# Novel type of phase transition in a system of self-driven particles.

@article{Vicsek1995NovelTO, title={Novel type of phase transition in a system of self-driven particles.}, author={Vicsek and Czir{\'o}k and Ben-Jacob and Cohen and Shochet}, journal={Physical review letters}, year={1995}, volume={75 6}, pages={ 1226-1229 } }

A simple model with a novel type of dynamics is introduced in order to investigate the emergence of self-ordered motion in systems of particles with biologically motivated interaction. In our model particles are driven with a constant absolute velocity and at each time step assume the average direction of motion of the particles in their neighborhood with some random perturbation $(\ensuremath{\eta})$ added. We present numerical evidence that this model results in a kinetic phase transition…

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## References

SHOWING 1-10 OF 24 REFERENCES

Models for contact-mediated pattern formation: cells that form parallel arrays

- BiologyJournal of mathematical biology
- 1990

Kinetic continuum models are derived for cells that crawl over a 2D substrate, undergo random reorientation, and turn in response to contact with a neighbor, and it is found that behavior depends on parameters such as total mass, random motility, adherence, and sloughing rates, as well as on broad aspects of the contact response.

Introduction to Phase Transitions and Critical Phenomena

- Physics
- 1971

This is a paperback edition of a distinguished book, originally published by Clarendon Press in 1971. It was then the first text on critical phenomena, a field that has enjoyed great activity for the…

Flocks, herds and schools: A distributed behavioral model

- Computer ScienceSIGGRAPH
- 1987

This paper explores an approach based on simulation as an alternative to scripting the paths of each bird individually, an elaboration of a particle systems, with the simulated birds being the particles.

Dynamical aspects of animal grouping: swarms, schools, flocks, and herds.

- Biology, MedicineAdvances in biophysics
- 1986

Fractal Growth Phenomena

- Materials Science
- 1989

Foreword, B. Mandelbrot introduction fractal geometry fractal measures methods for determining fractal dimensions local growth models diffusion-limited growth growing self-affine surfaces…

private communication [13] see

- e.g., R. D. Astumian and M. Bier Phys. Rev. Lett. 72,
- 1994

Physica A200

- 1993

Fractal Growth Phenomena. (Singapore, World Scientific

- Fractal Growth Phenomena. (Singapore, World Scientific
- 1992

Surface Disordering

- Surface Disordering
- 1992

Tenenbaum Physica A187

- Tenenbaum Physica A187
- 1992