2,550 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

### Momentum conservation and correlation analyses in heavy-ion collisions at ultrarelativistic energies

Global transverse-momentum conservation induces correlations between any
number of particles, which contribute in particular to the two- and
three-particle correlations measured in heavy-ion collisions. These
correlations are examined in detail, and their importance for studies of jets
and their interaction with the medium is discussed.Comment: 5 pages, 2 figures. v2: corrected typos and added a paragrap

### Statistics of 3-dimensional Lagrangian turbulence

We consider a superstatistical dynamical model for the 3-d movement of a
Lagrangian tracer particle embedded in a high-Reynolds number turbulent flow.
The analytical model predictions are in excellent agreement with recent
experimental data for flow between counter-rotating disks. In particular, we
calculate the Lagrangian scaling exponents zeta_j for our system, and show that
they agree well with the measured exponents reported in [X. Hu et al., PRL 96,
114503 (2006)]. Moreover, the model correctly predicts the shape of velocity
difference and acceleration probability densities, the fast decay of component
correlation functions and the slow decay of the modulus, as well as the
statistical dependence between acceleration components. Finally, the model
explains the numerically [P.K. Yeung and S.B. Pope, J. Fluid Mech. 207, 531
(1989)] and experimentally observed fact [B.W. Zeff et al., Nature 421, 146
(2003)] that enstrophy lags behind dissipation.Comment: 5 pages, 3 figures. Replaced by final version accepted by Phys. Rev.
Let

### 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

### A new modelling framework for statistical cumulus dynamics

We propose a new modelling framework suitable for the description of atmospheric convective systems as a collection of distinct plumes. The literature contains many examples of models for collections of plumes in which strong simplifying assumptions are made, a diagnostic dependence of convection on the large-scale environment and the limit of many plumes often being imposed from the outset. Some recent studies have sought to remove one or the other of those assumptions. The proposed framework removes both, and is explicitly time-dependent and stochastic in its basic character. The statistical dynamics of the plume collection are defined through simple probabilistic rules applied at the level of individual plumes, and van Kampen's system size expansion is then used to construct the macroscopic limit of the microscopic model. Through suitable choices of the microscopic rules, the model is shown to encompass previous studies in the appropriate limits, and to allow their natural extensions beyond those limits

### A generalization of the cumulant expansion. Application to a scale-invariant probabilistic model

As well known, cumulant expansion is an alternative way to moment expansion
to fully characterize probability distributions provided all the moments exist.
If this is not the case, the so called escort mean values (or q-moments) have
been proposed to characterize probability densities with divergent moments [C.
Tsallis et al, J. Math. Phys 50, 043303 (2009)]. We introduce here a new
mathematical object, namely the q-cumulants, which, in analogy to the
cumulants, provide an alternative characterization to that of the q-moments for
the probability densities. We illustrate this new scheme on a recently proposed
family of scale-invariant discrete probabilistic models [A. Rodriguez et al, J.
Stat. Mech. (2008) P09006; R. Hanel et al, Eur. Phys. J. B 72, 263268 (2009)]
having q-Gaussians as limiting probability distributions

### Generalized Fokker-Planck equation, Brownian motion, and ergodicity

Microscopic theory of Brownian motion of a particle of mass $M$ in a bath of
molecules of mass $m\ll M$ is considered beyond lowest order in the mass ratio
$m/M$. 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
$(m/M)^2$ and are found to make the stationary distribution non-Maxwellian.
Some relevant numerical simulations are also presented

### On-off intermittency over an extended range of control parameter

We propose a simple phenomenological model exhibiting on-off intermittency
over an extended range of control parameter. We find that the distribution of
the 'off' periods has as a power-law tail with an exponent varying continuously
between -1 and -2, at odds with standard on-off intermittency which occurs at a
specific value of the control parameter, and leads to the exponent -3/2. This
non-trivial behavior results from the competition between a strong slowing down
of the dynamics at small values of the observable, and a systematic drift
toward large values.Comment: 4 pages, 3 figure

### DERIVATION OF NONLINEAR ONSAGER RELATIONS FROM STATISTICAL MECHANICS

The long road that starts from the microscopic equations of motion and ends with the
phenomenological equations of the experimenter. is sketched. One type of system leads
to nonlinear macroscopic equations, but no reciprocal relations are found. The other type
(called diffusive type) leads to a nonlinear Fokker-Planck equation. For low temperature
the fluctuations are small and one is left with a set of non linear deterministic equations.
They obey the Onsager-Casimir relations

### 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

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