Complutense University Library

Coherent motions and clusters in a dissipative Morse ring chain

Makarov , Valeri A. and Dunkel, J. and Ebeling, Werner and Erdmann, U (2002) Coherent motions and clusters in a dissipative Morse ring chain. International Journal of Bifurcation and Chaos, 12 (11). pp. 2359-2377. ISSN 0218-1274

[img] PDF
Restricted to Repository staff only until 31 December 2020.

1MB

Official URL: http://www.worldscientific.com/doi/pdf/10.1142/S0218127402005923

View download statistics for this eprint

==>>> Export to other formats

Abstract

We study a one-dimensional ring chain of length L with N particles interacting via Morse potentials and influenced by dissipative forces (passive and active friction). We show that by negative friction the system can be driven far from the thermodynamic equilibrium states. For over-critical pumping with free energy several types of coherent motions including uniform rotations, optical oscillations and waves emerge in the ring. We also show the existence of a critical particle density n(c) = N/L-c, below that the particles spontaneously organize into clusters which can actively rotate. Additionally, the influence of white noise on the clustering is discussed.

Item Type:Article
Uncontrolled Keywords:Nonlinear friction; Active Brownian particles; Lennard-Jones-like interactions; Cluster formation; Brownian particles; Energy depots; Toda; Excitation; Solitons; Lattice
Subjects:Sciences > Mathematics > Differential equations
ID Code:16910
References:

Bolterauer, H. & Opper, M. [1981] \Solitons in the statistical mechanics of the Toda lattice," Z. Phys. B42, 155-161.

Christov, C. I. & Velarde, M. G. [1995] \Dissipative solitons," Physica D86, 323-347.

Chu, X. L. & Velarde, M. G. [1991] \Korteweg-de Vries soliton excitation in Benard-Marangoni convection," Phys. Rev. A43, 1094-1096.

Ebeling, W., Jenssen, M. & Romanowsky, Y. M. [1989] \Irreversible processes and selforganization," Teubner Texte Physik, Vol. 23 (Teubner Leipzig), pp. 7-24.

Ebeling, W. & Jenssen, M. [1991] \Soliton-assisted activation processes," Ber. Bunsenges. Phys. Chem. 95, 1356-1362.

Ebeling, W., Schweitzer, F. & Tilch, B. [1999] \Active Brownian particles with energy depots modelling animal mobility," BioSyst. 49, 17-29.

Ebeling, W., Erdmann, U., Dunkel, J. & Jenssen, M. [2000] \Nonlinear dynamics and fluctuations of dissipative Toda chains," J. Stat. Phys. 101, 443-457.

Erdmann, U., Ebeling, W., Schimansky-Geier, L. & Schweitzer, F. [2000] \Brownian particles far from equilibrium," Eur. Phys. J. B15, 105-113.

Feynman, R. P. [1972] Statistical Mechanics (Benjamin Mass.).

Guckenheimer, J. & Holmes, P. [1983] Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Vol. 42 (Springer).

Jenssen,M. & Ebeling,W. [2000] \Distribution functions and excitation spectra of Toda systems at intermediate temperatures," Physica D141, 117-132.

Kac, M., Uhlenbeck, G. E. & Hemmer, P. C. [1963] \On the van der Waals theory of the vapor-liquid equilibrium," J. Math. Phys. 4, 216-228.

Landa, P. [1996] Nonlinear Oscillations and Waves in Dynamical Systems (Kluwer Academic Publishers, Dordrecht).

Makarov, V., Ebeling, W. & Velarde, M. [2000] \Solitonlike waves on dissipative Toda lattices," Int. J. Bifurcation and Chaos 10, 1075-1089.

Makarov, V. A., del Rio, E., Ebeling, W. & Velarde, M. G. [2001] \Dissipative Toda-Rayleigh lattice and its oscillatory modes," Phys. Rev. E64, 036601.

Percus, J. K. [1987] \Exactly solvable models of classical many-body systems," Studies in Statist. Mech. 13, 1-158.

Rayleigh, J. W. [1945] The Theory of Sound, Vol. 1, 2nd edition (Dover, NY).

Schweitzer, F., Ebeling, W. & Tilch, B. [1998] \Complex motion of Brownian particles with energy depots," Phys. Rev. Lett. 80(23), 5044-5047.

Toda, M. [1983] Nonlinear Waves and Solitons (Kluwer Academic Publishing, Dordrecht).

Toda, M. & Saitoh, N. [1983] \The classical specific heat of the exponential lattice," J. Phys. Soc. Japan 52, 3703-3705.

Wiggins, S. [1996] Introduction to Applied Nonlinear Dynamical Systems and Chaos (Springer, Dordrecht).

Deposited On:15 Nov 2012 09:41
Last Modified:07 Feb 2014 09:38

Repository Staff Only: item control page