The role of the alloy structure in the magnetic behavior of granular systems

The effect of grain size, easy magnetization axis and anisotropy constant distributions in the irreversible magnetic behavior of granular alloys is considered. A simulated granular alloy is used to provide a realistic grain structure for the Monte Carlo simulation of the ZFC-FC curves. The effect of annealing and external field is also studied. The simulation curves are in good agreement with the FC and ZFC magnetization curves measured on melt spun Cu-Co ribbons.Comment: 13 pages, 10 figures, submitted to PR

On the signature of tensile blobs in the scattering function of a stretched polymer

We present Monte Carlo data for a linear chain with excluded volume subjected to a uniform stretching. Simulation of long chains (up to 6000 beads) at high stretching allows us to observe the signature of tensile blobs as a crossover in the scaling behavior of the chain scattering function for wave vectors perpendicular to stretching. These results and corresponding ones in the stretching direction allow us to verify for the first time Pincus prediction on scaling inside blobs. Outside blobs, the scattering function is well described by the Debye function for a stretched ideal chain.Comment: 4 pages, 4 figures, to appear in Physical Review Letter

Coupled Maps on Trees

We study coupled maps on a Cayley tree, with local (nearest-neighbor) interactions, and with a variety of boundary conditions. The homogeneous state (where every lattice site has the same value) and the node-synchronized state (where sites of a given generation have the same value) are both shown to occur for particular values of the parameters and coupling constants. We study the stability of these states and their domains of attraction. As the number of sites that become synchronized is much higher compared to that on a regular lattice, control is easier to effect. A general procedure is given to deduce the eigenvalue spectrum for these states. Perturbations of the synchronized state lead to different spatio-temporal structures. We find that a mean-field like treatment is valid on this (effectively infinite dimensional) lattice.Comment: latex file (25 pages), 4 figures included. To be published in Phys. Rev.

Exact formula for currents in strongly pumped diffusive systems

We analyze a generic model of mesoscopic machines driven by the nonadiabatic variation of external parameters. We derive a formula for the probability current; as a consequence we obtain a no-pumping theorem for cyclic processes satisfying detailed balance and demonstrate that the rectification of current requires broken spatial symmetry.Comment: 10 pages, accepted for publication in the Journal of Statistical Physic

Dynamics of heteropolymers in dilute solution: effective equation of motion and relaxation spectrum

The dynamics of a heteropolymer chain in solution is studied in the limit of long chain length. Using functional integral representation we derive an effective equation of motion, in which the heterogeneity of the chain manifests itself as a time-dependent excluded volume effect. At the mean field level, the heteropolymer chain is therefore dynamically equivalent to a homopolymer chain with both time-independent and time-dependent excluded volume effects. The perturbed relaxation spectrum is also calculated. We find that heterogeneity also renormalizes the relaxation spectrum. However, we find, to the lowest order in heterogeneity, that the relaxation spectrum does not exhibit any dynamic freezing, at the point when static (equilibrium) ``freezing'' transition occurs in heteropolymer. Namely, the breaking of fluctuation-dissipation theorem (FDT) proposed for spin glass dynamics does not have dynamic effect in heteropolymer, as far as relaxation spectrum is concerned. The implication of this result is discussed

Numerical Confirmation of Late-time t^{1/2} Growth in Three-dimensional Phase Ordering

Results for the late-time regime of phase ordering in three dimensions are reported, based on numerical integration of the time-dependent Ginzburg-Landau equation with nonconserved order parameter at zero temperature. For very large systems ($700^3$) at late times, $t \ge 150,$ the characteristic length grows as a power law, $R(t) \sim t^n$, with the measured $n$ in agreement with the theoretically expected result $n=1/2$ to within statistical errors. In this time regime $R(t)$ is found to be in excellent agreement with the analytical result of Ohta, Jasnow, and Kawasaki [Phys. Rev. Lett. {\bf 49}, 1223 (1982)]. At early times, good agreement is found between the simulations and the linearized theory with corrections due to the lattice anisotropy.Comment: Substantially revised and enlarged, submitted to PR

Chaotic Cascades with Kolmogorov 1941 Scaling

We define a (chaotic) deterministic variant of random multiplicative cascade models of turbulence. It preserves the hierarchical tree structure, thanks to the addition of infinitesimal noise. The zero-noise limit can be handled by Perron-Frobenius theory, just as the zero-diffusivity limit for the fast dynamo problem. Random multiplicative models do not possess Kolmogorov 1941 (K41) scaling because of a large-deviations effect. Our numerical studies indicate that deterministic multiplicative models can be chaotic and still have exact K41 scaling. A mechanism is suggested for avoiding large deviations, which is present in maps with a neutrally unstable fixed point.Comment: 14 pages, plain LaTex, 6 figures available upon request as hard copy (no local report #

Random Walks with Long-Range Self-Repulsion on Proper Time

We introduce a model of self-repelling random walks where the short-range interaction between two elements of the chain decreases as a power of the difference in proper time. Analytic results on the exponent $\nu$ are obtained. They are in good agreement with Monte Carlo simulations in two dimensions. A numerical study of the scaling functions and of the efficiency of the algorithm is also presented.Comment: 25 pages latex, 4 postscript figures, uses epsf.sty (all included) IFUP-Th 13/92 and SNS 14/9

Chaotic Scattering Theory, Thermodynamic Formalism, and Transport Coefficients

The foundations of the chaotic scattering theory for transport and reaction-rate coefficients for classical many-body systems are considered here in some detail. The thermodynamic formalism of Sinai, Bowen, and Ruelle is employed to obtain an expression for the escape-rate for a phase space trajectory to leave a finite open region of phase space for the first time. This expression relates the escape rate to the difference between the sum of the positive Lyapunov exponents and the K-S entropy for the fractal set of trajectories which are trapped forever in the open region. This result is well known for systems of a few degrees of freedom and is here extended to systems of many degrees of freedom. The formalism is applied to smooth hyperbolic systems, to cellular-automata lattice gases, and to hard sphere sytems. In the latter case, the goemetric constructions of Sinai {\it et al} for billiard systems are used to describe the relevant chaotic scattering phenomena. Some applications of this formalism to non-hyperbolic systems are also discussed.Comment: 35 pages, compressed file, follow directions in header for ps file. Figures are available on request from [email protected]

Dynamic scaling and quasi-ordered states in the two dimensional Swift-Hohenberg equation

The process of pattern formation in the two dimensional Swift-Hohenberg equation is examined through numerical and analytic methods. Dynamic scaling relationships are developed for the collective ordering of convective rolls in the limit of infinite aspect ratio. The stationary solutions are shown to be strongly influenced by the strength of noise. Stationary states for small and large noise strengths appear to be quasi-ordered and disordered respectively. The dynamics of ordering from an initially inhomogeneous state is very slow in the former case and fast in the latter. Both numerical and analytic calculations indicate that the slow dynamics can be characterized by a simple scaling relationship, with a characteristic dynamic exponent of $1/4$ in the intermediate time regime