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A small quantum scattering system (the microsystem) is studied in interaction with a large system (the macrosystem) described by unknown stochastic variables. The interaction between the two systems is diagonal for the microsystem in a…
Important gaps remain in our understanding of the thermodynamics and statistical physics of self-gravitating systems. Using mean field theory, here we investigate the equilibrium properties of several spherically symmetric model systems…
Defects such as voids are observed at multiple length scales of an additively manufactured composite material. Modeling such defects and their multiscale interaction is crucial for the materials performance prediction. In this work, we…
We consider a noise driven network of integrate-and-fire neurons. The network evolves as result of the activities of the neurons following spike-timing-dependent plasticity rules. We apply a self-consistent mean-field theory to the system…
Subdiffusion has been proposed as an explanation of various kinetic phenomena inside living cells. In order to fascilitate large-scale computational studies of subdiffusive chemical processes, we extend a recently suggested mesoscopic model…
Finite lattice models are a prototype for strongly correlated quantum systems and capture essential properties of condensed matter systems. With the dramatic progress in ultracold atoms in optical lattices, finite fermionic Hubbard systems…
We simulate the collective dynamics in spin lattices with long range interactions and collective decay in one, two and three dimensions. Starting from a dynamical mean-field approach derived by local factorization of the density operator we…
We investigate team optimal control of stochastic subsystems that are weakly coupled in dynamics (through the mean-field of the system) and are arbitrary coupled in the cost. The controller of each subsystem observes its local state and the…
We investigate the mean-field limit for interacting particle systems through a duality-based framework and obtain quantitative estimates on the convergence of marginals as well as on correlation functions. In particular, for merely…
We review some recent methods of subgrid-scale parameterization used in the context of climate modeling. These methods are developed to take into account (subgrid) processes playing an important role in the correct representation of the…
We study an interacting particle system whose dynamics depends on an interacting random environment. As the number of particles grows large, the transition rate of the particles slows down (perhaps because they share a common resource of…
Recent progress in treating the dynamically screened nature of the Coulomb interaction in strongly correlated lattice models and materials is reviewed with a focus on computational schemes based on the dynamical mean field approximation. We…
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…
Collaborative multi-agent robotic systems where agents coordinate by modifying a shared environment often result in undesired dynamical couplings that complicate the analysis and experiments when solving a specific problem or task.…
Recent advances in metagenomics have revealed macroecological patterns or "laws" describing robust statistical regularities across microbial communities. Stochastic logistic models (SLMs), which treat species as independent -- akin to ideal…
In order to understand the role of space in ecological communities where each species produces a certain type of resource and has varying abilities to exploit the resources produced by its own species and by the other species, we carry out…
We formulate theoretical modeling approaches and develop practical computational simulation methods for investigating the non-equilibrium statistical mechanics of fluid interfaces with passive and active immersed particles. Our approaches…
We consider large systems of stochastic interacting particles through discontinuous kernels which has vision geometrical constrains. We rigorously derive a Vlasov-Fokker-Planck type of kinetic mean-field equation from the corresponding…
In these lectures I will study some properties that are shared by many glassy systems. I will shown how some of these properties can be understood in the framework of the mean field approach based on the replica method and I will discuss…
Recent theoretical studies of statistical mechanical properties of systems with long range interactions are briefly reviewed. In these systems the interaction potential decays with a rate slower than 1/r^d at large distances r in d…