Anisotropic Scaling in Threshold Critical Dynamics of Driven Directed Lines

The dynamical critical behavior of a single directed line driven in a random medium near the depinning threshold is studied both analytically (by renormalization group) and numerically, in the context of a Flux Line in a Type-II superconductor with a bulk current $\vec J$. In the absence of transverse fluctuations, the system reduces to recently studied models of interface depinning. In most cases, the presence of transverse fluctuations are found not to influence the critical exponents that describe longitudinal correlations. For a manifold with $d=4-\epsilon$ internal dimensions, longitudinal fluctuations in an isotropic medium are described by a roughness exponent $\zeta_\parallel=\epsilon/3$ to all orders in $\epsilon$, and a dynamical exponent $z_\parallel=2-2\epsilon/9+O(\epsilon^2)$. Transverse fluctuations have a distinct and smaller roughness exponent $\zeta_\perp=\zeta_\parallel-d/2$ for an isotropic medium. Furthermore, their relaxation is much slower, characterized by a dynamical exponent $z_\perp=z_\parallel+1/\nu$, where $\nu=1/(2-\zeta_\parallel)$ is the correlation length exponent. The predicted exponents agree well with numerical results for a flux line in three dimensions. As in the case of interface depinning models, anisotropy leads to additional universality classes. A nonzero Hall angle, which has no analogue in the interface models, also affects the critical behavior.Comment: 26 pages, 8 Postscript figures packed together with RevTeX 3.0 manuscript using uufiles, uses multicol.sty and epsf.sty, e-mail [email protected] in case of problem

The Origin of a Repose Angle: Kinetics of Rearrangements for Granular Materials

A microstructural theory of dense granular materials is presented, based on two main ideas. Firstly, that macroscopic shear results form activated local rearrangements at a mesoscopic scale. Secondly, that the update frequency of microscopic processes is determined by granular temperature. In a shear cell, the resulting constitutive equations account for Bagnold's scaling and for the existence of a Coulomb criterion of yield. In the case of a granular flow down an inclined plane, they account for the rheology observed in recent experiments and for the temperature and velocity profiles measured numerically.Comment: submitted to PR

Finite Temperature Depinning of a Flux Line from a Nonuniform Columnar Defect

A flux line in a Type-II superconductor with a single nonuniform columnar defect is studied by a perturbative diagrammatic expansion around an annealed approximation. The system undergoes a finite temperature depinning transition for the (rather unphysical) on-the-average repulsive columnar defect, provided that the fluctuations along the axis are sufficiently large to cause some portions of the column to become attractive. The perturbative expansion is convergent throughout the weak pinning regime and becomes exact as the depinning transition is approached, providing an exact determination of the depinning temperature and the divergence of the localization length.Comment: RevTeX, 4 pages, 3 EPS figures embedded with epsf.st

A Ball in a Groove

We study the static equilibrium of an elastic sphere held in a rigid groove by gravity and frictional contacts, as determined by contact mechanics. As a function of the opening angle of the groove and the tilt of the groove with respect to the vertical, we identify two regimes of static equilibrium for the ball. In the first of these, at large opening angle or low tilt, the ball rolls at both contacts as it is loaded. This is an analog of the "elastic" regime in the mechanics of granular media. At smaller opening angles or larger tilts, the ball rolls at one contact and slides at the other as it is loaded, analogously with the "plastic" regime in the mechanics of granular media. In the elastic regime, the stress indeterminacy is resolved by the underlying kinetics of the ball response to loading.Comment: RevTeX 3.0, 4 pages, 2 eps figures included with eps

Onset of Propagation of Planar Cracks in Heterogeneous Media

The dynamics of planar crack fronts in hetergeneous media near the critical load for onset of crack motion are investigated both analytically and by numerical simulations. Elasticity of the solid leads to long range stress transfer along the crack front which is non-monotonic in time due to the elastic waves in the medium. In the quasistatic limit with instantaneous stress transfer, the crack front exhibits dynamic critical phenomenon, with a second order like transition from a pinned to a moving phase as the applied load is increased through a critical value. At criticality, the crack-front is self-affine, with a roughness exponent $\zeta =0.34\pm 0.02$. The dynamic exponent $z$ is found to be equal to $0.74\pm 0.03$ and the correlation length exponent $\nu =1.52\pm 0.02$. These results are in good agreement with those obtained from an epsilon expansion. Sound-travel time delays in the stress transfer do not change the static exponents but the dynamic exponent $z$ becomes exactly one. Real elastic waves, however, lead to overshoots in the stresses above their eventual static value when one part of the crack front moves forward. Simplified models of these stress overshoots are used to show that overshoots are relevant at the depinning transition leading to a decrease in the critical load and an apparent jump in the velocity of the crack front directly to a non-zero value. In finite systems, the velocity also shows hysteretic behaviour as a function of the loading. These results suggest a first order like transition. Possible implications for real tensile cracks are discussed.Comment: 51 pages + 20 figur

Gutenberg Richter and Characteristic Earthquake Behavior in Simple Mean-Field Models of Heterogeneous Faults

The statistics of earthquakes in a heterogeneous fault zone is studied analytically and numerically in the mean field version of a model for a segmented fault system in a three-dimensional elastic solid. The studies focus on the interplay between the roles of disorder, dynamical effects, and driving mechanisms. A two-parameter phase diagram is found, spanned by the amplitude of dynamical weakening (or ``overshoot'') effects (epsilon) and the normal distance (L) of the driving forces from the fault. In general, small epsilon and small L are found to produce Gutenberg-Richter type power law statistics with an exponential cutoff, while large epsilon and large L lead to a distribution of small events combined with characteristic system-size events. In a certain parameter regime the behavior is bistable, with transitions back and forth from one phase to the other on time scales determined by the fault size and other model parameters. The implications for realistic earthquake statistics are discussed.Comment: 21 pages, RevTex, 6 figures (ps, eps

Are Steadily Moving Crystals Unstable?

We study the dynamics of small fluctuations about the uniform state of a crystal moving through a dissipative medium, e.g. a sedimenting colloidal crystal or a moving flux lattice, using a set of continuum equations for the displacement fields, and a one-dimensional driven lattice-gas model for the coupled concentration and tilt fields. For the colloidal crystal we predict a continuous nonequilibrium phase transition to a clumped state above a critical Peclet number.Comment: 4 pages, revtex, 2 .eps figures, uses epsf.sty; To be published in Phys. Rev. Lett. This version is substantially rewritten but the essential content is the same as befor

Dynamics and Instabilities of Planar Tensile Cracks in Heterogeneous Media

The dynamics of tensile crack fronts restricted to advance in a plane are studied. In an ideal linear elastic medium, a propagating mode along the crack front with a velocity slightly less than the Rayleigh wave velocity, is found to exist. But the dependence of the effective fracture toughness $\Gamma(v)$ on the crack velocity is shown to destabilize the crack front if $(d\Gamma)/(dv)<0$. Short wavelength radiation due to weak random heterogeneities leads to this instability at low velocities. The implications of these results for the crack dynamics are discussed.Comment: 12 page

Lateral Separation of Macromolecules and Polyelectrolytes in Microlithographic Arrays

A new approach to separation of a variety of microscopic and mesoscopic objects in dilute solution is presented. The approach takes advantage of unique properties of a specially designed separation device (sieve), which can be readily built using already developed microlithographic techniques. Due to the broken reflection symmetry in its design, the direction of motion of an object in the sieve varies as a function of its self-diffusion constant, causing separation transverse to its direction of motion. This gives the device some significant and unique advantages over existing fractionation methods based on centrifugation and electrophoresis.Comment: 4 pages with 3 eps figures, needs RevTeX 3.0 and epsf, also available in postscript form http://cmtw.harvard.edu/~deniz

Anti-neuronal antibodies associated with headache with neurological deficits and cerebrospinal fluid lymphocytosis

5OCT333-335