58,829 research outputs found
Minimizers of the Landau-de Gennes energy around a spherical colloid particle
We consider energy minimizing configurations of a nematic liquid crystal
around a spherical colloid particle, in the context of the Landau-de Gennes
model. The nematic is assumed to occupy the exterior of a ball of radius r_0,
satisfy homeotropic weak anchoring at the surface of the colloid, and approach
a uniform uniaxial state at infinity. We study the minimizers in two different
limiting regimes: for balls which are small compared to the characteristic
length scale r_0>L. The relationship between the
radius and the anchoring strength W is also relevant. For small balls we obtain
a limiting quadrupolar configuration, with a "Saturn ring" defect for
relatively strong anchoring, corresponding to an exchange of eigenvalues of the
Q-tensor. In the limit of very large balls we obtain an axisymmetric minimizer
of the Oseen-Frank energy, and a dipole configuration with exactly one point
defect is obtained
Separation of colour degree of freedom from dynamics in a soliton cellular automaton
We present an algorithm to reduce the coloured box-ball system, a one
dimensional integrable cellular automaton described by motions of several
colour (kind) of balls, into a simpler monochrome system. This algorithm
extracts the colour degree of freedom of the automaton as a word which turns
out to be a conserved quantity of this dynamical system. It is based on the
theory of crystal basis and in particular on the tensor products of sl_n
crystals of symmetric and anti-symmetric tensor representations.Comment: 19 page
Structure and Phase transitions of Yukawa balls
In this review, an overview of structural properties and phase transitions in
finite spherical dusty (complex) plasma crystals -- so-called Yukawa balls --
is given. These novel kinds of Wigner crystals can be directly analyzed
experimentally with video cameras. The experiments clearly reveal a shell
structure and allow to determine the shell populations, to observe metastable
states and transitions between configurations as well as phase transitions. The
experimental observations of the static properties are well explained by a
rather simple theoretical model which treats the dust particles as being
confined by a parabolic potential and interacting via an isotropic Yukawa pair
potential. The excitation properties of the Yukawa balls such as normal modes
and the dynamic behavior, including the time-dependent formation of the crystal
requires, in addition, to include the effect of friction between the dust
particles and the neutral gas. Aside from first-principle molecular dynamics
and Monte Carlo simulations several analytical approaches are reviewed which
include shell models and a continuum theory. A summary of recent results and
theory-experiment comparisons is given and questions for future research
activities are outlined.Comment: Invited review, submitted to Contrib. Plasmas Physic
Total Chiral Symmetry Breaking during Crystallization: Who needs a "Mother Crystal"?
Processes that can produce states of broken chiral symmetry are of particular
interest to physics, chemistry and biology. Chiral symmetry breaking during
crystallization of sodium chlorate occurs via the production of secondary
crystals of the same handedness from a single "mother crystal" that seeds the
solution. Here we report that a large and "symmetric" population of D- and
L-crystals moves into complete chiral purity disappearing one of the
enantiomers. This result shows: (i) a new symmetry breaking process
incompatible with the hypothesis of a single "mother crystal"; (ii) that
complete symmetry breaking and chiral purity can be achieved from an initial
system with both enantiomers. These findings demand a new explanation to the
process of total symmetry breaking in crystallization without the intervention
of a "mother crystal" and open the debate on this fascinating phenomenon. We
present arguments to show that our experimental data can been explained with a
new model of "complete chiral purity induced by nonlinear autocatalysis and
recycling".Comment: 5 pages, 4 figures, Added reference
Non-equilibrium two-phase coexistence in a confined granular layer
We report the observation of the homogenous nucleation of crystals in a dense
layer of steel spheres confined between two horizontal plates vibrated
vertically. Above a critical vibration amplitude, two-layer crystals with
square symmetry were found to coexist in steady state with a surrounding
granular liquid. By analogy to equilibrium hard sphere systems, the phase
behavior can be explained through entropy maximization. However, dramatic
non-equilibrium effects are present, including a significant difference in the
granular temperatures of the two phases.Comment: 4 pages, 3 figures, RevTex4 forma
On a Periodic Soliton Cellular Automaton
We propose a box and ball system with a periodic boundary condition (pBBS).
The time evolution rule of the pBBS is represented as a Boolean recurrence
formula, an inverse ultradiscretization of which is shown to be equivalent with
the algorithm of the calculus for the 2Nth root. The relations to the pBBS of
the combinatorial R matrix of are also discussed.Comment: 17 pages, 5 figure
Analysis of a particle antiparticle description of a soliton cellular automaton
We present a derivation of a formula that gives dynamics of an integrable
cellular automaton associated with crystal bases. This automaton is related to
type D affine Lie algebra and contains usual box-ball systems as a special
case. The dynamics is described by means of such objects as carriers,
particles, and antiparticles. We derive it from an analysis of a recently
obtained formula of the combinatorial R (an intertwiner between tensor products
of crystals) that was found in a study of geometric crystals.Comment: LaTeX, 21 pages, 2 figure
The A^{(1)}_M automata related to crystals of symmetric tensors
A soliton cellular automaton associated with crystals of symmetric tensor
representations of the quantum affine algebra U'_q(A^{(1)}_M) is introduced. It
is a crystal theoretic formulation of the generalized box-ball system in which
capacities of boxes and carriers are arbitrary and inhomogeneous. Scattering
matrices of two solitons coincide with the combinatorial R matrices of
U'_q(A^{(1)}_{M-1}). A piecewise linear evolution equation of the automaton is
identified with an ultradiscrete limit of the nonautonomous discrete KP
equation. A class of N soliton solutions is obtained through the
ultradiscretization of soliton solutions of the latter.Comment: 45 pages, latex2e, 2 figure
Enhancement of mobilities in a pinned multidomain crystal
Mobility properties inside and around degenerate domains of an elastic
lattice partially pinned on a square array of traps are explored by means of a
fully controllable model system of macroscopic particles. We focus on the
different configurations obtained for filling ratios equal to 1 or 2 when the
pinning strength is lowered. These theoretically expected but never observed
configurations are degenerated, which implies the existence of a multidomain
crystal. We show that the distinction between trapped and untrapped particles
that is made in the case of strong pinning is not relevant for such a weaker
pinning. Indeed, one ought to distinguish between particles inside or around
the domains associated to positional degeneracies. The possible consequences on
the depinning dynamics of the lattice are discussed.Comment: 7 pages, 10 figures Version 2 : longer versio
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