Related papers: Neural network approach to time-dependent dividing…
Dynamics between reactants and products are often mediated by a rate-determining barrier and an associated dividing surface leading to the transition state theory rate. This framework is challenged when the barrier is time-dependent because…
In chemical or physical reaction dynamics, it is essential to distinguish precisely between reactants and products for all time. This task is especially demanding in time-dependent or driven systems because therein the dividing surface (DS)…
Chemical reactions in multidimensional systems are often described by a rank-1 saddle, whose stable and unstable manifolds intersect in the normally hyperbolic invariant manifold (NHIM). Trajectories started on the NHIM in principle never…
Transition state theory formally provides a simplifying approach for determining chemical reaction rates and pathways. Given an underlying potential energy surface for a reactive system, one can determine the dividing surface in phase space…
We introduce Neural Dynamical Systems (NDS), a method of learning dynamical models in various gray-box settings which incorporates prior knowledge in the form of systems of ordinary differential equations. NDS uses neural networks to…
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…
Chemical reaction rates must increasingly be determined in systems that evolve under the control of external stimuli. In these systems, when a reactant population is induced to cross an energy barrier through forcing from a temporally…
Reaction rates of chemical reactions under nonequilibrium conditions can be determined through the construction of the normally hyperbolic invariant manifold (NHIM) [and moving dividing surface (DS)] associated with the transition state…
Transition State Theory is a central cornerstone in reaction dynamics. Its key step is the identification of a dividing surface that is crossed only once by all reactive trajectories. This assumption is often badly violated, especially when…
Chemical reactions subjected to time-varying external forces cannot generally be described through a fixed bottleneck near the transition state barrier or dividing surface. A naive dividing surface attached to the instantaneous, but moving,…
The framework of transition state theory (TST) provides a powerful way for analyzing the dynamics of physical and chemical reactions. While TST has already been successfully used to obtain reaction rates for systems with a single…
The identification of trajectories that contribute to the reaction rate is the crucial dynamical ingredient in any classical chemical reactivity calculation. This problem often requires a full scale numerical simulation of the dynamics, in…
Glass transitions are widely observed in various types of soft matter systems. However, the physical mechanism of these transitions remains {elusive}, despite years of ambitious research. In particular, an important unanswered question is…
Many natural systems, such as neurons firing in the brain or basketball teams traversing a court, give rise to time series data with complex, nonlinear dynamics. We can gain insight into these systems by decomposing the data into segments…
A permanently increasing number of on-board automotive control systems requires new approaches to their digital mapping that improves functionality in terms of adaptability and robustness as well as enables their easier on-line software…
Recurrent Neural Networks (RNNs) have shown great success in modeling time-dependent patterns, but there is limited research on their learned representations of latent temporal features and the emergence of these representations during…
Spiking Neural Networks (SNN) are characterised by their unique temporal dynamics, but the properties and advantages of such computations are still not well understood. In order to provide answers, in this work we demonstrate how Spiking…
Data-driven models for predicting dynamic responses of linear and nonlinear systems are of great importance due to their wide application from probabilistic analysis to inverse problems such as system identification and damage diagnosis. In…
Dynamics play a critical role in computation. The principled evolution of states over time enables both biological and artificial networks to represent and integrate information to make decisions. In the past few decades, significant…
Classical transition state theory (TST) is the cornerstone of reaction rate theory. It postulates a partition of phase space into reactant and product regions, which are separated by a dividing surface that reactive trajectories must cross.…