316 on One Hundred Years of Boundary Layer Research, Proceedings of the IUTAM Symposium held at DLR-Göttingen, Germany, 2004, (eds. G. E. A. Meier and
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1 316 on One Hundred Years of Boundary Layer Research, Proceedings of the IUTAM Symposium held at DLR-Göttingen, Germany, 2004, (eds. G. E. A. Meier and K. R. Sreenivasan), Solid Mech. Appl., 129, Springer, 2006, pp [10] J. M. Hamilton, J. Kim and F. Waleffe, Regeneration mechanisms of near-wall turbulence structures, J. Fluid Mech., 287 (1995), [11] J. Kim, P. Moin and R. Moser, Turbulence statistics in fully developed channel flow at low Reynolds number, J. Fluid Mech., 177 (1987), [12] P. R. Spalart, R. D. Moser and M. M. Rogers, Spectral methods for the Navier Stokes equations with one infinite and two periodic directions, J. Comput. Phys., 96 (1991), [13] C. Canuto, M. Y. Hussaini, A. Quarteroni and T. A. Zang, Spectral method in fluid dynamics, Springer, New York, [14] G. B. McFadden, B. T. Murray and R. F. Boisvert, Elimination of spurious eigenvalues in the Chebyshev tau spectral method, J. Comput. Phys., 91 (1990), [15],,, [16] Y. Saad, Iterative methods for sparse linear systems, SIAM, Philadelphia, [17] J. E. Dennis, Jr. and R. B. Schnabel, Numerical methods for unconstrained optimization and nonlinear equations, SIAM, Philadelphia, [18] K. Pyragas, Continuous control of chaos by self-controlling feedback, Phys. Lett. A, 170 (1992), [19],,,, [20] J. Jiménez, G. Kawahara, M. P. Simens, M. Nagata and M. Shiba, Characterization of near-wall turbulence in terms of equilibrium and bursting solutions, Phys. Fluids, 17 (2005), , 16 pp. [21] S. K. Robinson, Coherent Motions in the Turbulent Boundary Layer, Annu. Rev. Fluid Mech., 23 (1991), ( ) ( ) AUTO
2 AUTO 317 ( ) CT, MRI MRI MRI AUTO E. J. Doedel [1] AUTO 1.2 AUTO AUTO E. J. Doedel [1] AUTO C FORTRAN C AUTO2000 FORTRAN AUTO07p AUTO07p AUTO C FORTRAN AUTO AUTO AUTO KNOPPIX/Math 2008 [19] AUTO07p AUTO AUTO AUTO 93
3 318 (AUTO ) AUTO 200 ([ 7 ]) AUTO AUTO Automatic (AUTO Automatic AUTO )AUTO ([18]) 2 AUTO AUTO AUTO 2.1 AUTO AUTO () 94
4 AUTO 319 AUTO 1 u t = (u + 1)(u 2 α), α < 1. (1) α u = 1 0 <α<1 u = ±α α <0 u = 1 u 0 lim t u(t) = 1 u(t) 1 α 0 (α = 0.001) u(0) = 0.5 (1) u(t) 1 u(t) 1 (1) lim t u(t) = 1 1 S t = 150 u = 1 lim t u(t) = 1 AE 0 2/3 AE 0 ( 95
5 320 ) α = u =0AUTO AUTO 2 ()AUTO α =0 α =0 u =0 AE (1) AUTO U 0 S AE ( 1 ) AE ( α <0 ) AUTO [ 5 ], [ 6 ], [15] [17] 96
6 AUTO 321 [2] [3] ( 2 ) u t = D u u xx + u 2 v (F + k)u, (2) v t = D v v xx u 2 v + F (1 v). 31 u(x, t) L (a) D u =10 5, D v =2 10 5, F =0.04, k = , L =1.6(b) D u =10 5, D v =2 10 5, F =0.025, k =0.0542, L =0.5 97
7 322 3 ( 4) (2) AUTO ( 5) AUTO AUTO AUTO LAPACK [ 4 ] [17] 4 [ 8 ], [ 9 ] AUTO AUTO AUTO 1) ([10] [14]) AUTO 98
8 AUTO u(x, t) D u =10 5, D v =2 10 5, L =0.5 (k, F) 3 99
9 324 5 F =0.04, L =0.3 AUTO AUTO k = (a), (b) k 2 (a) k = , (b) k = (a) (b) 100
10 AUTO AUTO AUTO first author AUTO first author AUTO 1) AUTO AUTO [ 1 ] E. J. Doedel, A. R. Champneys, T. F. Fairgrieve, Y. A. Kuznetsov, B. Sandstede and X. Wang, AUTO97: Continuation and bifurcation software for ordinary differential equations (with HomCont), (1997) concordia.ca/auto/ AUTO ; ac.jp/ ttks/auto/auto-j.html [ 2 ] J. E. Pearson, Complex patterns in a simple system, Science, 261 (1993), [ 3 ] P. Gray and S. K. Scott, Autocatalytic reactions in the isothermal, continuous stirred tank reactor: oscillations and instabilities in the system A +2B 3B, B C, Chem. Eng. Sci., 39 (1984), [ 4 ] Linear Algebra Package ; [ 5 ] Y. Nishiura and D. Ueyama, A skeleton structure of self-replicating dynamics, Physica D, 130 (1999), [ 6 ] Y. Nishiura and D. Ueyama, Spatio-temporal chaos for the Gray Scott model, Physica D, 150 (2001), [ 7 ] Y. Nishiura, D. Ueyama and T. Yanagita, Chaotic pulses for discrete reaction diffusion systems, SIAM J. Appl. Dyn. Syst., 4 (2005), [ 8 ] S. Ei, The motion of weakly interacting pulses in reaction-diffusion systems, J. Dynam. Differential Equations, 14 (2002), [ 9 ] S. Ei, Y. Nishiura and K. Ueda, 2 n -splitting or edge-splitting? A manner of splitting in dissipative systems, Japan J. Indust. Appl. Math.,
11 326 (2001), [10] Y. Nishiura, T. Teramoto and K. Ueda, Scattering and separators in dissipative systems, Phys. Rev. E, 67 (2003), , 7 pp. [11] M. Iima and Y. Nishiura, Collision of localized traveling-wave convection cells in binary fluid, GAKUTO Internat. Ser. Math. Sci. Appl., 22 (2005), [12],, In:,, 1454 (2005), [13] X. Yuan, T. Teramoto and Y. Nishiura, Heterogeneity-induced defect bifurcation and pulse dynamics for a three-component reactiondiffusion system, Phys. Rev. E, 75 (2007), , 12 pp. [14] Y. Nishiura, Y. Oyama and K. Ueda, Dynamics of traveling pulses in heterogeneous media of jump type, Hokkaido Math. J., 36 (2007), [15], (1),, 5,, [16],,, 5,, [17],,, 4,, [18],,, 18. [19] KNOPPIX/Math Project ; ( ) ( ) A. Kushner, V. Lychagin and V. Rubtsov: Contact Geometry and Non-linear Differential Equations, Encyclopedia Math. Appl., 101, Cambridge Univ. Press, 2007 xxii Monge Ampère Lie Lie 19 [Ma] [Mo] Cartan (e.g. [BGG]) 2 Monge Ampère Lie 102
Shunsuke Kobayashi 1 [6] [11] [7] u t = D 2 u 1 x 2 + f(u, v) + s L u(t, x)dx, L x (0.L), t > 0, Neumann 0 v t = D 2 v 2 + g(u, v), x (0, L), t > 0. x
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Shunsuke Kobayashi [6] [] [7] u t = D 2 u x 2 + fu, v + s L ut, xdx, L x 0.L, t > 0, Neumann 0 v t = D 2 v 2 + gu, v, x 0, L, t > 0. x2 u u v t, 0 = t, L = 0, x x. v t, 0 = t, L = 0.2 x x ut, x R vt, x
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1. A. M. Turing [18] 60 Turing A. Gierer H. Meinhardt [1] : (GM) ) a t = D a a xx µa + ρ (c a2 h + ρ 0 (0 < x < l, t > 0) h t = D h h xx νh + c ρ a 2 (0 < x < l, t > 0) a x = h x = 0 (x = 0, l) a = a(x,
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2006 11 28 1. (1) ẋ = ax = x(t) =Ce at C C>0 a0 x(t) 0(t )!! 1 0.8 0.6 0.4 0.2 2 4 6 8 10-0.2 (1) a =2 C =1 1. (1) τ>0 (2) ẋ(t) = ax(t τ) 4 2 2 4 6 8 10-2 -4 (2) a =2 τ =1!! 1. (2) A. (2)
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