308 research outputs found
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
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
Disclination in Lorentz Space-Time
The disclination in Lorentz space-time is studied in detail by means of
topological properties of -mapping. It is found the space-time
disclination can be described in term of a Dirac spinor. The size of the
disclination, which is proved to be the difference of two sets of su(2)% -like
monopoles expressed by two mixed spinors, is quantized topologically in terms
of topological invariantswinding number. The projection of space-time
disclination density along an antisymmetric tensor field is characterized by
Brouwer degree and Hopf index.Comment: Revtex, 7 page
Ordered droplet structures at the liquid crystal surface and elastic-capillary colloidal interactions
We demonstrate a variety of ordered patterns, including hexagonal structures
and chains, formed by colloidal particles (droplets) at the free surface of a
nematic liquid crystal (LC). The surface placement introduces a new type of
particle interaction as compared to particles entirely in the LC bulk. Namely,
director deformations caused by the particle lead to distortions of the
interface and thus to capillary attraction. The elastic-capillary coupling is
strong enough to remain relevant even at the micron scale when its
buoyancy-capillary counterpart becomes irrelevant.Comment: 10 pages, 3 figures, to be published in Physical Review Letter
Axially symmetric membranes with polar tethers
Axially symmetric equilibrium configurations of the conformally invariant
Willmore energy are shown to satisfy an equation that is two orders lower in
derivatives of the embedding functions than the equilibrium shape equation, not
one as would be expected on the basis of axial symmetry. Modulo a translation
along the axis, this equation involves a single free parameter c.If c\ne 0, a
geometry with spherical topology will possess curvature singularities at its
poles. The physical origin of the singularity is identified by examining the
Noether charge associated with the translational invariance of the energy; it
is consistent with an external axial force acting at the poles. A one-parameter
family of exact solutions displaying a discocyte to stomatocyte transition is
described.Comment: 13 pages, extended and revised version of Non-local sine-Gordon
equation for the shape of axi-symmetric membrane
Kramers rate theory of ionization and dissociation of bound states
Calculating the microscopic dissociation rate of a bound state, such as a
classical diatomic molecule, has been difficult so far. The problem was that
standard theories require an energy barrier over which the bound particle (or
state) escapes into the preferred low-energy state. This is not the case when
the long-range repulsion responsible for the barrier is either absent or
screened (as in Cooper pairs, ionized plasma, or biomolecular complexes). We
solve this classical problem by accounting for entropic memory at the
microscopic level. The theory predicts dissociation rates for arbitrary
potentials and is successfully tested on the example of plasma, where it yields
an estimate of ionization in the core of Sun in excellent agreement with
experiments. In biology, the new theory accounts for crowding in
receptor-ligand kinetics and protein aggregation
Points, Walls and Loops in Resonant Oscillatory Media
In an experiment of oscillatory media, domains and walls are formed under the
parametric resonance with a frequency double the natural one. In this bi-stable
system, %phase jumps by crossing walls. a nonequilibrium transition from
Ising wall to Bloch wall consistent with prediction is confirmed
experimentally. The Bloch wall moves in the direction determined by its
chirality with a constant speed. As a new type of moving structure in
two-dimension, a traveling loop consisting of two walls and Neel points is
observed.Comment: 9 pages (revtex format) and 6 figures (PostScript
Electric-field-induced nematic-cholesteric transition and 3-D director structures in homeotropic cells
We study the phase diagram of director structures in cholesteric liquid
crystals of negative dielectric anisotropy in homeotropic cells of thickness d
which is smaller than the cholesteric pitch p. The basic control parameters are
the frustration ratio d/p and the applied voltage U. Fluorescence Confocal
Polarising Microscopy allows us to directly and unambiguously determine the 3-D
director structures. The results are of importance for potential applications
of the cholesteric structures, such as switchable gratings and eyewear with
tunable transparency based.Comment: Will be published in Physical Review
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