Abstract
The experimentally observed non-Gaussian form of passive tracer distributions in media stirred by active swimmers (Leptos et al., Phys. Rev. Lett. 103, 198103 (2009)) are analyzed in terms of continuous time random walks. The walks are characterized by a trapping time distribution ψ(τ) with long time behaviour ψ(τ) ∝ τ −1−α and a step size distribution p(Δx) ∝ (Δx)−2−β. The experimentally observed behaviour that 〈x 2〉 ∝ t is obtained for a one-parameter family of exponents with β = 2α. However, the distribution function for this case is non-Gaussian and shows exponential tails. The shape of the distributions agrees rather well with the experimental observations from Leptos et al. and allows for the determination of the exponents.
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References
X.-L. Wu, A. Libchaber, Phys. Rev. Lett. 84, 3017 (2000).
C. Valeriani, M. Li, J. Novosel, J. Arlt, D. Marenduzzo, Soft Matter 7, 5228 (2011).
K.C. Leptos, J.S. Guasto, J.P. Gollub, A.I. Pesci, R.E. Goldstein, Phys. Rev. Lett. 103, 198103 (2009).
R. Metzler, J. Klafter, Phys. Rep. 339, 1 (2000).
D. Brockmann, Eur. Phys. J. ST 157, 173 (2008).
A. Visser, Marine Ecol. Progr. Ser. 222, 1 (2001).
E. Lauga, T.R. Powers, Rep. Prog. Phys. 72, 096601 (2009).
J.S. Guasto, R. Rusconi, R. Stocker, Annu. Rev. Fluid Mech. 44, 373 (2012).
H. Jiang, T.R. Osborn, C. Meneveau, J. Plankton Res. 24, 167 (2002).
H. Jiang, C. Meneveau, T.R. Osborn, J. Plankton Res. 24, 191 (2002).
E. Malkiel, J. Sheng, J. Katz, J.R. Strickler, J. Exp. Biol. 206, 3657 (2003).
K. Drescher, R.E. Goldstein, N. Michel, M. Polin, I. Tuval, Phys. Rev. Lett. 105, 168101 (2010).
K. Drescher, J. Dunkel, L.H. Cisneros, S. Ganguly, R.E. Goldstein, Proc. Natl. Acad. Sci. U.S.A. 108, 10940 (2011).
P.T. Underhill, J.P. Hernandez-Ortiz, M.D. Graham, Phys. Rev. Lett. 100, 248101 (2008).
H.C. Berg, Random Walks in Biology (Princeton University Press, 1993).
M. Polin, I. Tuval, K. Drescher, J.P. Gollub, R.E. Goldstein, Science 325, 487 (2009).
I.M. Zaid, J. Dunkel, J.M. Yeomans, J. R. Soc. Interface 8, 1314 (2011).
Z. Lin, J.-L. Thiffeault, S. Childress, J. Fluid Mech. 669, 167 (2011).
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Eckhardt, B., Zammert, S. Non-normal tracer diffusion from stirring by swimming microorganisms. Eur. Phys. J. E 35, 96 (2012). https://doi.org/10.1140/epje/i2012-12096-7
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DOI: https://doi.org/10.1140/epje/i2012-12096-7