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Perceptrons are the building blocks of many theoretical approaches to a wide range of complex systems, ranging from neural networks and deep learning machines, to constraint satisfaction problems, glasses and ecosystems. Despite their…
Hybrid particle-field methods are computationally efficient approaches for modelling soft matter systems. So far applications of these methodologies have been limited to constant volume conditions. Here, we reformulate particle-field…
The aim of this paper is to discuss the mathematical modeling of Brownian active particle systems, a recently popular paradigmatic system for self-propelled particles. We present four microscopic models with different types of repulsive…
A system of interacting Brownian particles subject to short-range repulsive potentials is considered. A continuum description in the form of a nonlinear diffusion equation is derived systematically in the dilute limit using the method of…
Interacting particle systems are in frequent use to model collective behaviour in various situations and applications. For many systems, the interaction between the agents is restricted to an underlying network structure and often, the…
We study a modified mean-field approximation for the Ising Model in arbitrary dimension. Instead of taking a "central" spin, or a small "drop" of fluctuating spins coupled to the effective field of their nearest neighbors as in the…
We study the 3-spin spherical model with mean-field interactions and Gaussian random couplings. For moderate system sizes of up to 20 spins, we obtain all stationary points of the energy landscape by means of the numerical polynomial…
Hydrodynamics provides a successful framework to effectively describe the dynamics of complex many-body systems ranging from subnuclear to cosmological scales by introducing macroscopic quantities such as particle densities and fluid…
In this paper a rigorous proof of the mean field limit for a pedestrian flow model in two dimensions is given by using a probabilistic method. The model under investigation is an interacting particle system coupled to the eikonal equation…
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…
Static and dynamical aspects of nuclear systems are described through an extended time-dependent mean-field approach. The foundations of the formalism are presented, with highlights on the estimation of average values and their…
A statistical theory of the mean field is developed. It is based on the proposition that the mean field can be obtained as an energy average. Moreover, it is assumed that the matrix elements of the residual interaction, obtained after the…
The method to calculate the grand partition function of a particle system, in which constituents interact with each other via potential, that include repulsive and attractive components, is proposed. The cell model, which was introduced to…
Interacting particle systems are known for their ability to generate large-scale self-organized structures from simple local interaction rules between each agent and its neighbors. In addition to studying their emergent behavior, a main…
Theoretical work has shed light on the phase behavior of idealized mixtures of many components with random interactions. But typical mixtures interact through particular physical features, leading to a structured, non-random interaction…
On the basis of a microscopic model of self-consistent field, the thermodynamics of the many-particle Fermi system at finite temperatures with account of three-body interactions is built and the quasiparticle equations of motion are…
We consider heterogeneously interacting diffusive particle systems and their large population limit. The interaction is of mean field type with weights characterized by an underlying graphon. A law of large numbers result is established as…
The main difficulty that arises in the analysis of most machine learning algorithms is to handle, analytically and numerically, a large number of interacting random variables. In this Ph.D manuscript, we revisit an approach based on the…
This article addresses reaction networks in which spatial and stochastic effects are of crucial importance. For such systems, particle-based models allow us to describe all microscopic details with high accuracy. However, they suffer from…
Simple elastic models of spin-crossover compounds are known empirically to exhibit classical critical behavior. We demonstrate how the long-ranged interactions responsible for this behavior arise naturally upon integrating out mechanical…