Related papers: Dominant Reaction Pathways in High Dimensional Sys…
The dominant reaction pathway (DRP) is a rigorous framework to microscopically compute the most probable trajectories, in non-equilibrium transitions. In the low-temperature regime, such dominant pathways encode the information about 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…
We study the role of quantum fluctuations of atomic nuclei in the real-time dynamics of non-equilibrium macro-molecular transitions. To this goal we introduce an extension of the Dominant Reaction Pathways (DRP) formalism, in which the…
For reaction-diffusion processes with at most bimolecular reactants, we derive well-behaved, numerically tractable, exact Langevin equations that govern a stochastic variable related to the response field in field theory. Using duality…
Finding representative reaction pathways is necessary for understanding mechanisms of molecular processes, but is considered to be extremely challenging. We propose a new method to construct reaction paths based on mean first-passage times.…
We propose an adaptive biasing algorithm aimed at enhancing the sampling of multimodal measures by Langevin dynamics. The underlying idea consists in generalizing the standard adaptive biasing force method commonly used in conjunction with…
Diffusion of a particle passing over the saddle point of a two-dimensional quadratic potential is studied via a set of coupled Langevin equations and the expression for the passing probability is obtained exactly. The passing probability is…
Effective dynamics using conditional expectation was proposed in [F. Legoll and T. Leli\`evre, Nonlinearity, 2010] to approximate the essential dynamics of high-dimensional diffusion processes along a given reaction coordinate. The…
We develop an efficient method to calculate probabilities of large deviations from the typical behavior (rare events) in reaction--diffusion systems. The method is based on a semiclassical treatment of underlying "quantum" Hamiltonian,…
Diffusion mediated reaction models are particularly ubiquitous in the description of physical, chemical or biological processes. The random walk schema is a useful tool for formulating these models. Recently, evanescent random walk models…
Patterns in reaction-diffusion systems near primary bifurcations can be studied locally and classified by means of amplitude equations. This is not possible for excitable reaction-diffusion systems. In this Letter we propose a global…
A computational procedure is developed for determining the conversion probability for reaction-diffusion systems in which a first-order catalytic reaction is performed over active particles. We apply this general method to systems on metric…
The paradigmatic model of the directed percolation process is studied near its second order phase transition between an absorbing and an active state. The model is first expressed in a form of Langevin equation and later rewritten into a…
Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a…
Characterizing thermally activated transitions in high-dimensional rugged energy surfaces is a very challenging task for classical computers. Here, we develop a quantum annealing scheme to solve this problem. First, the task of finding the…
We present a data-driven point of view for rare events, which represent conformational transitions in biochemical reactions modeled by over-damped Langevin dynamics on manifolds in high dimensions. We first reinterpret the transition state…
The two-dimensional barrier passage is studied in the framework of Langevin statistical reactive dynamics. The optimal incident angle for a particle diffusing in the dissipative non-orthogonal environment with various strengths of coupling…
Evaluating the linear response of a driven system to a change in environment temperature(s) is essential for understanding thermal properties of nonequilibrium systems. The system is kept in weak contact with possibly different fast…
We develop a theoretical approach to the protein folding problem based on out-of-equilibrium stochastic dynamics. Within this framework, the computational difficulties related to the existence of large time scale gaps in the protein folding…
A model has two main aims: predicting the behavior of a physical system and understanding its nature, that is how it works, at some desired level of abstraction. A promising recent approach to model building consists in deriving a…