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.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.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.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.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.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.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.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.
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.
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.
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].
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.
Thesis: a monumental work.
[pdf, abstract]
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.
Phys. Rev. E. 53, p. 3750 (1996).
[ps, abstract].
See the Physical Review E for the text of the paper.
Phys. Rev. E. 53, p. 1465 (1996).
[ps, html, abstract].
Europhys. Lett., 27 575 (1994).
[ps,abstract].
J. Chem. Phys. 103 3737 (1995).
[ps,pdf, abstract].
