345 research outputs found

### Fluctuation relation for a L\'evy particle

We study the work fluctuations of a particle subjected to a deterministic
drag force plus a random forcing whose statistics is of the L\'evy type. In the
stationary regime, the probability density of the work is found to have ``fat''
power-law tails which assign a relatively high probability to large
fluctuations compared with the case where the random forcing is Gaussian. These
tails lead to a strong violation of existing fluctuation theorems, as the ratio
of the probabilities of positive and negative work fluctuations of equal
magnitude behaves in a non-monotonic way. Possible experiments that could probe
these features are proposed.Comment: 5 pages, 2 figures, RevTeX4; v2: minor corrections and references
added; v3: typos corrected, new conclusion, close to published versio

### 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

### 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

### 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

### Chaotic Observer-based Synchronization Under Information Constraints

Limit possibilities of observer-based synchronization systems under
information constraints (limited information capacity of the coupling channel)
are evaluated. We give theoretical analysis for multi-dimensional
drive-response systems represented in the Lurie form (linear part plus
nonlinearity depending only on measurable outputs). It is shown that the upper
bound of the limit synchronization error (LSE) is proportional to the upper
bound of the transmission error. As a consequence, the upper and lower bounds
of LSE are proportional to the maximum rate of the coupling signal and
inversely proportional to the information transmission rate (channel capacity).
Optimality of the binary coding for coders with one-step memory is established.
The results are applied to synchronization of two chaotic Chua systems coupled
via a channel with limited capacity.Comment: 7 pages, 6 figures, 27 reference

### Early risk factors of overweight developmental trajectories during middle childhood

Background
Research is needed to identify early life risk factors associated with different developmental
paths leading to overweight by adolescence.
Objectives
To model heterogeneity in overweight development during middle childhood and identify
factors associated with differing overweight trajectories.
Methods
Data was drawn from the Quebec Longitudinal Study of Child Development (QLSCD; 1998-
2010). Trained research assistants measured height and weight according to a standardized
protocol and conducted yearly home interviews with the child’s caregiver (mother in
98% of cases). Information on several putative early life risk factors for the development of
overweight were obtained, including factors related to the child’s perinatal, early behavioral
family and social environment. Group-based trajectories of the probability of overweight (6-
12 years) were identified with a semiparametric method (n=1678). Logistic regression analyses were used to identify early risk factors (5 months- 5 years) associated with each
trajectory.
Results
Three trajectories of overweight were identified: “early-onset overweight” (11.0 %), “lateonset
overweight” (16.6%) and “never overweight” (72.5%). Multinomial analyses indicated
that children in the early and late-onset group, compared to the never overweight group,
had 3 common types of risk factors: parental overweight, preschool overweight history, and
large size for gestational age. Maternal overprotection (OR= 1.12, CI: 1.01-1.25), short
nighttime sleep duration (OR=1.66, CI: 1.07-2.57), and immigrant status (OR=2.01, CI:
1.05-3.84) were factors specific to the early-onset group. Finally, family food insufficiency
(OR=1.81, CI: 1.00-3.28) was weakly associated with membership in the late-onset trajectory
group.
Conclusions
The development of overweight in childhood follows two different trajectories, which have
common and distinct risk factors that could be the target of early preventive interventions

### The Value of Information for Populations in Varying Environments

The notion of information pervades informal descriptions of biological
systems, but formal treatments face the problem of defining a quantitative
measure of information rooted in a concept of fitness, which is itself an
elusive notion. Here, we present a model of population dynamics where this
problem is amenable to a mathematical analysis. In the limit where any
information about future environmental variations is common to the members of
the population, our model is equivalent to known models of financial
investment. In this case, the population can be interpreted as a portfolio of
financial assets and previous analyses have shown that a key quantity of
Shannon's communication theory, the mutual information, sets a fundamental
limit on the value of information. We show that this bound can be violated when
accounting for features that are irrelevant in finance but inherent to
biological systems, such as the stochasticity present at the individual level.
This leads us to generalize the measures of uncertainty and information usually
encountered in information theory

### Counting function fluctuations and extreme value threshold in multifractal patterns: the case study of an ideal $1/f$ noise

To understand the sample-to-sample fluctuations in disorder-generated
multifractal patterns we investigate analytically as well as numerically the
statistics of high values of the simplest model - the ideal periodic $1/f$
Gaussian noise. By employing the thermodynamic formalism we predict the
characteristic scale and the precise scaling form of the distribution of number
of points above a given level. We demonstrate that the powerlaw forward tail of
the probability density, with exponent controlled by the level, results in an
important difference between the mean and the typical values of the counting
function. This can be further used to determine the typical threshold $x_m$ of
extreme values in the pattern which turns out to be given by
$x_m^{(typ)}=2-c\ln{\ln{M}}/\ln{M}$ with $c=3/2$. Such observation provides a
rather compelling explanation of the mechanism behind universality of $c$.
Revealed mechanisms are conjectured to retain their qualitative validity for a
broad class of disorder-generated multifractal fields. In particular, we
predict that the typical value of the maximum $p_{max}$ of intensity is to be
given by $-\ln{p_{max}} = \alpha_{-}\ln{M} +
\frac{3}{2f'(\alpha_{-})}\ln{\ln{M}} + O(1)$, where $f(\alpha)$ is the
corresponding singularity spectrum vanishing at $\alpha=\alpha_{-}>0$. For the
$1/f$ noise we also derive exact as well as well-controlled approximate
formulas for the mean and the variance of the counting function without
recourse to the thermodynamic formalism.Comment: 28 pages; 7 figures, published version with a few misprints
corrected, editing done and references adde

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