149 research outputs found
Universal Dynamics of Phase-Field Models for Dendritic Growth
We compare time-dependent solutions of different phase-field models for
dendritic solidification in two dimensions, including a thermodynamically
consistent model and several ad hoc models. The results are identical when the
phase-field equations are operating in their appropriate sharp interface limit.
The long time steady state results are all in agreement with solvability
theory. No computational advantage accrues from using a thermodynamically
consistent phase-field model.Comment: 4 pages, 3 postscript figures, in latex, (revtex
Theory of spiral wave dynamics in weakly excitable media: asymptotic reduction to a kinematic model and applications
In a weakly excitable medium, characterized by a large threshold stimulus,
the free end of an isolated broken plane wave (wave tip) can either rotate
(steadily or unsteadily) around a large excitable core, thereby producing a
spiral pattern, or retract causing the wave to vanish at boundaries. An
asymptotic analysis of spiral motion and retraction is carried out in this
weakly excitable large core regime starting from the free-boundary limit of the
reaction-diffusion models, valid when the excited region is delimited by a thin
interface. The wave description is shown to naturally split between the tip
region and a far region that are smoothly matched on an intermediate scale.
This separation allows us to rigorously derive an equation of motion for the
wave tip, with the large scale motion of the spiral wavefront slaved to the
tip. This kinematic description provides both a physical picture and exact
predictions for a wide range of wave behavior, including: (i) steady rotation
(frequency and core radius), (ii) exact treatment of the meandering instability
in the free-boundary limit with the prediction that the frequency of unstable
motion is half the primary steady frequency (iii) drift under external actions
(external field with application to axisymmetric scroll ring motion in
three-dimensions, and spatial or/and time-dependent variation of excitability),
and (iv) the dynamics of multi-armed spiral waves with the new prediction that
steadily rotating waves with two or more arms are linearly unstable. Numerical
simulations of FitzHug-Nagumo kinetics are used to test several aspects of our
results. In addition, we discuss the semi-quantitative extension of this theory
to finite cores and pinpoint mathematical subtleties related to the thin
interface limit of singly diffusive reaction-diffusion models
Fracture in Mode I using a Conserved Phase-Field Model
We present a continuum phase-field model of crack propagation. It includes a
phase-field that is proportional to the mass density and a displacement field
that is governed by linear elastic theory. Generic macroscopic crack growth
laws emerge naturally from this model. In contrast to classical continuum
fracture mechanics simulations, our model avoids numerical front tracking. The
added phase-field smoothes the sharp interface, enabling us to use equations of
motion for the material (grounded in basic physical principles) rather than for
the interface (which often are deduced from complicated theories or empirical
observations). The interface dynamics thus emerges naturally. In this paper, we
look at stationary solutions of the model, mode I fracture, and also discuss
numerical issues. We find that the Griffith's threshold underestimates the
critical value at which our system fractures due to long wavelength modes
excited by the fracture process.Comment: 10 pages, 5 figures (eps). Added 2 figures and some text. Removed one
section (and a figure). To be published in PR
Noise Induced Coherence in Neural Networks
We investigate numerically the dynamics of large networks of globally
pulse-coupled integrate and fire neurons in a noise-induced synchronized state.
The powerspectrum of an individual element within the network is shown to
exhibit in the thermodynamic limit () a broadband peak and an
additional delta-function peak that is absent from the powerspectrum of an
isolated element. The powerspectrum of the mean output signal only exhibits the
delta-function peak. These results are explained analytically in an exactly
soluble oscillator model with global phase coupling.Comment: 4 pages ReVTeX and 3 postscript 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.
Dynamic Front Transitions and Spiral-Vortex Nucleation
This is a study of front dynamics in reaction diffusion systems near
Nonequilibrium Ising-Bloch bifurcations. We find that the relation between
front velocity and perturbative factors, such as external fields and curvature,
is typically multivalued. This unusual form allows small perturbations to
induce dynamic transitions between counter-propagating fronts and nucleate
spiral vortices. We use these findings to propose explanations for a few
numerical and experimental observations including spiral breakup driven by
advective fields, and spot splitting
Energy radiation of moving cracks
The energy radiated by moving cracks in a discrete background is analyzed.
The energy flow through a given surface is expressed in terms of a generalized
Poynting vector. The velocity of the crack is determined by the radiation by
the crack tip. The radiation becomes more isotropic as the crack velocity
approaches the instability threshold.Comment: 7 pages, embedded figure
A Phase-Field Model of Spiral Dendritic Growth
Domains of condensed-phase monolayers of chiral molecules exhibit a variety
of interesting nonequilibrium structures when formed via pressurization. To
model these domain patterns, we add a complex field describing the tilt degree
of freedom to an (anisotropic) complex-phase-field solidification model. The
resulting formalism allows for the inclusion of (in general, non-reflection
symmetric) interactions between the tilt, the solid-liquid interface, and the
bond orientation. Simulations demonstrate the ability of the model to exhibit
spiral dendritic growth.Comment: text plus Four postscript figure file
Electromigration of Single-Layer Clusters
Single-layer atom or vacancy clusters in the presence of electromigration are
studied theoretically assuming an isotropic medium. A variety of distinctive
behaviors distinguish the response in the three standard limiting cases of
periphery diffusion (PD), terrace diffusion (TD), and evaporation-condensation
(EC). A general model provides power laws describing the size dependence of the
drift velocity in these limits, consistent with established results in the case
of PD. The validity of the widely used quasistatic limit is calculated. Atom
and vacancy clusters drift in opposite directions in the PD limit but in the
same direction otherwise. In absence of PD, linear stability analysis reveals a
new type of morphological instability, not leading to island break-down. For
strong electromigration, Monte Carlo simulations show that clusters then
destabilize into slits, in contrast to splitting in the PD limit.
Electromigration affects the diffusion coefficient of the cluster and
morphological fluctuations, the latter diverging at the instability threshold.
An instrinsic attachment-detachment bias displays the same scaling signature as
PD in the drift velocity.Comment: 11 pages, 4 figure
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