Hostname: page-component-848d4c4894-8bljj Total loading time: 0 Render date: 2024-06-21T00:14:47.208Z Has data issue: false hasContentIssue false
  • English
  • Français

An information-theoretic approach to study fluid–structure interactions

Published online by Cambridge University Press:  13 June 2018

Peng Zhang ,
Maxwell Rosen ,
Sean D. Peterson  and
Maurizio Porfiri Open the ORCID record for Maurizio Porfiri [Opens in a new window]
Peng Zhang
Affiliation:
Department of Mechanical and Aerospace Engineering, New York University Tandon School of Engineering, Brooklyn, NY 11201, USA
Maxwell Rosen
Affiliation:
Department of Mechanical and Aerospace Engineering, New York University Tandon School of Engineering, Brooklyn, NY 11201, USA
Sean D. Peterson
Affiliation:
Department of Mechanical and Aerospace Engineering, New York University Tandon School of Engineering, Brooklyn, NY 11201, USA Department of Mechanical and Mechatronics Engineering, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
Maurizio Porfiri*
Affiliation:
Department of Mechanical and Aerospace Engineering, New York University Tandon School of Engineering, Brooklyn, NY 11201, USA
*
†Email address for correspondence: mporfiri@nyu.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

The question of causality is pervasive to fluid–structure interactions, where it finds its most alluring instance in the study of fish swimming in coordination. How and why fish align their bodies, synchronize their motion, and position in crystallized formations are yet to be fully understood. Here, we posit a model-free approach to infer causality in fluid–structure interactions through the information-theoretic notion of transfer entropy. Given two dynamical units, transfer entropy quantifies the reduction of uncertainty in predicting the future state of one of them due to additional knowledge about the past of the other. We demonstrate our approach on a system of two tandem airfoils in a uniform flow, where the pitch angle of one airfoil is actively controlled while the other is allowed to passively rotate. Through transfer entropy, we seek to unveil causal relationships between the airfoils from information transfer conducted by the fluid medium.

JFM classification

Waves/Free-surface Flows: Channel flow Biological Fluid Dynamics: Swimming/flying
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 848 , 10 August 2018 , pp. 968 - 986
Check for updates
Copyright
© 2018 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abdi, H. 2007 Bonferroni and Šidák corrections for multiple comparisons. In Encyclopedia of Measurement and Statistics (ed. Salkind, N.), pp. 103–107. Sage.Google Scholar
Abdulsadda, A. T. & Tan, X. 2012 An artificial lateral line system using IPMC sensor arrays. Intl J. Smart Nano Mater. 3 (3), 226–242.Google Scholar
Anderson, R. P., Jimenez, G., Bae, J. Y., Silver, D., Macinko, J. & Porfiri, M. 2016 Understanding policy diffusion in the US: an information-theoretical approach to unveil connectivity structures in slowly evolving complex systems. SIAM J. Appl. Dyn. Syst. 15 (3), 1384–1409.Google Scholar
Ashraf, I., Bradshaw, H., Ha, T.-T., Halloy, J., Godoy-Diana, R. & Thiria, B. 2017 Simple phalanx pattern leads to energy saving in cohesive fish schooling. Proc. Natl Acad. Sci. USA 114 (36), 9599–9604.CrossRefGoogle ScholarPubMed
Bossomaier, T., Barnett, L., Harr, M. & Lizier, J. T. 2016 An Introduction to Transfer Entropy: Information Flow in Complex Systems. Springer.Google Scholar
Butail, S., Mwaffo, V. & Porfiri, M. 2016 Model-free information-theoretic approach to infer leadership in pairs of zebrafish. Phys. Rev. E 93 (4), 042411.Google ScholarPubMed
Conaway, M. R. 1989 Analysis of repeated categorical measurements with conditional likelihood methods. J. Am. Stat. Assoc. 84 (405), 53–62.CrossRefGoogle Scholar
Cover, T. M. & Thomas, J. A. 2006 Elements of Information Theory. Wiley.Google Scholar
Ding, Y., Nawroth, J. C., McFall-Ngai, M. J. & Kanso, E. 2014 Mixing and transport by ciliary carpets: a numerical study. J. Fluid Mech. 743, 124–140.Google Scholar
Dowell, E. H. & Hall, K. C. 2001 Modeling of fluid–structure interaction. Annu. Rev. Fluid Mech. 33 (1), 445–490.CrossRefGoogle Scholar
Faes, L., Porta, A., Rossato, G., Adami, A., Tonon, D., Corica, A. & Nollo, G. 2013 Investigating the mechanisms of cardiovascular and cerebrovascular regulation in orthostatic syncope through an information decomposition strategy. Autonomic Neurosci.: Basic Clinical 178 (1), 76–82.CrossRefGoogle ScholarPubMed
Grabow, C., Macinko, J., Silver, D. & Porfiri, M. 2016 Detecting causality in policy diffusion processes. Chaos 26 (8), 083113.Google Scholar
Griffiths, S. W. & Magurran, A. E. 1998 Sex and schooling behaviour in the Trinidadian guppy. Animal Behav. 56 (3), 689–693.Google Scholar
Hlinka, J., Hartman, D., Vejmelka, M., Runge, J., Marwan, N., Kurths, J. & Paluš, M. 2013 Reliability of inference of directed climate networks using conditional mutual information. Entropy 15 (6), 2023–2045.Google Scholar
Hobeck, J. D. & Inman, D. J. 2012 Artificial piezoelectric grass for energy harvesting from turbulence-induced vibration. Smart Mater. Struct. 21 (10), 105024.Google Scholar
Hu, F., Nie, L.-J. & Fu, S.-J. 2015 Information dynamics in the interaction between a prey and a predator fish. Entropy 17 (10), 7230–7241.Google Scholar
Kiørboe, T., Andersen, A., Langlois, V. J. & Jakobsen, H. H. 2010 Unsteady motion: escape jumps in planktonic copepods, their kinematics and energetics. J. R. Soc. Interface 7 (52), 1591–1602.Google Scholar
Kleeman, R. 2002 Measuring dynamical prediction utility using relative entropy. J. Atmos. Sci. 59 (13), 2057–2072.Google Scholar
Kleeman, R. 2011 Information theory and dynamical system predictability. Entropy 13 (3), 612–649.Google Scholar
Lam, K., Li, J. Y. & So, R. M. C. 2003 Force coefficients and Strouhal numbers of four cylinders in cross flow. J. Fluids Struct. 18 (3), 305–324.Google Scholar
Lamb, H. 1945 Hydrodynamics. Dover.Google Scholar
Liao, J. C. 2007 A review of fish swimming mechanics and behaviour in altered flows. Phil. Trans. R. Soc. Lond. B 362 (1487), 1973–1993.CrossRefGoogle ScholarPubMed
Lizier, J. T. & Prokopenko, M. 2010 Differentiating information transfer and causal effect. Eur. Phys. J. B 73 (4), 605–615.Google Scholar
López, F., Matilla-García, M., Mur, J. & Ruiz-Marín, M. 2010 A non-parametric spatial independence test using symbolic entropy. Regional Sci. Urban Economics 40 (2), 106–115.Google Scholar
Majda, A., Kleeman, R. & Cai, D. 2002 A mathematical framework for quantifying predictability through relative entropy. Meth. Appl. Anal. 9 (3), 425–444.Google Scholar
Marschinski, R. & Kantz, H. 2002 Analysing the information flow between financial time series. Eur. Phys. J. B 30 (2), 275–281.Google Scholar
Mittal, R., Erath, B. D. & Plesniak, M. W. 2013 Fluid dynamics of human phonation and speech. Annu. Rev. Fluid Mech. 45 (1), 437–467.Google Scholar
Nakayama, S., Ruiz-Marín, M., Camacho, M. & Porfiri, M. 2017 Plasticity in leader–follower roles in human teams. Sci. Rep. 7, 14562.CrossRefGoogle ScholarPubMed
Orange, N. & Abaid, N. 2015 A transfer entropy analysis of leader–follower interactions in flying bats. Eur. Phys. J. 224 (17–18), 3279–3293.Google Scholar
Ozono, S. 1999 Flow control of vortex shedding by a short splitter plate asymmetrically arranged downstream of a cylinder. Phys. Fluids 11 (10), 2928–2934.Google Scholar
Paluš, M. & Vejmelka, M. 2007 Directionality of coupling from bivariate time series: how to avoid false causalities and missed connections. Phys. Rev. E 75 (5), 056211.Google Scholar
Partridge, B. L. 1982 The structure and function of fish schools. Sci. Am. 246 (6), 114–123.Google Scholar
Pitcher, T. J. 1998 Shoaling and shoaling behaviour in fishes. In Comparative Psychology: A Handbook (ed. Greenberg, G. & Haraway, M. M.), pp. 748–760. Garland.Google Scholar
Pitcher, T. J., Magurran, A. E. & Winfield, I. J. 1982 Fish in larger shoals find food faster. Behav. Ecol. Sociobiol. 10 (2), 149–151.Google Scholar
Porfiri, M. & Ruiz-Marín, M. 2017 Symbolic dynamics of animal interaction. J. Theor. Biol. 435, 145–156.CrossRefGoogle ScholarPubMed
Porfiri, M. & Ruiz-Marín, M. 2018 Information flow in a model of policy diffusion: an analytical study. IEEE Trans. Network Sci. Engng 5 (1), 42–54.CrossRefGoogle Scholar
Pozrikidis, C. 2010 Shear flow over cylindrical rods attached to a substrate. J. Fluids Struct. 26 (3), 393–405.CrossRefGoogle Scholar
Ristroph, L. & Zhang, J. 2008 Anomalous hydrodynamic drafting of interacting flapping flags. Phys. Rev. Lett. 101 (19), 194502.CrossRefGoogle ScholarPubMed
Rockwell, D. 1998 Vortex–body interactions. Annu. Rev. Fluid Mech. 30 (1), 199–229.Google Scholar
Ruiz-Marín, M., Matilla-García, M., Cordoba, J. A. G., Susillo-González, J. L., Romo-Astorga, A., González-Pérez, A., Ruiz, A. & Gayán, J. 2010 An entropy test for single-locus genetic association analysis. BMC Genetics 11 (1), 19.Google Scholar
Schreiber, T. 2000 Measuring information transfer. Phys. Rev. Lett. 85 (2), 461–464.CrossRefGoogle ScholarPubMed
Shannon, C. E. 1948 A mathematical theory of communication. Bell Syst. Tech. J. 27 (3), 379–423.CrossRefGoogle Scholar
Staniek, M. & Lehnertz, K. 2008 Symbolic transfer entropy. Phys. Rev. Lett. 100 (15), 158101.CrossRefGoogle ScholarPubMed
Strykowski, P. J. & Sreenivasan, K. R. 1990 On the formation and suppression of vortex shedding at low Reynolds numbers. J. Fluid Mech. 218, 71–107.CrossRefGoogle Scholar
Tomaru, T., Murakami, H., Niizato, T., Nishiyama, Y., Sonoda, K., Moriyama, T. & Gunji, Y.-P. 2016 Information transfer in a swarm of soldier crabs. Artif. Life Robot. 21 (2), 177–180.Google Scholar
Vicente, R., Wibral, M., Lindner, M. & Pipa, G. 2011 Transfer entropy: a model-free measure of effective connectivity for the neurosciences. J. Comput. Neurosci. 30 (1), 45–67.Google Scholar
Weihs, D. 1973 Hydromechanics of fish schooling. Nature 241 (5387), 290–291.CrossRefGoogle Scholar
Wibral, M., Pampu, N., Priesemann, V., Siebenhhner, F., Seiwert, H., Lindner, M., Lizier, J. T. & Vicente, R. 2013 Measuring information-transfer delays. PLoS One 8 (2), e55809.CrossRefGoogle ScholarPubMed
Wiener, N. 1956 The theory of prediction. Mod. Math. Engrs 1, 125–139.Google Scholar
Zhang, Z. & Grabchak, M. 2013 Bias adjustment for a nonparametric entropy estimator. Entropy 15 (6), 1999–2011.CrossRefGoogle Scholar
Supplementary material: File

Zhang et al. supplementary material

Zhang et al. supplementary material 1

Download Zhang et al. supplementary material(File)
File 583.3 KB