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To solve equations 1, 2, 3, and 4, we need to update the velocity, pressure, position of the boundary, and force acting on the boundary at timen+ 1using data from time n. The IBM does this in the following steps [57], with an additional step (4b) for IBAMR [68, 69]:

1. Find the force density,Fnon the immersed boundary, from the current boundary configuration

2. Use equation 3 to spread this boundary force from the Lagrangian boundary mesh to the Eulerian fluid lattice points.

3. Solve the Navier-Stokes equations, equations 1 and 2, on the Eulerian grid. Upon doing so, updateun+1 and pn+1 from un,pn, and fn. Note that a staggered grid projection scheme is used to perform this update.

4a. Update the material positionsXn+1 using the local fluid velocitiesUn+1 computed fromun+1

and equation 4.

4b. If on a selected time step for adaptive mesh refinement, refine the Eulerian grid in areas of the domain that contain the immersed structure or where the vorticity exceeds a predetermined threshold.

We note that step 4b is from the IBAMR implementation of the IBM. IBAMR is an IBM framework written in C++ that provides discretization and solver infrastructure for partial differential equations on block-structured locally refined Eulerian grids [104, 105] and on Lagrangian meshes. Adaptive Mesh Refinement (AMR) achieves higher accuracy between the Lagrangian and Eulerian mesh by increasing grid resolution in areas of the domain where the vorticity exceeds a certain threshold and in areas of the domain that contain an immersed boundary. AMR improves the computational efficiency by decreasing grid resolution in areas that do not necessitate high resolution.

APPENDIX B: THE IMMERSED BOUNDARY METHOD WITH FINITE ELEMENTS (IBFE)

We define the structure material coordinates to be X = (X, Y, Z) ∈ S, where S denotes the Lagrangian structure domain. The physical positions of X at time t is given byχ(X, t)∈Ω, where

Ω is the region in which the entire fluid-structure interaction domain occupies. Hence the space occupied by the structure at time tisχ(S, t)⊂Ω.The system of equations is as follows:

ρ " ∂u ∂t(x, t) +u(x, t)· ∇u(x, t) # =∇p(x, t) +µ∆u(x, t) +F(x, t) (8) ∇ ·u(x, t) = 0 (9) F(x, t) = Z S f(X, t)δ(x−χ(X, t))dX (10) ∂χ(X, t) ∂t =U(X, t) = Z Ω u(x, t)δ(x−χ(X, t))dx. (11)

We use the following equation to relate stress deformations of the immersed structure back to F(X, t), Z S f_elas(X, t)·φ(X)dX=− Z S Ppass(X, t) :∇Xφ(X)dX, (12)

where φ is a test function in this weak formulation that describesfelas in terms of the first Piola- Kirchhoff solid stress tensor, P. This stress tensor gives the current elastic deformation forces of the immersed structure in terms of its reference configuration. This stress tensor describes the passive elasticity of the polyp with a neo-Hookean material model, given by

Ppass=ηtot F−F−T, (13)

where_F= _∂∂χ_X is the deformation gradient andηtot is the elastic modulus of the material and can be

dependent onX. Assuming sufficient regularity, felas =∇X·Ppass. To move the boundary, a tether

force,ftarg, is applied that is proportional to the distance between the current configuration of the

boundary and the preferred configuration,χtarg(X, t), as follows:

where ktarg is a constant of proportionality that can be described as the stiffness of the tether force.

The total force acting on the boundary may then be written as

f(X, t) =ftarg(X, t) +felas(X, t) (15)

In comparison to the traditional IB method, IBFE does not use fiber models that describe individual Lagrangian point-to-point type deformation models. Rather IBFE builds upon a finite element framework to describe the Lagrangian body from a solid mechanics foundation. This in turn makes a more global-body approach to describe deformations of a structure, instead of individual point-set force deformation laws. The algorithm is much the same as the algorithm for traditional finite difference IB method, with the exception that deformation forces are computed differently.

REFERENCES

[1] W. Shakespeare, “Hamlet,” inThe Complete Works of William Shakespeare, (London, UK), pp. 870–907, Oxford University Press, 1957.

[2] G. Samson, Organic Compounds of Astatine. PhD thesis, Universiteit van Amsterdam, Amsterdam, the Netherlands, 1971.

[3] H. A. F. Gohar and H. M. Roushdy, “The neuromuscular system of the Xeniidae (Alcyonaria). I. Histological,” Publications of the Marine Biological Station Al-Ghardaqa (Red Sea), vol. 10, pp. 63–81, 1959.

[4] S. Vogel,Life in Moving Fluids. Princeton, NJ: Princeton University Press, 2 ed., 1994. [5] S. Vogel, Comparative biomechanics: life’s physical world. Princeton, NJ: Princeton University

Press, 2 ed., 2013.

[6] H. Toussaint and M. Truijens, “Biomechanical aspects of peak performance in human swimming,” Animal Biology, vol. 55, pp. 17–40, 2005.

[7] P. K. Kundu and I. M. Cohen,Fluid Mechanics. San Diego, CA: Academic Press, 2 ed., 2001. [8] D. J. T. Sumpter, Collective Animal Behavior. Princeton, NJ: Princeton University Press,

2010.

[9] I. D. Couzin, “Collective cognition in animal groups,” Trends in Cognitive Sciences, vol. 13, pp. 36–43, 2009.

[10] I. D. Couzin and N. R. Franks, “Self-organized lane formation and optimized traffic flow in army ants,” Proceedings of the Royal Society B, vol. 270, pp. 139–146, 2003.

[11] C. K. Hemelrijk and H. Hildenbrandt, “Schools of fish and flocks of birds: their shape and internal structure by self-organization,” Interface Focus, vol. 2, pp. 726–737, 2012.

[12] E. Lushi, H. Wioland, and R. E. Goldstein, “Fluid flows created by swimming bacteria drive self-organization in confined suspensions,” Proceedings of the National Academy of Sciences of the United States of America, vol. 111, pp. 9733–9738, 2014.

[13] I. D. Couzin, J. Krause, R. James, G. D. Ruxton, and N. R. Franks, “Collective memory and spatial sorting in animal groups,” Journal of Theoretical Biology, vol. 218, pp. 1–11, 2002. [14] A. Attanasi, A. Cavagna, L. D. Castillo, I. Giardina, S. Melillo, L. Parisi, O. Pohl, B. Rossaro,

E. Shen, E. Silvestri, and M. Viale, “Collective behaviour without collective order in wild swarms of midges,” PLoS Computational Biology, vol. 7, pp. 1–10, 2014.

[15] K. E. Fabricius and P. Alderslade,Soft Corals and Sea Fans: A Comprehensive Guide to the Tropical Shallow Water Genera of the Central-West Pacific, the Indian Ocean and the Red Sea.

Townsville, QLD, Australia: Australian Institute of Marine Science, 2001.

[16] E. H. Borneman,Aquarium Corals: Selection, Husbandry, and Natural History. Neptune City, NJ: T.F.H. Publications, 2001.

[17] J. B. P. A. Lamark, Histoire Naturelle des Animaux sans Vertèbres (Natural History of Invertebrate Animals), vol. 2. Paris, France: Verdière, 1816.

[18] E. Lieske and R. F. Myers, Coral Reef Guide: Red Sea. NY, NY: Harper Collins, 2 ed., 2004. [19] H. A. F. Gohar and H. M. Roushdy, “On the physiology of the neuromuscular system of

Heteroxenia (Alcyonaria),” Publications of the Marine Biological Station Al-Ghardaqa (Red Sea), vol. 10, pp. 91–143, 1959.

[20] H. A. F. Gohar, “Studies on the Xeniidae of the Red Sea: their ecology, physiology, taxonomy and phylogeny,” Publications of the Marine Biological Station Al-Ghardaqa (Red Sea), vol. 2, pp. 24–118, 1940.

[21] C. S. McFadden, A. M. Reynolds, and M. P. Janes, “DNA barcoding of xeniid soft corals (Octo- corallia: Alcyonacea:xeniidae) from Indonesia: species richness and phylogenetic relationships,” Systematics and Biodiversity, vol. 12, pp. 247–257, 2014.

[22] M. P. Janes, “Laboratory methods for the identification of soft corals (Octocorallia: Alcy- onacea),” inAdvances in Coral Husbandry in Public Aquariums (R. J. Leewis and M. Janse, eds.), vol. 2 ofPublic Aquarium Husbandry Series, ch. 46, pp. 413–426, Arnhem, the Nether- lands: Burgers’ Zoo, 2008.

[23] A. Halàsz, A. M. Reynolds, C. S. McFadden, R. J. Toonen, and Y. Benayahu, “Could polyp pulsation be the key to species boundaries in the genus Ovabunda (Octocorallia: Alcyonacea: Xeniidae)?,” Hydrobiologia, vol. 759, pp. 95–107, 2015.

[24] J. B. Lewis, “Feeding behavior and feeding ecology of the Octocorallia (Coelenterata: Antho- zoa),” Journal of Zoology, vol. 196, pp. 371–384, 1982.

[25] D. Schlichter, “Nutritional strategies of cnidarians: the absorption, translocation and utilization of dissolved nutrients byHeteroxenia fuscescens,” American Zoologist, vol. 22, pp. 659–669, 1982.

[26] L. Muscatine and C. Hand, “Direct evidence for the transfer of materials from symbiotic algae to the tissues of a coelenterate,” Proceedings of the National Academy of Sciences of the United States of America, vol. 44, pp. 1259–1263, 1958.

[27] M. L. J. V. Veghel, “Reproductive characteristics of the polymorphic Caribbean reef building coralMontastrea annularis. I. Gametogenesis and spawning behavior,”Marine Ecology Progress Series, vol. 109, pp. 209–219, 1994.

[28] P. T. Raimondi and A. N. C. Morse, “The consequences of complex larval behavior in a coral,” Ecology, vol. 81, pp. 3193–3211, 2000.

[29] M. Kremien, U. Shavit, T. Mass, and A. Genin, “Benefit of pulsation in soft corals,” Proceedings of the National Academy of Sciences of the United States of America, vol. 110, pp. 8978–8983, 2013.

[30] T. Mass, A. Genin, U. Shavit, M. Grinstein, and D. Tchernov, “Flow enhances photosynthesis in marine benthic autotrophs by increasing the efflux of oxygen from the organism to the water,” Proceedings of the National Academy of Sciences of the United States of America, vol. 107, pp. 2527–2531, 2010.

[31] C. Wild and M. S. Naumann, “Effect of active water movement on energy and nutrient acquisition in coral reef-associated benthic organisms,” Proceedings of the National Academy of Sciences of the United States of America, vol. 110, pp. 8767–8768, 2013.

[32] K. Stemmer, I. Burghardt, C. Mayer, G. B. Reinicke, H. Wägele, R. Tollrian, and F. Leese, “Morphological and genetic analyses of xeniid soft coral diversity (Octocorallia: Alcyonacea),” Organisms Diversity & Evolution, vol. 13, pp. 135–150, 2013.

[33] M. S. Studivan, W. I. Hatch, and C. L. Mitchelmore, “Responses of the soft coral Xenia elongata following acute exposure to a chemical dispersant,” SpringerPlus, vol. 4, p. 80, 2015. [34] V. N. Bednarz, M. S. Naumann, W. Niggl, and C. Wild, “Inorganic nutrient availability

affects organic matter fluxes and metabolic activity in the soft coral genusXenia,” Journal of Experimental Biology, vol. 20, pp. 3672–3679, 2012.

[35] O. H. Shapiro, V. I. Fernandez, M. Garren, J. S. Guasto, F. P. Debaillon-Vesque, E. Kramarsky- Winter, A. Vardi, and R. Stocker, “Vortical ciliary flows actively enhance mass transport in reef corals,” Proceedings of the National Academy of Sciences of the United States of America, vol. 111, no. 37, pp. 13391–13396, 2014.

[36] J. H. Costello and S. P. Colin, “Flow and feeding by swimming scyphomedusae,” Marine Biology, vol. 124, pp. 399–406, 1995.

[37] J. O. Dabiri, S. P. Colin, and J. H. Costello, “Fast-swimming hydromedusae exploit velar kinematics to form an optimal vortex wake,” Journal of Experimental Biology, vol. 209, pp. 2025–2033, 2006.

[38] A. P. Hoover, B. E. Griffith, and L. A. Miller, “Quantifying performance in the medusan mechanospace with an actively swimming three-dimensional jellyfish model,” Journal of Fluid Mechanics, vol. 813, pp. 1112–1155, 2017.

[39] J. Peng and J. O. Dabiri, “Transport of inertial particles by Lagrangian coherent structures: application to predator-prey interaction in jellyfish feeding,” Journal of Fluid Mechanics, vol. 623, pp. 75–84, 2009.

[40] A. Santhanakrishnan, M. Dollinger, C. L. Hamlet, S. P. Colin, and L. A. Miller, “Flow structure and transport characteristics of feeding and exchange currents generated by upside- down cassiopea jellyfish,” Journal of Experimental Biology, vol. 215, no. 14, pp. 2369–2381, 2012.

[41] J. M. Gosline and M. E. DeMont, “Jet-propelled swimming in squids,” Scientific American, vol. 252, pp. 96–103, 1985.

[42] I. K. Bartol, P. S. Krueger, J. T. Thompson, and W. J. Stewart, “Swimming dynamics and propulsive efficiency of squids throughout ontogeny,” Integrative and Comparative Biology, vol. 48, no. 6, pp. 720–733, 2008.

[43] J. L. Manuel and M. J. Dadswell, “Swimming of juvenile sea scallops,Placopecten magellanicus (Gmelin): A minimum size for effective swimming?,” Journal of Experimental Marine Biology and Ecology, vol. 174, pp. 137–175, 1993.

[44] J. L. Falter, R. J. Lowe, and Z. Zhang, “Toward a universal mass-momentum transfer rela- tionship for predicting nutrient uptake and metabolite exchange in benthic reef communities,” Geophysical Research Letters, vol. 43, no. 18, pp. 9764–9772, 2016.

[45] R. W. Bilger and M. J. Atkinson, “Anomalous mass transfer of phosphate on coral reef flats,” Limnology and Oceanography, vol. 37, no. 2, pp. 261–272, 1992.

[46] E. H. Kaplan, R. T. Peterson, and S. L. Kaplan,A Field Guide to Southeastern and Caribbean Seashores: Cape Hatteras to the Gulf Coast, Florida, and the Caribbean. Boston, MA: Houghton Mifflin Harcourt, 2 ed., 1988.

[47] W. K. Fitt and K. Costley, “The role of temperature in survival of the polyp stage of the tropical rhizostome jellyfishCassiopea xamachana,” Journal of Experimental Marine Biology and Ecology, vol. 222, pp. 79–91, 1998.

[48] C. Hamlet,Mathematical Modeling, Immersed Boundary Simulation, and Experimental Valida- tion of the Fluid Flow around the Upside-Down Jellyfish Cassiopea xamachana. PhD thesis,

University of North Carolina at Chapel Hill, Chapel Hill, NC, 2011.

[49] S. Childress and R. Dudley, “Transition from ciliary to flapping mode in a swimming mollusc: Flapping as a bifurcation inReω,” Journal of Fluid Mechanics, vol. 498, pp. 257–288, 2004.

[50] S. Alben and M. Shelley, “Coherent locomotion as an attracting state for a free flapping body,” Proceedings of the National Academy of Sciences of the United States of America, vol. 102, no. 32, pp. 11163–11166, 2005.

[51] C. Hamlet, A. Santhanakrishnan, and L. A. Miller, “A numerical study of the effects of bell pulsation dynamics and oral arms on the exchange currents generated by the upside-down jellyfishcassiopea xamachana,”Journal of Experimental Biology, vol. 214, no. 11, pp. 1911–1921, 2011.

[52] G. Herschlag and L. A. Miller, “Reynolds number limits for jet propulsion: A numerical study of simplified jellyfish,” Journal of Theoretical Biology, vol. 285, no. 1, pp. 2369–2381, 2011. [53] Photron, “Software downloads.” https://photron.com/software-downloads/, last checked

November 7, 2017.

[54] Z. J. Taylor, R. Gurka, G. A. Kopp, and A. Liberzon, “Long-duration time-resolved PIV to study unsteady aerodynamics,” IEEE Transactions on Instrumentation and Measurement, vol. 59, no. 12, pp. 3262–3269, 2010.

[55] T. L. Hedrick, “Software techniques for two- and three-dimensional kinematic measurements of biological and biomimetic systems,” Bioinspiration and Biomimetics, vol. 3, no. 3, p. 034001, 2008.

[56] C. S. Peskin, “Flow patterns around heart valves: a numerical method,” Journal of Computa- tional Physics, vol. 10, pp. 252–271, 1972.

[57] C. S. Peskin, “The immersed boundary method,” Acta Numerica, vol. 11, pp. 479–517, 2002. [58] C. S. Peskin and D. M. McQueen, “Fluid dynamics of the heart and its valves,” inCase Studies in Mathematical Modeling: Ecology, Physiology, and Cell Biology(F. R. Adler, M. A. Lewis, and J. C. Dalton, eds.), ch. 14, pp. 309–338, New Jersey: Prentice-Hall, 1996.

[59] A. J. Baird, L. D. Waldrop, and L. A. Miller, “Neuromechanical pumping: boundary flexibility and traveling depolarization waves drive flow within valveless, tubular hearts,” Japanese Journal of Industrial and Applied Mathematics, vol. 32, pp. 829–846, 2015.

[60] N. A. Battista, A. N. Lane, and L. A. Miller, “On the dynamic suction pumping of blood cells in tubular hearts,” inWomen in Mathematical Biology: Research Collaboration (A. Layton and L. A. Miller, eds.), vol. 8, ch. 11, pp. 211–231, New York, NY: Springer, 2017.

[61] N. A. Battista, A. N. Lane, J. Liu, and L. A. Miller, “Fluid dynamics in heart development: effects of hematocrit and trabeculation,” Mathematical Medicine and Biology, 2017.

[62] L. A. Miller, A. Santhanakrishnan, S. K. Jones, C. Hamlet, K. Mertens, and L. Zhu, “Re- configuration and the reduction of vortex-induced vibrations in broad leaves,” Journal of Experimental Biology, vol. 215, pp. 2716–2727, 2012.

[63] L. A. Miller and C. S. Peskin, “A computational fluid dynamics of clap and fling in the smallest insects,” Journal of Experimental Biology, vol. 208, pp. 3076–3090, 2009.

[64] S. K. Jones, R. Laurenza, T. L. Hedrick, B. E. Griffith, and L. A. Miller, “Lift- vs. drag-based mechanisms for vertical force production in the smallest flying insects,” Journal of Theoretical Biology, vol. 384, pp. 105–120, 2015.

[65] E. D. Tytell, C.-Y. Hsu, and L. J. Fauci, “The role of mechanical resonance in the neural control of swimming in fishes,” Zoology, vol. 117, pp. 48–56, 2014.

[66] A. P. Hoover and L. A. Miller, “A numerical study of the benefits of driving jellyfish bells at their natural frequency,” Journal of Theoretical Biology, vol. 374, pp. 13–25, 2015.

[67] N. A. Battista, W. C. Strickland, and L. A. Miller, “IB2d: a Python and MATLAB implemen- tation of the immersed boundary method,” Bioinspiration and Biomimetics, vol. 12, p. 036003, 2017.

[68] B. E. Griffith,Simulating the blood-muscle-valve mechanics of the heart by an adaptive and par- allel version of the immersed boundary method. PhD thesis, Courant Institute of Mathematics,

New York University, New York, NY, 2005.

[69] B. E. Griffith, “An adaptive and distributed-memory parallel implementation of the immersed boundary (IB) method.” https://github.com/IBAMR/IBAMR, 2014.

[70] H. Childs, E. Brugger, B. Whitlock, J. Meredith, S. Ahern, D. Pugmire, K. Biagas, M. Miller, C. Harrison, G. H. Weber, H. Krishnan, T. Fogal, A. Sanderson, C. Garth, E. W. Bethel, D. Camp, O. Rübel, M. urant, J. M. Favre, and P. Navrátil, “VisIt: an end-user tool for visualizing and analyzing very large data,” in High Performance Visualization - Enabling Extreme-Scale Scientific Insight, pp. 357–372, Oct 2012.

[71] G. Haller, “Lagrangian coherent structures from approximate velocity data,” Physics of Fluids, vol. 14, pp. 1851–1861, 2002.

[72] S. C. Shadden, F. Lekien, and J. E. Marsden, “Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows,” Physica D: Nonlinear Phenomena, vol. 212, pp. 271–304, 2005.

[73] S. C. Shadden, J. O. Dabiri, and J. E. Marsden, “Lagrangian analysis of fluid transport in empirical vortex ring flows,” Physics of Fluids, vol. 18, no. 4, p. 047105, 2006.

[74] J. Peng and J. O. Dabiri, “Transport of inertial particles by Lagrangian coherent structures: application to predator-prey interaction in jellyfish feeding,” Journal of Fluid Mechanics, vol. 623, pp. 75–84, 2009.

[75] M. M. Wilson, J. Peng, J. O. Dabiri, and J. D. Eldredge, “Lagrangian coherent structures in low Reynolds number swimming,” Journal of Physics: Condensed Matter, vol. 21, p. 204105, 2009.

[76] T. Sapsis, J. Peng, and G. Haller, “Instabilities on prey dynamics in jellyfish feeding,” Bulletin of Mathematical Biology, vol. 73, pp. 1841–1856, 2011.

[77] J. O. Dabiri, S. P. Colin, J. H. Costello, and M. Gharib, “Flow patterns generated by oblate medusan jellyfish: field measurements and laboratory analyses,” Journal of Experimental Biology, vol. 208, pp. 1257–1265, 2005.

[78] S. J. Schymanski and D. Or, “Wind increases leaf water use efficiency,” Plant, Cell and Environment, vol. 39, pp. 1448–1459, 2016.

[79] D. M. Gates, “Heat transfer in plants,” Scientific American, vol. 213, pp. 76–84, 1965. [80] J. Grace and J. Wilson, “The boundary layer over a populus leaf,” Journal of Experimental

Botany, vol. 27, pp. 231–241, 1975.

[81] J. M. Peters, N. Gravish, and S. A. Combes, “Wings as impellers: Honey bees co-opt flight system to induce nest ventilation and disperse pheromones,” Journal of Experimental Biology, vol. 220, pp. 2203–2209, 2017.

[82] C. M. Quick, A. M. Venugopal, A. A. Gashev, D. C. Zawieja, and R. H. Stewart, “Intrinsic pump-conduit behavior of lymphangions,” American Journal of Physiology ? Regulatory, Integrative and Comparative Physiology, vol. 292, pp. R1510–R1518, 2007.

[83] D. C. Zawieja, “Contractile physiology of lymphatics,” Lymphatic Research and Biology, vol. 7, pp. 87–96, 2009.

[84] K. R. Sutherland and D. Weihs, “Hydrodynamic advantages of swimming by salp chains,” Journal of the Royal Society Interface, vol. 14, p. 20170298, 2017.

[85] A. Weidenmüller, C. Kleindam, and J. Tautz, “Collective control of nest climate parameters in bumblebee colonies,” Animal Behaviour, vol. 63, pp. 1065–1071, 2002.

[86] A. Filella, F. Nadal, C. Sire, E. Kanso, and C. Eloy, “Hydrodynamic interactions influence fish collective behavior.” https://arxiv.org/abs/1705.07821, 2017.

[87] E. Schneidman, M. J. B. II, R. Segev, and W. Bialek, “Weak pairwise correlations imply strongly correlated network states in a neural population,” Nature, vol. 440, pp. 1007–1012, 2006.

[88] P. DeLellis, G. Polverino, G. Ustuner, N. Abaid, S. Macrí, E. M. Bollt, and M. Porfiri, “Collective behaviour across animal species,” Scientific Reports, vol. 4, p. 3723, 2014.

[89] S. Butail, V. Mwaffo, and M. Porfiri, “Model-free information-theoretic approach to infer

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