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We consider an aggregation model that consists of an active transport equation for the macroscopic population density, where the velocity has a nonlocal functional dependence on the density, modelled via an interaction potential. We set up…
We introduce a model of self-propelled particles carrying out a Brownian motion with a diffusion coefficient which depends on the local density of particles within a certain finite radius. Numerical simulations show that in a range of…
Zipf's law is the most common statistical distribution displaying scaling behavior. Cities, populations or firms are just examples of this seemingly universal law. Although many different models have been proposed, no general theoretical…
The emerging collective motions of swarms of interacting agents are a subject of great interest in application areas ranging from biology to physics and robotics. In this paper, we conduct a careful analysis of the collective dynamics of a…
This work presents a microscopic model to describe pedestrian flows based on the social force theory. The aim of this study is twofold: (1) developing a realistic model that can be used as a tool for designing pedestrian-friendly…
We give a comprehensive rate equation description for the irreversible growth of aggregates by migration from small to large aggregates. For a homogeneous rate K(i;j) at which monomers migrate from aggregates of size i to those of size j,…
Cellular self-assembly and organization are fundamental steps for the development of biological tissues. In this paper, within the framework of a cellular automata model, we address how an ordered tissue pattern spontaneously emerges from a…
Uncovering the mechanism leading to the scaling law in human trajectories is of fundamental importance in understanding many spatiotemporal phenomena. We propose a hierarchical geographical model to mimic the real traffic system, upon which…
We study the hydrodynamics of a system of agents who optimize either their individual utility (self-interest) or the collective welfare (cooperation). When agents act selfishly, their interactions are non-reciprocal, driving the system out…
In this paper we analyze the rural-urban migration phenomena as it is usually observed in economies which are in the early stages of industrialization. The analysis is conducted by means of a statistical mechanics approach which builds a…
Understanding urban mobility requires models that capture how people interact with and navigate the built environment. We present a scalable, generalizable agent-based framework in which daily schedules emerge from the interplay between…
Pedestrian crowds can very realistically be simulated with a social force model which describes the different influences affecting individual pedestrian motion by a few simple force terms. The model is able to reproduce the emergence of…
We analyze a simplistic model for run-and-tumble dynamics, motivated by observations of complex spatio-temporal patterns in colonies of myxobacteria. In our model, agents run with fixed speed either left or right, and agents turn with a…
Individual-based models of chemical or biological dynamics usually consider individual entities diffusing in space and performing a birth-death type dynamics. In this work we study the properties of a model in this class where the birth…
We study a minimal model of active transport in crowded single-file environments which generalises the emblematic model of single file diffusion to the case when the tracer particle (TP) performs either an autonomous directed motion or is…
New model equations are derived for dynamics of self-aggregation of finite-size particles. Differences from standard Debye-Huckel and Keller-Segel models are: a) the mobility $\mu$ of particles depends on the locally-averaged particle…
This paper examines the spatial agglomeration of workers and income in a continuous space-time framework. Local markets feature spatial spillovers and both exogenous and endogenous amenities. Workers relocate to maximise their instantaneous…
Large scale simulations of the movements of people in a ``virtual'' city and their analyses are used to generate new insights into understanding the dynamic processes that depend on the interactions between people. Models, based on these…
We introduce a kinetic framework for modeling the time evolution of the statistical distributions of the population densities in the three compartments of susceptible, infectious, and recovered individuals, under epidemic spreading driven…
We consider a single server queue that serves a finite population of $n$ customers that will enter the queue (require service) only once, also known as the $\Delta_{(i)}/G/1$ queue. This paper presents a method for analyzing heavy-traffic…