Shape Optimization of Swimming Sheets

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The swimming behavior of a flexible sheet which moves by propagating deformation waves along its body was first studied by G. I. Taylor in 1951. In addition to being of theoretical interest, this problem serves as a useful model of the locomotion of gastropods and various micro-organisms. Although the mechanics of swimming via wave propagation has been studied extensively, relatively little work has been done to define or describe optimal swimming by this mechanism.We carry out this objective for a sheet that is separated from a rigid substrate by a thin film of viscous Newtonian fluid. Using a lubrication approximation ... continued below

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Wilkening, J. & Hosoi, A.E. March 1, 2005.

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The swimming behavior of a flexible sheet which moves by propagating deformation waves along its body was first studied by G. I. Taylor in 1951. In addition to being of theoretical interest, this problem serves as a useful model of the locomotion of gastropods and various micro-organisms. Although the mechanics of swimming via wave propagation has been studied extensively, relatively little work has been done to define or describe optimal swimming by this mechanism.We carry out this objective for a sheet that is separated from a rigid substrate by a thin film of viscous Newtonian fluid. Using a lubrication approximation to model the dynamics, we derive the relevant Euler-Lagrange equations to optimize swimming speed and efficiency. The optimization equations are solved numerically using two different schemes: a limited memory BFGS method that uses cubic splines to represent the wave profile, and a multi-shooting Runge-Kutta approach that uses the Levenberg-Marquardt method to vary the parameters of the equations until the constraints are satisfied. The former approach is less efficient but generalizes nicely to the non-lubrication setting. For each optimization problem we obtain a one parameter family of solutions that becomes singular in a self-similar fashion as the parameter approaches a critical value. We explore the validity of the lubrication approximation near this singular limit by monitoring higher order corrections to the zeroth order theory and by comparing the results with finite element solutions of the full Stokes equations.

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  • 58th Annual Meeting of the Division of FluidDynamics, Chicago, IL, 11/20-22/2005

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  • Report No.: LBNL--59395
  • Grant Number: DE-AC02-05CH11231
  • Office of Scientific & Technical Information Report Number: 900788
  • Archival Resource Key: ark:/67531/metadc890103

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Office of Scientific & Technical Information Technical Reports

Reports, articles and other documents harvested from the Office of Scientific and Technical Information.

Office of Scientific and Technical Information (OSTI) is the Department of Energy (DOE) office that collects, preserves, and disseminates DOE-sponsored research and development (R&D) results that are the outcomes of R&D projects or other funded activities at DOE labs and facilities nationwide and grantees at universities and other institutions.

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  • March 1, 2005

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  • Sept. 22, 2016, 2:13 a.m.

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  • Sept. 22, 2017, 3:09 p.m.

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Wilkening, J. & Hosoi, A.E. Shape Optimization of Swimming Sheets, article, March 1, 2005; Berkeley, California. (digital.library.unt.edu/ark:/67531/metadc890103/: accessed November 22, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.