Geodesic
Nonlinear Tempering of Subdiffusion with Chemotaxis, Volume Filling, and Adhesion
S. Falconer1 ; A. Al-Sabbagh2 ; S. Fedotov1
1 School of Mathematics, The University of Manchester, Manchester M13 9PL, United Kingdom
2 Department of Mathematics, Al-Nahrain University, Jadiriya 64055, Baghdad, Iraq
Mathematical modelling of natural phenomena, Tome 10 (2015) no. 3, pp. 48-60

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The purpose of this paper is to implement nonlinear particle interactions into subdiffusive transport, involving chemotaxis and nonlinear effects such as volume filling and adhesion. We systematically derive nonlinear subdiffusive fractional equations with chemoattractant dependent forcing. We consider the diffusion limit of the master equation and analyse the role of nonlinear tempering in the stationary case. We study the interaction between attractive forces of anomalous aggregation and chemotaxis, with repulsive forces induced by nonlinear reactions. We show that this nonlinear interaction can prevent the phenomenon of anomalous aggregation when the local particle concentration grows too high. We also show that the effect of nonlinear tempering is to suppress the intermediate subdiffusive behaviour which results in a nonlinear advection diffusion equation in the long time limit.
DOI : 10.1051/mmnp/201510305

S. Falconer 1 ; A. Al-Sabbagh 2 ; S. Fedotov 1

1 School of Mathematics, The University of Manchester, Manchester M13 9PL, United Kingdom
2 Department of Mathematics, Al-Nahrain University, Jadiriya 64055, Baghdad, Iraq 
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S. Falconer; A. Al-Sabbagh; S. Fedotov. Nonlinear Tempering of Subdiffusion with Chemotaxis, Volume Filling, and Adhesion. Mathematical modelling of natural phenomena, Tome 10 (2015) no. 3, pp. 48-60. doi: 10.1051/mmnp/201510305

[1] E. Barkai, R. Metzler, J. Klafter Physical Review E 2000 132 138

[2] S. Fedotov Physical Review E 2011 1 5

[3] S. Fedotov Physical Review E 2013 032104

[4] S. Fedotov, S. Falconer Physical Review E 2012 1 6

[5] S. Fedotov, S. Falconer Physical Review E 2013 052139

[6] S. Fedotov, S. Falconer Physical Review E 2014 012107

[7] S. Fedotov, A. Ivanov, A.Y. Zubarev Mathematical Modelling of Natural Phenomena 2013 28 43

[8] S. Fedotov, N. Korabel Physical Review E 2015 042112

[9] S. Fedotov, V. Méndez Physical Review Letters 2008 218102

[10] S. Havlin, D. Movshovitz, B. Trus, G.H. Weiss Journal of Physics A 1985 L719

[11] T. Hillen, K. Painter Advances in Applied Mathematics 2001 280 301

[12] T. Hillen, K.J. Painter Journal of Mathematical Biology 2009 183 217

[13] S.T. Johnston, M.J. Simpson, R.E. Baker Physical Review E 2012 051922

[14] M.M. Meerschaert, P. Straka The Annals of Probability 2014 1699 1723

[15] V. Mendéz, S. Fedotov, W. Horsthemke. Reaction-transport systems: Mesoscopic foundations, fronts, and spatial instabilities. Springer, 2010.

[16] R. Metzler, J. Klafter Physics Reports 2000 1 77

[17] R. Metzler, J. Klafter, I.M. Sokolov Physical Review E 1998 1621 1633

[18] M. Raberto, E. Scalas, F. Mainardi Physica A: Statistical Mechanics and its Applications 2002 749 755

[19] M. Rausand, A. Høyland. System reliability theory: Models, statistical methods, and applications. Wiley Series in Probability and Statistics - Applied Probability and Statistics Section. Wiley, 2004.

[20] F. Santamaria, S. Wils, E. De Schutter, G.J. Augustine European Journal of Neuroscience 2011 561 568

[21] M.J. Saxton Biophysical Journal 2001 2226 40

[22] H. Scher, E.N. Montroll Physical Review B 1975 2455 2477

[23] P. Straka, S. Fedotov Journal of Theoretical Biology 2015 71 83

[24] M. Vlad, J. Ross Physical Review E 2002 1 11

[25] A. Yadav, W. Horsthemke Physical Review E 2006

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