Related papers: Complexity reduction in many particles systems wit…
Inspired by a PDE-ODE system of aggregation developed in the biomathematical literature, an interacting particle system representing aggregation at the level of individuals is investigated. It is proved that the empirical density of the…
We use the BBGKY hierarchy equations to calculate, perturbatively, the lowest order nonlinear correction to the two point correlation and the pair velocity for Gaussian initial conditions in a critical density matter dominated cosmological…
We investigate algorithmic control of a large swarm of mobile particles (such as robots, sensors, or building material) that move in a 2D workspace using a global input signal (such as gravity or a magnetic field). We show that a maze of…
Optimal control of large particle systems with collective dynamics by few agents is a subject of high practical importance (e.g. in evacuation dynamics), but still limited mathematical basis. In particular the transition from discrete…
The goal of this paper is to describe the various kinetic equations which arise from scaling limits of interacting particle systems. We provide a formalism which allows us to determine the kinetic equation for a given interaction potential…
Complex social systems are composed of interconnected individuals whose interactions result in group behaviors. Optimal control of a real-world complex system has many applications, including road traffic management, epidemic prevention,…
The goal of these expository notes is to give an introduction to random matrices for non-specialist of this topic focusing on the link between random matrices and systems of particles in interaction. We first recall some general results…
In this paper we continue the study of the derivation of different types of kinetic equations which arise from scaling limits of interacting particle systems. We began this study in \cite{NVW}. More precisely, we consider the derivation of…
Open quantum systems that feature non-Markovian dynamics are routinely solved using techniques such as the Hierarchical Equations of Motion (HEOM). However, their usage of the entire system density-matrix renders them intractable for…
In this article we study a system of $N$ particles, each of them being defined by the couple of a position (in $\mathbb{R}^d$) and a so-called orientation which is an element of a compact Riemannian manifold. This orientation can be seen as…
Starting from a many-body classical system governed by a trace-form entropy we derive, in the stochastic quantization picture, a family of non linear and non-Hermitian Schroedinger equations describing, in the mean filed approximation, a…
We investigate a two-dimensional system of active particles confined to a narrow annular domain. Despite the absence of explicit interactions among the velocities or the active forces of different particles, the system displays a transition…
We study fluctuation fields of orthogonal polynomials in the context of particle systems with duality. We thereby obtain a systematic orthogonal decomposition of the fluctuation fields of local functions, where the order of every term can…
We discuss the problem of two particles interacting via short-range interactions within a harmonic-oscillator trap. The interactions are organized according to their number of derivatives and defined in truncated model spaces made from a…
The quantum mechanics formalism introduced new revolutionary concepts challenging our everyday perceptions. Arguably, quantum entanglement, which explains correlations that cannot be reproduced classically, is the most notable of them.…
Filtering is concerned with online estimation of the state of a dynamical system from partial and noisy observations. In applications where the state of the system is high dimensional, ensemble Kalman filters are often the method of choice.…
A fast algorithm to study one-dimensional self-gravitating systems, and, more generally, systems that are Lagrangian integrable between collisions, is presented. The algorithm is event-driven, and uses a heap-ordered set of predicted future…
The BBGKY hierarchy of equations for a particle interacting with an ideal gas is investigated. Principal properties of its solutions are disclosed, as exact identities which connect probability distribution of path of the particle, its…
The Random Batch Method (RBM) is an effective technique to reduce the computational complexity when solving certain stochastic differential problems (SDEs) involving interacting particles. It can transform the computational complexity from…
Here we discuss a particle-based approach to deal with systems of many identical quantum objects (particles) which never employs labels to mark them. We show that it avoids both methodological problems and drawbacks in the study of quantum…