Document - Fractional kinetics emerging from ergodicity breaking in random media

2016

Journal article Open Access

Fractional kinetics emerging from ergodicity breaking in random media

Molina-García D., Pham T. M., Paradisi P., Manzo C., Pagnini G.

generalized grey Bronian motion (ggBm) 60G22 60J60 Anomalous diffusion 26A33 Statistical Mechanics (cond-mat.stat-mech) FOS: Physical sciences non-Gaussian fractional kinetics Signal Processing Brownian motion Heterogeneity Time Series Analysis Condensed Matter - Statistical Mechanics anomalous diffusion stochastic processes biophysics

We present a modeling approach for diffusion in a complex medium characterized by a random length scale. The resulting stochastic process shows subdiffusion with a behavior in qualitative agreement with single-particle tracking experiments in living cells, such as ergodicity breaking, p variation, and aging. In particular, this approach recapitulates characteristic features previously described in part by the fractional Brownian motion and in part by the continuous-time random walk. Moreover, for a proper distribution of the length scale, a single parameter controls the ergodic-to-nonergodic transition and, remarkably, also drives the transition of the diffusion equation of the process from nonfractional to fractional, thus demonstrating that fractional kinetics emerges from ergodicity breaking.

Source: Physical review. E (Print) 94 (2016). doi:10.1103/PhysRevE.94.052147

Publisher: American Physical Society, Ridge, NY, Stati Uniti d'America

Citations

[1] I. Golding and E. C. Cox, Phys. Rev. Lett. 96, 098102 (2006).
[2] I. Bronstein, Y. Israel, E. Kepten, S. Mai, Y. Shav-Tal, E. Barkai, and Y. Garini, Phys. Rev. Lett. 103, 018102 (2009).
[3] J.-H. Jeon, V. Tejedor, S. Burov, E. Barkai, C. SelhuberUnkel, K. Berg-S rensen, L. Oddershede, and R. Metzler, Phys. Rev. Lett. 106, 048103 (2011).
[4] A. V. Weigel, B. Simon, M. M. Tamkun, and D. Krapf, Proc. Natl. Acad. Sci. USA 108, 6438 (2011).
[5] S. M. A. Tabei, S. Burov, H. Y. Kim, A. Kuznetsov, T. Huynh, J. Jureller, L. H. Philipson, A. R. Dinner, and N. F. Scherer, Proc. Natl. Acad. Sci. USA 110, 4911 (2013).
[6] C. Manzo, J. A. Torreno-Pina, P. Massignan, G. J. Lapeyre, M. Lewenstein, and M. F. Garcia{Parajo, Phys. Rev. X 5, 011021 (2015).
[7] E. Barkai, Y. Garini, and R. Metzler, Phys. Today 65, 29 (2012).
[8] R. Metzler, J.-H. Jeon, A. G. Cherstvy, and E. Barkai, Phys. Chem. Chem. Phys. 16, 24128 (2014).
[9] C. Manzo and M. F. Garcia-Parajo, Rep. Progr. Phys. 78, 124601 (2015).
[10] W. Deng and E. Barkai, Phys. Rev. E 79, 011112 (2009).
[11] M. Magdziarz, A. Weron, K. Burnecki, and J. Klafter, Phys. Rev. Lett. 103, 180602 (2009).
[12] A. Lubelski, I. M. Sokolov, and J. Klafter, Phys. Rev. Lett. 100, 250602 (2008).
[13] Y. He, S. Burov, R. Metzler, and E. Barkai, Phys. Rev. Lett. 101, 058101 (2008).
[14] N. Goldenfeld and L. P. Kadano , Science 284, 87 (1999).
[15] S. Chandrasekhar, Rev. Modern Phys. 15, 1 (1943).
[16] G. Pagnini, A. Mura, and F. Mainardi, Int. J. Stoch. Anal. 2012, 427383 (2012).
[17] G. Pagnini, Physica A 409, 29 (2014).
[18] A. Mura and G. Pagnini, J. Phys. A: Math. Theor. 41, 285003 (2008).
[19] F. Mainardi, A. Mura, and G. Pagnini, Int. J. Di er. Equations 2010, 104505 (2010).
[20] G. Pagnini, Fract. Calc. Appl. Anal. 16, 436 (2013).
[21] F. Mainardi, G. Pagnini, and R. Goren o, Fract. Calc. Appl. Anal. 6, 441 (2003).
[22] G. Pagnini, Fract. Calc. Appl. Anal. 15, 117 (2012).
[23] T. Neusius, I. M. Sokolov, and J. C. Smith, Phys. Rev. E 80, 011109 (2009).
[24] S. Burov, R. Metzler, and E. Barkai, Proc. Natl. Acad. Sci. USA 107, 13228 (2010).
[25] G. Margolin and E. Barkai, J. Chem. Phys. 121, 1566 (2004).
[26] P. Paradisi, P. Allegrini, F. Barbi, S. Bianco, and P. Grigolini, AIP Conf. Proc. 800, 92 (2005).
[27] S. Bianco, P. Grigolini, and P. Paradisi, J. Chem. Phys. 123, 174704 (2005).
[28] O. Akin, P. Paradisi, and P. Grigolini, Physica A 371, 157 (2006).
[29] P. Paradisi, R. Cesari, and P. Grigolini, Cent. Eur. J. Phys. 7, 421 (2009).
[30] O. Akin, P. Paradisi, and P. Grigolini, J. Stat. Mech.: Theory Exp. , P01013 (2009), doi: 10.1088/1742- 5468/2009/01/P01013.
[31] J. H. P. Schulz, E. Barkai, and R. Metzler, Phys. Rev. Lett. 110, 020602 (2013).
[32] D. Molina-Garc a, T. M. Pham, and G. Pagnini, in Non-linear Systems, Nanotechnology, Recent Advances in Electrical Engineering Series, Vol. 55, edited by V. Mladenov, WSEAS (WSEAS Press, 2015) pp. 75{80, Proceedings of the 14th International Conference on NonLinear Analysis, Non-Linear Systems and Chaos (NOLASC '15), Rome, Italy, November 7{9, 2015. ISSN: 1790-5117; ISBN: 978-1-61804-345-0.

Metrics

Back to previous page

Cite as

BibTeX entry

@article{oai:it.cnr:prodotti:401217,
	title = {Fractional kinetics emerging from ergodicity breaking in random media},
	author = {Molina-García D. and Pham T.  M. and Paradisi P. and Manzo C. and Pagnini G.},
	publisher = {American Physical Society, Ridge, NY, Stati Uniti d'America},
	doi = {10.1103/physreve.94.052147 and 10.48550/arxiv.1508.01361},
	journal = {Physical review. E (Print)},
	volume = {94},
	year = {2016}
}