286 research outputs found
Instability patterns in ultrathin nematic films: comparison between theory and experiment
Motivated by recent experimental observations [U. Delabre et al, Langmuir 24,
3998, 2008] we reconsider an instability of ultrathin nematic films, spread on
liquid substrates. Within a continuum elastic theory of liquid crystals, in the
harmonic approximation, we find an analytical expressions for the critical
thickness as well as for the critical wavenumber, characterizing the onset of
instability towards the stripe phase. Comparing theoretical predictions with
experimental observations, we establish the utility of surface-like term such
as an azimuthal anchoring.Comment: 6 pages, 3 figures, LaTeX macros EPL draft, accepted for publication
in EP
Conical defects in growing sheets
A growing or shrinking disc will adopt a conical shape, its intrinsic
geometry characterized by a surplus angle at the apex. If growth is slow,
the cone will find its equilibrium. Whereas this is trivial if , the
disc can fold into one of a discrete infinite number of states if is
positive. We construct these states in the regime where bending dominates,
determine their energies and how stress is distributed in them. For each state
a critical value of is identified beyond which the cone touches itself.
Before this occurs, all states are stable; the ground state has two-fold
symmetry.Comment: 4 pages, 4 figures, LaTeX, RevTeX style. New version corresponds to
the one published in PR
Streamer Propagation as a Pattern Formation Problem: Planar Fronts
Streamers often constitute the first stage of dielectric breakdown in strong
electric fields: a nonlinear ionization wave transforms a non-ionized medium
into a weakly ionized nonequilibrium plasma. New understanding of this old
phenomenon can be gained through modern concepts of (interfacial) pattern
formation. As a first step towards an effective interface description, we
determine the front width, solve the selection problem for planar fronts and
calculate their properties. Our results are in good agreement with many
features of recent three-dimensional numerical simulations.Comment: 4 pages, revtex, 3 ps file
Fission of a multiphase membrane tube
A common mechanism for intracellular transport is the use of controlled
deformations of the membrane to create spherical or tubular buds. While the
basic physical properties of homogeneous membranes are relatively well-known,
the effects of inhomogeneities within membranes are very much an active field
of study. Membrane domains enriched in certain lipids in particular are
attracting much attention, and in this Letter we investigate the effect of such
domains on the shape and fate of membrane tubes. Recent experiments have
demonstrated that forced lipid phase separation can trigger tube fission, and
we demonstrate how this can be understood purely from the difference in elastic
constants between the domains. Moreover, the proposed model predicts timescales
for fission that agree well with experimental findings
Spin Relaxation Resonances Due to the Spin-Axis Interaction in Dense Rubidium and Cesium Vapor
Resonances in the magnetic decoupling curves for the spin relaxation of dense
alkali-metal vapors prove that much of the relaxation is due to the spin-axis
interaction in triplet dimers. Initial estimates of the spin-axis coupling
coefficients for the dimers are 290 MHz for Rb; 2500 MHz for Cs.Comment: submitted to Physical Review Letters, text + 3 figure
Regular dendritic patterns induced by non-local time-periodic forcing
The dynamic response of dendritic solidification to spatially homogeneous
time-periodic forcing has been studied. Phase-field calculations performed in
two dimensions (2D) and experiments on thin (quasi 2D) liquid crystal layers
show that the frequency of dendritic side-branching can be tuned by oscillatory
pressure or heating. The sensitivity of this phenomenon to the relevant
parameters, the frequency and amplitude of the modulation, the initial
undercooling and the anisotropies of the interfacial free energy and molecule
attachment kinetics, has been explored. It has been demonstrated that besides
the side-branching mode synchronous with external forcing as emerging from the
linear Wentzel-Kramers-Brillouin analysis, modes that oscillate with higher
harmonic frequencies are also present with perceptible amplitudes.Comment: 15 pages, 23 figures, Submitted to Phys. Rev.
Morphogenesis of growing soft tissues
Recently, much attention has been given to a noteworthy property of some soft
tissues: their ability to grow. Many attempts have been made to model this
behaviour in biology, chemistry and physics. Using the theory of finite
elasticity, Rodriguez has postulated a multiplicative decomposition of the
geometric deformation gradient into a growth-induced part and an elastic one
needed to ensure compatibility of the body. In order to fully explore the
consequences of this hypothesis, the equations describing thin elastic objects
under finite growth are derived. Under appropriate scaling assumptions for the
growth rates, the proposed model is of the Foppl-von Karman type. As an
illustration, the circumferential growth of a free hyperelastic disk is
studied.Comment: 4 pages, 3 figure
1D Aging
We derive exact expressions for a number of aging functions that are scaling
limits of non-equilibrium correlations, R(tw,tw+t) as tw --> infinity with t/tw
--> theta, in the 1D homogenous q-state Potts model for all q with T=0 dynamics
following a quench from infinite temperature. One such quantity is (the
two-point, two-time correlation function) when
n/sqrt(tw) --> z. Exact, closed-form expressions are also obtained when one or
more interludes of infinite temperature dynamics occur. Our derivations express
the scaling limit via coalescing Brownian paths and a ``Brownian space-time
spanning tree,'' which also yields other aging functions, such as the
persistence probability of no spin flip at 0 between tw and tw+t.Comment: 4 pages (RevTeX); 2 figures; submitted to Physical Review Letter
Propagation and Structure of Planar Streamer Fronts
Streamers often constitute the first stage of dielectric breakdown in strong
electric fields: a nonlinear ionization wave transforms a non-ionized medium
into a weakly ionized nonequilibrium plasma. New understanding of this old
phenomenon can be gained through modern concepts of (interfacial) pattern
formation. As a first step towards an effective interface description, we
determine the front width, solve the selection problem for planar fronts and
calculate their properties. Our results are in good agreement with many
features of recent three-dimensional numerical simulations.
In the present long paper, you find the physics of the model and the
interfacial approach further explained. As a first ingredient of this approach,
we here analyze planar fronts, their profile and velocity. We encounter a
selection problem, recall some knowledge about such problems and apply it to
planar streamer fronts. We make analytical predictions on the selected front
profile and velocity and confirm them numerically.
(abbreviated abstract)Comment: 23 pages, revtex, 14 ps file
Pattern formation in directional solidification under shear flow. I: Linear stability analysis and basic patterns
An asymptotic interface equation for directional solidification near the
absolute stabiliy limit is extended by a nonlocal term describing a shear flow
parallel to the interface. In the long-wave limit considered, the flow acts
destabilizing on a planar interface. Moreover, linear stability analysis
suggests that the morphology diagram is modified by the flow near the onset of
the Mullins-Sekerka instability. Via numerical analysis, the bifurcation
structure of the system is shown to change. Besides the known hexagonal cells,
structures consisting of stripes arise. Due to its symmetry-breaking
properties, the flow term induces a lateral drift of the whole pattern, once
the instability has become active. The drift velocity is measured numerically
and described analytically in the framework of a linear analysis. At large flow
strength, the linear description breaks down, which is accompanied by a
transition to flow-dominated morphologies, described in a companion paper.
Small and intermediate flows lead to increased order in the lattice structure
of the pattern, facilitating the elimination of defects. Locally oscillating
structures appear closer to the instability threshold with flow than without.Comment: 20 pages, Latex, accepted for Physical Review
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