Related papers: Reactive trajectories and the transition path proc…
We present a numerical method for computing optimal transition pathways and transition rates in systems of stochastic differential equations (SDEs). In particular, we compute the most probable transition path of stochastic equations by…
Transition states and minimum energy paths are essential to understand and predict chemical reactivity. Double-ended methods represent a standard approach for their determination. We introduce a new double-ended method that optimizes…
We construct path integrals for stochastic hybrid reaction-diffusion (RD) processes, in which the reaction terms depend on the discrete state of a randomly switching environment. We proceed by spatially discretizing a given RD system and…
In this paper, we discuss and compare two probabilistic approaches for associating a stochastic differential equation with a McKean-type partial differential equation featuring a reaction term and path-dependent coefficients. The…
Transition path sampling is a method for estimating the rates of rare events in molecular systems based on the gradual transformation of a path distribution containing a small fraction of reactive trajectories into a biased distribution in…
We study diffusion-controlled processes in nonequilibrium steady states, where standard rate theory assumptions break down. Using transition path theory, we generalize the relations between reactive probability fluxes and measures of the…
We introduce a path sampling method for obtaining statistical properties of an arbitrary stochastic dynamics. The method works by decomposing a trajectory in time, estimating the probability of satisfying a progress constraint, modifying…
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…
The run-and-tumble particle (RTP) is one of the simplest examples of an active particle in which the direction of constant motion randomly switches. In the one-dimensional (1D) case this means switching between rightward and leftward…
We propose an efficient method to compute reaction rate constants of thermally activated processes occurring in many-body systems at finite temperature. The method consists in two steps: first, paths are sampled using a transition path…
A time-dependent no-recrossing dividing surface is shown to lead to a new criterion for identifying reactive trajectories well before they are evolved to infinite time. Numerical dynamics simulations of a dissipative anharmonic…
The time evolution of many physical, chemical, and biological systems can be modelled by stochastic transitions between the minima of the potential energy surface describing the system of interest. We show that in cases where there are two…
We consider a population of $N$ labeled random walkers moving on a substrate, and an excitation jumping among the walkers upon contact. The label $\mathcal{X}(t)$ of the walker carrying the excitation at time $t$ can be viewed as a…
Adaptive multilevel splitting algorithms have been introduced rather recently for estimating tail distributions in a fast and efficient way. In particular, they can be used for computing the so-called reactive trajectories corresponding to…
This paper deals with the process $X = (X_t)_{t\in [0,T]}$ defined by the stochastic differential equation (SDE) $dX_t = (a(X_t) + b(Y_t))dt +\sigma(X_t)dW_1(t)$, where $W_1$ is a Brownian motion and $Y$ is an exogenous process. The first…
The process of fluctuations of trajectory observables of stochastic systems is related to processes with independent increments from the risk theory. The first-passage times of variables of the thermodynamics of trajectories, in particular,…
We present a method to study rare nonadiabatic dynamics in open quantum systems using transition path sampling and quantum jump trajectories. As with applications of transition path sampling to classical dynamics, the method does not rely…
Sampled structure sequences obtained, for instance, from real-time reactivity explorations or first-principles molecular dynamics simulations contain valuable information about chemical reactivity. Eventually, such sequences allow for the…
We discuss two independent methods of solution of a master equation whose biased jump transition rates account for long jumps of L\'{e}vy-stable type and nonetheless admit a Boltzmannian (thermal) equilibrium to arise in the large time…
We consider the system of stochastic differential equation $dX_t = A(X_{t-}) \, dZ_t$, $ X_0 = x$, driven by cylindrical $\alpha$-stable process $Z_t$ in $\mathbb{R}^d$. We assume that $A(x) = (a_{ij}(x))$ is diagonal and $a_{ii}(x)$ are…