104 research outputs found
Mesoscale model of dislocation motion and crystal plasticity
A consistent, small scale description of plastic motion in a crystalline
solid is presented based on a phase field description. By allowing for
independent mass motion given by the phase field, and lattice distortion, the
solid can remain in mechanical equilibrium on the timescale of plastic motion.
Singular (incompatible) strains are determined by the phase field, to which
smooth distortions are added to satisfy mechanical equilibrium. A numerical
implementation of the model is presented, and used to study a benchmark
problem: the motion of an edge dislocation dipole in a hexagonal lattice. The
time dependence of the dipole separation agrees with classical elasticity
without any adjustable parameters.Comment: 5 pages, 3 figure
Grain boundary dynamics in stripe phases of non potential systems
We describe numerical solutions of two non potential models of pattern
formation in nonequilibrium systems to address the motion and decay of grain
boundaries separating domains of stripe configurations of different
orientations. We first address wavenumber selection because of the boundary,
and possible decay modes when the periodicity of the stripe phases is different
from the selected wavenumber for a stationary boundary. We discuss several
decay modes including long wavelength undulations of the moving boundary as
well as the formation of localized defects and their subsequent motion. We find
three different regimes as a function of the distance to the stripe phase
threshold and initial wavenumber, and then correlate these findings with domain
morphology during domain coarsening in a large aspect ratio configuration.Comment: 8 pages, 8 figure
Tilt grain boundary instabilities in three dimensional lamellar patterns
We identify a finite wavenumber instability of a 90 tilt grain
boundary in three dimensional lamellar phases which is absent in two
dimensional configurations. Both a stability analysis of the slowly varying
amplitude or envelope equation for the boundary, and a direct numerical
solution of an order parameter model equation are presented. The instability
mode involves two dimensional perturbations of the planar base boundary, and is
suppressed for purely one dimensional perturbations. We find that both the most
unstable wavenumbers and their growth rate increase with , the
dimensionless distance away from threshold of the lamellar phase.Comment: 11 pages, 7 figures, to be published in Phys. Rev.
Kinematics and dynamics of disclination lines in three-dimensional nematics
An exact kinematic law for the motion of disclination lines in nematic liquid
crystals as a function of the tensor order parameter is derived.
Unlike other order parameter fields that become singular at their respective
defect cores, the tensor order parameter remains regular. Following earlier
experimental and theoretical work, the disclination core is defined to be the
line where the uniaxial and biaxial order parameters are equal, or
equivalently, where the two largest eigenvalues of cross. This
allows an exact expression relating the velocity of the line to spatial and
temporal derivatives of on the line, to be specified by a
dynamical model for the evolution of the nematic. By introducing a linear core
approximation for , analytical results are given for several
prototypical configurations, including line interactions and motion, loop
annihilation, and the response to external fields and shear flows. Behaviour
that follows from topological constraints or defect geometry is highlighted.
The analytic results are shown to be in agreement with three dimensional
numerical calculations based on a singular Maier-Saupe free energy that allows
for anisotropic elasticity.Comment: 24 pages, 15 figure
Stability of parallel/perpendicular domain boundaries in lamellar block copolymers under oscillatory shear
We introduce a model constitutive law for the dissipative stress tensor of
lamellar phases to account for low frequency and long wavelength flows. Given
the uniaxial symmetry of these phases, we argue that the stress tensor must be
the same as that of a nematic but with the local order parameter being the
slowly varying lamellar wavevector. This assumption leads to a dependence of
the effective dynamic viscosity on orientation of the lamellar phase. We then
consider a model configuration comprising a domain boundary separating
laterally unbounded domains of so called parallel and perpendicularly oriented
lamellae in a uniform, oscillatory, shear flow, and show that the configuration
can be hydrodynamically unstable for the constitutive law chosen. It is argued
that this instability and the secondary flows it creates can be used to infer a
possible mechanism for orientation selection in shear experiments.Comment: 26 pages, 10 figure
Motion of buoyant particles and coarsening of solid-liquid mixtures in a random acceleration field
Flow induced by a random acceleration field (g-jitter) is considered in two
related situations that are of interest for microgravity fluid experiments: the
random motion of an isolated buoyant particle and coarsening of a solid-liquid
mixture. We start by analyzing in detail actual accelerometer data gathered
during a recent microgravity mission, and obtain the values of the parameters
defining a previously introduced stochastic model of this acceleration field.
We then study the motion of a solid particle suspended in an incompressible
fluid that is subjected to such random accelerations. The displacement of the
particle is shown to have a diffusive component if the correlation time of the
stochastic acceleration is finite or zero, and mean squared velocities and
effective diffusion coefficients are obtained explicitly. Finally, the effect
of g-jitter on coarsening of a solid-liquid mixture is considered. Corrections
due to the induced fluid motion are calculated, and estimates are given for
coarsening of Sn-rich particles in a Sn-Pb eutectic fluid, experiment to be
conducted in microgravity in the near future.Comment: 25 pages, 4 figures (included). Also at
http://www.scri.fsu.edu/~vinals/ross2.p
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