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Optimally swimming stokesian robots
1. | CMAP UMR 7641, CNRS, École Polytechnique, Route de Saclay, 91128 Palaiseau Cedex, France, France |
2. | SISSA, International School of Advanced Studies, Via Bonomea 265, 34136 Trieste, Italy, Italy |
References:
[1] |
A. A. Agrachev, D. Barilari and U. Boscain, Introduction to Riemannian and sub-Riemannian geometry,, Not Yet Published, ().
|
[2] |
A. A. Agrachev and Y. L. Sachkov, "Control Theory From the Geometric Viewpoint," Springer Heidelberg, 2004. |
[3] |
F. Alouges, A. DeSimone and L. Heltai, Numerical strategies for stroke optimization of axisymmetric microswimmers, Math. Models Methods Appl. Sci., 2 (2011), 361-387.
doi: 10.1142/S0218202511005088. |
[4] |
F. Alouges, A. DeSimone and A. Lefebvre, Optimal strokes for low Reynolds number swimmers: An example, J. Nonlinear Sci., 18 (2008), 277-302.
doi: 10.1007/s00332-007-9013-7. |
[5] |
F. Alouges, A. DeSimone and A. Lefebvre, Biological fluid dynamics, nonlinear partial differential equations, Encyclopedia of Complexity and Systems Science, 2009. |
[6] |
F. Alouges, A. DeSimone and A. Lefebvre, Optimal strokes for axisymmetric microswimmers, The European Physical Journal E, 28 (2009), 279-284. |
[7] |
M. Arroyo, L. Heltai, D. Millàn and A. DeSimone, Reverse engineering the euglenoid movement, Proceedings of the National Academy of Sciences of the United States of America, 109 (2012), 17874-17879. |
[8] |
J. E. Avron, O. Gat and O. Kenneth, Optimal swimming at low reynolds numbers, Phys. Rev. Lett., 93 (2004), 186001. |
[9] |
W. Bangerth, R. Hartmann and G. Kanschat, deal.II: Differential Equations Analysis Library,, Technical Reference., ().
|
[10] |
W. Bangerth, R. Hartmann and G. Kanschat, deal.II-a general-purpose object-oriented finite element library, ACM Trans. Math. Softw., 33 (2007).
doi: 10.1145/1268776.1268779. |
[11] |
R. A. Bartlett, Mathematical and high level overview of moocho, Technical Report SAND2009-3969, Sandia National Laboratories, (2009). |
[12] |
A. Bressan, Impulsive control of Lagrangian systems and locomotion in fluids, Discrete Contin. Dyn. Syst., 20 (2008), 1-35.
doi: 10.3934/dcds.2008.20.1. |
[13] |
T. Chambrion and A. Munnier, Generalized scallop theorem for Linear swimmers,, preprint, ().
|
[14] |
G. Dal Maso, A. DeSimone and M. Morandotti, An existence and uniqueness result for the motion of self-propelled microswimmers, SIAM J. Math. Anal., 43 (2011), 1345-1368.
doi: 10.1137/10080083X. |
[15] |
R. Dreyfus, J. Baudry and H. A. Stone, Purcell's "rotator'': mechanical rotation at low Reynolds number, The European Physical Journal B-Condensed Matter and Complex Systems, 47 (2005), 161-164. |
[16] |
R. Dreyfus, J. Baudry, M. L. Roper, M. Fermigier, H. A. Stone and J. Bibette, Microscopic artificial swimmer, Nature, 437 (2005), 862-865. |
[17] |
J. H. Hannay and J. F. Nye, Fibonacci numerical integration on a sphere, J. Phys. A, 37 (2004), 11591-11601.
doi: 10.1088/0305-4470/37/48/005. |
[18] |
J. Happel and H. Brenner, "Low Reynolds Number Hydrodynamics with Special Applications to Particulate Media," Prentice-Hall Inc., Englewood Cliffs, N.J., 1965. |
[19] |
R. M. Harshey, Bacterial motility on a surface: many ways to a common goal, Annual Reviews in Microbiology, 57 (2003), 249-273. |
[20] |
M. A. Heroux et al, An overview of the Trilinos project, ACM Trans. Math. Softw., 31 (2005), 397-423.
doi: 10.1145/1089014.1089021. |
[21] |
V. Jurdjevic, "Geometric Control Theory," Cambridge Univ. Press, 1997. |
[22] |
A. Y. Khapalov, Local controllability for a "Swimming'' model, SIAM J. Control Optim., 46 (2007), 655-682.
doi: 10.1137/050638424. |
[23] |
J. Koiller, K. Ehlers and R. Montgomery, Problems and progress in microswimming, J. Nonlinear Sci., 6 (1996), 507-541.
doi: 10.1007/s003329900021. |
[24] |
E. Lauga and T. R. Powers, The hydrodynamics of swimming microorganisms, Rep. Prog. Phys., 72 (2009), 096601.
doi: 10.1088/0034-4885/72/9/096601. |
[25] |
A. Lefebvre-Lepot and B. Merlet, A stokesian submarine, ESAIM: Proc., 28 (2009), 150-161. |
[26] |
M. J. Lighthill, On the squirming motion of nearly spherical deformable bodies through liquids at very small Reynolds numbers, Comm. Pure Appl. Math., 5 (1952), 109-118. |
[27] |
J. Lohéac, J.-F. Scheid and M. Tucsnak, Controllability and time optimal control for low reynolds numbers swimmers, Acta Appl. Math., 123 (2013), 175-200.
doi: 10.1007/s10440-012-9760-9. |
[28] |
A. Najafi and R. Golestanian, Simple swimmer at low Reynolds number: Three linked spheres, Phys. Rev. E, 69 (2004), 062901. |
[29] |
C. Pozrikidis, "Boundary Integral and Singularity Methods for Linearized Viscous Flow," Cambridge Texts in Applied Mathematics. Cambridge Univ. Press, Cambridge, 1992.
doi: 10.1017/CBO9780511624124. |
[30] |
C. Pozrikidis, "A practical Guide to Boundary Element Methods with the Software Library BEMLIB," Chapman & Hall/CRC, Boca Raton, FL, 2002.
doi: 10.1201/9781420035254. |
[31] |
E. M. Purcell, Life at low Reynolds numbers, Am. J. Phys, 45 (1977), 3-11. |
[32] |
J. San Martín, T. Takahashi and M. Tucsnak, A control theoretic approach to the swimming of microscopic organisms, Quart. Appl. Math, 65 (2007), 405-424. |
[33] |
A. Shapere and F. Wilczek, Geometry of self-propulsion at low Reynolds number, J. Fluid Mech., 198 (1989), 557-585.
doi: 10.1017/S002211208900025X. |
[34] |
G. Taylor, Analysis of the swimming of microscopic organisms, Proc. Roy. Soc. London. Ser. A, 209 (1951), 447-461. |
show all references
References:
[1] |
A. A. Agrachev, D. Barilari and U. Boscain, Introduction to Riemannian and sub-Riemannian geometry,, Not Yet Published, ().
|
[2] |
A. A. Agrachev and Y. L. Sachkov, "Control Theory From the Geometric Viewpoint," Springer Heidelberg, 2004. |
[3] |
F. Alouges, A. DeSimone and L. Heltai, Numerical strategies for stroke optimization of axisymmetric microswimmers, Math. Models Methods Appl. Sci., 2 (2011), 361-387.
doi: 10.1142/S0218202511005088. |
[4] |
F. Alouges, A. DeSimone and A. Lefebvre, Optimal strokes for low Reynolds number swimmers: An example, J. Nonlinear Sci., 18 (2008), 277-302.
doi: 10.1007/s00332-007-9013-7. |
[5] |
F. Alouges, A. DeSimone and A. Lefebvre, Biological fluid dynamics, nonlinear partial differential equations, Encyclopedia of Complexity and Systems Science, 2009. |
[6] |
F. Alouges, A. DeSimone and A. Lefebvre, Optimal strokes for axisymmetric microswimmers, The European Physical Journal E, 28 (2009), 279-284. |
[7] |
M. Arroyo, L. Heltai, D. Millàn and A. DeSimone, Reverse engineering the euglenoid movement, Proceedings of the National Academy of Sciences of the United States of America, 109 (2012), 17874-17879. |
[8] |
J. E. Avron, O. Gat and O. Kenneth, Optimal swimming at low reynolds numbers, Phys. Rev. Lett., 93 (2004), 186001. |
[9] |
W. Bangerth, R. Hartmann and G. Kanschat, deal.II: Differential Equations Analysis Library,, Technical Reference., ().
|
[10] |
W. Bangerth, R. Hartmann and G. Kanschat, deal.II-a general-purpose object-oriented finite element library, ACM Trans. Math. Softw., 33 (2007).
doi: 10.1145/1268776.1268779. |
[11] |
R. A. Bartlett, Mathematical and high level overview of moocho, Technical Report SAND2009-3969, Sandia National Laboratories, (2009). |
[12] |
A. Bressan, Impulsive control of Lagrangian systems and locomotion in fluids, Discrete Contin. Dyn. Syst., 20 (2008), 1-35.
doi: 10.3934/dcds.2008.20.1. |
[13] |
T. Chambrion and A. Munnier, Generalized scallop theorem for Linear swimmers,, preprint, ().
|
[14] |
G. Dal Maso, A. DeSimone and M. Morandotti, An existence and uniqueness result for the motion of self-propelled microswimmers, SIAM J. Math. Anal., 43 (2011), 1345-1368.
doi: 10.1137/10080083X. |
[15] |
R. Dreyfus, J. Baudry and H. A. Stone, Purcell's "rotator'': mechanical rotation at low Reynolds number, The European Physical Journal B-Condensed Matter and Complex Systems, 47 (2005), 161-164. |
[16] |
R. Dreyfus, J. Baudry, M. L. Roper, M. Fermigier, H. A. Stone and J. Bibette, Microscopic artificial swimmer, Nature, 437 (2005), 862-865. |
[17] |
J. H. Hannay and J. F. Nye, Fibonacci numerical integration on a sphere, J. Phys. A, 37 (2004), 11591-11601.
doi: 10.1088/0305-4470/37/48/005. |
[18] |
J. Happel and H. Brenner, "Low Reynolds Number Hydrodynamics with Special Applications to Particulate Media," Prentice-Hall Inc., Englewood Cliffs, N.J., 1965. |
[19] |
R. M. Harshey, Bacterial motility on a surface: many ways to a common goal, Annual Reviews in Microbiology, 57 (2003), 249-273. |
[20] |
M. A. Heroux et al, An overview of the Trilinos project, ACM Trans. Math. Softw., 31 (2005), 397-423.
doi: 10.1145/1089014.1089021. |
[21] |
V. Jurdjevic, "Geometric Control Theory," Cambridge Univ. Press, 1997. |
[22] |
A. Y. Khapalov, Local controllability for a "Swimming'' model, SIAM J. Control Optim., 46 (2007), 655-682.
doi: 10.1137/050638424. |
[23] |
J. Koiller, K. Ehlers and R. Montgomery, Problems and progress in microswimming, J. Nonlinear Sci., 6 (1996), 507-541.
doi: 10.1007/s003329900021. |
[24] |
E. Lauga and T. R. Powers, The hydrodynamics of swimming microorganisms, Rep. Prog. Phys., 72 (2009), 096601.
doi: 10.1088/0034-4885/72/9/096601. |
[25] |
A. Lefebvre-Lepot and B. Merlet, A stokesian submarine, ESAIM: Proc., 28 (2009), 150-161. |
[26] |
M. J. Lighthill, On the squirming motion of nearly spherical deformable bodies through liquids at very small Reynolds numbers, Comm. Pure Appl. Math., 5 (1952), 109-118. |
[27] |
J. Lohéac, J.-F. Scheid and M. Tucsnak, Controllability and time optimal control for low reynolds numbers swimmers, Acta Appl. Math., 123 (2013), 175-200.
doi: 10.1007/s10440-012-9760-9. |
[28] |
A. Najafi and R. Golestanian, Simple swimmer at low Reynolds number: Three linked spheres, Phys. Rev. E, 69 (2004), 062901. |
[29] |
C. Pozrikidis, "Boundary Integral and Singularity Methods for Linearized Viscous Flow," Cambridge Texts in Applied Mathematics. Cambridge Univ. Press, Cambridge, 1992.
doi: 10.1017/CBO9780511624124. |
[30] |
C. Pozrikidis, "A practical Guide to Boundary Element Methods with the Software Library BEMLIB," Chapman & Hall/CRC, Boca Raton, FL, 2002.
doi: 10.1201/9781420035254. |
[31] |
E. M. Purcell, Life at low Reynolds numbers, Am. J. Phys, 45 (1977), 3-11. |
[32] |
J. San Martín, T. Takahashi and M. Tucsnak, A control theoretic approach to the swimming of microscopic organisms, Quart. Appl. Math, 65 (2007), 405-424. |
[33] |
A. Shapere and F. Wilczek, Geometry of self-propulsion at low Reynolds number, J. Fluid Mech., 198 (1989), 557-585.
doi: 10.1017/S002211208900025X. |
[34] |
G. Taylor, Analysis of the swimming of microscopic organisms, Proc. Roy. Soc. London. Ser. A, 209 (1951), 447-461. |
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