1,056 research outputs found
Transient rectification of Brownian diffusion with asymmetric initial distribution
In an ensemble of non-interacting Brownian particles, a finite systematic
average velocity may temporarily develop, even if it is zero initially. The
effect originates from a small nonlinear correction to the dissipative force,
causing the equation for the first moment of velocity to couple to moments of
higher order. The effect may be relevant when a complex system dissociates in a
viscous medium with conservation of momentum
Fidelity of holonomic quantum computations in the case of random errors in the values of control parameters
We investigate the influence of random errors in external control parameters
on the stability of holonomic quantum computation in the case of arbitrary
loops and adiabatic connections. A simple expression is obtained for the case
of small random uncorrelated errors. Due to universality of mathematical
description our results are valid for any physical system which can be
described in terms of holonomies. Theoretical results are confirmed by
numerical simulations.Comment: 7 pages, 3 figure
Generalized Fokker-Planck equation, Brownian motion, and ergodicity
Microscopic theory of Brownian motion of a particle of mass in a bath of
molecules of mass is considered beyond lowest order in the mass ratio
. The corresponding Langevin equation contains nonlinear corrections to
the dissipative force, and the generalized Fokker-Planck equation involves
derivatives of order higher than two. These equations are derived from first
principles with coefficients expressed in terms of correlation functions of
microscopic force on the particle. The coefficients are evaluated explicitly
for a generalized Rayleigh model with a finite time of molecule-particle
collisions. In the limit of a low-density bath, we recover the results obtained
previously for a model with instantaneous binary collisions. In general case,
the equations contain additional corrections, quadratic in bath density,
originating from a finite collision time. These corrections survive to order
and are found to make the stationary distribution non-Maxwellian.
Some relevant numerical simulations are also presented
How accurate are the non-linear chemical Fokker-Planck and chemical Langevin equations?
The chemical Fokker-Planck equation and the corresponding chemical Langevin
equation are commonly used approximations of the chemical master equation.
These equations are derived from an uncontrolled, second-order truncation of
the Kramers-Moyal expansion of the chemical master equation and hence their
accuracy remains to be clarified. We use the system-size expansion to show that
chemical Fokker-Planck estimates of the mean concentrations and of the variance
of the concentration fluctuations about the mean are accurate to order
for reaction systems which do not obey detailed balance and at
least accurate to order for systems obeying detailed balance,
where is the characteristic size of the system. Hence the chemical
Fokker-Planck equation turns out to be more accurate than the linear-noise
approximation of the chemical master equation (the linear Fokker-Planck
equation) which leads to mean concentration estimates accurate to order
and variance estimates accurate to order . This
higher accuracy is particularly conspicuous for chemical systems realized in
small volumes such as biochemical reactions inside cells. A formula is also
obtained for the approximate size of the relative errors in the concentration
and variance predictions of the chemical Fokker-Planck equation, where the
relative error is defined as the difference between the predictions of the
chemical Fokker-Planck equation and the master equation divided by the
prediction of the master equation. For dimerization and enzyme-catalyzed
reactions, the errors are typically less than few percent even when the
steady-state is characterized by merely few tens of molecules.Comment: 39 pages, 3 figures, accepted for publication in J. Chem. Phy
Coarse grained dynamics of the freely cooling granular gas in one dimension
We study the dynamics and structure of clusters in the inhomogeneous
clustered regime of a freely cooling granular gas of point particles in one
dimension. The coefficient of restitution is modeled as or 1 depending
on whether the relative speed is greater or smaller than a velocity scale
. The effective fragmentation rate of a cluster is shown to rise
sharply beyond a dependent time scale. This crossover is coincident
with the velocity fluctuations within a cluster becoming order . Beyond
this crossover time, the cluster size distribution develops a nontrivial power
law distribution, whose scaling properties are related to those of the velocity
fluctuations. We argue that these underlying features are responsible behind
the recently observed nontrivial coarsening behaviour in the one dimensional
freely cooling granular gas.Comment: 7 Pages, 9 Figure
Stochastic dynamics beyond the weak coupling limit: thermalization
We discuss the structure and asymptotic long-time properties of coupled
equations for the moments of a Brownian particle's momentum derived
microscopically beyond the lowest approximation in the weak coupling parameter.
Generalized fluctuation-dissipation relations are derived and shown to ensure
convergence to thermal equilibrium at any order of perturbation theory.Comment: 6+ page
Positive Feedback Regulation Results in Spatial Clustering and Fast Spreading of Active Signaling Molecules on a Cell Membrane
Positive feedback regulation is ubiquitous in cell signaling networks, often
leading to binary outcomes in response to graded stimuli. However, the role of
such feedbacks in clustering, and in spatial spreading of activated molecules,
has come to be appreciated only recently. We focus on the latter, using a
simple model developed in the context of Ras activation with competing negative
and positive feedback mechanisms. We find that positive feedback, in the
presence of slow diffusion, results in clustering of activated molecules on the
plasma membrane, and rapid spatial spreading as the front of the cluster
propagates with a constant velocity (dependent on the feedback strength). The
advancing fronts of the clusters of the activated species are rough, with
scaling consistent with the Kardar-Parisi-Zhang (KPZ) equation in one
dimension. Our minimal model is general enough to describe signal transduction
in a wide variety of biological networks where activity in the
membrane-proximal region is subject to feedback regulation.Comment: 37 pages, 8 figures. Journal of Chemical Physics (in press
The Accuracy of Perturbative Master Equations
We consider open quantum systems with dynamics described by master equations
that have perturbative expansions in the system-environment interaction. We
show that, contrary to intuition, full-time solutions of order-2n accuracy
require an order-(2n+2) master equation. We give two examples of such
inaccuracies in the solutions to an order-2n master equation: order-2n
inaccuracies in the steady state of the system and order-2n positivity
violations, and we show how these arise in a specific example for which exact
solutions are available. This result has a wide-ranging impact on the validity
of coupling (or friction) sensitive results derived from second-order
convolutionless, Nakajima-Zwanzig, Redfield, and Born-Markov master equations.Comment: 6 pages, 0 figures; v2 updated references; v3 updated references,
extension to full-time and nonlocal regime
Intermittent quakes and record dynamics in the thermoremanent magnetization of a spin-glass
A novel method for analyzing the intermittent behavior of linear response
data in aging systems is presented and applied to spin-glass thermoremanent
magnetization (TRM) (Rodriguez et al. Phys. Rev. Lett. 91, 037203, 2003).
The probability density function (PDF) of magnetic fluctuations is shown to
have an asymmetric exponential tail, demonstrating that the demagnetization
process is carried by intermittent, significant, spin rearrangements or
\emph{quakes}. These quakes are most pronounced shortly after the field
removal, and in the non-equilibrium aging regime .
For a broad temperature range, we study the dependence of the TRM decay rate on
, the time since the initial quench and on , the time at which the
magnetic field is cut. The and dependence of the rate is extracted
numerically from the data and described analytically using the assumption that
the linear response is subordinated to the intermittent process which
spasmodically release the initial imbalances created by the quench.Comment: 8 pages, 9 figures. The paper has been expanded and restructured, the
figures have been enlarged and improved. Final version, to appear in Phy.
Rev.
Demographic growth and the distribution of language sizes
It is argued that the present log-normal distribution of language sizes is,
to a large extent, a consequence of demographic dynamics within the population
of speakers of each language. A two-parameter stochastic multiplicative process
is proposed as a model for the population dynamics of individual languages, and
applied over a period spanning the last ten centuries. The model disregards
language birth and death. A straightforward fitting of the two parameters,
which statistically characterize the population growth rate, predicts a
distribution of language sizes in excellent agreement with empirical data.
Numerical simulations, and the study of the size distribution within language
families, validate the assumptions at the basis of the model.Comment: To appear in Int. J. Mod. Phys. C (2008
- …