Understanding collective properties of driven particle systems is significant for naturally occurring aggregates and because the knowledge gained can be used as building blocks for the design of artificial ones. We model self-propelling biological or artificial individuals interacting through pairwise attractive and repulsive forces. For the first time, we are able to predict stability and morphology of organization starting from the shape of the two-body interaction. We present a coherent theory, based on fundamental statistical mechanics, for all possible phases of collective motion.

Motivated by empirical observations of spatio-temporal clusters of crime across a wide variety of urban settings, we present a model to study the emergence, dynamics, and steady-state properties of crime hotspots. We focus on a two-dimensional lattice model for residential burglary, where each site is characterized by a dynamic attractiveness variable, and where each criminal is represented as a random walker. The dynamics of criminals and of the attractiveness field are coupled to each other via specific biasing and feedback mechanisms. Depending on parameter choices, we observe and describe several regimes of aggregation, including hotspots of high criminal activity. On the basis of the discrete system, we also derive a continuum model; the two are in good quantitative agreement for large system sizes. By means of a linear stability analysis we are able to determine the parameter values that will lead to the creation of stable hotspots. We discuss our model and results in the context of established criminological and sociological findings of criminal behavior.

We study a class of swarming problems wherein particles evolve dynamically via pairwise interaction potentials and a velocity selection mechanism. We find that the swarming system undergoes various changes of state as a function of the selfpropulsion and interaction potential parameters. In this paper, we utilize a procedure which, in a definitive way, connects a class of individual-based models to their continuum formulations and determine criteria for the validity of the latter. H-stability of the interaction potential plays a fundamental role in determining both the validity of the continuum approximation and the nature of the aggregation state transitions. We perform a linear stability analysis of the continuum model and compare the results to the simulations of the individual-based one.

We present a kinetic theory for swarming systems of interacting, self-propelled discrete particles. Starting from the Liouville equation for the many-body problem we derive a kinetic equation for the single particle probability distribution function and the related macroscopic hydrodynamic equations. General solutions include flocks of constant density and fixed velocity and other non-trivial morphologies such as compactly supported rotating mills. The kinetic theory approach leads us to the identification of macroscopic structures otherwise not recognized as solutions of the hydrodynamic equations, such as double mills of two superimposed flows. We find the conditions allowing for the existence of such solutions and compare to the case of single mills.

The morphology of surfaces of arbitrary orientation in the presence of step and kink Ehrlich-Schwoebel effects (SESE and KESE) during growth is studied within the framework of a model in which steps are continuous lines, and is illustrated by a simple solid-on-solid model. For vicinal surfaces KESE induces an instability often stronger than that from SESE. The possibility of stable kink flow growth is analyzed. Fluctuations can shift the stability threshold. KESE also induces mound formation. [S0031-9007(99)09023-7]

Criminality is a big challenge at several different levels. This is particularly evident -even for microcriminality -in urban areas (in Europe and North America the percent of population living in urban areas is around 85%). It is considered by sociologists among the most important indexes affecting the (perception of the) quality of life in a given place.Starting from the seminal paper by G. Becker [3], the study of crime and criminality from the point of view of economics has been developed in several directions. And the role of mathematical, statistical, and physical models has been steadily increasing. Thus, the paper [6] appears to be extremely timely and useful.Generally speaking, models are often more descriptive than predictive, in the sense that it is not expected that they predict e.g. the number of burglaries or car thefts that will occur in a given district over a given period of time. Nevertheless, they can be instrumental in describing the mechanisms by which it can be foreseen that a concentration of crimes can appear in particular zones (hot spots), or the "contagion" that criminal behaviour can have on particular classes of individuals. This description can in turn suggest how to contrast the phenomena.Therefore, modelling the diffusion of criminal (or simply unlawful) behaviour in urban areas can be a tool that administrations and police authorities can use in order to choose optimal strategies to combat crime. And this is particularly important in a horizon of budget cuts that impose the best use of the existing (scarce) resources, optimization of strategies, logistics etc.Another feature of the models is the fact that they allow to perform simulations to mimic the response of the system to changes of parameters, of external inputs or constraints. Of course "for complex phenomena as criminality (

In this paper, we study cooperative control algorithms using pairwise interactions, for the purpose of controlling flocks of unmanned vehicles. An important issue is the role the potential plays in the stability and possible collapse of the group as agent number increases. We model a set of interacting Dubins vehicles with fixed turning angle and speed. We perform simulations for a large number of agents and we show experimental realizations of the model on a testbed with a small number of vehicles. In both cases, critical thresholds exist between coherent, stable, and scalable flocking and dispersed or collapsing motion of the group.

We develop a mathematical framework aimed at analyzing repeat and nearrepeat effects in crime data. Parsing burglary data from Long Beach, CA according to different counting methods, we determine the probability distribution functions for the time interval s between repeat offenses. We then compare these observed distributions to theoretically derived distributions in which the repeat effects are due solely to persistent risk heterogeneity. We find that risk heterogeneity alone cannot explain the observed distributions, while a form of event dependence (boosts) can. Using this information, we model repeat victimization as a series of random events, the likelihood of which changes each time an offense occurs. We are able to estimate typical time scales for repeat burglary events in Long Beach by fitting our data to this model. Computer simulations of this model using these observed parameters agree with the empirical data.