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Dynamics of channel incision in a granular bed driven by
subsurface water flow (under review)
We propose a dynamical model for channels incised into an erodible bed
by subsurface water flow. The model is validated by the time-resolved
topographic measurements of channel growth in a laboratory-scale
experiment. Surface heights in the experiment are measured via a
novel laser-aided imaging technique. Erosion rate in the model is
composed of the diffusive and advective components as well as a simple
driving term due to the seeping water. Steady driving conditions may
exist whenever channels are incised into a flat and level erodible bed
by a watertable replentished via steady (on average) rainfall. Under
such steady driving conditions, the model predicts an asymptotically
self-similar growing shape for the channel transects. Vice versa,
given a transects shape which evolved under steady driving conditions
and an estimate of the erosion rate at the bottom of the channel
(which is constant under steady driving), granular transport
coefficients can be inferred from the static channel shape. We report
an estimate of these transport coefficients for the system of ravines
incised into unconsolidated sand in the Appalachicola River basin,
Florida.
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Low-temperature dynamics of kinks on Ising interfaces (PRE,
2005)
The anisotropic motion of an interface driven by its intrinsic
curvature or by an external field is investigated in the context of
the kinetic Ising model in both two and three dimensions. We derive in
two dimensions (2D) a continuum evolution equation for the density of
kinks by a time-dependent and nonlocal mapping to the asymmetric
exclusion process. Whereas kinks execute random walks biased by the
external field and pile up vertically on the physical 2D lattice, they
execute hard-core biased random walks on a transformed 1D
lattice. Their density obeys a nonlinear diffusion equation which can
be transformed into the standard expression for the interface
velocity, v = M[(gamma+gamma'')kappa + H], where M, gamma + gamma'',
and kappa are the interface mobility, stiffness, and curvature,
respectively. In 3D, we obtain the velocity of a curved interface near
the <100> orientation from an analysis of the self-similar evolution
of 2D shrinking terraces. We show that this velocity is consistent
with the one predicted from the 3D tensorial generalization of the law
for anisotropic curvature-driven motion. In this generalization, both
the interface stiffness tensor and the curvature tensor are singular
at the <100> orientation. However, their product, which determines the
interface velocity, is smooth. In addition, we illustrate how this
kink-based kinetic description provides a useful framework for
studying more complex situations by modeling the effect of immobile
dilute impurities.
Link to the
paper at the PRE website
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Threshold phenomena in erosion driven by subsurface flow
(JGR, 2004)
We study channelization and slope destabilization driven by subsurface
(groundwater) flow in a laboratory experiment. The pressure of the
water entering the sand pile from below as well as the slope of the
sand pile are varied. We present quantitative understanding of the
three modes of sediment mobilization in this experiment: surface
erosion, fluidization, and slumping. The onset of erosion is
controlled not only by shear stresses caused by surfical flows but
also by hydrodynamic stresses deriving from subsurface flows. These
additional forces require modification of the critical Shields
criterion. Whereas surface flows alone can mobilize surface grains
only when the water flux exceeds a threshold, subsurface flows cause
this threshold to vanish at slopes steeper than a critical angle
substantially smaller than the maximum angle of stability. Slopes
above this critical angle are unstable to channelization by any amount
of fluid reaching the surface.
Link
to the paper at the JGR's website
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Unsteady Crack Motion and Branching in a Phase-Field Model of
Brittle Fracture (PRL, 2004)
Crack propagation is studied numerically using a continuum phase-field
approach to mode III brittle fracture. The results shed light on the
physics that controls the speed of accelerating cracks and the
characteristic branching instability at a fraction of the wave speed.
Link to the
paper at the PRE website
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Grain shape, grain boundary mobility and the Herring relation
(Acta Materialia, 2004)
Motivated by recent experiments on grain boundary migration in Al, we
examine the question: does interface mobility depend on the nature of
the driving force? We investigate this question in the Ising model and
conclude that the answer is "no." This conclusion highlights the
importance of including the second derivative of the interface energy
with respect to inclination gamma'' in the Herring relation in order
to correctly describe the motion of grain boundaries driven by
capillarity. The importance of this term can be traced to the entropic
part of gamma'', which can be highly anisotropic, such that the
reduced mobility (i.e., the product of interface stiffness gamma +
gamma'' and mobility) can be nearly isotropic even though the mobility
itself is highly anisotropic. The cancellation of these two
anisotropies (associated with stiffness and mobility) originates in
the Ising model from the fact that the number of geometrically
necessary kinks, and hence the kink configurational entropy, varies
rapidly with inclination near low-energy/low mobility, but slowly near
high-energy/high-mobility interfaces, where the kink density is
high. This implies that the stiffness is high where the mobility is
low and vice versa. Consequently, the grain shape can appear isotropic
or highly anisotropic depending on whether its motion is driven by
curvature or an external field, respectively, but the mobility itself
is independent of driving force. We discuss the implications of these
results for interpreting experimental observations and computer
simulations of microstructural evolution, where gamma'' is routinely
neglected.
Link to the
paper at Acta Materialia's website
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Tracer diffusion in a dislocated lamellar system (PRL, 2002)
Many lamellar systems exhibit strongly anisotropic diffusion. When the
diffusion across the lamellae is slow, an alternative mechanism for
transverse transport becomes important. A tracer particle can
propagate across the lamellae by encircling a screw dislocation. We
calculate the statistical properties of this mode of transverse
transport. When either positive or negative dislocations are in
excess, transport across the lamellae is ballistic. When the average
dislocation charge is zero, the mean square of the normal displacement
grows like T logT for large times. To obtain this result, the
trajectory of the tracer must be smoothed over distances of order of
the dislocation core size.
Text of the paper
in PRL
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Phase field model of premelting of grain boundaries (Physica
D, 2002)
We present a phase field model of solidification which includes the
effects of the crystalline orientation in the solid phase. This model
describes grain boundaries as well as solid-liquid boundaries within a
unified framework. With an appropriate choice of coupling of the
phase field variable to the gradient of the crystalline orientation
variable in the free energy, we find that high angle boundaries
undergo a premelting transition. As the melting temperature is
approached from below, low angle grain boundaries remain narrow. The
width of the liquid layer at high angle grain boundaries diverges
logarithmically. In addition, for some choices of model coupling,
there may be a discontinuous jump in the width of the fluid layer as
function of temperature.
Text of the paper in Physica D.
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Sharp interface limit of phase-field model of crystal grains
(PRE, 2001)
We constructed a minimal phase field model of grains in a
polycrystal. The ingredients are a two locally defined order
parameters: degree of bond orientational order and average local
orientation and a non-analytic free energy density. The resulting
evolution equation must be interpreted with some care. In this paper
we study a sharp interface limit of this model which allows us to
extract the grain boundary energy, mobility and the rotation rate of
the grains.
See the Physical
Review E for the text of the paper.
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Rate-and-State Theory of Plastic Deformation
Near a
Circular Hole (PRE, 1999)
In this paper we look at how a circular hole in a thin plate grows
when tensile stress is applied far away. We show how results
predicted by conventional plasticity theories emerge from a the theory
developed in a preceding work.
[ps, pdf, abstract].
See the Physical
Review E for the text of the paper.
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Dynamic ductile to brittle transition
in a
one-dimensional model of viscoplasticity
Why are some things brittle and shatter on impact and others do
not. The answer lies in understanding the violent processes near the
tip of a running crack where strain rates can reach 10,000,000!
M. L. Falk and J. S. Langer developed a fully dynamic plasticity model
that works at such high strain rates. It is based on an molecular
dynamics simulation of an amorphous material. In this paper we apply
this model to a one-dimensional peeling model to take a stab at
understanding ductility and brittleness.
[ps,
abstract].
See the Physical Review E for the text of the paper.
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Critical examination of cohesive-zone models
in the
theory of dynamic fracture
This paper is an attempt to describe dynamic fracture instability
using rate-dependent cohesive-zone models. Published in the Journal
of the Mechanics and Physics of Solids.
[ps, abstract].
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Properties of Ridges in Elastic Membranes
Investigation of ridge properties that are relevant to describing
crumpled elastic membranes.
Phys. Rev. E. 55, p. 1577
(1997).
[ps,
abstract].
See the Physical Review
E for the text of the paper.
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Thesis: a monumental work.
[pdf, abstract]
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Stretching Ridges in a Crumpled Elastic Sheet
Science,
Volume 270, Number 5241, Issue of 1 December 1995, pp. 1482-1485
[ps,
abstract].
There are more
pictures here.
- A technical analysis of the ridge singularity in thin plates
based on von Karman plate equations.
Phys. Rev. E. 53, p. 3750 (1996).
[ps, abstract].
See the Physical Review E for the text of the paper.
- Candy wrapper noise and its glassy properties.
Phys. Rev. E. 53, p. 1465 (1996).
[ps,
html, abstract].
- Shape transition of a droplet in electric field.
Europhys. Lett., 27 575 (1994).
[ps,abstract].
- Surface energy anisotropy of dipolar lattices.
J. Chem. Phys. 103 3737 (1995).
[ps,pdf,
abstract].