Annihilation of edge dislocations in smectic A liquid crystals
This paper presents a theoretical study of the annihilation of edge dislocations in the same smectic plane in a bulk smectic-A phase. We use a time-dependent Landau-Ginzburg approach where the smectic ordering is described by the complex order parameter psi( r--> ,t) =eta e(iphi) . This quantity allows both the degree of layering and the position of the layers to be monitored. We are able to follow both precollision and postcollision regimes, and distinguish different early and late behaviors within these regimes. The early precollision regime is driven by changes in the phi ( r--> ) configuration. The relative velocity of the defects is approximately inversely proportional to the interdefect separation distance. In the late precollision regime the symmetry changes within the cores of defects also become influential. Following the defect collision, in the early postcollision stage, bulk layer order is approached exponentially in time. At very late times, however, there seems to be a long-time power-law tail in the order parameter fluctuation relaxation
Discrete symmetries and 1/3-quantum vortices in condensates of F=2 cold atoms
In this Letter we study discrete symmetries of mean field manifolds of
condensates of F=2 cold atoms, and various unconventional quantum vortices.
Discrete quaternion symmetries result in two species of spin defects that can
only appear in integer vortices while {\em cyclic} symmetries are found to
result in a phase shift of (or ) and therefore 1/3- (or 2/3-)
quantum vortices in condensates. We also briefly discuss 1/3-quantum vortices
in condensates of trimers.Comment: 4 pages, 2 figures included; published versio
A stochastic derivation of the geodesic rule
We argue that the geodesic rule, for global defects, is a consequence of the
randomness of the values of the Goldstone field in each causally
connected volume. As these volumes collide and coalescence, evolves by
performing a random walk on the vacuum manifold . We derive a
Fokker-Planck equation that describes the continuum limit of this process. Its
fundamental solution is the heat kernel on , whose leading
asymptotic behavior establishes the geodesic rule.Comment: 12 pages, No figures. To be published in Int. Jour. Mod. Phys.
Nematic liquid crystal dynamics under applied electric fields
In this paper we investigate the dynamics of liquid crystal textures in a
two-dimensional nematic under applied electric fields, using numerical
simulations performed using a publicly available LIquid CRystal Algorithm
(LICRA) developed by the authors. We consider both positive and negative
dielectric anisotropies and two different possibilities for the orientation of
the electric field (parallel and perpendicular to the two-dimensional lattice).
We determine the effect of an applied electric field pulse on the evolution of
the characteristic length scale and other properties of the liquid crystal
texture network. In particular, we show that different types of defects are
produced after the electric field is switched on, depending on the orientation
of the electric field and the sign of the dielectric anisotropy.Comment: 7 pages, 12 figure
Defect kinetics and dynamics of pattern coarsening in a two-dimensional smectic-A system
Two-dimensional simulations of the coarsening process of the
isotropic/smectic-A phase transition are presented using a high-order Landau-de
Gennes type free energy model. Defect annihilation laws for smectic
disclinations, elementary dislocations, and total dislocation content are
determined. The computed evolution of the orientational correlation length and
disclination density is found to be in agreement with previous experimental
observations showing that disclination interactions dominate the coarsening
process. The mechanism of smectic disclination movement, limited by the
absorption and emission of elementary dislocations, is found to be facilitated
by curvature walls connecting interacting disclinations. At intermediate times
in the coarsening process, split-core dislocation formation and interactions
displaying an effective disclination quadrupole configuration are observed.
This work provides the framework for further understanding of the formation and
dynamics of the diverse set of curvature defects observed in smectic liquid
crystals and other layered material systems
Elasticity-mediated self-organization and colloidal interactions of solid spheres with tangential anchoring in a nematic liquid crystal
Using laser tweezers and fluorescence confocal polarizing microscopy, we
study colloidal interactions of solid microspheres in the nematic bulk caused
by elastic distortions around the particles with strong tangential surface
anchoring. The particles aggregate into chains directed at about 30 degrees to
the far field director and, at higher concentrations, form complex kinetically
trapped structures. We characterize the distance and angular dependencies of
the colloidal interaction forces.Comment: 6 pages, 5 figure
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