Reaction–diffusion with stochastic decay rates

Abstract

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 fluctuations in both transport times and decay rates. We introduce and analyze a model framework that explicitly connects microscopic fluctuations with the mescoscopic description. For broad distributions of transport and reaction time scales we compute the particle density and derive the equations governing its evolution, finding power-law decay of the survival probability, and spatially varying decay that leads to subdiffusion and an asymptotically stationary surviving-particle density. These anomalies are clearly attributable to non-Markovian effects that couple transport and chemical properties in both reaction and diffusion terms.

Invariants of motion with stochastic resetting and space-time coupled returns

“…Stochastic motion with stochastic resetting is of considerable interest due to its broad applicability in statistical [1][2][3][4][5][6][7], chemical [8][9][10][11][12], and biological physics [13,14]; and due to its importance in computer science [15,16], computational physics [17,18], population dynamics [19][20][21], queuing theory [22][23][24] and the theory of search and first-passage [25][26][27]. Particularly, in statistical physics, such motion has become a focal point of recent studies owing to the rich non-equilibrium [2][3][4][5][6][28][29][30] and first-passage [31][32][33][34][35][36] phenomena it displays.…”

Landau-like expansion for phase transitions in stochastic resetting

“…Michaelis-Menten chemical reaction. Michaelis-Menten chemical reactions are an integral part of first passage under restart (FPUR) formalism [42][43][44][45][46]. Here we will assume a two-state model of this reaction where an enzyme (E) binds with a substrate (S) to form two alternative metastable states: ES 1 with probability p or ES 2 otherwise [see Fig.…”

Stochastic model for filtration by porous materials

“…Following [53] we, now, exchange the integration over x with summation over n since the two variables are independent and we break the expectation value in two terms, one averaging over all indices up to n − 1 and the one averaging over the last index n:…”

“…To evaluate the Laplace inverse transform of the previous expression, it has been shown [53] (in the framework of a reactive-diffusive system) that the behavior of eq. (C6) is dominated by the numerator alone.…”