#### 19 Citations

Number of common sites visited by N random walkers.

- Mathematics, Physics
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2012

The mean number of common sites, W(N)(t), visited by N independent random walkers each of length t and all starting at the origin at t = 0 in d dimensions is computed analytically. Expand

Application of cellular automata to sewer network optimization problems

- Mathematics
- 2011

Abstract A Cellular Automata approach is introduced in this paper for the optimal design of sewer network problems. The solution of sewer network optimization problems requires the determination of… Expand

The elements of probabilistic time geography

- Geography, Computer Science
- GeoInformatica
- 2011

This paper starts with the standard assumption of time geography (no further knowledge), and develops the appropriate probability distribution by three equivalent approaches. Expand

Optimal solution of large-scale reservoir-operation problems: Cellular-automata versus heuristic-search methods

- Mathematics
- 2009

A novel cellular-automata approach is developed in this article for the optimal solution of large-scale reservoir-operation problems. The aim of this article is to show how cellular automata can be… Expand

Elliptic equation for random walks. Application to transport in microporous media

- Mathematics
- 2007

We consider a process of random walks with arbitrary residence time distribution. We show that in many cases this process may not be described by the classical (Fick) parabolic diffusion equation,… Expand

A Survey on Cellular Automata ∗

- 2003

A cellular automaton is a decentralized computing model providing an excellent platform for performing complex computation with the help of only local information. Researchers, scientists and… Expand

Multiparticle random walks on a deformable medium.

- Mathematics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2002

The results show that the randomly distributed particles in the beginning will be self-organized into a cluster pattern in the intermediate stage, and then return to the random distribution patterns in the late stage. Expand

Survival probability and order statistics of diffusion on disordered media.

- Mathematics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2002

We investigate the first passage time t(j,N) to a given chemical or Euclidean distance of the first j of a set of N>>1 independent random walkers all initially placed on a site of a disordered… Expand

Note: About the Random Walk from Many Injection Points

- Mathematics
- 1999

The random walk on a discrete lattice has been analysed in completely different fields such as chemistry [1, 2], ecology [3, 4], and general physics [5, 6]. The general idea has been to insert a… Expand

Absence of PS integrins or laminin A affects extracellular adhesion, but not intracellular assembly, of hemiadherens and neuromuscular junctions in Drosophila embryos.

- Biology, Medicine
- Developmental biology
- 1998

It is suggested that neuromuscular contact in part requires basement membrane adhesion to the general muscle surface, and this form of adhesion is completely abolished in the absence of laminin A. Expand

#### References

SHOWING 1-8 OF 8 REFERENCES

Territory covered by N diffusing particles

- Mathematics
- Nature
- 1992

THE number of distinct sites visited by a random walker after t steps is of great interest1–21, as it provides a direct measure of the territory covered by a diffusing particle. Thus, this quantity… Expand

On reptation in polymer melts

- Chemistry
- 1986

A rederivation of the basic scaling laws for polymer reptation in a condensed phase yield directly for the coefficient of self‐diffusion. Dr∼M−2, where M is proportional to the polymer molecular… Expand

On the Williams-Watts function of dielectric relaxation.

- Chemistry, Medicine
- Proceedings of the National Academy of Sciences of the United States of America
- 1984

This work derives this form of varphi(alpha)(t) from the following random-walk model: if the diffusion of defects toward dipoles is executed as a continuous-time random walk composed of an alternation of steps and pauses and the pausing-time distribution function has a long tail of the form psi(t) infinity t(-1-alpha), then the relaxation function has the above fractional exponential form. Expand

Walks, walls, wetting, and melting

- Materials Science
- 1984

New results concerning the statistics of, in particular,p random walkers on a line whose paths do not cross are reported, extended, and interpreted. A general mechanism yielding phase transitions in… Expand

Kinetics of electron trapping reactions in amorphous solids; a non-Gaussian diffusion model

- Materials Science
- 1977

Reptation of a Polymer Chain in the Presence of Fixed Obstacles

- Chemistry
- 1971

We discuss possible motions for one polymer molecule P (of mass M) performing wormlike displacements inside a strongly cross‐linked polymeric gel G. The topological requirement that P cannot… Expand