Matches in SemOpenAlex for { <https://semopenalex.org/work/W4313408972> ?p ?o ?g. }
- W4313408972 abstract "Using an approach based on the diffusion analog of the Cattaneo-Vernotte differential model, we find the exact analytical solution to the corresponding time-dependent linear hyperbolic initial boundary value problem, describing irreversible diffusion-controlled reactions under Smoluchowski's boundary condition on a spherical sink. By means of this solution, we extend exact analytical calculations for the time-dependent classical Smoluchowski rate coefficient to the case that includes the so-called inertial effects, occurring in the host media with finite relaxation times. We also present a brief survey of Smoluchowski's theory and its various subsequent refinements, including works devoted to the description of the short-time behavior of Brownian particles. In this paper, we managed to show that a known Rice's formula, commonly recognized earlier as an exact reaction rate coefficient for the case of hyperbolic diffusion, turned out to be only its approximation being a uniform upper bound of the exact value. Here, the obtained formula seems to be of great significance for bridging a known gap between an analytically estimated rate coefficient on the one hand and molecular dynamics simulations together with experimentally observed results for the short times regime on the other hand. A particular emphasis has been placed on the rigorous mathematical treatment and important properties of the relevant initial boundary value problems in parabolic and hyperbolic diffusion theories." @default.
- W4313408972 created "2023-01-06" @default.
- W4313408972 creator A5027919998 @default.
- W4313408972 date "2023-01-23" @default.
- W4313408972 modified "2023-10-13" @default.
- W4313408972 title "Accurate analytical calculation of the rate coefficient for the diffusion-controlled reactions due to hyperbolic diffusion" @default.
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