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The dynamics of phase transitions plays a crucial r\^ole in the so-called interface between high energy particle physics and cosmology. Many of the interesting results generated during the last fifteen years or so rely on simplified…
Cell cultures exhibit rich and complex behaviors driven by dynamic metabolic interactions among cells. In this work, we present a model that captures these interactions through a framework inspired by statistical mechanics. Using Monte…
We are interested in modelling Darwinian evolution, resulting from the interplay of phenotypic variation and natural selection through ecological interactions. Our models are rooted in the microscopic, stochastic description of a population…
Experiments with pedestrians revealed that the geometry of the domain, as well as the incentive of pedestrians to reach a target as fast as possible have a strong influence on the overall dynamics. In this paper, we propose and validate…
The aim of this work is to put forward a statistical mechanics theory of social interaction, generalizing econometric discrete choice models. After showing the formal equivalence linking econometric multinomial logit models to equilibrium…
In this work we investigate the behaviour of a human crowd in a cross-flow. We first analyse the results of a set of controlled experiments in which subjects were divided into two groups, in such a way to explore different density settings,…
This work deals with a mesoscopic and deterministic theory for the collective dynamics of Water Coherence Domains, and it represents a continuation of a previous work published in Plos ONE…
The chaotical dynamics is studied in different Friedmann-Robertson- Walker cosmological models with scalar (inflaton) field and hydrodynamical matter. The topological entropy is calculated for some particular cases. Suggested scheme can be…
This paper studies a flocking model in which the interaction between agents is described by a general local nonlinear function depending on the distance between agents.
Quantitative predictions about the processes that promote species coexistence are a subject of active research in ecology. In particular, competitive interactions are known to shape and maintain ecological communities, and situations where…
The flocking of self-propelled particles in heterogeneous environments is relevant to both natural and artificial systems. The Vicsek model is a canonical choice to investigate such systems due to the minimal number of parameters required…
This paper presents a position-based flocking model for interacting agents, balancing cohesion-separation and alignment to achieve stable collective motion. The model modifies a position-velocity-based approach by approximating velocity…
Traditional approaches to ecosystem modelling have relied on spatially homogeneous approximations to interaction, growth and death. More recently, spatial interaction and dispersal have also been considered. While these leads to certain…
The behavior of interacting populations typically displays irregular temporal and spatial patterns that are difficult to reconcile with an underlying deterministic dynamics. A classical example is the heterogeneous distribution of plankton…
Many real-world systems can be modeled as networks of interacting oscillatory units. Collective dynamics that are of functional relevance for the oscillator network, such as switching between metastable states, arise through the interplay…
Modeling of crowds of pedestrians has been considered in this paper from different aspects. Based on fractional microscopic model that may be much more close to reality, a fractional macroscopic model has been proposed using conservation…
Large animal groups -- bird flocks, fish schools, insect swarms -- are often assumed to form by gradual aggregation of sparsely distributed individuals. Using a mathematically precise framework based on time-varying directed interaction…
Quantifying population dynamics is a fundamental challenge in ecology and evolutionary biology, particularly for species that are cryptic, microscopic, or extinct. Traditional approaches rely on continuous representations of population…
We review the observations and the basic laws describing the essential aspects of collective motion -- being one of the most common and spectacular manifestation of coordinated behavior. Our aim is to provide a balanced discussion of the…
We use topological data analysis as a tool to analyze the fit of mathematical models to experimental data. This study is built on data obtained from motion tracking groups of aphids in [Nilsen et al., PLOS One, 2013] and two random walk…