New dynamic scaling in increasing systems

• Authors: Juan Pastor , Javier Galeano
• Languages of publication: EN

Abstracts

EN

We report a new dynamic scaling ansatz for systems whose system size is increasing with time. We apply this new hypothesis in the Eden model in two geometries. In strip geometry, we impose the system to increase with a power law, L ∼ h
a. In increasing linear clusters, if a < 1/z, where z is the dynamic exponent, the correlation length reaches the whole system, and we find two regimes: the first, where the interface fluctuations initially grow with an exponent β = 0.3, and the second, where a crossover comes out and fluctuations evolve as h
aα. If a = 1/z, there is not a crossover and fluctuations keep on growing in a unique regimen with the same exponent β. In particular, in circular geometry, a = 1, we find this kind of regime and in consequence, a unique regime holds.

Keywords

EN

Eden model; System Growth; Dynamic Scaling

Discipline

• 68.35.Ct: Interface structure and roughness
• 05.40.-a: Fluctuation phenomena, random processes, noise, and Brownian motion(for fluctuations in superconductivity, see 74.40.-n; for statistical theory and fluctuations in nuclear reactions, see 24.60.-k; for fluctuations in plasma, see 52.25.Gj; for nonlinear dynamics and chaos, see 05.45.-a)

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2007
• Volume: 5
• Issue: 4
• Pages: 539-548

Dates

published

1 - 12 - 2007

online

1 - 12 - 2007

Contributors

author

Juan Pastor

• Dpt. Ciencia y Tecnología Aplicadas a la I.T. Agrícola, E.U.I.T. Agrícola, Ciudad Universitaria s/n, Universidad Politécnica de Madrid, E-28040, Madrid, Spain

author

Javier Galeano

• Dpt. Ciencia y Tecnología Aplicadas a la I.T. Agrícola, E.U.I.T. Agrícola, Ciudad Universitaria s/n, Universidad Politécnica de Madrid, E-28040, Madrid, Spain

References

• [1] A. J. Koch and H. Meinhardt: “Biological pattern-formation - From basic mechanisms to complex structures”, Rev. Mod. Phys., Vol. 66, (1994), pp. 1481–1507. http://dx.doi.org/10.1103/RevModPhys.66.1481[Crossref]
• [2] M. C. Cross and P. C. Hohenberg: “Pattern-formation outside of equilibrium”, Rev. Mod. Phys., Vol. 65, (1993), pp. 851–1112. http://dx.doi.org/10.1103/RevModPhys.65.851[Crossref]
• [3] A.-L. Barabási and H. E. Stanley: Fractal Concepts in Surface Growth, Cambridge University Press, Cambridge, 1995.
• [4] P. Meakin: Fractals, Scaling and Growth far from Equilibrium, Cambridge University Press, Cambridge, 1998.
• [5] M. Eden, “A probabilistic model for morphogenesis”. In H. P. Yockey, R. L. Platzman and H. Quastler(Eds.): Symposium on Information Theory of Biology, Pergamon Press, New York, 1958, pp. 359–370.
• [6] M. Eden: “A two-dimensional growth process”, In: J. Neyman (Eds.): Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability, Vol. IV, Univ. of California Press, Berkeley, 1961, pp. 223–239.
• [7] R. Jullien and R. Botet:“Scaling properties of the surface of the Eden model in d = 2, 3, 4”, J. Phys. A, Vol. 18, (1985), pp. 2279–2287. http://dx.doi.org/10.1088/0305-4470/18/12/026[Crossref]
• [8] M. Plischke, Z. Rácz, and D. Liu: “Time-reversal invariance and universality of two-dimensional growth models”, Phys. Rev. B, Vol. 35, (1987), pp. 3485–3495. http://dx.doi.org/10.1103/PhysRevB.35.3485[Crossref]
• [9] F. Family and T. Vicsek: “Scaling of the active zone in the eden process on percolation networks and the ballistic deposition model”, J. Phys. A, Vol. 18, (1985), pp. L75–L81. http://dx.doi.org/10.1088/0305-4470/18/2/005[Crossref]
• [10] J. J. Ramasco, J. M. López, and M. A. Rodríguez: “Generic dynamic scaling in kinetic roughening”, Phys. Rev. Lett., Vol. 84, (2000), pp. 2199–2202. http://dx.doi.org/10.1103/PhysRevLett.84.2199[Crossref]
• [11] P. Meakin, R. Jullien, and R. Botet:“Large-scale numerical investigation of the surface of Eden clusters”, Europhys. Lett., Vol. 1, (1986), pp. 609–615. http://dx.doi.org/10.1209/0295-5075/1/12/001[Crossref]
• [12] J. G. Zabolitzky and D. Stauffer: “Simulation of large Eden clusters”, Phys. Rev. A, Vol. 34, (1986), pp. 1523–1530. http://dx.doi.org/10.1103/PhysRevA.34.1523[Crossref]
• [13] P. Freche, D. Stauffer, and H. E. Stanley: “Surface-structure and anisotropy of Eden Clusters”, J. Phys. A, Vol. 18, (1985), pp. L1163–1168. http://dx.doi.org/10.1088/0305-4470/18/18/009[Crossref]
• [14] L. R. Paiva and S. C. Ferreira Jr.: J. Phys. A-Math. Theor, Vol. 40, (2007), pp. F43–F49. http://dx.doi.org/10.1088/1751-8113/40/1/F05[Crossref]
• [15] A. Brú, S. Albertos, J. L. Subiza, J. L. García-Asenjo, and I. Brú: “The universal dynamics of tumor growth”, Biophys. J., Vol. 85, (2003), pp. 2984–2961. http://dx.doi.org/10.1016/S0006-3495(03)74715-8[Crossref]
• [16] J. Galeano, J. Buceta, K. Juarez, B. Pumariño, J. de la Torre, and J. M. Iriondo: “Dynamical scaling analysis of plant callus growth”, Europhys. Lett., Vol. 63, (2003), pp. 83–89. http://dx.doi.org/10.1209/epl/i2003-00481-1[Crossref]

Identifiers

DOI

10.2478/s11534-007-0043-4