Numerical approximation of a coagulation-fragmentation model for animal group size statistics

We study numerically a coagulation-fragmentation model derived by Niwa [17] and further elaborated by Degond et al. [5]. In [5] a unique equi- librium distribution of group sizes is shown to exist in both cases of continuous and discrete group size distributions. We provide a numerical investigation of these equilibria using three different methods to approximate the equilibrium: a recursive algorithm based on the work of Ma et. al. [12], a Newton method and the resolution of the time-dependent problem. All three schemes are val- idated by showing that they approximate the predicted small and large size asymptotic behaviour of the equilibrium accurately. The recursive algorithm is used to investigate the transition from discrete to continuous size distributions and the time evolution scheme is exploited to show uniform convergence to equilibrium in time and to determine convergence rates

Kinetic models for topological nearest-neighbor interactions

We consider systems of agents interacting through topological interactions. These have been shown to play an important part in animal and human behavior. Precisely, the system consists of a finite number of particles characterized by their positions and velocities. At random times a randomly chosen particle, the follower, adopts the velocity of its closest neighbor, the leader. We study the limit of a system size going to infinity and, under the assumption of propagation of chaos, show that the limit kinetic equation is a non-standard spatial diffusion equation for the particle distribution function. We also study the case wherein the particles interact with their K closest neighbors and show that the corresponding kinetic equation is the same. Finally, we prove that these models can be seen as a singular limit of the smooth rank-based model previously studied in Blanchet and Degond (J Stat Phys 163:41–60, 2016). The proofs are based on a combinatorial interpretation of the rank as well as some concentration of measure arguments

Asymptotic-Preserving methods and multiscale models for plasma physics

The purpose of the present paper is to provide an overview of As ymptotic- Preserving methods for multiscale plasma simulations by ad dressing three sin- gular perturbation problems. First, the quasi-neutral lim it of fluid and kinetic models is investigated in the framework of non magnetized as well as magne- tized plasmas. Second, the drift limit for fluid description s of thermal plasmas under large magnetic fields is addressed. Finally efficient nu merical resolutions of anisotropic elliptic or diffusion equations arising in ma gnetized plasma simu- lation are reviewed

Modelling tissue self-organization: from micro to macro models

In this chapter, we present recent works concerned with the derivation of a macroscopic model for complex interconnected fiber networks from an agent-based model, with applications to, but not limited to, adipose tissue self-organization. Starting from an agent-based model for interconnected fibers interacting through alignment interactions and having the ability to create and suppress cross-links, the formal limit of large number of individuals is first investigated. It leads to a kinetic system of two equations: one for the individual fiber distribution function and one for the distribution function of connected fiber pairs. The hydrodynamic limit, in a regime of instantaneous fiber linking/unlinking then leads to a macroscopic model describing the evolution of the fiber local density and mean orientation. These works are the first attempt to derive a macroscopic model for interconnected fibers from an agent-based formulation and represent a first step towards the formulation of a large scale synthetic tissue model which will serve for the investigation of large scale effects in tissue homeostasis

Transport of congestion in two-phase compressible/incompressible flows

We study the existence of weak solutions to the two-phase fluid model with congestion constraint. The model encompasses the flow in the uncongested regime (compressible) and the congested one (incompressible) with the free boundary separating the two phases. The congested regime appears when the density in the uncongested regime achieves a threshold value that describes the comfort zone of individuals. This quantity is prescribed initially and transported along with the flow. We prove that this system can be approximated by the fully compressible Navier–Stokes system with a singular pressure, supplemented with transport equation for the congestion density. We also present the application of this approximation for the purposes of numerical simulations in the one-dimensional domain

Phase Transitions in a Kinetic Flocking Model of Cucker-Smale Type

We consider a collective behavior model in which individuals try to imitate each others' velocity and have a preferred speed. We show that a phase change phenomenon takes place as diffusion decreases, bringing the system from a “disordered” to an “ordered” state. This effect is related to recently noticed phenomena for the diffusive Vicsek model. We also carry out numerical simulations of the system and give further details on the phase transition

Symmetry-breaking phase-transitions in highly concentrated semen

New experimental evidence of self-motion of a confined active suspension is presented. Depositing fresh semen sample in an annular shaped micro- fluidic chip leads to a spontaneous vortex state of the fluid at sufficiently large sperm concentration. The rotation occurs unpredictably clockwise or counterclockwise and is robust and stable. Furthermore, for highly active and concentrated semen, richer dynamics can occur such as self-sustained or damped rotation oscillations. Experimental results obtained with systematic dilution provide a clear evidence of a phase transition toward collective motion associated with local alignment of spermatozoa akin to the Vicsek model. A macroscopic theory based on previously derived Self-Organized Hydrodynamics (SOH) models is adapted to this context and provides predictions consistent with the observed stationary motion

Are tumor cell lineages solely shaped by mechanical forces?

This paper investigates cell proliferation dynamics in small tumor cell aggregates using an individual-based model (IBM). The simulation model is designed to study the morphology of the cell population and of the cell lineages as well as the impact of the orientation of the division plane on this morphology. Our IBM model is based on the hypothesis that cells are incompressible objects that grow in size and divide once a threshold size is reached, and that newly born cell adhere to the existing cell cluster. We performed comparisons between the simulation model and experimental data by using several statistical indicators. The results suggest that the emergence of particular morphologies can be explained by simple mechanical interactions

Modelling tissue self-organization: from micro to macro models

In this chapter, we present recent works concerned with the derivation of a macroscopic model for complex interconnected fiber networks from an agent-based model, with applications to, but not limited to, adipose tissue self-organization. Starting from an agent-based model for interconnected fibers interacting through alignment interactions and having the ability to create and suppress cross-links, the formal limit of large number of individuals is first investigated. It leads to a kinetic system of two equations: one for the individual fiber distribution function and one for the distribution function of connected fiber pairs. The hydrodynamic limit, in a regime of instantaneous fiber linking/unlinking then leads to a macroscopic model describing the evolution of the fiber local density and mean orientation. These works are the first attempt to derive a macroscopic model for interconnected fibers from an agent-based formulation and represent a first step towards the formulation of a large scale synthetic tissue model which will serve for the investigation of large scale effects in tissue homeostasis

Equilibrage Modal de Rotors Flexibles

SIGLEINIST T 75567 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc