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Ying Z, Zhang H, Wang L, Melnik R. A two-dimensional hydrodynamics prediction framework for mantle-undulated propulsion robot using multiple proper orthogonal decomposition and long short term memory neural network. BIOINSPIRATION & BIOMIMETICS 2023; 19:016005. [PMID: 37976535 DOI: 10.1088/1748-3190/ad0daf] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/04/2023] [Accepted: 11/17/2023] [Indexed: 11/19/2023]
Abstract
In this paper, a deep learning based framework has been developed to predict hydrodynamic forces on a mantle-undulated propulsion robot (MUPRo). A multiple proper orthogonal decomposition (MPOD) algorithm has been proposed to efficiently identify fluid features near the undulating mantle of the MUPRo globally and locally. The results indicate that theL2error of the solution states near the undulating boundary of the proposed MPOD algorithm converges almost linearly to 0.2%. Furthermore, a hydrodynamics prediction framework has been developed based on the proposed MPOD algorithm, where a long short-term memory neural network predicts the temporal coefficients of the MPOD spatial modes. The developed framework achieves economical and reliable predictions of hydrodynamic forces acting on the undulating boundary compared to simulations and experiments. Moreover, theL2error of the developed framework is one to two orders of magnitude lower than that of the frameworks based on the classical POD algorithm when the degrees of freedom are consistent. Finally, the reliability of the proposed MPOD-NIROM is discussed through an offline parameter planning case of an aquatic-inspired robot. The model presented in this paper can provide support for the offline parameter planning of aquatic-inspired robots.
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Affiliation(s)
- Zixiang Ying
- State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, 310027 Hangzhou, People's Republic of China
| | - Haozhi Zhang
- State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, 310027 Hangzhou, People's Republic of China
| | - Linxiang Wang
- State Key Laboratory of Fluid Power and Mechatronic Systems, Zhejiang University, 310027 Hangzhou, People's Republic of China
| | - Roderick Melnik
- MS2Discovery Interdisciplinary Research Institute, Wilfrid Laurier University, Waterloo N2L 3L5, ON, Canada
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Santiago M, Battista NA, Miller LA, Khatri S. Passive concentration dynamics incorporated into the library IB2d, a two-dimensional implementation of the immersed boundary method. BIOINSPIRATION & BIOMIMETICS 2022; 17:036003. [PMID: 35026749 DOI: 10.1088/1748-3190/ac4afa] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/23/2021] [Accepted: 01/13/2022] [Indexed: 06/14/2023]
Abstract
In this paper, we present an open-source software library that can be used to numerically simulate the advection and diffusion of a chemical concentration or heat density in a viscous fluid where a moving, elastic boundary drives the fluid and acts as a source or sink. The fully-coupled fluid-structure interaction problem of an elastic boundary in a viscous fluid is solved using Peskin's immersed boundary method. The addition or removal of the concentration or heat density from the boundary is solved using an immersed boundary-like approach in which the concentration is spread from the immersed boundary to the fluid using a regularized delta function. The concentration or density over time is then described by the advection-diffusion equation and numerically solved. This functionality has been added to our software library,IB2d, which provides an easy-to-use immersed boundary method in two dimensions with full implementations in MATLAB and Python. We provide four examples that illustrate the usefulness of the method. A simple rubber band that resists stretching and absorbs and releases a chemical concentration is simulated as a first example. Complete convergence results are presented for this benchmark case. Three more biological examples are presented: (1) an oscillating row of cylinders, representative of an idealized appendage used for filter-feeding or sniffing, (2) an oscillating plate in a background flow is considered to study the case of heat dissipation in a vibrating leaf, and (3) a simplified model of a pulsing soft coral where carbon dioxide is taken up and oxygen is released as a byproduct from the moving tentacles. This method is applicable to a broad range of problems in the life sciences, including chemical sensing by antennae, heat dissipation in plants and other structures, the advection-diffusion of morphogens during development, filter-feeding by marine organisms, and the release of waste products from organisms in flows.
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Affiliation(s)
- Matea Santiago
- Department of Mathematics, University of Arizona, PO Box 210089, Tucson, AZ 85721, United States of America
| | - Nicholas A Battista
- Department of Mathematics and Statistics, The College of New Jersey, 2000 Pennington Rd., Ewing, NJ 08628, United States of America
| | - Laura A Miller
- Department of Mathematics, University of Arizona, PO Box 210089, Tucson, AZ 85721, United States of America
| | - Shilpa Khatri
- Department of Applied Mathematics, University of California Merced, 5200 North Lake Rd., Merced, CA 95343, United States of America
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Exploring the sensitivity in jellyfish locomotion under variations in scale, frequency, and duty cycle. J Math Biol 2021; 83:56. [PMID: 34731319 DOI: 10.1007/s00285-021-01678-z] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2020] [Revised: 08/04/2021] [Accepted: 10/13/2021] [Indexed: 10/19/2022]
Abstract
Jellyfish have been called one of the most energy-efficient animals in the world due to the ease in which they move through their fluid environment, by product of their bell kinematics coupled with their morphological, muscular, material properties. We investigated jellyfish locomotion by conducting in silico comparative studies and explored swimming performance across different fluid scales (i.e., Reynolds Number), bell contraction frequencies, and contraction phase kinematics (duty cycle) for a jellyfish with a fineness ratio of 1 (ratio of bell height to bell diameter). To study these relationships, an open source implementation of the immersed boundary method was used (IB2d) to solve the fully coupled fluid-structure interaction problem of a flexible jellyfish bell in a viscous fluid. Thorough 2D parameter subspace explorations illustrated optimal parameter combinations in which give rise to enhanced swimming performance. All performance metrics indicated a higher sensitivity to bell actuation frequency than fluid scale or duty cycle, via Sobol sensitivity analysis, on a higher performance parameter subspace. Moreover, Pareto-like fronts were identified in the overall performance space involving the cost of transport and forward swimming speed. Patterns emerged within these performance spaces when highlighting different parameter regions, which complemented the global sensitivity results. Lastly, an open source computational model for jellyfish locomotion is offered to the science community that can be used as a starting place for future numerical experimentation.
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Baldwin T, Battista NA. Hopscotching jellyfish: combining different duty cycle kinematics can lead to enhanced swimming performance. BIOINSPIRATION & BIOMIMETICS 2021; 16:066021. [PMID: 34584025 DOI: 10.1088/1748-3190/ac2afe] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/17/2021] [Accepted: 09/28/2021] [Indexed: 06/13/2023]
Abstract
Jellyfish (Medusozoa) have been deemed the most energy-efficient animals in the world. Their bell morphology and relatively simple nervous systems make them attractive to robotocists. Although, the science community has devoted much attention to understanding their swimming performance, there is still much to be learned about the jet propulsive locomotive gait displayed by prolate jellyfish. Traditionally, computational scientists have assumed uniform duty cycle kinematics when computationally modeling jellyfish locomotion. In this study we used fluid-structure interaction modeling to determine possible enhancements in performance from shuffling different duty cycles together across multiple Reynolds numbers and contraction frequencies. Increases in speed and reductions in cost of transport were observed as high as 80% and 50%, respectively. Generally, the net effects were greater for cases involving lower contraction frequencies. Overall, robust duty cycle combinations were determined that led to enhanced or impeded performance.
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Affiliation(s)
- Tierney Baldwin
- Department of Mathematics and Statistics, The College of New Jersey, 2000 Pennington Road, Ewing Township, NJ 08628, United States of America
| | - Nicholas A Battista
- Department of Mathematics and Statistics, The College of New Jersey, 2000 Pennington Road, Ewing Township, NJ 08628, United States of America
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Fujita S, Kuranaga E, Nakajima YI. Regeneration Potential of Jellyfish: Cellular Mechanisms and Molecular Insights. Genes (Basel) 2021; 12:758. [PMID: 34067753 PMCID: PMC8156412 DOI: 10.3390/genes12050758] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/21/2021] [Revised: 05/09/2021] [Accepted: 05/14/2021] [Indexed: 01/20/2023] Open
Abstract
Medusozoans, the Cnidarian subphylum, have multiple life stages including sessile polyps and free-swimming medusae or jellyfish, which are typically bell-shaped gelatinous zooplanktons that exhibit diverse morphologies. Despite having a relatively complex body structure with well-developed muscles and nervous systems, the adult medusa stage maintains a high regenerative ability that enables organ regeneration as well as whole body reconstitution from the part of the body. This remarkable regeneration potential of jellyfish has long been acknowledged in different species; however, recent studies have begun dissecting the exact processes underpinning regeneration events. In this article, we introduce the current understanding of regeneration mechanisms in medusae, particularly focusing on cellular behaviors during regeneration such as wound healing, blastema formation by stem/progenitor cells or cell fate plasticity, and the organism-level patterning that restores radial symmetry. We also discuss putative molecular mechanisms involved in regeneration processes and introduce a variety of novel model jellyfish species in the effort to understand common principles and diverse mechanisms underlying the regeneration of complex organs and the entire body.
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Affiliation(s)
- Sosuke Fujita
- Graduate School of Life Sciences, Tohoku University, Sendai 980-8578, Miyagi, Japan; (S.F.); (E.K.)
| | - Erina Kuranaga
- Graduate School of Life Sciences, Tohoku University, Sendai 980-8578, Miyagi, Japan; (S.F.); (E.K.)
| | - Yu-ichiro Nakajima
- Graduate School of Life Sciences, Tohoku University, Sendai 980-8578, Miyagi, Japan; (S.F.); (E.K.)
- Frontier Research Institute for Interdisciplinary Sciences, Tohoku University, Sendai 980-8577, Miyagi, Japan
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Costello JH, Colin SP, Dabiri JO, Gemmell BJ, Lucas KN, Sutherland KR. The Hydrodynamics of Jellyfish Swimming. ANNUAL REVIEW OF MARINE SCIENCE 2021; 13:375-396. [PMID: 32600216 DOI: 10.1146/annurev-marine-031120-091442] [Citation(s) in RCA: 24] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Jellyfish have provided insight into important components of animal propulsion, such as suction thrust, passive energy recapture, vortex wall effects, and the rotational mechanics of turning. These traits are critically important to jellyfish because they must propel themselves despite severe limitations on force production imposed by rudimentary cnidarian muscular structures. Consequently, jellyfish swimming can occur only by careful orchestration of fluid interactions. Yet these mechanics may be more broadly instructive because they also characterize processes shared with other animal swimmers, whose structural and neurological complexity can obscure these interactions. In comparison with other animal models, the structural simplicity, comparative energetic efficiency, and ease of use in laboratory experimentation allow jellyfish to serve as favorable test subjects for exploration of the hydrodynamic bases of animal propulsion. These same attributes also make jellyfish valuable models for insight into biomimetic or bioinspired engineeringof swimming vehicles. Here, we review advances in understanding of propulsive mechanics derived from jellyfish models as a pathway toward the application of animal mechanics to vehicle designs.
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Affiliation(s)
- John H Costello
- Department of Biology, Providence College, Providence, Rhode Island 02918, USA;
| | - Sean P Colin
- Department of Marine Biology and Environmental Science, Roger Williams University, Bristol, Rhode Island 02809, USA;
| | - John O Dabiri
- Graduate Aerospace Laboratories and Department of Mechanical and Civil Engineering, California Institute of Technology, Pasadena, California 91125, USA;
| | - Brad J Gemmell
- Department of Integrative Biology, University of South Florida, Tampa, Florida 33620, USA;
| | - Kelsey N Lucas
- School for Environment and Sustainability, University of Michigan, Ann Arbor, Michigan 48109, USA;
| | - Kelly R Sutherland
- Oregon Institute of Marine Biology, University of Oregon, Eugene, Oregon 97403, USA;
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Senter DM, Douglas DR, Strickland WC, Thomas SG, Talkington AM, Miller LA, Battista NA. A semi-automated finite difference mesh creation method for use with immersed boundary software IB2d and IBAMR. BIOINSPIRATION & BIOMIMETICS 2020; 16:10.1088/1748-3190/ababb0. [PMID: 32746437 PMCID: PMC7970534 DOI: 10.1088/1748-3190/ababb0] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/11/2019] [Accepted: 08/03/2020] [Indexed: 06/11/2023]
Abstract
Numerous fluid-structure interaction problems in biology have been investigated using the immersed boundary method. The advantage of this method is that complex geometries, e.g., internal or external morphology, can easily be handled without the need to generate matching grids for both the fluid and the structure. Consequently, the difficulty of modeling the structure lies often in discretizing the boundary of the complex geometry (morphology). Both commercial and open source mesh generators for finite element methods have long been established; however, the traditional immersed boundary method is based on a finite difference discretization of the structure. Here we present a software library for obtaining finite difference discretizations of boundaries for direct use in the 2D immersed boundary method. This library provides tools for extracting such boundaries as discrete mesh points from digital images. We give several examples of how the method can be applied that include passing flow through the veins of insect wings, within lymphatic capillaries, and around starfish using open-source immersed boundary software.
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Affiliation(s)
- D Michael Senter
- Dept. of Mathematics, CB 3250, University of North Carolina, Chapel Hill, NC, 27599, United States of America
- Bioinformatics. and Comp. Biology, CB 7264, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, United States of America
| | - Dylan R Douglas
- Dept. of Mathematics, CB 3250, University of North Carolina, Chapel Hill, NC, 27599, United States of America
- Department of Mathematics, University of Arizona, 617 N. Santa Rita Ave. P.O. Box 210089 Tucson, AZ 85721-0089, United States of America
| | - W Christopher Strickland
- Dept. of Mathematics, CB 3250, University of North Carolina, Chapel Hill, NC, 27599, United States of America
- Dept. of Mathematics, 1403 Circle Drive, University of Tennessee at Knoxville, Knoxville, TN 37919, United States of America
| | - Steven G Thomas
- Dept. of Mathematics, CB 3250, University of North Carolina, Chapel Hill, NC, 27599, United States of America
| | - Anne M Talkington
- Dept. of Mathematics, CB 3250, University of North Carolina, Chapel Hill, NC, 27599, United States of America
- Bioinformatics. and Comp. Biology, CB 7264, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, United States of America
| | - Laura A Miller
- Dept. of Mathematics, CB 3250, University of North Carolina, Chapel Hill, NC, 27599, United States of America
- Bioinformatics. and Comp. Biology, CB 7264, University of North Carolina at Chapel Hill, Chapel Hill, NC 27599, United States of America
- Department of Mathematics, University of Arizona, 617 N. Santa Rita Ave. P.O. Box 210089 Tucson, AZ 85721-0089, United States of America
| | - Nicholas A Battista
- Dept. of Mathematics and Statistics, The College of New Jersey, 2000 Pennington Rd., Ewing, NJ 08628, United States of America
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Battista NA. Swimming Through Parameter Subspaces of a Simple Anguilliform Swimmer. Integr Comp Biol 2020; 60:1221-1235. [DOI: 10.1093/icb/icaa130] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
Synopsis
Computational scientists have investigated swimming performance across a multitude of different systems for decades. Most models depend on numerous model input parameters and performance is sensitive to those parameters. In this article, parameter subspaces are qualitatively identified in which there exists enhanced swimming performance for an idealized, simple swimming model that resembles a Caenorhabditis elegans, an organism that exhibits an anguilliform mode of locomotion. The computational model uses the immersed boundary method to solve the fluid-interaction system. The 1D swimmer propagates itself forward by dynamically changing its preferred body curvature. Observations indicate that the swimmer’s performance appears more sensitive to fluid scale and stroke frequency, rather than variations in the velocity and acceleration of either its upstroke or downstroke as a whole. Pareto-like optimal fronts were also identified within the data for the cost of transport and swimming speed. While this methodology allows one to locate robust parameter subspaces for desired performance in a straight-forward manner, it comes at the cost of simulating orders of magnitude more simulations than traditional fluid–structure interaction studies.
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Affiliation(s)
- Nicholas A Battista
- Department of Mathematics and Statistics, The College of New Jersey, 2000 Pennington Road, Ewing Township, NJ 08628, USA
- Department of Mathematics and Statistics, The College of New Jersey, 2000 Pennington Road, Ewing Township, NJ 08628, USA
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Abstract
While pendulums have been around for millennia and have even managed to swing their way into undergraduate curricula, they still offer a breadth of complex dynamics to which some has still yet to have been untapped. To probe into the dynamics, we developed a computational fluid dynamics (CFD) model of a pendulum using the open-source fluid-structure interaction (FSI) software, IB2d. Beyond analyzing the angular displacements, speeds, and forces attained from the FSI model alone, we compared its dynamics to the canonical damped pendulum ordinary differential equation (ODE) model that is familiar to students. We only observed qualitative agreement after a few oscillation cycles, suggesting that there is enhanced fluid drag during our setup’s initial swing, not captured by the ODE’s linearly-proportional-velocity damping term, which arises from the Stokes Drag Law. Moreover, we were also able to investigate what otherwise could not have been explored using the ODE model, that is, the fluid’s response to a swinging pendulum—the system’s underlying fluid dynamics.
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