1,062 research outputs found
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
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
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
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 and transmission 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
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