Monte Carlo Dynamics of driven Flux Lines in Disordered Media

We show that the common local Monte Carlo rules used to simulate the motion of driven flux lines in disordered media cannot capture the interplay between elasticity and disorder which lies at the heart of these systems. We therefore discuss a class of generalized Monte Carlo algorithms where an arbitrary number of line elements may move at the same time. We prove that all these dynamical rules have the same value of the critical force and possess phase spaces made up of a single ergodic component. A variant Monte Carlo algorithm allows to compute the critical force of a sample in a single pass through the system. We establish dynamical scaling properties and obtain precise values for the critical force, which is finite even for an unbounded distribution of the disorder. Extensions to higher dimensions are outlined.Comment: 4 pages, 3 figure

The depinning transition of a driven interface in the random-field Ising model around the upper critical dimension

We investigate the depinning transition for driven interfaces in the random-field Ising model for various dimensions. We consider the order parameter as a function of the control parameter (driving field) and examine the effect of thermal fluctuations. Although thermal fluctuations drive the system away from criticality the order parameter obeys a certain scaling law for sufficiently low temperatures and the corresponding exponents are determined. Our results suggest that the so-called upper critical dimension of the depinning transition is five and that the systems belongs to the universality class of the quenched Edward-Wilkinson equation.Comment: accepted for publication in Phys. Rev.

Influence of Hot Band Annealing on Cold-Rolled Microstructure and Recrystallization in AA 6016

The influence of an intermediate heat treatment at the end of hot rolling and before cold rolling on Cube texture formation during the final solution annealing of AA 6016 is investigated. Three hot bands with different initial grain sizes and textures are considered: the first one without annealing before cold rolling, while the other two hot bands are heat treated at 540 °C for 1 hour in air before being cold rolled. One of the heat-treated hot bands was left to cool down in air and the other inside the furnace. Electron-backscatter diffraction (EBSD) maps of the cold-rolled specimens and crystal plasticity simulations show no difference in the amount of Cube remaining in the microstructure at the end of cold rolling for all three specimens. The initial grain size of the hot band has no influence on the Cube texture fraction left in the microstructure at the end of cold rolling for thickness reductions higher than 65 pct. Nevertheless, the grain size of the hot band affects the shape and distribution of the Cube grains left in the microstructure and the kernel average misorientation in the cold-rolled specimens. Moreover, the heat treatment decreases the intensity of the beta fiber components (Brass, Copper, and S) in the hot band and promotes the formation of a cold-rolled microstructure with a low kernel average misorientation. Both these factors lower the probability of preferential Cube nucleation during solution annealing and keep the Cube volume fraction after recrystallization below 10 pct, while it reaches 25 pct without intermediate annealing

Higher correlations, universal distributions and finite size scaling in the field theory of depinning

Recently we constructed a renormalizable field theory up to two loops for the quasi-static depinning of elastic manifolds in a disordered environment. Here we explore further properties of the theory. We show how higher correlation functions of the displacement field can be computed. Drastic simplifications occur, unveiling much simpler diagrammatic rules than anticipated. This is applied to the universal scaled width-distribution. The expansion in d=4-epsilon predicts that the scaled distribution coincides to the lowest orders with the one for a Gaussian theory with propagator G(q)=1/q^(d+2 \zeta), zeta being the roughness exponent. The deviations from this Gaussian result are small and involve higher correlation functions, which are computed here for different boundary conditions. Other universal quantities are defined and evaluated: We perform a general analysis of the stability of the fixed point. We find that the correction-to-scaling exponent is omega=-epsilon and not -epsilon/3 as used in the analysis of some simulations. A more detailed study of the upper critical dimension is given, where the roughness of interfaces grows as a power of a logarithm instead of a pure power.Comment: 15 pages revtex4. See also preceding article cond-mat/030146

Origin of the roughness exponent in elastic strings at the depinning threshold

Within a recently developed framework of dynamical Monte Carlo algorithms, we compute the roughness exponent $\zeta$ of driven elastic strings at the depinning threshold in 1+1 dimensions for different functional forms of the (short-range) elastic energy. A purely harmonic elastic energy leads to an unphysical value for $\zeta$. We include supplementary terms in the elastic energy of at least quartic order in the local extension. We then find a roughness exponent of $\zeta \simeq 0.63$, which coincides with the one obtained for different cellular automaton models of directed percolation depinning. The quartic term translates into a nonlinear piece which changes the roughness exponent in the corresponding continuum equation of motion. We discuss the implications of our analysis for higher-dimensional elastic manifolds in disordered media.Comment: 4 pages, 2 figure

Critical behavior of a traffic flow model

The Nagel-Schreckenberg traffic flow model shows a transition from a free flow regime to a jammed regime for increasing car density. The measurement of the dynamical structure factor offers the chance to observe the evolution of jams without the necessity to define a car to be jammed or not. Above the jamming transition the dynamical structure factor exhibits for a given k-value two maxima corresponding to the separation of the system into the free flow phase and jammed phase. We obtain from a finite-size scaling analysis of the smallest jam mode that approaching the transition long range correlations of the jams occur.Comment: 5 pages, 7 figures, accepted for publication in Physical Review

Velocity-force characteristics of a driven interface in a disordered medium

Using a dynamic functional renormalization group treatment of driven elastic interfaces in a disordered medium, we investigate several aspects of the creep-type motion induced by external forces below the depinning threshold $f_c$: i) We show that in the experimentally important regime of forces slightly below $f_c$ the velocity obeys an Arrhenius-type law $v\sim\exp[-U(f)/T]$ with an effective energy barrier $U(f)\propto (f_{c}-f)$ vanishing linearly when f approaches the threshold $f_c$. ii) Thermal fluctuations soften the pinning landscape at high temperatures. Determining the corresponding velocity-force characteristics at low driving forces for internal dimensions d=1,2 (strings and interfaces) we find a particular non-Arrhenius type creep $v\sim \exp[-(f_c(T)/f)^{\mu}]$ involving the reduced threshold force $f_c(T)$ alone. For d=3 we obtain a similar v-f characteristic which is, however, non-universal and depends explicitly on the microscopic cutoff.Comment: 9 pages, RevTeX, 3 postscript figure