Category: Transport Processes

Categories
diffusion fluid flow Nonequilibrium Pattern Formation

Pattern Formation at Liquid Interfaces

B. Heidel, C. Knobler, R. Hilfer, R. Bruinsma

Physical Review Letters 60, 2492 (1988)
10.1103/PhysRevLett.60.2492

submitted on
Monday, January 11, 1988

Although many examples of pattern formation resulting from chemical reactions at liquid interfaces are known, few have been studied in detail. We report a quantitative study of patterns formed by the photoproduction of Fe++ and its subsequent reaction to form Turnbull’s Blue. The experiment leads to the postulation of a mechanism in which autocatalysis is enhanced by double diffusion. The phase diagram contains a line of phase transitions whose critical behavior is discussed.



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Categories
Fractals Mathematics Stochastic Processes Transport Processes

Probabilistic Interpretation of the Einstein Relation

R. Hilfer, A. Blumen

Physical Review A 37, 578 (1988)
10.1103/PhysRevA.37.578

submitted on
Monday, June 8, 1987

We present a probabilistic picture for the Einstein relation which holds for arbitrarily connected structures. The diffusivity is related to mean first-passage times, while the conductance is given as a direct-passage probability. The fractal Einstein relation is an immediate consequence of our result. In addition, we derive a star-triangle transformation for Markov chains and calculate the exact values of the fracton (spectral) dimension for treelike structures. We point to the relevance of the probabilistic interpretation for simulation and experiment.



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