Perturbation of magnetostatic modes observed by ferromagnetic resonance force microscopy

Magnetostatic modes of yttrium iron garnet (YIG) films are investigated by ferromagnetic resonance force microscopy. A thin-film "probe" magnet at the tip of a compliant cantilever introduces a local inhomogeneity in the internal field of the YIG sample. This influences the shape of the sample's magnetostatic modes, thereby measurably perturbing the strength of the force coupled to the cantilever. We present a theoretical model that explains these observations; it shows that the tip-induced variation of the internal field creates either a local "potential barrier" or "potential well" for the magnetostatic waves. The data and model together indicate that local magnetic imaging of ferromagnets is possible, even in the presence of long-range spin coupling, through the introduction of localized magnetostatic modes predicted to arise from sufficiently strong tip fields

Mean flow and spiral defect chaos in Rayleigh-Benard convection

We describe a numerical procedure to construct a modified velocity field that does not have any mean flow. Using this procedure, we present two results. Firstly, we show that, in the absence of mean flow, spiral defect chaos collapses to a stationary pattern comprising textures of stripes with angular bends. The quenched patterns are characterized by mean wavenumbers that approach those uniquely selected by focus-type singularities, which, in the absence of mean flow, lie at the zig-zag instability boundary. The quenched patterns also have larger correlation lengths and are comprised of rolls with less curvature. Secondly, we describe how mean flow can contribute to the commonly observed phenomenon of rolls terminating perpendicularly into lateral walls. We show that, in the absence of mean flow, rolls begin to terminate into lateral walls at an oblique angle. This obliqueness increases with Rayleigh number.Comment: 14 pages, 19 figure

Kinetics of Ordering in Fluctuation-Driven First-Order Transitions: Simulations and Dynamical Renormalization

Many systems where interactions compete with each other or with constraints are well described by a model first introduced by Brazovskii. Such systems include block copolymers, alloys with modulated phases, Rayleigh-Benard Cells and type-I superconductors. The hallmark of this model is that the fluctuation spectrum is isotropic and has a minimum at a nonzero wave vector represented by the surface of a d-dimensional hyper-sphere. It was shown by Brazovskii that the fluctuations change the free energy structure from a $\phi ^{4}$ to a $\phi ^{6}$ form with the disordered state metastable for all quench depths. The transition from the disordered to the periodic, lamellar structure changes from second order to first order and suggests that the dynamics is governed by nucleation. Using numerical simulations we have confirmed that the equilibrium free energy function is indeed of a $\phi ^{6}$ form. A study of the dynamics, however, shows that, following a deep quench, the dynamics is described by unstable growth rather than nucleation. A dynamical calculation, based on a generalization of the Brazovskii calculations shows that the disordered state can remain unstable for a long time following the quench.Comment: 18 pages, 15 figures submitted to PR

Pattern Formation of Ion Channels with State Dependent Electrophoretic Charges and Diffusion Constants in Fluid Membranes

A model of mobile, charged ion channels in a fluid membrane is studied. The channels may switch between an open and a closed state according to a simple two-state kinetics with constant rates. The effective electrophoretic charge and the diffusion constant of the channels may be different in the closed and in the open state. The system is modeled by densities of channel species, obeying simple equations of electro-diffusion. The lateral transmembrane voltage profile is determined from a cable-type equation. Bifurcations from the homogeneous, stationary state appear as hard-mode, soft-mode or hard-mode oscillatory transitions within physiologically reasonable ranges of model parameters. We study the dynamics beyond linear stability analysis and derive non-linear evolution equations near the transitions to stationary patterns.Comment: 10 pages, 7 figures, will be submitted to Phys. Rev.

Damped finite-time-singularity driven by noise

We consider the combined influence of linear damping and noise on a dynamical finite-time-singularity model for a single degree of freedom. We find that the noise effectively resolves the finite-time-singularity and replaces it by a first-passage-time or absorbing state distribution with a peak at the singularity and a long time tail. The damping introduces a characteristic cross-over time. In the early time regime the probability distribution and first-passage-time distribution show a power law behavior with scaling exponent depending on the ratio of the non linear coupling strength to the noise strength. In the late time regime the behavior is controlled by the damping. The study might be of relevance in the context of hydrodynamics on a nanometer scale, in material physics, and in biophysics.Comment: 9 pages, 4 eps-figures, revtex4 fil

Grain boundary pinning and glassy dynamics in stripe phases

We study numerically and analytically the coarsening of stripe phases in two spatial dimensions, and show that transient configurations do not achieve long ranged orientational order but rather evolve into glassy configurations with very slow dynamics. In the absence of thermal fluctuations, defects such as grain boundaries become pinned in an effective periodic potential that is induced by the underlying periodicity of the stripe pattern itself. Pinning arises without quenched disorder from the non-adiabatic coupling between the slowly varying envelope of the order parameter around a defect, and its fast variation over the stripe wavelength. The characteristic size of ordered domains asymptotes to a finite value $R_g \sim \lambda_0\ \epsilon^{-1/2}\exp(|a|/\sqrt{\epsilon})$, where$\epsilon\ll 1$is the dimensionless distance away from threshold,$\lambda_0$the stripe wavelength, and$a$ a constant of order unity. Random fluctuations allow defect motion to resume until a new characteristic scale is reached, function of the intensity of the fluctuations. We finally discuss the relationship between defect pinning and the coarsening laws obtained in the intermediate time regime.Comment: 17 pages, 8 figures. Corrected version with one new figur

Limit cycle induced by multiplicative noise in a system of coupled Brownian motors

We study a model consisting of $N$ nonlinear oscillators with {\em global periodic} coupling and {\em local multiplicative} and additive noises. The model was shown to undergo a nonequilibrium phase transition towards a broken-symmetry phase exhibiting noise-induced "ratchet" behavior. A previous study \cite{[7]} focused on the relationship between the character of thehysteresis loop, the number of ``homogeneous'' mean-field solutions and the shape of the stationary mean-field probability distribution function. Here we show --as suggested by the absence of stable solutions when the load force is beyond a critical value-- the existence of a limit cycle induced by both:multiplicative noise and {\em global periodic} coupling.Comment: Submitted to Phys. Rev. E, RevTex, 18 pgs, 5 figure

Dynamics of systems with isotropic competing interactions in an external field: a Langevin approach

We study the Langevin dynamics of a ferromagnetic Ginzburg-Landau Hamiltonian with a competing long-range repulsive term in the presence of an external magnetic field. The model is analytically solved within the self consistent Hartree approximation for two different initial conditions: disordered or zero field cooled (ZFC), and fully magnetized or field cooled (FC). To test the predictions of the approximation we develop a suitable numerical scheme to ensure the isotropic nature of the interactions. Both the analytical approach and the numerical simulations of two-dimensional finite systems confirm a simple aging scenario at zero temperature and zero field. At zero temperature a critical field $h_c$ is found below which the initial conditions are relevant for the long time dynamics of the system. For $h < h_c$ a logarithmic growth of modulated domains is found in the numerical simulations but this behavior is not captured by the analytical approach which predicts a $t^1/2$ growth law at $T = 0$

Dynamics of fluctuations in a fluid below the onset of Rayleigh-B\'enard convection

We present experimental data and their theoretical interpretation for the decay rates of temperature fluctuations in a thin layer of a fluid heated from below and confined between parallel horizontal plates. The measurements were made with the mean temperature of the layer corresponding to the critical isochore of sulfur hexafluoride above but near the critical point where fluctuations are exceptionally strong. They cover a wide range of temperature gradients below the onset of Rayleigh-B\'enard convection, and span wave numbers on both sides of the critical value for this onset. The decay rates were determined from experimental shadowgraph images of the fluctuations at several camera exposure times. We present a theoretical expression for an exposure-time-dependent structure factor which is needed for the data analysis. As the onset of convection is approached, the data reveal the critical slowing-down associated with the bifurcation. Theoretical predictions for the decay rates as a function of the wave number and temperature gradient are presented and compared with the experimental data. Quantitative agreement is obtained if allowance is made for some uncertainty in the small spacing between the plates, and when an empirical estimate is employed for the influence of symmetric deviations from the Oberbeck-Boussinesq approximation which are to be expected in a fluid with its density at the mean temperature located on the critical isochore.Comment: 13 pages, 10 figures, 52 reference