Related papers: Collective behaviours: from biochemical kinetics t…
The dynamical properties and diffusive behavior of a collection of mutually interacting particles are numerically investigated for two types of long-range interparticle interactions: Coulomb-electrostatic and dipole-electrodynamic. It is…
The thermodynamics and the dynamics of particle systems with infinite-range coupling display several unusual and new features with respect to systems with short-range interactions. The Hamiltonian Mean Field (HMF) model represents a…
This paper presents a unified mathematical theory of swarms where the dynamics of social behaviors interacts with the mechanical dynamics of self-propelled particles. The term behavioral swarms is introduced to characterize the specific…
Mass action systems capture chemical reaction networks in homogeneous and dilute solutions. We suggest a notion of generalized mass action systems that admits arbitrary nonnegative power-law rate functions and serves as a more realistic…
Analysis of large continuous-time stochastic systems is a computationally intensive task. In this work we focus on population models arising from chemical reaction networks (CRNs), which play a fundamental role in analysis and design of…
Ensemble inequivalence has been observed in several systems. In particular it has been recently shown that negative specific heat can arise in the microcanonical ensemble in the thermodynamic limit for systems with long-range interactions.…
Collective behavior in animals has long been modeled through self-propelled particle models, which reproduce striking group-level phenomena through abstract interaction forces. Yet these models are fundamentally descriptive: they leave open…
The use of mathematical methods for the analysis of chemical reaction systems has a very long history, and involves many types of models: deterministic versus stochastic, continuous versus discrete, and homogeneous versus spatially…
The kinetics of chemical reactions are determined by the law of mass action, which has been successfully applied to homogeneous, dilute mixtures. At non-dilute conditions, interactions among the components can give rise to coexisting…
Motivated by the recent experimental observations on clustering of motor proteins on microtubule filament, we study an open system of two parallel totally asymmetric simple exclusion processes under asymmetric coupling conditions, which…
The aim of this work is to implement a statistical mechanics theory of social interaction, generalizing econometric discrete choice models. A class of simple mean field discrete models is introduced and discussed both from the theoretical…
We introduce contextual behavioural metrics (CBMs) as a novel way of measuring the discrepancy in behaviour between processes, taking into account both quantitative aspects and contextual information. This way, process distances by…
The theory of biochemical processes needs simple but realistic models of phenomena underlying microscopic dynamics of proteins. Many experiments performed in the 1980s have demonstrated that within the protein native state, apart from usual…
In recent years, kinetic equations have been used to model many social phenomena. A key feature of these models is that transition rate kernels involve Dirac delta functions, which capture sudden, discontinuous state changes. Here, we study…
The paper presents a method by which the mean field dynamics of a population of dynamical systems with parameter diversity and global coupling can be described in terms of a few macroscopic degrees of freedom. The method applies to…
An analytical method to compute thermodynamic properties of a given Hamiltonian system is proposed. This method combines ideas of both dynamical systems and ensemble approaches to thermodynamics, providing de facto a possible alternative to…
It is standard in chemistry to represent a sequence of reactions by a single overall reaction, often called a complex reaction in contrast to an elementary reaction. Photosynthesis $6 \text{CO}_2+6 \text{H}_2\text{O} \to \…
We construct and analyze a random graph model for discrete choice with social interaction and several groups of equal size. We concentrate on the case of two groups of equal sizes and we allow the interaction strength within a group to…
We present a strategy capable of describing basic features of the dynamics of crowds. The behaviour of the crowd is considered from a twofold perspective. We examine both the large scale behaviour of the crowd, and phenomena happening at…
These lecture notes want to illustrate the close connection between statistical mechanics and field theory not only on the formal level, i.e. that many concepts of one area can easily be taken over to the other one, but also on the level of…