345 research outputs found

    Fluctuation relation for a L\'evy particle

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    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

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    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

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    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

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    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

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    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

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    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

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    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/f1/f noise

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    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/f1/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 xmx_m of extreme values in the pattern which turns out to be given by xm(typ)=2clnlnM/lnMx_m^{(typ)}=2-c\ln{\ln{M}}/\ln{M} with c=3/2c=3/2. Such observation provides a rather compelling explanation of the mechanism behind universality of cc. 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 pmaxp_{max} of intensity is to be given by lnpmax=αlnM+32f(α)lnlnM+O(1)-\ln{p_{max}} = \alpha_{-}\ln{M} + \frac{3}{2f'(\alpha_{-})}\ln{\ln{M}} + O(1), where f(α)f(\alpha) is the corresponding singularity spectrum vanishing at α=α>0\alpha=\alpha_{-}>0. For the 1/f1/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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