Related papers: Sample to sample fluctuations in fragmentation and…
This text surveys different probabilistic aspects of a model which is used to describe the evolution of an object that falls apart randomly as time passes. Each point of view yields useful techniques to establish properties of such random…
We provide information about the asymptotic regimes for a homogeneous fragmentation of a finite set. We establish a phase transition for the asymptotic behaviours of the shattering times, defined as the first instants when all the blocks of…
We investigate the propagation of random fluctuations through biochemical networks in which the concentrations of species are large enough so that the unperturbed problem is well-described by ordinary differential equation. We characterize…
Fractal properties are usually characterized by means of various statistical tools which deal with spatial average quantities. Here we focus on the determination of fluctuations around the average counts and we develop a test for the study…
We consider the limiting behavior of fluctuations of small noise diffusions with multiple scales around their homogenized deterministic limit. We allow full dependence of the coefficients on the slow and fast motion. These processes arise…
We present results from an individual particle based model for the collision, coagulation and fragmentation of heavy drops moving in a turbulent flow. Such a model framework can help to bridge the gap between the full hydrodynamic…
We investigate the time behavior of the fragmentation model with Kolmogorov time scales and space contraction resembling the random $\beta$-model of turbulence. The space averages computed at any instant using the entire spatial realization…
We present a brief introduction to the statistical properties of systems with large fluctuations. We point out that for such systems the relevant statistical quantities are scaling exponents and the nature of fluctuations is completely…
We study statistical properties of galaxy structures in several samples extracted from the 2dF Galaxy Redshift Survey. In particular, we measured conditional fluctuations by means of the scale-length method and determined their probability…
Order parameter fluctuations (the largest cluster size distribution) are studied within a three-dimensional bond percolation model on small lattices. Cumulant ratios measuring the fluctuations exhibit distinct features near the percolation…
Many fluctuating systems consist of macroscopic structures in addition to noisy signals. Thus, for this class of fluctuating systems, the scaling behaviors are very complicated. Such phenomena are quite commonly observed in Nature, ranging…
Extending recent work on stress fluctuations in complex fluids and amorphous solids we describe in general terms the ensemble average $v(\Delta t)$ and the standard deviation $\delta v(\Delta t)$ of the variance $v[\mathbf{x}]$ of time…
We derive exact statistical properties of a class of recursive fragmentation processes. We show that introducing a fragmentation probability 0<p<1 leads to a purely algebraic size distribution in one dimension, P(x) ~ x^{-2p}. In d…
An approach for understanding the behavior of multiplicity distributions in restricted phase-space intervals derived on the basis of global observables is proposed. We obtain a unifying connection between local multiparticle clusters and…
The fluctuations are termed mesoscopic, when their typical size is essentially larger then the average distance between the nearest neighbors, while being much smaller than the overall system size. Since the features of mesoscopic…
We study the equilibrium fluctuations for a gradient exclusion process with conductances in random environments, which can be viewed as a central limit theorem for the empirical distribution of particles when the system starts from an…
Are spinodal instabilities the leading mechanism in the fragmentation of a fermionic system? Numerous experimental indications suggest such a scenario and stimulated much effort in giving a suitable description, without being finalised in a…
The flow of frictionless granular particles is studied with stress-controlled discrete element modeling simulations for systems varying in size from 300 to 100,000 particles. The volume fraction and shear stress ratio $\mu$ are relatively…
In a class of heterogeneous random networks, where each node dynamics is a random dynamical system, interacting with neighbor nodes via a random coupling function, we characterize the hub behavior as the mean-field, subject to statistically…
Fluctuation scaling is observed phenomenon from complex networks through finance to ecology. It means that the variance and the mean of a specific quantity are related as $\ev{\sigma^2|n}\propto \ev{n|A}^{2\alpha}$ with $1/2\geq \alpha \geq…