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Geometric aspects of transformations of forces acting upon a swimmer in a 3-D incompressible fluid
1. | Department of Mathematics, Washington State University, Pullman, WA 99164-3113, United States |
References:
[1] |
F. Alouges, A. DeSimone and A. Lefebvre, Optimal strokes for low reynolds number Sswimmers: An example, J. Nonlinear Sci., 18 (2008), 27-302. |
[2] |
J. M. Ball, J. E. Mardsen and M. Slemrod, Controllable for distributed bilinear systems, SIAM J. Control. Opt., (1982), 575-597. |
[3] |
L. E. Becker, S. A. Koehler and H. A. Stone, On self-propulsion of micro-machines at low Reynolds number: Purcell's three-link swimmer, J. Fluid Mech., 490 (2003), 15-35. |
[4] |
S. Childress, "Mechanics of Swimming and Flying," Cambridge University Press, 1981. |
[5] |
Gi. Dal Maso, A. DeSimone and M. Morandotti, An existence and uniqueness result for the motion of self-propelled micro-swimmers, SIAM J. Math. Anal., 43 (2011), 1345-1368.
doi: 10.1137/10080083X. |
[6] |
T. Fakuda, et al, Steering mechanism and swimming experiment of micro mobile robot in water, Proc. Micro Electro Mechanical Systems (MEMS'95), (1995), 300-305. |
[7] |
L. J. Fauci and C. S. Peskin, A computational model of aquatic animal locomotion, J. Comp. Physics, 77 (1988), 85-108.
doi: 10.1016/0021-9991(88)90158-1. |
[8] |
L. J. Fauci, Computational modeling of the swimming of biflagellated algal cells, Contemporary Mathematics, 141 (1993), 91-102.
doi: 10.1090/conm/141/1212579. |
[9] |
G. P. Galdi, On the steady self-propelled motion of a body in a viscous incompressible fluid, Arch. Ration. Mech. Anal., 148 (1999), 53-88.
doi: 10.1007/s002050050156. |
[10] |
G. P. Galdi, On the motion of a rigid body in a viscous liquid: A mathematical analysis with applications, in "Handbook of Mathematical Fluid Mechanics" (eds. S. Friedlander and D. Serre), Elsevier Science, (2002), 653-791. |
[11] |
J. Gray, Study in animal locomotion IV - the propulsive power of the dolphin, J. Exp. Biology, 10 (1032), 192-199. |
[12] |
J. Gray and G. J. Hancock, The propulsion of sea-urchin spermatozoa, J. Exp. Biol., 32 802, 1955. |
[13] |
S. Guo, et al., Afin type of micro-robot in pipe, Proc. of the 2002 Int. Symp. on micromechatronics and human science (MHS 2002), (2002), 93-98. |
[14] |
M. E. Gurtin, "Introduction to Continuum Mechanics,'' Academic Press, 1981. |
[15] |
M. F. Hawthorne, J. I. Zink, J. M. Skelton, M. J. Bayer, Ch. Liu, E. Livshits, R. Baer and D. Neuhauser, Electrical or photocontrol of rotary motion of a metallacarborane, Science, 303, 1849, 2004. |
[16] |
V. Happel, and H. Brenner, "Low Reynolds Number Hydrodynamics with Special Applications to Particulate Media," Prentice Hall, 1965. |
[17] |
S. Hirose, "Biologically Inspired Robots: Snake-Like Locomotors and Manipulators," Oxford University Press, Oxford, 1993. |
[18] |
E. Kanso, J. E. Marsden, C. W. Rowley and J. Melli-Huber, Locomotion of articulated bodies in a perfect fluid, J. Nonlinear Science, 15 (2005), 255-289. |
[19] |
A. Y. Khapalov, The well-posedness of a model of an apparatus swimming in the 2-D Stokes fluid, Techn. Rep. 2005-5, Washington State University, Department of Mathematics, http://www.math.wsu.edu/TRS/2005-5.pdf). |
[20] |
A. Y. Khapalov, Local controllability for a "swimming'' model, SIAM J. Cont. Opt., 46 (2007), 655-682.
doi: 10.1137/050638424. |
[21] |
A. Y. Khapalov, Geometric aspects of controllability for a swimming phenomenon, Appl. Math. Optim., 57 (2008), 98-124.
doi: 10.1007/s00245-007-9013-x. |
[22] |
A. Y. Khapalov, Micro motions of a 2-D swimming model governed by multiplicative controls, Nonlinear Analysis: Theory, Methods and Appl.: Special Issue: WCNA 2008, 71 (2009), 1970-1979. |
[23] |
A. Y. Khapalov and S. Eubanks, The wellposedness of a 2-D swimming model governed in the nonstationary Stokes fluid by multiplicative controls, Applicable Analysis, 88 (2009), 1763-1783.
doi: 10.1080/00036810903401222. |
[24] |
A. Y. Khapalov, "Controllability of Partial Differential Equations Governed by Multiplicative Controls,'' Lecture Notes in Mathematics Series, Vol. 1995, Springer-Verlag Berlin Heidelberg, 284p., 2010. |
[25] |
J. Koiller, F. Ehlers and R. Montgomery, Problems and progress in microswimming, J. Nonlinear Sci., 6 (1996), 507-541. |
[26] |
L. G. Leal, The Slow Motion of Slender Rod-Like Particles in a Second- Order Fluid, J. Fluid Mech., 69 (1975), 305-337. |
[27] |
M. J. Lighthill, "Mathematics of Biofluid Dynamics,'' Philadelphia, Society for Industrial and Applied Mathematics, 1975. |
[28] |
R. Mason and J. W. Burdick, Experiments in carangiform robotic fish locomotion, Proc. IEEE Int. Conf. Robotics and Automation, (2000), 428-435. |
[29] |
K. A. McIsaac and J. P. Ostrowski, Motion planning for dynamic eel-like robots, Proc. IEEE Int. Conf. Robotics and Automation, San Francisco, (2000), 1695-1700. |
[30] |
S. Martinez and J. Cort'es, Geometric control of robotic locomotion systems, Proc. X Fall Workshop on Geometry and Physics, Madrid, 2001, Publ. de la RSME, 4 (2001), 183-198. |
[31] |
K. A. Morgansen, V. Duindam, R. J. Mason, J. W. Burdick and R. M. Murray, Nonlinear control methods for planar carangiform robot fish locomotion, Proc. IEEE Int. Conf. Robotics and Automation, (2001), 427-434. |
[32] |
C. S. Peskin, Numerical analysis of blood flow in the heart, J. Comp. Physics, 25 (1977), 220-252.
doi: 10.1016/0021-9991(77)90100-0. |
[33] |
C. S. Peskin and D. M. McQueen, A general method for the computer simulation of biological systems interacting with fluids, SEB Symposium on biological fluid dynamics, Leeds, England, July 5-8, 1994. |
[34] |
J. San Martin, T. Takashi and M. Tucsnak, A control theoretic approach to the swimming of microscopic organisms, Quart. Appl. Math., 65 (2007), 405-424. |
[35] |
J. San Martin, J.-F. Scheid, T. Takashi and M. Tucsnak, An initial and boundary value problem modeling of fish-like swimming, Arch. Ration. Mech. Anal., 188 (2008), 429-455.
doi: 10.1007/s00205-007-0092-2. |
[36] |
A. Shapere and F. Wilczeck, Geometry of self-propulsion at low Reynolds number, J. Fluid Mech., 198 (1989), 557-585. |
[37] |
M. Sigalotti and J.-C. Vivalda, Controllability properties of a class of systems modeling swimming microscopic organisms, ESAIM: COCV, Published online August 11, 2009. |
[38] |
G. I. Taylor, Analysis of the swimming of microscopic organisms, Proc. R. Soc. Lond. A, 209 (1951), 447-461. |
[39] |
G. I. Taylor, Analysis of the swimming of long and narrow animals, Proc. R. Soc. Lond. A, 214 (1952). |
[40] | |
[41] |
M. S. Trintafyllou, G. S. Trintafyllou and D. K. P. Yue, Hydrodynamics of fishlike swimming, Ann. Rev. Fluid Mech., 32 (2000), 33-53.
doi: 10.1146/annurev.fluid.32.1.33. |
[42] |
E. D. Tytell, C.-Y. Hsu, T. L. Williams, A. H. Cohen and L. J. Fauci, Interactions between internal forces, body stiffness, and fluid environment in a neuromechanical model of lamprey swimming, Proc. Natl Acad Sci USA, 107 (2010), 19832-19837.
doi: 10.1073/pnas.1011564107. |
[43] |
T. Y. Wu, Hydrodynamics of swimming fish and cetaceans, Adv. Appl. Math., 11 (1971), 1-63. |
show all references
References:
[1] |
F. Alouges, A. DeSimone and A. Lefebvre, Optimal strokes for low reynolds number Sswimmers: An example, J. Nonlinear Sci., 18 (2008), 27-302. |
[2] |
J. M. Ball, J. E. Mardsen and M. Slemrod, Controllable for distributed bilinear systems, SIAM J. Control. Opt., (1982), 575-597. |
[3] |
L. E. Becker, S. A. Koehler and H. A. Stone, On self-propulsion of micro-machines at low Reynolds number: Purcell's three-link swimmer, J. Fluid Mech., 490 (2003), 15-35. |
[4] |
S. Childress, "Mechanics of Swimming and Flying," Cambridge University Press, 1981. |
[5] |
Gi. Dal Maso, A. DeSimone and M. Morandotti, An existence and uniqueness result for the motion of self-propelled micro-swimmers, SIAM J. Math. Anal., 43 (2011), 1345-1368.
doi: 10.1137/10080083X. |
[6] |
T. Fakuda, et al, Steering mechanism and swimming experiment of micro mobile robot in water, Proc. Micro Electro Mechanical Systems (MEMS'95), (1995), 300-305. |
[7] |
L. J. Fauci and C. S. Peskin, A computational model of aquatic animal locomotion, J. Comp. Physics, 77 (1988), 85-108.
doi: 10.1016/0021-9991(88)90158-1. |
[8] |
L. J. Fauci, Computational modeling of the swimming of biflagellated algal cells, Contemporary Mathematics, 141 (1993), 91-102.
doi: 10.1090/conm/141/1212579. |
[9] |
G. P. Galdi, On the steady self-propelled motion of a body in a viscous incompressible fluid, Arch. Ration. Mech. Anal., 148 (1999), 53-88.
doi: 10.1007/s002050050156. |
[10] |
G. P. Galdi, On the motion of a rigid body in a viscous liquid: A mathematical analysis with applications, in "Handbook of Mathematical Fluid Mechanics" (eds. S. Friedlander and D. Serre), Elsevier Science, (2002), 653-791. |
[11] |
J. Gray, Study in animal locomotion IV - the propulsive power of the dolphin, J. Exp. Biology, 10 (1032), 192-199. |
[12] |
J. Gray and G. J. Hancock, The propulsion of sea-urchin spermatozoa, J. Exp. Biol., 32 802, 1955. |
[13] |
S. Guo, et al., Afin type of micro-robot in pipe, Proc. of the 2002 Int. Symp. on micromechatronics and human science (MHS 2002), (2002), 93-98. |
[14] |
M. E. Gurtin, "Introduction to Continuum Mechanics,'' Academic Press, 1981. |
[15] |
M. F. Hawthorne, J. I. Zink, J. M. Skelton, M. J. Bayer, Ch. Liu, E. Livshits, R. Baer and D. Neuhauser, Electrical or photocontrol of rotary motion of a metallacarborane, Science, 303, 1849, 2004. |
[16] |
V. Happel, and H. Brenner, "Low Reynolds Number Hydrodynamics with Special Applications to Particulate Media," Prentice Hall, 1965. |
[17] |
S. Hirose, "Biologically Inspired Robots: Snake-Like Locomotors and Manipulators," Oxford University Press, Oxford, 1993. |
[18] |
E. Kanso, J. E. Marsden, C. W. Rowley and J. Melli-Huber, Locomotion of articulated bodies in a perfect fluid, J. Nonlinear Science, 15 (2005), 255-289. |
[19] |
A. Y. Khapalov, The well-posedness of a model of an apparatus swimming in the 2-D Stokes fluid, Techn. Rep. 2005-5, Washington State University, Department of Mathematics, http://www.math.wsu.edu/TRS/2005-5.pdf). |
[20] |
A. Y. Khapalov, Local controllability for a "swimming'' model, SIAM J. Cont. Opt., 46 (2007), 655-682.
doi: 10.1137/050638424. |
[21] |
A. Y. Khapalov, Geometric aspects of controllability for a swimming phenomenon, Appl. Math. Optim., 57 (2008), 98-124.
doi: 10.1007/s00245-007-9013-x. |
[22] |
A. Y. Khapalov, Micro motions of a 2-D swimming model governed by multiplicative controls, Nonlinear Analysis: Theory, Methods and Appl.: Special Issue: WCNA 2008, 71 (2009), 1970-1979. |
[23] |
A. Y. Khapalov and S. Eubanks, The wellposedness of a 2-D swimming model governed in the nonstationary Stokes fluid by multiplicative controls, Applicable Analysis, 88 (2009), 1763-1783.
doi: 10.1080/00036810903401222. |
[24] |
A. Y. Khapalov, "Controllability of Partial Differential Equations Governed by Multiplicative Controls,'' Lecture Notes in Mathematics Series, Vol. 1995, Springer-Verlag Berlin Heidelberg, 284p., 2010. |
[25] |
J. Koiller, F. Ehlers and R. Montgomery, Problems and progress in microswimming, J. Nonlinear Sci., 6 (1996), 507-541. |
[26] |
L. G. Leal, The Slow Motion of Slender Rod-Like Particles in a Second- Order Fluid, J. Fluid Mech., 69 (1975), 305-337. |
[27] |
M. J. Lighthill, "Mathematics of Biofluid Dynamics,'' Philadelphia, Society for Industrial and Applied Mathematics, 1975. |
[28] |
R. Mason and J. W. Burdick, Experiments in carangiform robotic fish locomotion, Proc. IEEE Int. Conf. Robotics and Automation, (2000), 428-435. |
[29] |
K. A. McIsaac and J. P. Ostrowski, Motion planning for dynamic eel-like robots, Proc. IEEE Int. Conf. Robotics and Automation, San Francisco, (2000), 1695-1700. |
[30] |
S. Martinez and J. Cort'es, Geometric control of robotic locomotion systems, Proc. X Fall Workshop on Geometry and Physics, Madrid, 2001, Publ. de la RSME, 4 (2001), 183-198. |
[31] |
K. A. Morgansen, V. Duindam, R. J. Mason, J. W. Burdick and R. M. Murray, Nonlinear control methods for planar carangiform robot fish locomotion, Proc. IEEE Int. Conf. Robotics and Automation, (2001), 427-434. |
[32] |
C. S. Peskin, Numerical analysis of blood flow in the heart, J. Comp. Physics, 25 (1977), 220-252.
doi: 10.1016/0021-9991(77)90100-0. |
[33] |
C. S. Peskin and D. M. McQueen, A general method for the computer simulation of biological systems interacting with fluids, SEB Symposium on biological fluid dynamics, Leeds, England, July 5-8, 1994. |
[34] |
J. San Martin, T. Takashi and M. Tucsnak, A control theoretic approach to the swimming of microscopic organisms, Quart. Appl. Math., 65 (2007), 405-424. |
[35] |
J. San Martin, J.-F. Scheid, T. Takashi and M. Tucsnak, An initial and boundary value problem modeling of fish-like swimming, Arch. Ration. Mech. Anal., 188 (2008), 429-455.
doi: 10.1007/s00205-007-0092-2. |
[36] |
A. Shapere and F. Wilczeck, Geometry of self-propulsion at low Reynolds number, J. Fluid Mech., 198 (1989), 557-585. |
[37] |
M. Sigalotti and J.-C. Vivalda, Controllability properties of a class of systems modeling swimming microscopic organisms, ESAIM: COCV, Published online August 11, 2009. |
[38] |
G. I. Taylor, Analysis of the swimming of microscopic organisms, Proc. R. Soc. Lond. A, 209 (1951), 447-461. |
[39] |
G. I. Taylor, Analysis of the swimming of long and narrow animals, Proc. R. Soc. Lond. A, 214 (1952). |
[40] | |
[41] |
M. S. Trintafyllou, G. S. Trintafyllou and D. K. P. Yue, Hydrodynamics of fishlike swimming, Ann. Rev. Fluid Mech., 32 (2000), 33-53.
doi: 10.1146/annurev.fluid.32.1.33. |
[42] |
E. D. Tytell, C.-Y. Hsu, T. L. Williams, A. H. Cohen and L. J. Fauci, Interactions between internal forces, body stiffness, and fluid environment in a neuromechanical model of lamprey swimming, Proc. Natl Acad Sci USA, 107 (2010), 19832-19837.
doi: 10.1073/pnas.1011564107. |
[43] |
T. Y. Wu, Hydrodynamics of swimming fish and cetaceans, Adv. Appl. Math., 11 (1971), 1-63. |
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