International Journal of Physics
ISSN (Print): 2333-4568 ISSN (Online): 2333-4576 Website: Editor-in-chief: B.D. Indu
Open Access
Journal Browser
International Journal of Physics. 2018, 6(1), 26-29
DOI: 10.12691/ijp-6-1-5
Open AccessArticle

Effect of Viscosity on Nonlinear Tempering for Anomalous Diffusion of Viscous Particle: A Subdiffusive Case

Norodin A. Rangaig1, , Caironesa T. Pada1 and Vernie C. Convicto1

1Department of Physics, Mindanao State University-Main Campus, 9700 Marawi City, Philippines

Pub. Date: January 29, 2018

Cite this paper:
Norodin A. Rangaig, Caironesa T. Pada and Vernie C. Convicto. Effect of Viscosity on Nonlinear Tempering for Anomalous Diffusion of Viscous Particle: A Subdiffusive Case. International Journal of Physics. 2018; 6(1):26-29. doi: 10.12691/ijp-6-1-5


In this study, we introduced another parameter on nonlinear particle interaction into sub- diffusive transport involving nonlinear effects such as adhesion, volume filling, etc. We also introduce an additional variable which is the effect of viscosity on the nonlinear escape rate of particle which affects the resulting integral escape rate. This paper focuses only on the in- vestigation of the effect of the added variable on the total escape rate. Lastly, we can see the importance of this study when dealing viscous macroparticles.

random walk nonlinear interaction structured density structured viscosity escape rate

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit


[1]  S. Bochner, Diffusion equation and stochastic processes, Proceedings of the National Academy of Sciences, vol. 35, no. 7, pp. 368370, 1949.
[2]  H. Gu, J.-R. Liang, and Y.-X. Zhang, On a time-changed geometric Brownian motion and its application in financial market, Acta Physica Polonica B, vol. 43, no. 8, pp. 16671681, 2012.
[3]  J. Janczura and A. Wyomanska, Anomalous diffusion models: different types of subordinator distribution, Acta Physica Polonica B, vol. 43, no. 5, pp. 10011016, 2012.
[4]  C. Song, T. Koren, P. Wang, and A. Barabasi, Modelling the scaling properties of human mobility, Nature Physics, vol. 6, no. 10, pp. 818823, 2010.
[5]  M.J Saxton, Anomalous Subdiffusion in Flouresence Photobleaching Recovery: A Monte Carlo Study, Biophysical Journal, 1985.
[6]  S. Fedotov, and V. Mendez, Non-Markovian Model for Transport and Reaction of Particles in Spiny Dendrites, Phys. Rev. Lett., 101: 218102, 2008.
[7]  D. Kleinhans and R. Friedrich, Continuous-time random walks: simulation of continuous tra- jectories, Physical Review E, vol. 76, no. 6, Article ID 061102, 2007.
[8]  M.Magdziarz, Langevin picture of subdiffusion with infinitely divisiblewaiting times, Journal of Statistical Physics, vol. 135, no. 4, pp. 763772, 2009.
[9]  M. Magdziarz, Stochastic representation of subdiffusion processes with time-dependent drift, Stochastic Processes and Their Applications, vol. 119, no. 10, pp. 32383252, 2009.
[10]  E. Scalas, The application of continuous-time randomwalks in finance and economics, Physica A: StatisticalMechanics and its Applications, vol. 362, no. 2, pp. 225239, 2006.
[11]  M. Magdziarz, A. Weron, and K. Weron, Fractional Fokker- Planck dynamics: stochastic representation and computer simulation, Physical Review EStatistical, Nonlinear, and Soft Matter Physics, vol. 75, no. 1, Article ID016708, 2007.
[12]  S. Fedotov, and S. Falconer, Subdiffusive Master Equation with Space-Dependent Anomalous Exponent and Structural Instability, Phys. Rev. E, 85(3):1-6, 2012.
[13]  P. Straka and S. Fedotov, Transport Equation for Subdiffusion with Nonlinear Particle Inter- action, arXiv preprint: 1404.6869, 2014.
[14]  S. Falconer, A. Al-Sabbagh, and S. Fedotov, Nonlinear Tempering of Subdiffusion with Chemo- taxis, 2015.
[15]  T. Hillen, and K. Painter, Global Existence foe a Parabolic Chemotaxis Model with Prevention of Overcrowding. Adv. in Appl. Math., 26(4): pp. 280-301, 2001.
[16]  S. Fedotov, and S. Falconer, Random Death Process for the Regularization of Subdiffusive fractional Equation, Phys. Rev. E, 87:052139, 2013.
[17]  S. Fedotov, and S. Falconer, Nonlinear Degradation-enhanced Transport of Morphogens Per- forming Subdiffusion, Phys. Rev. E, 89:012107, 2014.