Nonlinear stability of flock solutions in second-order swarming models

In this paper we consider interacting particle systems which are frequently used to model collective behavior in animal swarms and other applications. We study the stability of orientationally aligned formations called flock solutions, one of the typical patterns emerging from such dynamics. We provide an analysis showing that the nonlinear stability of flocks in second-order models entirely depends on the linear stability of the first-order aggregation equation. Flocks are shown to be nonlinearly stable as a family of states under reasonable assumptions on the interaction potential. Furthermore, we numerically verify that commonly used potentials satisfy these hypotheses and investigate the nonlinear stability of flocks by an extensive case-study of uniform perturbations.Comment: 22 pages, 1 figure, 1 tabl

Convergence of a linearly transformed particle method for aggregation equations

We study a linearly transformed particle method for the aggregation equation with smooth or singular interaction forces. For the smooth interaction forces, we provide convergence estimates in $L^1$ and $L^\infty$ norms depending on the regularity of the initial data. Moreover, we give convergence estimates in bounded Lipschitz distance for measure valued solutions. For singular interaction forces, we establish the convergence of the error between the approximated and exact flows up to the existence time of the solutions in $L^1 \cap L^p$ norm

An improved version of the Hughes model for pedestrian flow

Roger Hughes proposed a macroscopic model for pedestrian dynamics, in which individuals seek to minimize their travel time but try to avoid regions of high density. One of the basic assumptions is that the overall density of the crowd is known to every agent. In this paper we present a modification of the Hughes model to include local effects, namely limited vision, and a conviction towards decision making. The modified velocity field enables smooth turning and temporary waiting behavior. We discuss the modeling in the micro- and macroscopic setting as well as the efficient numerical simulation of either description. Finally we illustrate the model with various numerical experiments and evaluate the behavior with respect to the evacuation time and the overall performance

The dissipative linear Boltzmann equation for hard spheres

We prove the existence and uniqueness of an equilibrium state with unit mass to the dissipative linear Boltzmann equation with hard--spheres collision kernel describing inelastic interactions of a gas particles with a fixed background. The equilibrium state is a universal Maxwellian distribution function with the same velocity as field particles and with a non--zero temperature lower than the background one, which depends on the details of the binary collision. Thanks to the H--theorem we then prove strong convergence of the solution to the Boltzmann equation towards the equilibrium.Comment: 17 pages, submitted to Journal of Statistical Physic

Gastrointestinal parasites in captive and free-ranging Cebus albifrons in the Western Amazon, Ecuador

Currently, there is a lack of surveys that report the occurrence of gastrointestinal parasites in the whiteheaded capuchin monkey (Cebus albifrons). We therefore assessed the presence and richness (= number of different parasite genera) of parasites in C. albifrons in wildlife refuges (n = 11) and in a free-ranging group near a human village (n = 15) in the Ecuadorian Amazon. In the 78 samples collected (median of 3 samples per animal), we identified a total of 6 genera of gastrointestinal parasites, representing protozoa, nematodes, acanthocephalans and cestodes. We observed a high prevalence (84%) across the 26 individuals, with the most prevalent parasite being Strongyloides sp. (76.9%), followed by Hymenolepis sp. (38.5%) and Prosthenorchis elegans (11.5%). We found Entamoeba histolytica/dispar/moskovskii/nuttalli and Capillaria sp. in only a minority of the animals (3.8%). In addition, we observed unidentified strongyles in approximately one-third of the animals (34.6%). We found a total of 6 parasite genera for the adult age group, which showed higher parasite richness than the subadult age group (5) and the juvenile age group (3). Faecal egg/cyst counts were not significantly different between captive and free-ranging individuals or between sexes or age groups. The free-ranging group had a higher prevalence than the captive group; however, this difference was not significant. The only genus common to captive and free-ranging individuals was Strongyloides sp. The high prevalence of gastrointestinal parasites and the presence of Strongyloides in both populations support results from previous studies in Cebus species. This high prevalence could be related to the high degree of humidity in the region. For the free-ranging group, additional studies are required to gain insights into the differences in parasite prevalence and intensity between age and sex groups. Additionally, our study demonstrated that a serial sampling of each individual increases the test sensitivity