Festschrift for Prof. Şefik Süzer's 60th birthday

[No abstract available

Stability of Monomer-Dimer Piles

We measure how strong, localized contact adhesion between grains affects the maximum static critical angle, theta_c, of a dry sand pile. By mixing dimer grains, each consisting of two spheres that have been rigidly bonded together, with simple spherical monomer grains, we create sandpiles that contain strong localized adhesion between a given particle and at most one of its neighbors. We find that tan(theta_c) increases from 0.45 to 1.1 and the grain packing fraction, Phi, decreases from 0.58 to 0.52 as we increase the relative number fraction of dimer particles in the pile, nu_d, from 0 to 1. We attribute the increase in tan(theta_c(nu_d)) to the enhanced stability of dimers on the surface, which reduces the density of monomers that need to be accomodated in the most stable surface traps. A full characterization and geometrical stability analysis of surface traps provides a good quantitative agreement between experiment and theory over a wide range of nu_d, without any fitting parameters.Comment: 11 pages, 12 figures consisting of 21 eps files, submitted to PR

Velocity Correlations in Dense Gravity Driven Granular Chute Flow

We report numerical results for velocity correlations in dense, gravity-driven granular flow down an inclined plane. For the grains on the surface layer, our results are consistent with experimental measurements reported by Pouliquen. We show that the correlation structure within planes parallel to the surface persists in the bulk. The two-point velocity correlation function exhibits exponential decay for small to intermediate values of the separation between spheres. The correlation lengths identified by exponential fits to the data show nontrivial dependence on the averaging time \dt used to determine grain velocities. We discuss the correlation length dependence on averaging time, incline angle, pile height, depth of the layer, system size and grain stiffness, and relate the results to other length scales associated with the rheology of the system. We find that correlation lengths are typically quite small, of the order of a particle diameter, and increase approximately logarithmically with a minimum pile height for which flow is possible, \hstop, contrary to the theoretical expectation of a proportional relationship between the two length scales.Comment: 21 pages, 16 figure

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

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

A Model Ground State of Polyampholytes

The ground state of randomly charged polyampholytes is conjectured to have a structure similar to a necklace, made of weakly charged parts of the chain, compacting into globules, connected by highly charged stretched `strings'. We suggest a specific structure, within the necklace model, where all the neutral parts of the chain compact into globules: The longest neutral segment compacts into a globule; in the remaining part of the chain, the longest neutral segment (the 2nd longest neutral segment) compacts into a globule, then the 3rd, and so on. We investigate the size distributions of the longest neutral segments in random charge sequences, using analytical and Monte Carlo methods. We show that the length of the n-th longest neutral segment in a sequence of N monomers is proportional to N/(n^2), while the mean number of neutral segments increases as sqrt(N). The polyampholyte in the ground state within our model is found to have an average linear size proportional to sqrt(N), and an average surface area proportional to N^(2/3).Comment: 8 two-column pages. 5 eps figures. RevTex. Submitted to Phys. Rev.

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

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

Roughness at the depinning threshold for a long-range elastic string

In this paper, we compute the roughness exponent zeta of a long-range elastic string, at the depinning threshold, in a random medium with high precision, using a numerical method which exploits the analytic structure of the problem (`no-passing' theorem), but avoids direct simulation of the evolution equations. This roughness exponent has recently been studied by simulations, functional renormalization group calculations, and by experiments (fracture of solids, liquid meniscus in 4He). Our result zeta = 0.390 +/- 0.002 is significantly larger than what was stated in previous simulations, which were consistent with a one-loop renormalization group calculation. The data are furthermore incompatible with the experimental results for crack propagation in solids and for a 4He contact line on a rough substrate. This implies that the experiments cannot be described by pure harmonic long-range elasticity in the quasi-static limit.Comment: 4 pages, 3 figure