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Mathematical retroreflectors
1. | Department of Mathematics, University of Aveiro, Aveiro 3810-193 |
References:
[1] |
P. Bachurin, K. Khanin, J. Marklof and A. Plakhov, Perfect retroreflectors and billiard dynamics, J. Modern Dynam., 5 (2011), 33-48.
doi: 10.3934/jmd.2011.5.33. |
[2] |
K. I. Borg, L. H. Söderholm and H. Essén, Force on a spinning sphere moving in a rarefied gas, Physics of Fluids, 15 (2003), 736-741.
doi: 10.1063/1.1541026. |
[3] |
L. Bunimovich, Mushrooms and other billiards with divided phase space, Chaos, 11 (2001), 802-808.
doi: 10.1063/1.1418763. |
[4] |
J. E. Eaton, On spherically symmetric lenses, Trans. IRE Antennas Propag., 4 (1952), 66-71. |
[5] |
P. D. F. Gouveia, "Computação de Simetrias Variacionais e Optimização da Resistência Aerodinâmica Newtoniana," (Portuguese) [Computation of Variational Symmetries and Optimization of Newtonian Aerodynamic Resistance], Ph.D thesis, University of Aveiro, Portugal, 2007. |
[6] |
P. Gouveia, A. Plakhov and D. Torres, Two-dimensional body of maximum mean resistance, Applied Math. and Computation, 215 (2009), 37-52.
doi: 10.1016/j.amc.2009.04.030. |
[7] |
S. G. Ivanov and A. M. Yanshin, Forces and moments acting on bodies rotating around a symmetry axis in a free molecular flow, Fluid Dyn., 15 (1980), 449-453.
doi: 10.1007/BF01089985. |
[8] |
K. Moe and M. M. Moe, Gas-surface interactions and satellite drag coefficients, Planet. Space Sci., 53 (2005), 793-801.
doi: 10.1016/j.pss.2005.03.005. |
[9] |
I. Newton, "Philosophiae Naturalis Principia Mathematica," London: Streater, 1687. |
[10] |
A. Plakhov, Billiards in unbounded domains reversing the direction of motion of a particle, Russ. Math. Surv., 61 (2006), 179-180.
doi: 10.1070/RM2006v061n01ABEH004308. |
[11] |
A. Plakhov, Billiards and two-dimensional problems of optimal resistance, Arch. Ration. Mech. Anal., 194 (2009), 349-382.
doi: 10.1007/s00205-008-0137-1. |
[12] |
A. Plakhov and P. Gouveia, Problems of maximal mean resistance on the plane, Nonlinearity, 20 (2007), 2271-2287.
doi: 10.1088/0951-7715/20/9/013. |
[13] |
A. Plakhov, Scattering in billiards and problems of Newtonian aerodynamics, Russ. Math. Surv., 64 (2009), 873-938.
doi: 10.1070/RM2009v064n05ABEH004642. |
[14] |
S. Tabachnikov, "Billiards," Paris: Société Mathématique de France, 1995. |
[15] |
C.-T. Wang, Free molecular flow over a rotating sphere, AIAA J., 10 (1972), 713-714.
doi: 10.2514/3.50192. |
show all references
References:
[1] |
P. Bachurin, K. Khanin, J. Marklof and A. Plakhov, Perfect retroreflectors and billiard dynamics, J. Modern Dynam., 5 (2011), 33-48.
doi: 10.3934/jmd.2011.5.33. |
[2] |
K. I. Borg, L. H. Söderholm and H. Essén, Force on a spinning sphere moving in a rarefied gas, Physics of Fluids, 15 (2003), 736-741.
doi: 10.1063/1.1541026. |
[3] |
L. Bunimovich, Mushrooms and other billiards with divided phase space, Chaos, 11 (2001), 802-808.
doi: 10.1063/1.1418763. |
[4] |
J. E. Eaton, On spherically symmetric lenses, Trans. IRE Antennas Propag., 4 (1952), 66-71. |
[5] |
P. D. F. Gouveia, "Computação de Simetrias Variacionais e Optimização da Resistência Aerodinâmica Newtoniana," (Portuguese) [Computation of Variational Symmetries and Optimization of Newtonian Aerodynamic Resistance], Ph.D thesis, University of Aveiro, Portugal, 2007. |
[6] |
P. Gouveia, A. Plakhov and D. Torres, Two-dimensional body of maximum mean resistance, Applied Math. and Computation, 215 (2009), 37-52.
doi: 10.1016/j.amc.2009.04.030. |
[7] |
S. G. Ivanov and A. M. Yanshin, Forces and moments acting on bodies rotating around a symmetry axis in a free molecular flow, Fluid Dyn., 15 (1980), 449-453.
doi: 10.1007/BF01089985. |
[8] |
K. Moe and M. M. Moe, Gas-surface interactions and satellite drag coefficients, Planet. Space Sci., 53 (2005), 793-801.
doi: 10.1016/j.pss.2005.03.005. |
[9] |
I. Newton, "Philosophiae Naturalis Principia Mathematica," London: Streater, 1687. |
[10] |
A. Plakhov, Billiards in unbounded domains reversing the direction of motion of a particle, Russ. Math. Surv., 61 (2006), 179-180.
doi: 10.1070/RM2006v061n01ABEH004308. |
[11] |
A. Plakhov, Billiards and two-dimensional problems of optimal resistance, Arch. Ration. Mech. Anal., 194 (2009), 349-382.
doi: 10.1007/s00205-008-0137-1. |
[12] |
A. Plakhov and P. Gouveia, Problems of maximal mean resistance on the plane, Nonlinearity, 20 (2007), 2271-2287.
doi: 10.1088/0951-7715/20/9/013. |
[13] |
A. Plakhov, Scattering in billiards and problems of Newtonian aerodynamics, Russ. Math. Surv., 64 (2009), 873-938.
doi: 10.1070/RM2009v064n05ABEH004642. |
[14] |
S. Tabachnikov, "Billiards," Paris: Société Mathématique de France, 1995. |
[15] |
C.-T. Wang, Free molecular flow over a rotating sphere, AIAA J., 10 (1972), 713-714.
doi: 10.2514/3.50192. |
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