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On a unified treatment of diffusion and kinetic processes
Author(s) -
Ulmer W.
Publication year - 1983
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560230607
Subject(s) - soliton , brownian motion , nonlinear system , fick's laws of diffusion , eigenfunction , diffusion , constant (computer programming) , reaction–diffusion system , physics , diffusion equation , non equilibrium thermodynamics , statistical physics , classical mechanics , quantum mechanics , eigenvalues and eigenvectors , economy , computer science , economics , programming language , service (business)
By the means of gauge invariance of the continuity equation Fick's law of diffusion can be extended to also comprehend the chemical reaction. In the case of first‐order reactions a complete set of eigenfunctions is obtained. These solutions provide a tool for pattern recognition in biochemical and biological problems (e.g., formation of chromosome banding). The transport equation, including reactions of second order, exhibits soliton solutions describing the propagation of a kinetic process in a medium (molecular chain, fluids, etc.). A relationship to the soliton solutions of the nonlinear Schrödinger equation and Korteweg–de Vries equation of hydrodynamics is also indicated. The propagation of a reactive process (transition state) occurs in many problems of molecular biology. The Brownian motion of ions undergoing a reaction of first order in a constant magnetic field is also exactly solved.