TY - JOUR
T1 - Loopy Lévy flights enhance tracer diffusion in active suspensions
AU - Kanazawa, Kiyoshi
AU - Sano, Tomohiko G.
AU - Cairoli, Andrea
AU - Baule, Adrian
N1 - Funding Information:
Acknowledgements We thank D. Mizuno, H. Takayasu, M. Takayasu, H. Hayakawa and F. van Wijland for discussions. This work was supported by a Grant-in-Aid for JSPS Fellows (grant number 16J05315), JSPS KAKENHI (grant numbers 16K16016 and 18K13519) and a Research Fellowship granted by the Royal Commission for the Exhibition of 1851. A.C. acknowledges the hospitality of the Yukawa Institute for Theoretical Physics, Kyoto University as well as financial support. Simulations and numerical calculations were carried out using the Cray XC40 supercomputer at Yukawa Institute for Theoretical Physics in Kyoto University.
Publisher Copyright:
© 2020, The Author(s), under exclusive licence to Springer Nature Limited.
PY - 2020/3/19
Y1 - 2020/3/19
N2 - Brownian motion is widely used as a model of diffusion in equilibrium media throughout the physical, chemical and biological sciences. However, many real-world systems are intrinsically out of equilibrium owing to energy-dissipating active processes underlying their mechanical and dynamical features1. The diffusion process followed by a passive tracer in prototypical active media, such as suspensions of active colloids or swimming microorganisms2, differs considerably from Brownian motion, as revealed by a greatly enhanced diffusion coefficient3–10 and non-Gaussian statistics of the tracer displacements6,9,10. Although these characteristic features have been extensively observed experimentally, there is so far no comprehensive theory explaining how they emerge from the microscopic dynamics of the system. Here we develop a theoretical framework to model the hydrodynamic interactions between the tracer and the active swimmers, which shows that the tracer follows a non-Markovian coloured Poisson process that accounts for all empirical observations. The theory predicts a long-lived Lévy flight regime11 of the loopy tracer motion with a non-monotonic crossover between two different power-law exponents. The duration of this regime can be tuned by the swimmer density, suggesting that the optimal foraging strategy of swimming microorganisms might depend crucially on their density in order to exploit the Lévy flights of nutrients12. Our framework can be applied to address important theoretical questions, such as the thermodynamics of active systems13, and practical ones, such as the interaction of swimming microorganisms with nutrients and other small particles14 (for example, degraded plastic) and the design of artificial nanoscale machines15.
AB - Brownian motion is widely used as a model of diffusion in equilibrium media throughout the physical, chemical and biological sciences. However, many real-world systems are intrinsically out of equilibrium owing to energy-dissipating active processes underlying their mechanical and dynamical features1. The diffusion process followed by a passive tracer in prototypical active media, such as suspensions of active colloids or swimming microorganisms2, differs considerably from Brownian motion, as revealed by a greatly enhanced diffusion coefficient3–10 and non-Gaussian statistics of the tracer displacements6,9,10. Although these characteristic features have been extensively observed experimentally, there is so far no comprehensive theory explaining how they emerge from the microscopic dynamics of the system. Here we develop a theoretical framework to model the hydrodynamic interactions between the tracer and the active swimmers, which shows that the tracer follows a non-Markovian coloured Poisson process that accounts for all empirical observations. The theory predicts a long-lived Lévy flight regime11 of the loopy tracer motion with a non-monotonic crossover between two different power-law exponents. The duration of this regime can be tuned by the swimmer density, suggesting that the optimal foraging strategy of swimming microorganisms might depend crucially on their density in order to exploit the Lévy flights of nutrients12. Our framework can be applied to address important theoretical questions, such as the thermodynamics of active systems13, and practical ones, such as the interaction of swimming microorganisms with nutrients and other small particles14 (for example, degraded plastic) and the design of artificial nanoscale machines15.
UR - http://www.scopus.com/inward/record.url?scp=85082083589&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85082083589&partnerID=8YFLogxK
U2 - 10.1038/s41586-020-2086-2
DO - 10.1038/s41586-020-2086-2
M3 - Article
C2 - 32188948
AN - SCOPUS:85082083589
VL - 579
SP - 364
EP - 367
JO - Nature Cell Biology
JF - Nature Cell Biology
SN - 1465-7392
IS - 7799
ER -