Related papers: Coagulation-fragmentation model for animal group-s…
We study the condensation phenomenon for the invariant measures of the mean-field model of reversible coagulation-fragmentation processes conditioned to a supercritical density of particles. It is shown that when the parameters of the…
At the macroscopic scale, many important models of collective motion fall into the class of kinematic flows for which both velocity and diffusion terms depend only on particle density. When total particle numbers are fixed and finite,…
The objective of statistical physics is to understand macroscopic behavior of a many-body system from the interactions of the constituents of that system. When many-body systems reach critical states, simple universal and scaling behaviors…
A cluster theory based mathematical model was developed and used to simulate the dynamics of a system composed of a large number of interacting agents-clusters with different size. The case of a system formed by a constant total number of…
The complex formations exhibited by schooling fish have long been the object of fascination for biologists and physicists. However, the physical and sensory mechanisms leading to organized collective behavior remain elusive. On the physical…
We present a generalized dynamical model describing the sharing of information, and corresponding herd behavior, in a population based on the recent model proposed by Eguiluz and Zimmermann. By introducing a size-dependent probability for…
Following some recent works, we investigate the problem of optimising the total population size for logistic diffusive models with respect to resources distributions. Using the spatially heterogeneous Fisher-KPP equation, we obtain a…
The effect of introducing a mass dependent diffusion rate ~ m^{-alpha} in a model of coagulation with single-particle break up is studied both analytically and numerically. The model with alpha=0 is known to undergo a nonequilibrium phase…
We consider several one-species population dynamics model with finite and infinite carrying capacity, time dependent growth and effort rates and solve them analytically. We show that defining suitable scaling functions for a given time, one…
Processes of coalescence and fragmentation are used to understand the time-evolution of the mass distribution of various systems and may result in a steady state or in stable deterministic or stochastic cycles. Motivated by applications in…
This paper studies the scaling properties of recruitment fluctuations in randomly varying environments, for abundant marine species with extreme reproductive behavior. Fisheries stock-recruitment data from the North Atlantic display…
We investigate finite size scaling in percolating widthless stick systems with variable aspect ratios in an extensive Monte Carlo simulation study. A generalized scaling function is introduced to describe the scaling behavior of the…
Pitman~(1999) describes a duality relationship between fragmentation and coagulation operators. An explicit relationship is described for the two-parameter Poisson-Dirichlet laws, with parameters {\footnotesize $(\alpha,\theta)$} and…
Animal behavior is shaped by a myriad of mechanisms acting on a wide range of scales, which hampers quantitative reasoning and the identification of general principles. Here, we combine data analysis and theory to investigate the…
A bonded particle model is used to explore how variations in the material properties of brittle, isotropic solids affect critical behavior in fragmentation. To control material properties, a new model is proposed which includes breakable…
We present a quantitative continuum theory of ``flocking'': the collective coherent motion of large numbers of self-propelled organisms. Our model predicts the existence of an ``ordered phase'' of flocks, in which all members of the flock…
We study the collective dynamics of a population of particles/organisms subject to self-consistent attraction-repulsion interactions and an external velocity field. The starting point of our analysis is a mean-field kinetic model and we…
Growth-fragmentation processes describe systems of particles in which each particle may grow larger or smaller, and divide into smaller ones as time proceeds. Unlike previous studies, which have focused mainly on the self-similar case, we…
This chapter focuses on the derivation of a doubly nonlocal Fisher-KPP model, which is a macroscopic nonlocal evolution equation describing population dynamics in the large population limit. The derivation starts from a microscopic…
We determine the basic phase diagram of the fish school model derived from data by Gautrais etal (PLoS Comp. Biol. 8, e1002678 (2012)), exploring its parameter space beyond the parameter values determined experimentally on groups of barred…