Related papers: Exact dynamical coarse-graining without time-scale…
The generalized Langevin equation is a model for the motion of coarse-grained particles where dissipative forces are represented by a memory term. The numerical realization of such a model requires the implementation of a stochastic…
The dynamics of physical systems that require high-dimensional representation can often be captured in a few meaningful degrees of freedom called collective variables (CVs). However, identifying CVs is challenging and constitutes a…
It is quite generally assumed that the overdamped Langevin equation provides a quantitative description of the dynamics of a classical Brownian particle in the long time limit. We establish and investigate a paradigm anomalous diffusion…
In light of the recently developed complete GJ set of single random variable stochastic, discrete-time St{\o}rmer-Verlet algorithms for statistically accurate simulations of Langevin equations, we investigate two outstanding questions: 1)…
In order to illustrate the adaptation of traditional continuum numerical techniques to the study of complex network systems, we use the equation-free framework to analyze a dynamically evolving multigraph. This approach is based on coupling…
We present results on the ballistic and diffusive behavior of the Langevin dynamics in a periodic potential that is driven away from equilibrium by a space-time periodic driving force, extending some of the results obtained by Collet and…
Many complex systems, ranging from migrating cells to animal groups, exhibit stochastic dynamics described by the underdamped Langevin equation. Inferring such an equation of motion from experimental data can provide profound insight into…
Coarse graining enables the investigation of molecular dynamics for larger systems and at longer timescales than is possible at atomic resolution. However, a coarse graining model must be formulated such that the conclusions we draw from it…
We study analytically and by event-driven molecular dynamics simulations the nonergodic and aging properties of force-free cooling granular gases with both constant and velocity-dependent (viscoelastic) restitution coefficient $\varepsilon$…
The measured time series from complex systems are renowned for their intricate stochastic behavior, characterized by random fluctuations stemming from external influences and nonlinear interactions. These fluctuations take diverse forms,…
Score-based generative models (SGMs) have demonstrated remarkable synthesis quality. SGMs rely on a diffusion process that gradually perturbs the data towards a tractable distribution, while the generative model learns to denoise. The…
We propose a new method called the N-particle underdamped Langevin algorithm for optimizing a special class of non-linear functionals defined over the space of probability measures. Examples of problems with this formulation include…
Diffusion maps approximate the generator of Langevin dynamics from simulation data. They afford a means of identifying the slowly-evolving principal modes of high-dimensional molecular systems. When combined with a biasing mechanism,…
Spatio-temporal processes in environmental applications are often assumed to follow a Gaussian model, possibly after some transformation. However, heterogeneity in space and time might have a pattern that will not be accommodated by…
We unify the variational hypocoercivity framework established by D. Albritton, S. Armstrong, J.-C. Mourrat, and M. Novack, with the notion of second-order lifts of reversible diffusion processes, recently introduced by A. Eberle and F.…
We survey an area of recent development, relating dynamics to theoretical computer science. We discuss the theoretical limits of simulation and computation of interesting quantities in dynamical systems. We will focus on central objects of…
Systems governed by a multivariate Langevin equation featuring an exact potential exhibit straightforward dynamics but are often difficult to recognize because, after a general coordinate change, the gradient flow becomes obscured by the…
General self-consistent expressions for the coefficients of diffusion and dynamical friction in a stable, bound, multicomponent self-gravitating and inhomogeneous system are derived. They account for the detailed dynamics of the colliding…
A generalized understanding of protein dynamics is an unsolved scientific problem, the solution of which is critical to the interpretation of the structure-function relationships that govern essential biological processes. Here, we approach…
Coarse-graining complex molecular systems to lower-dimensional reaction coordinates is a powerful approach for capturing their effective dynamics. The generalized Langevin equation (GLE) provides an exact framework for modeling…