Abstract
We investigate the dynamics of Brownian particles which are active in the sense that they take up energy from the environment, which can be stored in a internal energy depot and used for different activities. As one example, we consider the generation of a self-consistent field, which in turn affects the movement of the particles. The dynamics can in this case be described by coupled reactiondiffusion equations, but will be more efficiently simulated by means of Langevin equations for the active particles. As another example, we discuss the active motion of Brownian particles which can be described by a non-linear, velocity-dependent friction function. Provided a supercritical supply of energy, the active particles are able to perform non-trivial motion, such as “uphill” motion against the direction of an external force, or motion on a stochastic limit cycle.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Albano, E. V. 1996: Self-organized collective displacements of self-driven individuals, Physical Review Letters 77, 2129–2132.
Derenyi, I.; Vicsek, T. 1995: Cooperative Transport of Brownian Particles, Physical Review Letters 75, 374–377.
Ebeling, W.; Schweitzer, F.; Tilch, B. 1999: Active Brownian Particles with Energy Depots Modelling Animal Mobility, BioSystems 49, 17–29.
Ebeling, W.; Schweitzer, F.; Tilch, B. 2000: Statistical Mechanics of Driven Canonical-Dissipative Systems and Applications to Swarm Dynamics (submitted for publication).
Erdmann, U.; Ebeling, W.; Schimansky-Geier, L.; Schweitzer, F. 1999: Brownian Particles far from Equilibrium, European Physical Journal B 15/1 (2000) 105–113.
Feistel, R.; Ebeling, W. 1989: Evolution of Complex Systems. Self-Organization, Entropy and Development, Dordrecht: Kluwer.
Promherz, P.; Zeiler, A. 1994: Dissipative condensation of ion channels described by a Langevin-Kelvin equation, Physics Letters A 190, 33–37.
Helbing, D.; Schweitzer, F.; Keltsch, J.; Molnar, P. 1997: Active Walker Model for the Formation of Human and Animal Trail Systems, Physical Review E 56, 2527–2539.
Helbing, D.; Vicsek, T. 1999: Optimal Self-Organization, New Journal of Physics 1, 13.1–13.17.
Klimontovich, Yu. L. 1994: Nonlinear Brownian Motion, Physics-Uspekhi 37, 737–766.
Makarov, V., Ebeling, W., Velarde, M. 2000: Soliton-like waves on disipative Toda lattices, Interational Journal of Bifurcation & Chaos, in press.
Mikhailov, A. S.; Meinkohn, D. 1997: Self-Motion in Physico-Chemical Systems Far from Thermal Equilibrium, in: L. Schimansky-Geier, T. Pöschel (eds.): Stochastic Dynamics, Berlin: Springer, pp. 334–345.
Rayleigh, J. W. 1945: The Theory of Sound, 2nd edition, New York: Dover.
Rosé, H.; Hempel, H.; Schimansky-Geier, L. 1994: Stochastic Dynamics of Catalytic CO Oxidation on Pt(100), Physica A 206, 421.
Schienbein, M.; Gruler, H. 1993: Langevin Equation, Fokker-Planck Equation and Cell Migration, Bulletin of Mathematical Biology 55, 585–608.
Schimansky-Geier, L.; Mieth, M.; Rosé, H.; Malchow, H. 1995: Structure Formation by Active Brownian Particles, Physics Letters A 207, 140–146.
Schimansky-Geier, L.; Schweitzer, F.; Mieth, M. 1997: Interactive Structure Fromation with Brownian Particles, in: F. Schweitzer (ed.): Self-Organization of Complex Structures: From Individual to Collective Dynamics, London: Gordon and Breach, pp. 101–118.
Schweitzer, F.; Ebeling, W.; Tilch, B. 1998: Complex Motion of Brownian Particles with Energy Depots, Physical Review Letters 80, 5044–5047.
Schweitzer, F.; Holyst, J. 2000: Modelling Collective Opinion Formation by Means of Active Brownian Particles, European Physical Journal B (in press).
Schweitzer, F.; Lao, K.; Family, F. 1997: Active Random Walkers Simulate Trunk Trail Formation by Ants, BioSystems 41, 153–166.
Schweitzer, F.; Schimansky-Geier, L. 1994: Clustering of Active Walkers in a Two-Component System, Physica A 206, 359–379.
Schweitzer, F.; Tilch, B.; Ebeling, W. 2000: Uphill Motion of Active Brownian Particles in Piecewise Linear Potentials, European Physical Journal B 14, 157–168.
Tilch, B.; Schweitzer, F.; Ebeling, W. 1999: Directed Motion of Brownian Particles with Internal Energy Depot, Physica A 273, 294–314.
Vicsek, T.; Czirok, A.; Ben-Jacob, E.; Cohen, I.; Shochet. O. 1995: Novel Type of Phase Transition in a System of Self-Driven Particles, Physical Review Letters 75, 1226–1229.
Willebrand, H.; Niedernostheide, F. J.; Ammelt, E.; Dohmen, R.; Purwins, H.G. 1991: Spatio-Temporal Oscillations During Filament Splitting in Gas Discharge Systems, Physics Letters A 152, 437–445.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Schweitzer, F. (2000). Active Motion of Brownian Particles. In: Freund, J.A., Pöschel, T. (eds) Stochastic Processes in Physics, Chemistry, and Biology. Lecture Notes in Physics, vol 557. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45396-2_10
Download citation
DOI: https://doi.org/10.1007/3-540-45396-2_10
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-41074-4
Online ISBN: 978-3-540-45396-3
eBook Packages: Springer Book Archive