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Biomixing by chemotaxis and efficiency of biological reactions: The critical reaction case

Publication ,  Journal Article
Kiselev, A; Ryzhik, L
Published in: Journal of Mathematical Physics
November 27, 2012

Many phenomena in biology involve both reactions and chemotaxis. These processes can clearly influence each other, and chemotaxis can play an important role in sustaining and speeding up the reaction. In continuation of our work [A. Kiselev and L. Ryzhik, "Biomixing by chemotaxis and enhancement of biological reactions," Comm. Partial Differential Equations37, 298-318 (2012)]10.1080/03605302.2011.589879, we consider a model with a single density function involving diffusion, advection, chemotaxis, and absorbing reaction. The model is motivated, in particular, by the studies of coral broadcast spawning, where experimental observations of the efficiency of fertilization rates significantly exceed the data obtained from numerical models that do not take chemotaxis (attraction of sperm gametes by a chemical secreted by egg gametes) into account. We consider the case of the weakly coupled quadratic reaction term, which is the most natural from the biological point of view and was left open in Kiselev and Ryzhik ["Biomixing by chemotaxis and enhancement of biological reactions," Comm. Partial Differential Equations37, 298-318 (2012)]10.1080/03605302.2011.589879. The result is that similarly to Kiselev and Ryzhik ["Biomixing by chemotaxis and enhancement of biological reactions," Comm. Partial Differential Equations37, 298-318 (2012)]10.1080/03605302.2011.589879, the chemotaxis plays a crucial role in ensuring efficiency of reaction. However, mathematically, the picture is quite different in the quadratic reaction case and is more subtle. The reaction is now complete even in the absence of chemotaxis, but the timescales are very different. Without chemotaxis, the reaction is very slow, especially for the weak reaction coupling. With chemotaxis, the timescale and efficiency of reaction are independent of the coupling parameter. © 2012 American Institute of Physics.

Duke Scholars

Published In

Journal of Mathematical Physics

DOI

ISSN

0022-2488

Publication Date

November 27, 2012

Volume

53

Issue

11

Related Subject Headings

  • Mathematical Physics
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 02 Physical Sciences
  • 01 Mathematical Sciences
 

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Kiselev, A., & Ryzhik, L. (2012). Biomixing by chemotaxis and efficiency of biological reactions: The critical reaction case. Journal of Mathematical Physics, 53(11). https://doi.org/10.1063/1.4742858
Kiselev, A., and L. Ryzhik. “Biomixing by chemotaxis and efficiency of biological reactions: The critical reaction case.” Journal of Mathematical Physics 53, no. 11 (November 27, 2012). https://doi.org/10.1063/1.4742858.
Kiselev A, Ryzhik L. Biomixing by chemotaxis and efficiency of biological reactions: The critical reaction case. Journal of Mathematical Physics. 2012 Nov 27;53(11).
Kiselev, A., and L. Ryzhik. “Biomixing by chemotaxis and efficiency of biological reactions: The critical reaction case.” Journal of Mathematical Physics, vol. 53, no. 11, Nov. 2012. Scopus, doi:10.1063/1.4742858.
Kiselev A, Ryzhik L. Biomixing by chemotaxis and efficiency of biological reactions: The critical reaction case. Journal of Mathematical Physics. 2012 Nov 27;53(11).

Published In

Journal of Mathematical Physics

DOI

ISSN

0022-2488

Publication Date

November 27, 2012

Volume

53

Issue

11

Related Subject Headings

  • Mathematical Physics
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 02 Physical Sciences
  • 01 Mathematical Sciences