Mathematical aspects of application of fractional multidimensional Fokker-Plank equation to the theory of rate of chemical reactions based on spectroscopy experiments with examples.

Authors

  • Michael Fundator 1Division of Behavioral and Social Sciences and Education, the National Academy of Sciences, Engineering, and Medicine, USA. 2Board on Physics and Astronomy, the National Academy of Sciences, Engineering, and Medicine, USA.

DOI:

https://doi.org/10.14738/aivp.93.10478

Keywords:

fractional dimension, multidimensional Fokker-Plank equation, Hausdorff dimension, barrier crossing.

Abstract

Different types of spectroscopy experiments carried by multiple teams suggest some discrepancies between one-dimensional (1D) Kramers’ theory for the rate of chemical reactions with hydrodynamic Stokes-Einstein friction model. The disagreement continued despite multidimensional (multi-D), or non-Markovian, or not-exactly hydrodynamic modifications by Grote-Hynes, Hubbard, and other authors. The proposed fractional dimensional modification to multi-D model is based on theoretical and experimental findings of dimensional disagreement and deceptive simplicity between curves for barrier crossing at equilibrium and the boundary of the curves. Comparison of less anomalous fractional derivative exponents of 1.9 and 1.7 with more anomalous of 1.5 and 1.3 suggest Sierpinski carpet, Cesaro’s, and different attractors’ curves.

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Published

2021-07-08

How to Cite

Fundator, M. (2021). Mathematical aspects of application of fractional multidimensional Fokker-Plank equation to the theory of rate of chemical reactions based on spectroscopy experiments with examples. European Journal of Applied Sciences, 9(3), 577–580. https://doi.org/10.14738/aivp.93.10478