1,994 research outputs found
Phase Field Modeling of Fast Crack Propagation
We present a continuum theory which predicts the steady state propagation of
cracks. The theory overcomes the usual problem of a finite time cusp
singularity of the Grinfeld instability by the inclusion of elastodynamic
effects which restore selection of the steady state tip radius and velocity. We
developed a phase field model for elastically induced phase transitions; in the
limit of small or vanishing elastic coefficients in the new phase, fracture can
be studied. The simulations confirm analytical predictions for fast crack
propagation.Comment: 5 pages, 11 figure
Crack growth by surface diffusion in viscoelastic media
We discuss steady state crack growth in the spirit of a free boundary
problem. It turns out that mode I and mode III situations are very different
from each other: In particular, mode III exhibits a pronounced transition
towards unstable crack growth at higher driving forces, and the behavior close
to the Griffith point is determined entirely through crack surface dissipation,
whereas in mode I the fracture energy is renormalized due to a remaining finite
viscous dissipation. Intermediate mixed-mode scenarios allow steady state crack
growth with higher velocities, leading to the conjecture that mode I cracks can
be unstable with respect to a rotation of the crack front line
Breakdown of Scale Invariance in the Phase Ordering of Fractal Clusters
Our numerical simulations with the Cahn-Hilliard equation show that
coarsening of fractal clusters (FCs) is not a scale-invariant process. On the
other hand, a typical coarsening length scale and interfacial area of the FC
exhibit power laws in time, while the mass fractal dimension remains invariant.
The initial value of the lower cutoff is a relevant length scale. A
sharp-interface model is formulated that can follow the whole dynamics of a
diffusion controlled growth, coarsening, fragmentation and approach to
equilibrium in a system with conserved order parameter.Comment: 4 pages, 4 figures, RevTex, submitted to PR
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
Quasiperiodic Tip Splitting in Directional Solidification
We report experimental results on the tip splitting dynamics of seaweed
growth in directional solidification of succinonitrile alloys with
poly(ethylene oxide) or acetone as solutes. The seaweed or dense branching
morphology was selected by solidifying grains which are oriented close to the
{111} plane. Despite the random appearance of the growth, a quasiperiodic tip
splitting morphology was observed in which the tip alternately splits to the
left and to the right. The tip splitting frequency f was found to be related to
the growth velocity V as a power law f V^{1.5}. This finding
is consistent with the predictions of a tip splitting model that is also
presented. Small anisotropies are shown to lead to different kinds of seaweed
morphologies.Comment: 4 pages, 7 figures, submitted to Physical Review Letter
The universality class of fluctuating pulled fronts
It has recently been proposed that fluctuating ``pulled'' fronts propagating
into an unstable state should not be in the standard KPZ universality class for
rough interface growth. We introduce an effective field equation for this class
of problems, and show on the basis of it that noisy pulled fronts in {\em d+1}
bulk dimensions should be in the universality class of the {\em (d+1)+1}D KPZ
equation rather than of the {\em d+1}D KPZ equation. Our scenario ties together
a number of heretofore unexplained observations in the literature, and is
supported by previous numerical results.Comment: 4 pages, 2 figure
Multisensory integration across exteroceptive and interoceptive domains modulates self-experience in the rubber-hand illusion
Identifying with a body is central to being a conscious self. The now classic “rubber hand illusion” demonstrates that the experience of body ownership can be modulated by manipulating the timing of exteroceptive(visual and tactile)body-related feedback. Moreover,the strength of this modulation is related to individual differences in sensitivity to internal bodily signals(interoception). However the interaction of exteroceptive and interoceptive signals in determining the experience of body-ownership within an individual remains poorly understood.Here, we demonstrate that this depends on the online integration of exteroceptive and interoceptive signals by implementing an innovative “cardiac rubber hand illusion” that combined computer-generated augmented-reality with feedback of interoceptive (cardiac) information. We show that both subjective and objective measures of virtual-hand ownership are enhanced by cardio-visual feedback in-time with the actual heartbeat,as compared to asynchronous feedback. We further show that these measures correlate with individual differences in interoceptive sensitivity,and are also modulated by the integration of proprioceptive signals instantiated using real-time visual remapping of finger movements to the virtual hand.Our results demonstrate that interoceptive signals directly influence the experience of body ownership via multisensory integration,and they lend support to models of conscious selfhood based on interoceptive predictive coding
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
Metastable lifetimes in a kinetic Ising model: Dependence on field and system size
The lifetimes of metastable states in kinetic Ising ferromagnets are studied
by droplet theory and Monte Carlo simulation, in order to determine their
dependences on applied field and system size. For a wide range of fields, the
dominant field dependence is universal for local dynamics and has the form of
an exponential in the inverse field, modified by universal and nonuniversal
power-law prefactors. Quantitative droplet-theory predictions are numerically
verified, and small deviations are shown to depend nonuniversally on the
details of the dynamics. We identify four distinct field intervals in which the
field dependence and statistical properties of the lifetimes are different. The
field marking the crossover between the weak-field regime, in which the decay
is dominated by a single droplet, and the intermediate-field regime, in which
it is dominated by a finite droplet density, vanishes logarithmically with
system size. As a consequence the slow decay characteristic of the former
regime may be observable in systems that are macroscopic as far as their
equilibrium properties are concerned.Comment: 18 pages single spaced. RevTex Version 3. FSU-SCRI-94-1
Fermi-edge singularities in linear and non-linear ultrafast spectroscopy
We discuss Fermi-edge singularity effects on the linear and nonlinear
transient response of an electron gas in a doped semiconductor. We use a
bosonization scheme to describe the low energy excitations, which allows to
compute the time and temperature dependence of the response functions. Coherent
control of the energy absorption at resonance is analyzed in the linear regime.
It is shown that a phase-shift appears in the coherent control oscillations,
which is not present in the excitonic case. The nonlinear response is
calculated analytically and used to predict that four wave-mixing experiments
would present a Fermi-edge singularity when the exciting energy is varied. A
new dephasing mechanism is predicted in doped samples that depends linearly on
temperature and is produced by the low-energy bosonic excitations in the
conduction band.Comment: long version; 9 pages, 4 figure
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