相关论文: A Controlled Mean Field Model for Chiplet Populati…
Many complex dynamical systems in the real world, including ecological, climate, financial, and power-grid systems, often show critical transitions, or tipping points, in which the system's dynamics suddenly transit into a qualitatively…
We are interested in exploring interacting particle systems that can be seen as microscopic models for a particular structure of coupled transport flux arising when different populations are jointly evolving. The scenarios we have in mind…
We study the convergence of stochastic time-discretization schemes for evolution equations driven by random velocity fields, including examples like stochastic gradient descent and interacting particle systems. Using a unified framework…
Motivated by structured parasite populations in aquaculture we consider a class of size-structured population models, where individuals may be recruited into the population with distributed states at birth. The mathematical model which…
We consider interacting agent systems with a large number of stochastic agents (or particles) influenced by a fixed number of external stochastic lead agents. Such examples arise, for example in models of opinion dynamics, where a small…
Animal morphogenesis often involves significant shape changes of epithelial tissue sheets. Great progress has been made in understanding the underlying cellular driving forces and their coordination through biomechanical feedback loops.…
We provide a review of recently-develop dynamical mean-field theory (DMFT) approaches to the general problem of strongly correlated electronic systems with disorder. We first describe the standard DMFT approach, which is exact in the limit…
An efficient microcanonical dynamics has been recently introduced for Ising spin models embedded in a generic connected graph even in the presence of disorder i.e. with the spin couplings chosen from a random distribution. Such a dynamics…
We study interacting particle systems driven by noise, modeling phenomena such as opinion dynamics. We are interested in systems that exhibit phase transitions i.e. non-uniqueness of stationary states for the corresponding McKean-Vlasov…
We study stochastic particle systems on a complete graph and derive effective mean-field rate equations in the limit of diverging system size, which are also known from cluster aggregation models. We establish the propagation of chaos under…
Although coarse-grained models have been widely used to explain exotic phenomena in complex fluids, such as droplet formation in living cells, these conventional approaches often fail to capture the intricate microscopic degrees of freedom…
An economic modeling approach for cavity quantum electrodynamics is provided by mean-field dynamics, wherein the optical field is described classically while a self-consistent interaction with quantum emitters is incorporated through the…
Quite recently I have proposed a nonperturbative dynamical effective field model (DEFM) to quantitatively describe the dynamics of interacting ferrofluids. Its predictions compare very well with the results from simulations. In this paper I…
With the rapid development of AI and robotics, transporting a large swarm of networked robots has foreseeable applications in the near future. Existing research in swarm robotics has mainly followed a bottom-up philosophy with predefined…
A two populations mean-field monomer-dimer model including both hard-core and attractive interactions between dimers is considered. The pressure density in the thermodynamic limit is proved to satisfy a three-dimensional variational…
Residual deep neural networks are formulated as interacting particle systems leading to a description through neural differential equations, and, in the case of large input data, through mean-field neural networks. The mean-field…
Dynamical Mean-Field Theory (DMFT) is a powerful theoretical framework for analyzing systems with many interacting degrees of freedom. This tutorial provides an accessible introduction to DMFT. We begin with a linear model where the DMFT…
A simple model to handle the flow of people in emergency evacuation situations is considered: at every point x, the velocity U(x) that individuals at x would like to realize is given. Yet, the incompressibility constraint prevents this…
We propose and investigate a one-parameter probabilistic mixture of one-dimensional elementary cellular automata under the guise of a model for the dynamics of a single-species unstructured population with nonoverlapping generations in…
By considering a quantum critical Lipkin-Meshkov-Glick model we analyze a new type of Landau-Zener transitions where the population transfer is mediated by interaction rather than from a direct diabatic coupling. For this scenario, at a…