1,681 research outputs found
Comment on ``Connection between the Burgers equation with an elastic forcing term and a stochastic process''
In the above mentioned paper by E. Moreau and O. Vall\'{e}e [Phys. Rev. {\bf
E 73}, 016112, (2006)], the one-dimensional Burgers equation with an elastic
(attractive) forcing term has been claimed to be connected with the
Ornstein-Uhlenbeck process. We point out that this connection is valid only in
case of the repulsive forcing.Comment: Phys. Rev. E Commen
The Brownian gyrator: a minimal heat engine on the nano-scale
A Brownian particle moving in the vicinity of a generic potential minimum
under the influence of dissipation and thermal noise from two different heat
baths is shown to act as a minimal heat engine, generating a systematic torque
onto the physical object at the origin of the potential and an opposite torque
onto the medium generating the dissipation.Comment: Phys. Rev. Lett., in pres
Nonequilibrium Steady State Driven by a Nonlinear Drift Force
We investigate the properties of the nonequilibrium steady state for the
stochastic system driven by a nonlinear drift force and influenced by noises
which are not identically and independently distributed. The nonequilibrium
steady state (NESS) current results from a residual part of the drift force
which is not cancelled by the diffusive action of noises. From our previous
study for the linear drift force the NESS current was found to circulate on the
equiprobability surface with the maximum at a stable fixed point of the drift
force. For the nonlinear drift force, we use the perturbation theory with
respect to the cubic and quartic coefficients of the drift force. We find an
interesting potential landscape picture where the probability maximum shifts
from the fixed point of the drift force and, furthermore, the NESS current has
a nontrivial circulation which flows off the equiprobability surface and has
various centers not located at the probability maximum. The theoretical result
is well confirmed by the computer simulation.Comment: 10 pages, 4 figure
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.
Jamming at zero temperature, zero friction, and finite applied shear stress
Via molecular dynamics simulations, we unveil the hysteretic nature of the
jamming transition of soft repulsive frictionless spheres, as it occurs varying
the volume fraction or the shear stress. In a given range of control parameters
the system may be found both in a flowing and in an jammed state, depending on
the preparation protocol. The hysteresis is due to an underlying energy
landscape with many minima, as explained by a simple model, and disappears in
the presence of strong viscous forces and in the small limit. In this
limit, structural quantities are continuous at the transition, while the
asymptotic values of two time quantities such as the self-intermediate
scattering function are discontinuous, giving to the jamming transition a mixed
first-order second-order character close to that found at the glass transition
of thermal systems
Steering the potential barriers: entropic to energetic
We propose a new mechanism to alter the nature of the potential barriers when
a biased Brownian particle under goes a constrained motion in narrow, periodic
channel. By changing the angle of the external bias, the nature of the
potential barriers changes from purely entropic to energetic which in turn
effects the diffusion process in the system. At an optimum angle of the bias,
the nonlinear mobility exhibits a striking bell-shaped behavior. Moreover, the
enhancement of the scaled effective diffusion coefficient can be efficiently
controlled by the angle of the bias. This mechanism enables the proper design
of channel structures for transport of molecules and small particles. The
approximative analytical predictions have been verified by precise Brownian
dynamic simulations.Comment: (6 pages, 7 figures) Submitted to PR
Detecting charge noise with a Josephson junction: A problem of thermal escape in presence of non-Gaussian fluctuations
Motivated by several experimental activities to detect charge noise produced
by a mesoscopic conductor with a Josephson junction as on-chip detector, the
switching rate out of its zero-voltage state is studied. This process is
related to the fundamental problem of thermal escape in presence of
non-Gaussian fluctuations. In the relevant case of weak higher than second
order cumulants, an effective Fokker-Planck equation is derived, which is then
used to obtain an explicit expression for the escape rate. Specific results for
the rate asymmetry due to the third moment of current noise allow to analyse
experimental data and to optimize detection circuits.Comment: 4 pages, 1 figure; minor typos corrected, some revisions in the tex
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
Separation of suspended particles by arrays of obstacles in microfluidic devices
The stochastic transport of suspended particles through a periodic pattern of
obstacles in microfluidic devices is investigated by means of the Fokker-Planck
equation. Asymmetric arrays of obstacles have been shown to induce the
continuous separation of DNA molecules of different length. The analysis
presented here of the asymptotic distribution of particles in a unit cell of
these systems shows that separation is only possible in the presence of a
driving force with a non-vanishing normal component at the surface of the solid
obstacles. In addition, vector separation, in which different species move, in
average, in different directions within the device, is driven by differences on
the force acting on the various particles and not by differences in the
diffusion coefficient. Monte-Carlo simulations performed for different
particles and force fields agree with the numerical solutions of the
Fokker-Planck equation in the periodic system
Drift without flux: Brownian walker with a space dependent diffusion coefficient
Space dependent diffusion of micrometer sized particles has been directly
observed using digital video microscopy. The particles were trapped between two
nearly parallel walls making their confinement position dependent.
Consequently, not only did we measure a diffusion coefficient which depended on
the particles' position, but also report and explain a new effect: a drift of
the particles' individual positions in the direction of the diffusion
coefficient gradient, in the absence of any external force or concentration
gradient.Comment: 4 pages, 4 ps figures, include
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