Related papers: Homogeneous Boltzmann-type equations on graphs: A …
In this paper, we propose a novel approach that employs kinetic equations to describe the collective dynamics emerging from graph-mediated pairwise interactions in multi-agent systems. We formally show that for large graphs and specific…
In this paper, we present a critical collection of essential mathematical tools and techniques for the analysis of Boltzmann-type kinetic equations, which in recent years have established themselves as a flexible and powerful paradigm to…
The application of classical methods of statistical mechanics, originally developed by Ludwig Boltzmann in gas dynamics, to the description of social phenomena is a successful story that we try to outline in this paper. On one hand, it is…
A kinetic inhomogeneous Boltzmann-type equation is proposed to model the dynamics of the number of agents in a large market depending on the estimated value of an asset and the rationality of the agents. The interaction rules take into…
A broad set of empirical phenomenon in the study of social, economic and machine behaviour can be modelled as complex systems with averaging dynamics. However many of these models naturally result in consensus or consensus-like outcomes. In…
Interacting systems are ubiquitous in nature and engineering, ranging from particle dynamics in physics to functionally connected brain regions. These interacting systems can be modeled by graphs where edges correspond to the interactions…
In this paper, we propose a Boltzmann-type kinetic description of mass-varying interacting multi-agent systems. Our agents are characterised by a microscopic state, which changes due to their mutual interactions, and by a label, which…
It is shown, that the Boltzmann-like equations allow the formulation of a very general model for behavioral changes. This model takes into account spontaneous (or externally induced) behavioral changes and behavioral changes by pair…
In this paper we study binary interaction schemes with uncertain parameters for a general class of Boltzmann-type equations with applications in classical gas and aggregation dynamics. We consider deterministic (i.e., a priori averaged) and…
In this work we review some recent development in the mathematical modelling of quantitative sociology by means of statistical mechanics. After a short pedagogical introduction to static and dynamic properties of many body systems, we…
A linear Boltzmann equation with nonautonomous collision operator is rigorously derived in the Boltzmann-Grad limit for the deterministic dynamics of a Rayleigh gas where a tagged particle is undergoing hard-sphere collisions with…
We study the possibility of applying statistical mechanics to generally covariant quantum theories with a vanishing Hamiltonian. We show that (under certain appropiate conditions) this makes sense, in spite of the absence of a notion of…
Choice models for populations of agents on graphs are studied in terms of statistical thermodynamics. Equations of state are derived and discussed for different connectivity schemes, utility approximations, and temperature and volume…
The traffic modelling often keeps the mesoscopic scale in the theoretical sphere because the integro-differential nature of its equations. In the present work we suggest to use the lattice Boltzmann method to overcome these difficulties. In…
Dynamical complex systems composed of interactive heterogeneous agents are prevalent in the world, including urban traffic systems and social networks. Modeling the interactions among agents is the key to understanding and predicting the…
In the last decade, stochastic models have shown to be very useful for quantitative modelling of social processes. Here, a configurational master equation for the description of behavioral changes by pair interactions of individuals is…
We review the statistical mechanics approach to the study of the emerging collective behavior of systems of heterogeneous interacting agents. The general framework is presented through examples is such contexts as ecosystem dynamics and…
A kinetic model for the Boltzmann equation is proposed and explored as a practical means to investigate the properties of a dilute granular gas. It is shown that all spatially homogeneous initial distributions approach a universal…
A linear Boltzmann equation is derived in the Boltzmann-Grad scaling for the deterministic dynamics of many interacting particles with random initial data. We study a Rayleigh gas where a tagged particle is undergoing hard-sphere collisions…
We propose and investigate general kinetic models %of Boltzmann type with transition probabilities that can describe the simultaneous change of multiple microscopic states of the interacting agents. These models can be applied to many…