Related papers: From Localization to Stochastics in BBGKY Collecti…
Solutions to the BBGKY hierarchy of equations for molecular Brownian particle in ideal gas are considered, and exact relations are derived between probability distribution of path of the particle, its derivatives in respect to gas density…
In this paper, a high-order/low-order (HOLO) method is combined with a micro-macro (MM) decomposition to accelerate iterative solvers in fully implicit time-stepping of the BGK equation for gas dynamics. The MM formulation represents a…
This paper presents a revolutionary approach to the characterization, forecast, and control of collective systems. Collective systems are an ensemble of conservatively interacting entities. The evolution of the entities are determined by…
The main goal of the present article is to extend the Bogolyubov method for deriving kinetic equations to dissipative many-body systems. The basic conjecture underlying the Bogolyubov approach is the functional hypothesis, according to…
People organize in groups and contagions spread across them. A simple stochastic process, yet complex to model due to dynamical correlations within and between groups. Moreover, groups can evolve if agents join or leave in response to…
A new direct integration method is established to construct the solutions of the stationary BBGKY hierarchy, assuming the usual form of the equilibrium correlation functions, for infinite classical systems of particles interacting via a…
In this paper, a physics-oriented stochastic kinetic scheme will be developed that includes random inputs from both flow and electromagnetic fields via a hybridization of stochastic Galerkin and collocation methods. Based on the BGK-type…
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…
Based on multiple simulation trajectories, which started from dispersively selected initial conformations, the weighted ensemble dynamics method is designed to robustly and systematically explore the hierarchical structure of complex…
The Fokker-Planck equations for stochastic dynamical systems, with non-Gaussian $\alpha-$stable symmetric L\'evy motions, have a nonlocal or fractional Laplacian term. This nonlocality is the manifestation of the effect of non-Gaussian…
This paper presents a position-based flocking model for interacting agents, balancing cohesion-separation and alignment to achieve stable collective motion. The model modifies a position-velocity-based approach by approximating velocity…
Collective motion and self-organization of interacting particles, such as flocking and swarming, can be viewed as nonequilibrium analogues of collective dynamics in gases. Motivated by the analogy between gas mixtures and Cucker--Smale…
We study spatially non-homogeneous kinetic models for vehicular traffic flow. Classical formulations, as for instance the BGK equation, lead to unconditionally unstable solutions in the congested regime of traffic. We address this issue by…
We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of…
We explore analytically and numerically agglomeration driven by advection and localized source. The system is inhomogeneous in one dimension, viz. along the direction of advection. We analyze a simplified model with mass-independent…
We develop a systematic framework for the model reduction of multivariate geometric Brownian motions (GBMs), a fundamental class of stochastic processes with broad applications in mathematical finance, population biology, and statistical…
Numerous problems in development, regeneration, and disease involve simultaneous evolution of both spatial organization and the internal state of the constituents in addition to local interactions and crowding. This motivates us to study a…
We develop a generalized hyperdynamics method, which is able to simulate slow dynamics in atomistic general (both energy and entropy-dominated) systems. We show that a few functionals of the pair correlation function, involving two-body…
Many biological processes are supported by special molecules, called motor proteins or molecular motors, that transport cellular cargoes along linear protein filaments and can reversibly associate to their tracks. Stimulated by these…
A probabilistic analysis of the direct simulation of a homogeneous gas is given. A hierarchy of equations similar to the BBGKY hierarchy for the reduced probability densities is derived. By invoking the molecular chaos assumption, an…