Related papers: Pathwise estimates for effective dynamics: the cas…

This paper is devoted to the development of a theoretical and computational framework to efficiently sample the statistically significant thermally activated reaction pathways, in multi-dimensional systems obeying Langevin dynamics. We show…

We consider complex dynamical systems showing metastable behavior but no local separation of fast and slow time scales. The article raises the question of whether such systems exhibit a low-dimensional manifold supporting its effective…

A modified method of functional constraints is used to construct the exact solutions of nonlinear equations of reaction-diffusion type with delay and which are associated with variable coefficients. This study considers a most generalized…

Finding optimal reaction coordinates and predicting accurate kinetic rates for activated processes are two of the foremost challenges of molecular simulations. We introduce an algorithm that tackles the two problems at once: starting from a…

Several different methods exist for efficient approximation of paths in multiscale stochastic chemical systems. Another approach is to use bursts of stochastic simulation to estimate the parameters of a stochastic differential equation…

Reaction coordinates are widely used throughout chemical physics to model and understand complex chemical transformations. We introduce a definition of the natural reaction coordinate, suitable for condensed phase and biomolecular systems,…

Nonlinear response occurs naturally when a strong perturbation takes a system far from equilibrium. Despite of its omnipresence in nanoscale systems, it is difficult to predict in a general and efficient way. Here we introduce a way to…

Motivated by stochastic convection-diffusion problems we derive a posteriori error estimates for non-stationary non-linear convection-diffusion equations acting as a deterministic paradigm. The problem considered here neither fits into the…

Using equilibrium fluctuations to understand the response of a physical system to an externally imposed perturbation is the basis for linear response theory, which is widely used to interpret experiments and shed light on microscopic…

In this paper we consider a system of three fractional differential equations describing a nonlinear reaction. Our analysis includes both analytical technique and numerical simulation. This allows us to control the efficiency of the…

The primary emphasis of this work on kinetics is to illustrate the a posteriori approach to applications, where focus on data leads to novel outcomes, rather than the a priori tendencies of applied analysis which imposes constructs on the…

Reaction Coordinates (RCs) are indicators of hidden, low-dimensional mechanisms that govern the long-term behavior of high-dimensional stochastic processes. We present a novel and general variational characterization of optimal RCs and…

Complex multidimensional stochastic dynamics can be approximately described as diffusion along reaction coordinates (RCs). If the RCs are optimally selected, the diffusive model allows one to compute important properties of the dynamics…

Coarse-graining is central to reducing dimensionality in molecular dynamics, and is typically characterized by a mapping which projects the full state of the system to a smaller class of variables. While extensive literature has been…

The development of efficient and robust dynamic models is fundamental in the field of systems and control engineering. In this paper, a new formulation for the dynamic model of nonlinear mechanical systems, that can be applied to different…

We present a nonlinear dynamical approximation method for time-dependent Partial Differential Equations (PDEs). The approach makes use of parametrized decoder functions, and provides a general, and principled way of understanding and…

Kinematical relativistic effects are analyzed within the plane-wave impulse approximation for outgoing nucleon polarized responses in coincidence electron scattering. Following recent approaches for non-relativistic reductions of the…

The discovery of transition pathways to unravel distinct reaction mechanisms and, in general, rare events that occur in molecular systems is still a challenge. Recent advances have focused on analyzing the transition path ensemble using the…

The reduction of high-dimensional systems to effective models on a smaller set of variables is an essential task in many areas of science. For stochastic dynamics governed by diffusion processes, a general procedure to find effective…

Understanding mechanisms of rare but important events in complex molecular systems, such as protein folding or ligand (un)binding, requires accurately mapping transition paths from an initial to a final state. The committor is the ideal…