1. Hoa NguyenHoa Nguyen Center for Computational Science, Tulane University Collaborators Lisa FauciLisa Fauci, Department of Mathematics, Tulane University Peter Jumars Lee Karp-BossPeter Jumars and Lee Karp-Boss, School of Marine Sciences, University of Maine Magdalena MusielakMagdalena Musielak, Department of Mathematics, The George Washington University

2. Phytoplankton Copyright of Smithsonian Environmental Research Center Phytoplankton are the foundation of the oceanic food chain. Thalassiosira nordenskioeldii Copyright of the Biodiversity Institute of Ontario

3. Introduction Object: Individual non-motile diatom. Goal: Understand the effects of spines on diatoms in shear flow. Method: the Immersed Boundary Method (IBM) developed by Charles Peskin ([1], [2]). Thalassiosira nordenskioeldii Copyright of the Biodiversity Institute of Ontario Our simulation of a simplified model of the above diatom in shear flow (Re = 8.26 x 10 -4 ) [1] C. S. Peskin; Numerical analysis of blood flow in the heart, J. Compu. Phys. 25, 1977, pp. 220 - 252. [2] C. S. Peskin; The immersed boundary method, Acta Numerica 11, 2002, pp. 459- 517.

4. Immersed Boundary Method (IBM)

5. Spring Force Model of a plankter with eight spines (left) and detail of how the spines attach to the cell body (right).

6. Discretization: Spherical Centroidal Voronoi Tessellation The triangulation on the unit sphere is the dual mesh of the Spherical Centroidal Voronoi Tessellation (SCVT), as coded by Lili Ju [6]. We map this triangulation to a surface (such as an ellipsoid, a flat disc or a plankter’s cell body) to create a discretization of the structure.

7. Fluid Solver: Immersed Boundary Method with Adaptive Mesh Refinement (IBAMR) B.E. Griffith, R.D. Hornung, D.M. McQueen, and C.S. Peskin. An adaptive, formally second order accurate version of the immersed boundary method. Journal of Computational Physics. 223: 10-49 (2007). Re = 8.26

8. Jeffery Orbit

9. Ellipsoid in Shear Flow Variation of φ with time (where φ = rotation angle relative to the initial position). The period from the simulation is about 1.55 s, compared with the theoretical period T = 1.59 s.

10. Flat Disc in Shear Flow The period from the simulation is about 6.4 s, compared with the experimental period T = 7.6 s in Goldsmith and Mason’s paper [5] from 1962. Re = 3.03 x 10 -4 (oil) Re = 1.56 (water)

11. Plankter in Shear Flow The cell body has the same diameter as the disc, except that the top and bottom are dome-shaped (height = 0.006 cm). The spine length = 0.052 cm. Spine angle = 0 o Spine angle = 45 o Plankter without spines (Re = 3.03 x 10 -4 ) Plankter with eight spines (Re = 8.26 x 10 -4 )

12. Observe that the plankter with spines at different angles has a longer period than the one without spines. Simulations and Results T = 6.5 s T = 8.89 s T = 7.17 s

13. Research Extensions Different morphologies and chains of cells. Nutrient transport and acquisition. Computational models and laboratory experiments. unsteady shear and vortical background flows. Plankter without springs internal to the cell body and spines. Hideki Fujioka Ricardo Cortez Special thanks to Hideki Fujioka and Ricardo Cortez at the Center for Computational Science, Tulane University.

14. Thanks for your attention! This work is supported by NSF OCE 0724598.