Geometric and projection effects in Kramers-Moyal analysis

Kramers-Moyal coefficients provide a simple and easily visualized method with which to analyze stochastic time series, particularly nonlinear ones. One mechanism that can affect the estimation of the coefficients is geometric projection effects. For some biologically-inspired examples, these effects are predicted and explored with a non-stochastic projection operator method, and compared with direct numerical simulation of the systems' Langevin equations. General features and characteristics are identified, and the utility of the Kramers-Moyal method discussed. Projections of a system are in general non-Markovian, but here the Kramers-Moyal method remains useful, and in any case the primary examples considered are found to be close to Markovian.Comment: Submitted to Phys. Rev.

Exact corrections for finite-time drift and diffusion coefficients

Real data are constrained to finite sampling rates, which calls for a suitable mathematical description of the corrections to the finite-time estimations of the dynamic equations. Often in the literature, lower order discrete time approximations of the modeling diffusion processes are considered. On the other hand, there is a lack of simple estimating procedures based on higher order approximations. For standard diffusion models, that include additive and multiplicative noise components, we obtain the exact corrections to the empirical finite-time drift and diffusion coefficients, based on It\^o-Taylor expansions. These results allow to reconstruct the real hidden coefficients from the empirical estimates. We also derive higher-order finite-time expressions for the third and fourth conditional moments, that furnish extra theoretical checks for that class of diffusive models. The theoretical predictions are compared with the numerical outcomes of some representative artificial time-series.Comment: 18 pages, 5 figure

Analysis of stochastic time series in the presence of strong measurement noise

A new approach for the analysis of Langevin-type stochastic processes in the presence of strong measurement noise is presented. For the case of Gaussian distributed, exponentially correlated, measurement noise it is possible to extract the strength and the correlation time of the noise as well as polynomial approximations of the drift and diffusion functions from the underlying Langevin equation.Comment: 12 pages, 10 figures; corrected typos and reference

Phase space dynamics of overdamped quantum systems

The phase space dynamics of dissipative quantum systems in strongly condensed phase is considered. Based on the exact path integral approach it is shown that the Wigner transform of the reduced density matrix obeys a time evolution equation of Fokker-Planck type valid from high down to very low temperatures. The effect of quantum fluctuations is discussed and the accuracy of these findings is tested against exact data for a harmonic system.Comment: 7 pages, 2 figures, to appear in Euro. Phys. Let

Creep of current-driven domain-wall lines: intrinsic versus extrinsic pinning

We present a model for current-driven motion of a magnetic domain-wall line, in which the dynamics of the domain wall is equivalent to that of an overdamped vortex line in an anisotropic pinning potential. This potential has both extrinsic contributions due to, e.g., sample inhomogeneities, and an intrinsic contribution due to magnetic anisotropy. We obtain results for the domain-wall velocity as a function of current for various regimes of pinning. In particular, we find that the exponent characterizing the creep regime depends strongly on the presence of a dissipative spin transfer torque. We discuss our results in the light of recent experiments on current-driven domain-wall creep in ferromagnetic semiconductors, and suggest further experiments to corroborate our model.Comment: For figure in GIF format, see http://www.phys.uu.nl/~duine/mapping.gif v2: (hopefully) visible EPS figure added. v2: expanded new versio

Collective motion of binary self-propelled particle mixtures

In this study, we investigate the phenomenon of collective motion in binary mixtures of self-propelled particles. We consider two particle species, each of which consisting of pointlike objects that propel with a velocity of constant magnitude. Within each species, the particles try to achieve polar alignment of their velocity vectors, whereas we analyze the cases of preferred polar, antiparallel, as well as perpendicular alignment between particles of different species. Our focus is on the effect that the interplay between the two species has on the threshold densities for the onset of collective motion and on the nature of the solutions above onset. For this purpose, we start from suitable Langevin equations in the particle picture, from which we derive mean field equations of the Fokker-Planck type and finally macroscopic continuum field equations. We perform particle simulations of the Langevin equations, linear stability analyses of the Fokker-Planck and macroscopic continuum equations, and we numerically solve the Fokker-Planck equations. Both, spatially homogeneous and inhomogeneous solutions are investigated, where the latter correspond to stripe-like flocks of collectively moving particles. In general, the interaction between the two species reduces the threshold density for the onset of collective motion of each species. However, this interaction also reduces the spatial organization in the stripe-like flocks. The most interesting behavior is found for the case of preferred perpendicular alignment between different species. There, a competition between polar and truly nematic orientational ordering of the velocity vectors takes place within each particle species. Finally, depending on the alignment rule for particles of different species and within certain ranges of particle densities, identical and inverted spatial density profiles can be found for the two particle species.Comment: 16 pages, 10 figure

Noise-induced dynamical transition in systems with symmetric absorbing states

We investigate the effect of noise strength on the macroscopic ordering dynamics of systems with symmetric absorbing states. Using an explicit stochastic microscopic model, we present evidence for a phase transition in the coarsening dynamics, from an Ising-like to a voter-like behavior, as the noise strength is increased past a nontrivial critical value. By mapping to a thermal diffusion process, we argue that the transition arises due to locally-absorbing states being entered more readily in the high-noise regime, which in turn prevents surface tension from driving the ordering process.Comment: v2 with improved introduction and figures, to appear in PRL. 4 pages, 4 figure

Thermally-Assisted Current-Driven Domain Wall Motion

Starting from the stochastic Landau-Lifschitz-Gilbert equation, we derive Langevin equations that describe the nonzero-temperature dynamics of a rigid domain wall. We derive an expression for the average drift velocity of the domain wall as a function of the applied current, and find qualitative agreement with recent magnetic semiconductor experiments. Our model implies that at any nonzero temperature the average domain-wall velocity initially varies linearly with current, even in the absence of non-adiabatic spin torques.Comment: 4 pages, 2 figure

Theory of Single File Diffusion in a Force Field

The dynamics of hard-core interacting Brownian particles in an external potential field is studied in one dimension. Using the Jepsen line we find a very general and simple formula relating the motion of the tagged center particle, with the classical, time dependent single particle reflection ${\cal R}$ and transmission ${\cal T}$ coefficients. Our formula describes rich physical behaviors both in equilibrium and the approach to equilibrium of this many body problem.Comment: 4 Phys. Rev. page

Role of an intermediate state in homogeneous nucleation

We explore the role of an intermediate state (phase) in homogeneous nucleation phenomenon by examining the decay process through a doubly-humped potential barrier. As a generic model we use the fourth- and sixth-order Landau potentials and analyze the Fokker-Planck equation for the one-dimensional thermal diffusion in the system characterized by a triple-well potential. In the low temperature case we apply the WKB method to the decay process and obtain the decay rate which is accurate for a wide range of depth and curvature of the middle well. In the case of a deep middle well, it reduces to a doubly-humped-barrier counterpart of the Kramers escape rate: the barrier height and the curvature of an initial well in the Kramers rate are replaced by the arithmetic mean of higher(or outer) and lower(or inner) partial barriers and the geometric mean of curvatures of the initial and intermediate wells, respectively. It seems to be a universal formula. In the case of a shallow-enough middle well, Kramers escape rate is alternatively evaluated within the standard framework of the mean-first-passage time problem, which certainly supports the WKB result. The criteria whether or not the existence of an intermediate state can enhance the decay rate are revealed.Comment: 9pages, 11figure