Avalanches and the Renormalization Group for Pinned Charge-Density Waves

The critical behavior of charge-density waves (CDWs) in the pinned phase is studied for applied fields increasing toward the threshold field, using recently developed renormalization group techniques and simulations of automaton models. Despite the existence of many metastable states in the pinned state of the CDW, the renormalization group treatment can be used successfully to find the divergences in the polarization and the correlation length, and, to first order in an $\epsilon = 4-d$ expansion, the diverging time scale. The automaton models studied are a charge-density wave model and a ``sandpile'' model with periodic boundary conditions; these models are found to have the same critical behavior, associated with diverging avalanche sizes. The numerical results for the polarization and the diverging length and time scales in dimensions $d=2,3$ are in agreement with the analytical treatment. These results clarify the connections between the behaviour above and below threshold: the characteristic correlation lengths on both sides of the transition diverge with different exponents. The scaling of the distribution of avalanches on the approach to threshold is found to be different for automaton and continuous-variable models.Comment: 29 pages, 11 postscript figures included, REVTEX v3.0 (dvi and PS files also available by anonymous ftp from external.nj.nec.com in directory /pub/alan/cdwfigs

Vortex Dynamics and Defects in Simulated Flux Flow

We present the results of molecular dynamic simulations of a two-dimensional vortex array driven by a uniform current through random pinning centers at zero temperature. We identify two types of flow of the driven array near the depinning threshold. For weak disorder the flux array contains few dislocation and moves via correlated displacements of patches of vortices in a {\it crinkle} motion. As the disorder strength increases, we observe a crossover to a spatially inhomogeneous regime of {\it plastic} flow, with a very defective vortex array and a channel-like structure of the flowing regions. The two regimes are characterized by qualitatively different spatial distribution of vortex velocities. In the crinkle regime the distribution of vortex velocities near threshold has a single maximum that shifts to larger velocities as the driving force is increased. In the plastic regime the distribution of vortex velocities near threshold has a clear bimodal structure that persists upon time-averaging the individual velocities. The bimodal structure of the velocity distribution reflects the coexistence of pinned and flowing regions and is proposed as a quantitative signature of plastic flow.Comment: 12 pages, 13 embedded PostScript figure

Dynamic Ordering and Transverse Depinning of a Driven Elastic String in a Disordered Media

We examine the dynamics of an elastic string interacting with quenched disorder driven perpendicular and parallel to the string. We show that the string is the most disordered at the depinning transition but with increasing drive partial ordering is regained. For low drives the noise power is high and we observe a 1/f^2 noise signature crossing over to a white noise character with low power at higher drives. For the parallel driven moving string there is a finite transverse critical depinning force with the depinning transition occuring by the formation of running kinks.Comment: 4 pages, 4 postscript figure

Velocity-force characteristics of an interface driven through a periodic potential

We study the creep dynamics of a two-dimensional interface driven through a periodic potential using dynamical renormalization group methods. We find that the nature of weak-drive transport depends qualitatively on whether the temperature $T$ is above or below the equilibrium roughening transition temperature $T_c$. Above $T_c$, the velocity-force characteristics is Ohmic, with linear mobility exhibiting a jump discontinuity across the transition. For $T \le T_c$, the transport is highly nonlinear, exhibiting an interesting crossover in temperature and weak external force $F$. For intermediate drive, $F>F_*$, we find near $T_c^{-}$ a power-law velocity-force characteristics $v(F)\sim F^\sigma$, with $\sigma-1\propto \tilde{t}$, and well-below $T_c$, $v(F)\sim e^{-(F_*/F)^{2\tilde{t}}}$, with $\tilde{t}=(1-T/T_c)$. In the limit of vanishing drive ($F\ll F_*$) the velocity-force characteristics crosses over to $v(F)\sim e^{-(F_0/F)}$, and is controlled by soliton nucleation.Comment: 18 pages, submitted to Phys. Rev.

A Legendre spectral element method for eigenvalues in hydrodynamic stability

A Legendre polynomial-based spectral technique is developed to be applicable to solving eigenvalue problems which arise in linear and nonlinear stability questions in porous media, and other areas of Continuum Mechanics. The matrices produced in the corresponding generalised eigenvalue problem are sparse, reducing the computational and storage costs, where the superimposition of boundary conditions is not needed due to the structure of the method. Several eigenvalue problems are solved using both the Legendre polynomial-based and Chebyshev tau techniques. In each example, the Legendre polynomial-based spectral technique converges to the required accuracy utilising less polynomials than the Chebyshev tau method, and with much greater computational efficiency. © 2005 Elsevier B.V. All rights reserved