×

zbMATH — the first resource for mathematics

Fluid-structure interaction for the classroom: interpolation, hearts, and swimming! (English) Zbl 1459.65017
MSC:
65D05 Numerical interpolation
65D07 Numerical computation using splines
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
97M10 Modeling and interdisciplinarity (aspects of mathematics education)
97M60 Biology, chemistry, medicine (aspects of mathematics education)
97N40 Numerical analysis (educational aspects)
97N50 Interpolation and approximation (educational aspects)
97N80 Mathematical software, computer programs (educational aspects)
92C10 Biomechanics
Software:
IB2d; Matlab; VisIt
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Adobe Systems, Designing Multiple Master Typefaces, 1997, https://www.adobe.com/content/dam/acom/en/devnet/font/pdfs/5091.Design_MM_Fonts.pdf.
[2] S. Alben, L. A. Miller, and J. Peng, Efficient kinematics for jet-propelled swimming, J. Fluid Mech., 733 (2013), pp. 100-133. · Zbl 1294.76297
[3] A. J. Baird, T. King, and L. A. Miller, Numerical study of scaling effects in peristalsis and dynamic suction pumping, Biol. Fluid Dynam. Model. Comput. Appl., 628 (2014), pp. 129-148. · Zbl 1311.76152
[4] N. A. Battista, A. J. Baird, and L. A. Miller, A mathematical model and MATLAB code for muscle-fluid-structure simulations, Integr. Comp. Biol., 55 (2015), pp. 901-911.
[5] N. A. Battista, D. Douglas, A. Lane, L. Samsa, J. Liu, and L. Miller, Vortex dynamics in embryonic trabeculated ventricles, J. Cardiovasc. Dev. Dis., 6 (2019), art. 6.
[6] N. A. Battista, A. N. Lane, J. Liu, and L. A. Miller, Fluid dynamics of heart development: Effects of trabeculae and hematocrit, Math. Med. Biol., 35 (2018), pp. 493-516. · Zbl 1410.92032
[7] N. A. Battista, A. N. Lane, and L. A. Miller, On the dynamic suction pumping of blood cells in tubular hearts, in Women in Mathematical Biology: Research Collaboration, A. Layton and L. A. Miller, eds., Springer, New York, 2017, pp. 211-231. · Zbl 1401.92049
[8] N. A. Battista and M. S. Mizuhara, Fluid-Structure Interaction for the Classroom: Speed, Accuracy, Convergence, and Jellyfish!, preprint, https://arxiv.org/abs/1902.07615, 2019.
[9] N. A. Battista, W. C. Strickland, A. Barrett, and L. A. Miller, IB \(2\) d Reloaded: A more powerful Python and MATLAB implementation of the immersed boundary method, Math. Methods Appl. Sci., 41 (2018), pp. 8455-8480. · Zbl 1407.92007
[10] N. A. Battista, W. C. Strickland, and L. A. Miller, IB2d: A Python and MATLAB implementation of the immersed boundary method, Bioinspir. Biomim., 12 (2017), art. 036003.
[11] J. Baumgart and B. M. Friedrich, Fluid dynamics: Swimming across scales, Nature Phys., 10 (2014), pp. 711-712.
[12] A. D. Becker, H. Masoud, J. W. Newbolt, M. Shelley, and L. Ristroph, Hydrodynamic schooling of flapping swimmers, Nature Commun., 6 (2015), art. 8514.
[13] I. Borazjani and F. Sotiropoulos, Numerical investigation of the hydrodynamics of carangiform swimming in the transitional and inertial flow regimes, J. Exp. Biol., 211 (2008), pp. 1541-1558.
[14] R. L. Burden, D. J. Faires, and A. M. Burden, Numerical Analysis, 10th ed., Cengage Learning, Boston, MA, 2014. · Zbl 0913.65003
[15] 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. Durant, 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, Chapman and Hall/CRC Press, 2012, pp. 357-372.
[16] C. Hamlet, K. A. Hoffman, E. D. Tytell, and L. J. Fauci, The role of curvature feedback in the energetics and dynamics of lamprey swimming: A closed-loop model, PLoS Comput. Biol., 14 (2018), art. e1006324.
[17] C. Hamlet and L. A. Miller, Feeding currents of the upside-down jellyfish in the presence of background flow, Bull. Math. Biol., 74 (2012), pp. 2547-2569. · Zbl 1267.92056
[18] M. Heath, Scientific Computing, McGraw-Hill, New York, 2002.
[19] G. Hershlag and L. A. Miller, Reynolds number limits for jet propulsion: A numerical study of simplified jellyfish, J. Theoret. Biol., 285 (2011), pp. 84-95. · Zbl 1397.92054
[20] S. K. Jones, R. Laurenza, T. L. Hedrick, B. E. Griffith, and L. A. Miller, Lift- vs. drag-based for vertical force production in the smallest flying insects, J. Theoret. Biol., 384 (2015), pp. 105-120. · Zbl 1343.92050
[21] D. Kincaid and W. Cheney, Numerical Analysis, AMS, Providence, RI, 2002. · Zbl 0877.65002
[22] J. Lee, M. E. Moghadam, E. Kung, H. Cao, T. Beebe, Y. Miller, B. L. Roman, C.-L. Lien, N. C. Chi, A. L. Marsden, and T. K. Hsiai, Moving domain computational fluid dynamics to interface with an embryonic model of cardiac morphogenesis, PLoS One, 8 (2013), art. e72924.
[23] S. Marcus, M. Frigura-Iliasa, D. Vatau, and L. Matiu-Iovan, New interpolation tools for digital signal processing, in 2016 International Conference on Information and Digital Technologies (IDT), 2016, pp. 266-270.
[24] T. McMillen and P. Holmes, An elastic rod model for anguilliform swimming, J. Math. Biol., 53 (2006), pp. 843-886. · Zbl 1113.92005
[25] T. McMillen, T. Williams, and P. Holmes, Nonlinear muscles, passive viscoelasticity and body taper conspire to create neuromechanical phase lags in anguilliform swimmers, PLoS Comput. Biol., 4 (2008), art. e1000157.
[26] J. G. Miles and N. A. Battista, Naut your everyday jellyfish model: Exploring how tentacles and oral arms impact locomotion, Fluids, 4 (2019), art. 169.
[27] L. A. Miller and C. S. Peskin, A computational fluid dynamics of clap and fling in the smallest insects, J. Exp. Biol., 208 (2009), pp. 3076-3090.
[28] L. T. Nielsen, S. S. Asadzadeh, J. Dolger, J. H. Walther, T. Kiorboe, and A. Andersen, Hydrodynamics of microbial filter feeding, Proc. Natl. Acad. Sci. USA, 114 (2017), pp. 9373-9378.
[29] F. Pallasdies, S. Goedeke, W. Braun, and R. Memmesheimer, From single neurons to behavior in the jellyfish Aurelia aurita, eLife, 8 (2019), art. e50084
[30] C. S. Peskin, The immersed boundary method, Acta Numer., 11 (2002), pp. 479-517. · Zbl 1123.74309
[31] S. Ruck and H. Oertel, Fluid-structure interaction simulation of an avian flight model, J. Exp. Biol., 213 (2010), pp. 4180-4192.
[32] C. Runge, Über empirische Funktionen und die Interpolation zwischen äquidistanten Ordinaten, Z. Math. Phys., 46 (1901), pp. 224-243. · JFM 32.0272.02
[33] J. E. Samson, N. A. Battista, S. Khatri, and L. A. Miller, Pulsing corals: A story of scale and mixing, BIOMATH, 6 (2017), art. 1712169. · Zbl 1406.92140
[34] F. E. Su, Mathematics for human flourishing, Amer. Math. Monthly, 124 (2017), pp. 483-493. · Zbl 1391.97013
[35] M. Unser, Splines: A perfect fit for signal and image processing, IEEE Signal Process. Mag., 16 (1999), pp. 22-38.
[36] J. Vince, Vector Analysis for Computer Graphics, Springer, Berlin, Germany, 2007. · Zbl 1138.68620
[37] World Wide Web Consortium (W3C), SVG 1.1, 2nd ed., 2011, https://www.w3.org/TR/SVG11/fonts.html.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.