*J. Klafter and I. M. Sokolov*

- Published in print:
- 2011
- Published Online:
- December 2013
- ISBN:
- 9780199234868
- eISBN:
- 9780191775024
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199234868.001.0001
- Subject:
- Physics, Soft Matter / Biological Physics

The name “random walk” for a problem of a displacement of a point in a sequence of independent random steps was coined by Karl Pearson in 1905 in a question posed to readers of “Nature”. The same ...
More

The name “random walk” for a problem of a displacement of a point in a sequence of independent random steps was coined by Karl Pearson in 1905 in a question posed to readers of “Nature”. The same year, a similar problem was formulated by Albert Einstein in one of his Annus Mirabilis works. Even earlier problem was posed by Louis Bachelier in his thesis devoted to the theory of financial speculations in 1900. Nowadays theory of random walks was proved useful in physics and chemistry (diffusion, reactions, mixing in flows), economics, biology (from animal spread to motion of subcellular structures) and in many other disciplines. The random walk approach serves not only as a model of simple diffusion but of many complex sub‐ and superdiffusive transport processes as well. This book discusses main variants of the random walks and gives the most important mathematical tools for their theoretical description.Less

The name “random walk” for a problem of a displacement of a point in a sequence of independent random steps was coined by Karl Pearson in 1905 in a question posed to readers of “Nature”. The same year, a similar problem was formulated by Albert Einstein in one of his *Annus Mirabilis* works. Even earlier problem was posed by Louis Bachelier in his thesis devoted to the theory of financial speculations in 1900. Nowadays theory of random walks was proved useful in physics and chemistry (diffusion, reactions, mixing in flows), economics, biology (from animal spread to motion of subcellular structures) and in many other disciplines. The random walk approach serves not only as a model of simple diffusion but of many complex sub‐ and superdiffusive transport processes as well. This book discusses main variants of the random walks and gives the most important mathematical tools for their theoretical description.

*J. Klafter and I.M. Sokolov*

- Published in print:
- 2011
- Published Online:
- December 2013
- ISBN:
- 9780199234868
- eISBN:
- 9780191775024
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199234868.003.0009
- Subject:
- Physics, Soft Matter / Biological Physics

One of the important applications of random walks in physics and chemistry is connected with the description of reactions in situations when standard schemes based on classical kinetics fail to give ...
More

One of the important applications of random walks in physics and chemistry is connected with the description of reactions in situations when standard schemes based on classical kinetics fail to give correct results. The failure of classical reaction‐ or reaction‐diffusion schemes is often due to fluctuation effects which are considered in this chapter on a specific example of an A+B‐〉B reaction scheme (catalytic decay). Again, the chapter first introduces a relevant tool, configurational averaging, and discusses the reactions between immobile reactants, as well as trapping and target problems. The first one corresponds to the case of mobile A and immobile B, the second one to a vice versa situation. The kinetics of these two seemingly similar reactions differ drastically. Considering mobile particles performing CTRW with power‐law waiting times unveils additional interesting aspects of the problem.Less

One of the important applications of random walks in physics and chemistry is connected with the description of reactions in situations when standard schemes based on classical kinetics fail to give correct results. The failure of classical reaction‐ or reaction‐diffusion schemes is often due to fluctuation effects which are considered in this chapter on a specific example of an A+B‐〉B reaction scheme (catalytic decay). Again, the chapter first introduces a relevant tool, configurational averaging, and discusses the reactions between immobile reactants, as well as trapping and target problems. The first one corresponds to the case of mobile A and immobile B, the second one to a vice versa situation. The kinetics of these two seemingly similar reactions differ drastically. Considering mobile particles performing CTRW with power‐law waiting times unveils additional interesting aspects of the problem.