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Persistence of a Single Phytoplankton Species in a Water Column with Time-Periodic Light Intensity

Lee, Russell B
http://orcid.org/0000-0002-1031-3735
http://rave.ohiolink.edu/etdc/view?acc_num=osu1618752381895118

Abstract Details

2021, Master of Mathematical Sciences, Ohio State University, Mathematical Sciences.
We study a nonlocal reaction-diffusion-advection equation which models the growth of a single phytoplakton species. The persistence of a phytoplankton species in a eutrophic water column is considered, where the species are limited only by light its metabolism. In particular, we study the dependence of the critical death rate on several environmental factors. Previous studies have determined some necessary and sufficient conditions for the persistence in the case where the light intensity at the surface is constant in time. However, this is the ideal situation, as the light intensity at the surface is consistently changing over time (due to diurnal and seasonal cycles), implying that it should be treated as a time-periodic function. We introduce frequency as a new parameter to reflect this temporal variation of the environment. We aim to reveal how the critical death rate depends on the frequency, turbulent diffusion, and the drift. Previously studied theoretical results have determined that the critical death rate is monotone decreasing in both frequency and drift. However, the dependence on turbulent diffusion is far from fully understood. In this thesis, we will discuss recent results of principal eigenvalues of linear time-periodic parabolic operators, then numerically investigate the dependence of the critical death rate on the frequency, the drift rate, and more importantly, the diffusion rate. In doing so, some conjectures concerning the critical death rate are formulated to stimulate future investigations.
Yuan Lou, PhD (Advisor)
King-Yeung Lam, PhD (Committee Member)
44 p.
Mathematics
Phytoplankton, time-periodic, light intensity, single species

Recommended Citations

Citations

  • Lee, R. B. (2021). Persistence of a Single Phytoplankton Species in a Water Column with Time-Periodic Light Intensity [Master's thesis, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1618752381895118

    APA Style (7th edition)

  • Lee, Russell. Persistence of a Single Phytoplankton Species in a Water Column with Time-Periodic Light Intensity. 2021. Ohio State University, Master's thesis. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1618752381895118.

    MLA Style (8th edition)

  • Lee, Russell. "Persistence of a Single Phytoplankton Species in a Water Column with Time-Periodic Light Intensity." Master's thesis, Ohio State University, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=osu1618752381895118

    Chicago Manual of Style (17th edition)

osu1618752381895118
41
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