2,401 research outputs found
Long delay times in reaction rates increase intrinsic fluctuations
In spatially distributed cellular systems, it is often convenient to
represent complicated auxiliary pathways and spatial transport by time-delayed
reaction rates. Furthermore, many of the reactants appear in low numbers
necessitating a probabilistic description. The coupling of delayed rates with
stochastic dynamics leads to a probability conservation equation characterizing
a non-Markovian process. A systematic approximation is derived that
incorporates the effect of delayed rates on the characterization of molecular
noise, valid in the limit of long delay time. By way of a simple example, we
show that delayed reaction dynamics can only increase intrinsic fluctuations
about the steady-state. The method is general enough to accommodate nonlinear
transition rates, allowing characterization of fluctuations around a
delay-induced limit cycle.Comment: 8 pages, 3 figures, to be published in Physical Review
Dark matter density profiles: A comparison of nonextensive theory with N-body simulations
Density profiles of simulated galaxy cluster-sized dark matter haloes are
analysed in the context of a recently introduced nonextensive theory of dark
matter and gas density distributions. Nonextensive statistics accounts for
long-range interactions in gravitationally coupled systems and is derived from
the fundamental concept of entropy generalisation. The simulated profiles are
determined down to radii of ~1% of R_200. The general trend of the relaxed,
spherically averaged profiles is accurately reproduced by the theory. For the
main free parameter kappa, measuring the degree of coupling within the system,
and linked to physical quantities as the heat capacity and the polytropic index
of the self-gravitating ensembles, we find a value of -15. The significant
advantage over empirical fitting functions is provided by the physical content
of the nonextensive approach.Comment: 6 pages, 3 figures, accepted for publication in A&
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
Analytical results for a Fokker-Planck equation in the small noise limit
We present analytical results for the lowest cumulants of a stochastic
process described by a Fokker-Planck equation with nonlinear drift. We show
that, in the limit of small fluctuations, the mean, the variance and the
covariance of the process can be expressed in compact form with the help of the
Lambert W function. As an application, we discuss the interplay of noise and
nonlinearity far from equilibrium.Comment: 5 pages, 4 figure
A variational approach to moment-closure approximations for the kinetics of biomolecular reaction networks
Approximate solutions of the chemical master equation and the chemical
Fokker-Planck equation are an important tool in the analysis of biomolecular
reaction networks. Previous studies have highlighted a number of problems with
the moment-closure approach used to obtain such approximations, calling it an
ad-hoc method. In this article, we give a new variational derivation of
moment-closure equations which provides us with an intuitive understanding of
their properties and failure modes and allows us to correct some of these
problems. We use mixtures of product-Poisson distributions to obtain a flexible
parametric family which solves the commonly observed problem of divergences at
low system sizes. We also extend the recently introduced entropic matching
approach to arbitrary ansatz distributions and Markov processes, demonstrating
that it is a special case of variational moment closure. This provides us with
a particularly principled approximation method. Finally, we extend the above
approaches to cover the approximation of multi-time joint distributions,
resulting in a viable alternative to process-level approximations which are
often intractable.Comment: Minor changes and clarifications; corrected some typo
Classical no-cloning theorem under Liouville dynamics by non-Csisz\'ar f-divergence
The Csisz\'ar f-divergence, which is a class of information distances, is
known to offer a useful tool for analysing the classical counterpart of the
cloning operations that are quantum mechanically impossible for the factorized
and marginality classical probability distributions under Liouville dynamics.
We show that a class of information distances that does not belong to this
divergence class also allows for the formulation of a classical analogue of the
quantum no-cloning theorem. We address a family of nonlinear Liouville-like
equations, and generic distances, to obtain constraints on the corresponding
functional forms, associated with the formulation of classical analogue of the
no-cloning principle.Comment: 6 pages, revised, published versio
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
A new view of the spin echo diffusive diffraction on porous structures
Analysis with the characteristic functional of stochastic motion is used for
the gradient spin echo measurement of restricted motion to clarify details of
the diffraction-like effect in a porous structure. It gives the diffusive
diffraction as an interference of spin phase shifts due to the back-flow of
spins bouncing at the boundaries, when mean displacement of scattered spins is
equal to the spin phase grating prepared by applied magnetic field gradients.
The diffraction patterns convey information about morphology of the surrounding
media at times long enough that opposite boundaries are restricting
displacements. The method explains the dependence of diffraction on the time
and width of gradient pulses, as observed at the experiments and the
simulations. It also enlightens the analysis of transport properties by the
spin echo, particularly in systems, where the motion is restricted by structure
or configuration
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
Local Quasiconvexity of Groups acting on Small Cancellation Complexes
Given a group acting cellularly and cocompactly on a simply-connected
2-complex, we provide a criterion establishing that all finitely generated
subgroups have quasiconvex orbits. This work generalizes the "perimeter
method". As an application, we show that high-powered one-relator products A
\ast B / \nclose{r^n} are coherent if and are coherent.Comment: version 1. 14 pages, 4 figure
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