Related papers: Reaction kinetics in the few-encounter limit
Classical chemical kinetics use rate-equation models to describe how a reaction proceeds in time. Such models are sufficient for describing state transitions in a reaction where coherences between different states do not arise, or in other…
Chemical reaction network theory is a powerful framework to describe and analyze chemical systems. While much about the concentration profile in an equilibrium state can be determined in terms of the graph structure, the overall reaction's…
Based on the mean first passage time (MFPT) theory, we derive the expression of the MFPT in the energy-diffusion controlled regime with a power-law distribution. We discuss the finite barrier effect (i.e. thermal energy is not small with…
Turing's mechanism is often invoked to explain periodic patterns in nature, although direct experimental support is scarce. Turing patterns form in reaction-diffusion systems when the activating species diffuse much slower than the…
The first passage time for a single diffusing particle has been studied extensively, but the first passage time of a system of many diffusing particles, as is often the case in physical systems, has received little attention until recently.…
The usual Kramers theory of reaction rates in a condensed medium predict the rate to have an $\eta^{-1}$ dependence, $\eta$ being the viscosity of the medium. However, experiments on ligand binding to proteins performed long ago, showed the…
In most natural sciences there is currently the insight that it is necessary to bridge gaps between different processes which can be observed on different scales. This is especially true in the field of chemical reactions where the…
Classical theories of chemical kinetics assume independent reactions in dilute solutions, whose rates are determined by mean concentrations. In condensed matter, strong interactions alter chemical activities and create inhomogeneities that…
First passage phenomena arise across physics, biology, and finance when stochastic processes first reach a threshold, triggering downstream events. Examples include the irreversible exit from a domain, a biochemical reaction, a financial…
Understanding anomalous transport and reaction kinetics due to microscopic physical and chemical disorder is a long-standing goal in many fields including geophysics, biology, and engineering. We consider reaction-diffusion characterized by…
Plasmas in which there is a threshold for a dominant reaction to take place (such as recombination or attachment) will have particle distributions that evolve as the reaction progresses. The form of the Boltzmann collision term in such a…
New theorems for the moments of the first passage time of one dimensional nonlinear stochastic processes with an entrance boundary are formulated. This important class of one dimensional stochastic processes results among others from…
The mean first-passage time (MFPT) for a Brownian particle to surmount a potential barrier of height $\Delta U$ is a fundamental quantity governing a wide array of physical and chemical processes. According to the Arrhenius Law, the MFPT…
Chemical reactions generically require that particles come into contact. In practice, reaction is often imperfect and can necessitate multiple random encounters between reactants. In confined geometries, despite notable recent advances,…
The efficiency of an encounter-controlled two-channel reaction between two independently-mobile reactants on a lattice is characterized by the mean number $\rt$ of steps to reaction. The two reactants are distinguished by their mass with…
We revise the encounter-based approach to imperfect diffusion-controlled reactions, which employs the statistics of encounters between a diffusing particle and the reactive region to implement surface reactions. We extend this approach to…
We consider viscous, heat conducting mixtures of molecularly miscible chemical species forming a fluid in which the constituents can undergo chemical reactions. Assuming a common temperature for all components, we derive a closed system of…
We investigate how confinement may drastically change both the probability density of the first-encounter time and the related survival probability in the case of two diffusing particles. To obtain analytical insights into this problem, we…
Universal intermittent dynamics in a random catalytic reaction network, induced by smallness in the molecule number is reported. Stochastic simulations for a random catalytic reaction network subject to a flow of chemicals show that the…
Activated processes from chemical reactions up to conformational transitions of large biomolecules are hampered by barriers which are overcome only by the input of some free energy of activation. Hence, the characteristic and…