Related papers: Identifying Reaction Pathways in Phase Space via A…
We discuss the symbolic dynamics of biochemical networks with separate timescales. We show that symbolic dynamics of monomolecular reaction networks with separated rate constants can be described by deterministic, acyclic automata with a…
We use local diffusion maps to assess the quality of two types of collective variables (CVs) for a recently published hydrogen combustion benchmark dataset~\cite{guan2022benchmark} that contains ab initio molecular dynamics trajectories and…
For over a century, termolecular, or third order, chemical reactions have been explained by the Lindemann Hinshelwood mechanism, assuming sequential stabilization via bimolecular encounters. Here, we demonstrate that barrierless…
Models of reaction diffusion processes usually employ discrete lattice models with particles interacting at the same site, resulting in localized reactions in the continuum limit. Here, various non-local interactions are considered, and two…
In this paper we construct a path integral formulation of quantum mechanics on noncommutative phase-space. We first map the system to an equivalent system on the noncommutative plane. Then by applying the formalism of representing a quantum…
Raman spectroscopy is a powerful and non-invasive method for analysis of chemicals and detection of unknown substances. However, Raman signal is so weak that background noise can distort the actual Raman signal. These baseline shifts that…
An asymptotic theory is developed for general non-integrable boundary quantum field theory in 1+1 dimensions based on the Langrangean description. Reflection matrices are defined to connect asymptotic states and are shown to be related to…
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…
Characterizing the phase space distribution of particle beams in accelerators is a central part of accelerator understanding and performance optimization. However, conventional reconstruction-based techniques either use simplifying…
We develop a data-driven method to learn chemical reaction networks from trajectory data. Modeling the reaction system as a continuous-time Markov chain and assuming the system is fully observed, our method learns the propensity functions…
The asymptotic iteration method (AIM) is used to obtain both special exact solutions and general approximate solutions for a Hydrogen-like atom confined in a spherical box of arbitrary radius R. Critical box radii, at which states are no…
A variety of natural phenomena comprises a huge number of competing reactions and short-lived intermediates. Any study of such processes requires the discovery and accurate modeling of their underlying reaction network. However, this task…
Oscillators are ubiquitous in nature, and usually associated with the existence of an asymptotic phase that governs the long-term dynamics of the oscillator. % We show that asymptotic phase can be estimated using a carefully chosen series…
We consider a unified framework of sequential change-point detection and hypothesis testing modeled by means of hidden Markov chains. One observes a sequence of random variables whose distributions are functionals of a hidden Markov chain.…
We study the two-dimensional reduction of the Michaelis-Menten reaction of enzyme kinetics. First, we prove the existence and uniqueness of a slow manifold between the horizontal and vertical isoclines. Second, we determine the concavity of…
This paper concerns the use of asymptotic expansions for the efficient solving of forward and inverse problems involving a nonlinear singularly perturbed time-dependent reaction--diffusion--advection equation. By using an asymptotic…
By separating the effect of substituents from chemical process variables, such as reaction mechanism, solvent, or temperature, the Hammett equation enables control of chemical reactivity throughout chemical space. We used global regression…
This article investigates the non-stationary reaction-diffusion-advection equation, emphasizing solutions with internal layers and the associated inverse problems. We examine a nonlinear singularly perturbed partial differential equation…
We present a numerical path-integral iteration scheme for the low dimensional reduced density matrix of a time-dependent quantum dissipative system. Our approach simultaneously accounts for the combined action of a microscopically modelled…
We review recent results on quantum reactive scattering from a phase space perspective. The approach uses classical and quantum versions of normal form theory and the perspective of dynamical systems theory. Over the past ten years the…