151 research outputs found
Stick-slip motion of solids with dry friction subject to random vibrations and an external field
We investigate a model for the dynamics of a solid object, which moves over a
randomly vibrating solid surface and is subject to a constant external force.
The dry friction between the two solids is modeled phenomenologically as being
proportional to the sign of the object's velocity relative to the surface, and
therefore shows a discontinuity at zero velocity. Using a path integral
approach, we derive analytical expressions for the transition probability of
the object's velocity and the stationary distribution of the work done on the
object due to the external force. From the latter distribution, we also derive
a fluctuation relation for the mechanical work fluctuations, which incorporates
the effect of the dry friction.Comment: v1: 23 pages, 9 figures; v2: Reference list corrected; v3: Published
version, typos corrected, references adde
Joint Probability Distributions for a Class of Non-Markovian Processes
We consider joint probability distributions for the class of coupled Langevin
equations introduced by Fogedby [H.C. Fogedby, Phys. Rev. E 50, 1657 (1994)].
We generalize well-known results for the single time probability distributions
to the case of N-time joint probability distributions. It is shown that these
probability distribution functions can be obtained by an integral transform
from distributions of a Markovian process. The integral kernel obeys a partial
differential equation with fractional time derivatives reflecting the
non-Markovian character of the process.Comment: 13 pages, 1 figur
Nonequilibrium statistical mechanics of shear flow: invariant quantities and current relations
In modeling nonequilibrium systems one usually starts with a definition of
the microscopic dynamics, e.g., in terms of transition rates, and then derives
the resulting macroscopic behavior. We address the inverse question for a class
of steady state systems, namely complex fluids under continuous shear flow: how
does an externally imposed shear current affect the microscopic dynamics of the
fluid? The answer can be formulated in the form of invariant quantities, exact
relations for the transition rates in the nonequilibrium steady state, as
discussed in a recent letter [A. Baule and R. M. L. Evans, Phys. Rev. Lett.
101, 240601 (2008)]. Here, we present a more pedagogical account of the
invariant quantities and the theory underlying them, known as the
nonequilibrium counterpart to detailed balance (NCDB). Furthermore, we
investigate the relationship between the transition rates and the shear current
in the steady state. We show that a fluctuation relation of the
Gallavotti-Cohen type holds for systems satisfying NCDB.Comment: 24 pages, 11 figure
Path integral approach to random motion with nonlinear friction
Using a path integral approach, we derive an analytical solution of a
nonlinear and singular Langevin equation, which has been introduced previously
by P.-G. de Gennes as a simple phenomenological model for the stick-slip motion
of a solid object on a vibrating horizontal surface. We show that the optimal
(or most probable) paths of this model can be divided into two classes of
paths, which correspond physically to a sliding or slip motion, where the
object moves with a non-zero velocity over the underlying surface, and a
stick-slip motion, where the object is stuck to the surface for a finite time.
These two kinds of basic motions underlie the behavior of many more complicated
systems with solid/solid friction and appear naturally in de Gennes' model in
the path integral framework.Comment: 18 pages, 3 figure
Brownian motion with dry friction: Fokker-Planck approach
We solve a Langevin equation, first studied by de Gennes, in which there is a
solid-solid or dry friction force acting on a Brownian particle in addition to
the viscous friction usually considered in the study of Brownian motion. We
obtain both the time-dependent propagator of this equation and the velocity
correlation function by solving the associated time-dependent Fokker-Planck
equation. Exact results are found for the case where only dry friction acts on
the particle. For the case where both dry and viscous friction forces are
present, series representations of the propagator and correlation function are
obtained in terms of parabolic cylinder functions. Similar series
representations are also obtained for the case where an external constant force
is added to the Langevin equation.Comment: 18 pages, 13 figures (in color
Single particle tracking in systems showing anomalous diffusion: the role of weak ergodicity breaking
Anomalous diffusion has been widely observed by single particle tracking
microscopy in complex systems such as biological cells. The resulting time
series are usually evaluated in terms of time averages. Often anomalous
diffusion is connected with non-ergodic behaviour. In such cases the time
averages remain random variables and hence irreproducible. Here we present a
detailed analysis of the time averaged mean squared displacement for systems
governed by anomalous diffusion, considering both unconfined and restricted
(corralled) motion. We discuss the behaviour of the time averaged mean squared
displacement for two prominent stochastic processes, namely, continuous time
random walks and fractional Brownian motion. We also study the distribution of
the time averaged mean squared displacement around its ensemble mean, and show
that this distribution preserves typical process characteristic even for short
time series. Recently, velocity correlation functions were suggested to
distinguish between these processes. We here present analytucal expressions for
the velocity correlation functions. Knowledge of the results presented here are
expected to be relevant for the correct interpretation of single particle
trajectory data in complex systems.Comment: 15 pages, 15 figures; References adde
On distributions of functionals of anomalous diffusion paths
Functionals of Brownian motion have diverse applications in physics,
mathematics, and other fields. The probability density function (PDF) of
Brownian functionals satisfies the Feynman-Kac formula, which is a Schrodinger
equation in imaginary time. In recent years there is a growing interest in
particular functionals of non-Brownian motion, or anomalous diffusion, but no
equation existed for their PDF. Here, we derive a fractional generalization of
the Feynman-Kac equation for functionals of anomalous paths based on
sub-diffusive continuous-time random walk. We also derive a backward equation
and a generalization to Levy flights. Solutions are presented for a wide number
of applications including the occupation time in half space and in an interval,
the first passage time, the maximal displacement, and the hitting probability.
We briefly discuss other fractional Schrodinger equations that recently
appeared in the literature.Comment: 25 pages, 4 figure
Feynman-Kac equation for anomalous processes with space-and time-dependent forces
Invited contribution to the J. Phys. A special issue Emerging Talent
Sensitivity of MEG and EEG to Source Orientation
An important difference between magnetoencephalography
(MEG) and electroencephalography (EEG)
is that MEG is insensitive to radially oriented sources. We
quantified computationally the dependency of MEG and
EEG on the source orientation using a forward model with
realistic tissue boundaries. Similar to the simpler case of a
spherical head model, in which MEG cannot see radial
sources at all, for most cortical locations there was a source
orientation to which MEG was insensitive. The median
value for the ratio of the signal magnitude for the source
orientation of the lowest and the highest sensitivity was
0.06 for MEG and 0.63 for EEG. The difference in the
sensitivity to the source orientation is expected to contribute
to systematic differences in the signal-to-noise ratio
between MEG and EEG.National Institutes of Health (U.S.) (Grant NS057500)National Institutes of Health (U.S.) (Grant NS037462)National Institutes of Health (U.S.) (Grant HD040712)National Center for Research Resources (U.S.) (P41RR14075)Mind Research Networ
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