Kwan-tai Leung

Tricritical Behavior in Rupture Induced by Disorder

We discover a qualitatively new behavior for systems where the load transfer has limiting stress amplification as in real fiber composites. We find that the disorder is a relevant field leading to tricriticality, separating a first-order regime where rupture occurs without significant precursors from a second-order regime where the macroscopic elastic coefficient exhibits power law behavior. Our results are based on analytical analysis of fiber bundle models and numerical simulations of a two-dimensional tensorial spring-block system in which stick-slip motion and fracture compete. {copyright} {ital 1997} {ital The American Physical Society}

Spiral cracks in drying precipitates

We investigate the formation of spiral crack patterns during the desiccation of thin layers of precipitates in contact with a substrate. This symmetry-breaking fracturing mode is found to arise naturally not from torsion forces but from a propagating stress front induced by the foldup of the fragments. We model their formation mechanism using a coarse-grain model for fragmentation and successfully reproduce the spiral cracks. Fittings of experimental and simulation data show that the spirals are logarithmic. Theoretical aspects of the logarithmic spirals are discussed. In particular we show that this occurs generally when the crack speed is proportional to the propagating speed of stress front.

Pattern formation and selection in quasistatic fracture.

Fracture in quasistatically driven systems is studied by means of a discrete spring-block model. Developed from close comparison with desiccation experiments, it describes crack formation induced by friction on a substrate. The model produces cellular, hierarchical patterns of cracks, characterized by a mean fragment size linear in the layer thickness, in agreement with experiments. The selection of a stationary fragment size is explained by exploiting the correlations prior to cracking. A scaling behavior associated with the thickness and substrate coupling, derived and confirmed by simulations, suggests why patterns have similar morphology despite their disparity in scales.

Pattern formation: Spiral cracks without twisting

A fascinating class of patterns, often encountered in nature as meandering cracks on rocks, dried-out fields and tectonic plates, is produced by the fracture of solids. Here we describe the observation and modelling of an unusual type of pattern consisting of spiral cracks in fragments of a thin layer of drying precipitate. We find that this symmetry-breaking cracking mode arises naturally not from twisting forces, but from a propagating stress front induced by the fold-up of the fragments.

Phase transition in a spring-block model of surface fracture

A simple and robust spring-block model obeying threshold dynamics is introduced to study surface fracture of an overlayer subject to stress induced by adhesion to a substrate. We find a novel phase transition in the crack morphology and fragment-size statistics when the strain and the substrate coupling are varied. Across the transition, the cracks display in succession short-range, power law and long-range correlations. The study of stress release prior to cracking yields useful information on the cracking process.

RESPONSE IN KINETIC ISING MODEL TO OSCILLATING MAGNETIC FIELDS

Abstract Ising models obeying Glauber dynamics in a temporally oscillating magnetic field are analyzed. In the context of stochastic resonance, the response in the magnetization is calculated by means of both a mean-field theory with linear-response approximation, and the time-dependent Ginzburg-Landau equation. Analytic results for the temperature and frequency dependent response, including the resonance temperature, compare favorably with simulation data.

NONTRIVIAL STOCHASTIC RESONANCE TEMPERATURE FOR THE KINETIC ISING MODEL

The kinetic Ising model in a weak oscillating magnetic field is studied in the context of stochastic resonance. The signal-to-noise ratio calculated with simulations is found to peak at a nontrivial resonance temperature above the equilibrium critical temperature T_c. We argue that its appearance is closely related to the vanishing of the kinetic coefficient at T_c. Comparisons with various theoretical results in one and higher dimensions are made.

NOVEL PHASES AND FINITE-SIZE SCALING IN TWO-SPECIES ASYMMETRIC DIFFUSIVE PROCESSES

We study a stochastic lattice gas of particles undergoing asymmetric diffusion in two dimensions. Transitions between a low-density uniform phase and high-density nonuniform phases characteized by localized or extended structure are found. We develop a mean-field theory which relates coarse-grained parameters to microscopic ones. Detailed predictions for finite-size ([ital L]) scaling and density profiles agree excellently with simulations. Unusual large-[ital L] behavior of the transition point parallel to that of self-organized sandpile models is found.

Drifting spatial structures in a system with oppositely driven species

A system consisting of two conservative, oppositely driven species of particles with excluded volume interaction alone is studied on a torus. The system undergoes a phase transition between a homogeneous and an inhomogeneous phase, as the particle densities are varied. Focusing on the inhomogeneous phase with generally unequal numbers of the two species, the spatial structure is found to drift counter-intuitively against the majority species at a constant velocity that depends on the external field, system size, and particle densities. Such dependences are derived from a coarse-grained continuum theory, and a microscopic mechanism for the drift is explained. With virtually no tuning parameter, various theoretical predictions, notably a field-system-size scaling, agree extremely well with the simulations.

ANISOTROPIC FINITE-SIZE SCALING ANALYSIS OF A THREE-DIMENSIONAL DRIVEN-DIFFUSIVE SYSTEM

We study the standard three-dimensional driven diffusive system on a simple cubic lattice where particle jumping along a given lattice direction are biased by an infinitely strong field, while those along other directions follow the usual Kawasaki dynamics. Our goal is to determine which of the several existing theories for critical behavior is valid. We analyze finite-size scaling properties using a range of system shapes and sizes far exceeding previous studies. Four different analytic predictions are tested against the numerical data. Binder and Wangs prediction does not fit the data well. Among the two slightly different versions of Leung, the one including the effects of a dangerous irrelevant variable appears to be better. Recently proposed isotropic finite-size scaling is inconsistent with our data from cubic systems, where systematic deviations are found, especially in scaling at the critical temperature.