Phyllotaxis and patterns on plants

More documents

Recommendations

Info

Amplitude Equations 1. Representationw(r, α, t) = ∑ A s m(r, t)e is ∫ l mdr−imα + (∗)where A m (r, t)e i ∫ l mdr is WKB approximation for Hankel functionsH s m(kr) in the r >> 1, m/r finite limit with l 2 m = k 2 − m 2 /r 2g(r, α, t) = ∑ B s m(r, t)e is ∫ l mdr−imα + (∗)Alan C. Newell, Zhiying Sun, Patrick D. Shipman<strong>Phyllotaxis</strong> <strong>and</strong> <strong>patterns</strong> on plants
Amplitude Equations 1. EquationsLinear∂A m∂t∂+ (2il m∂r + i ∂l m+ i l m∂r r )2 A m = (ɛ − (lm 2 + m2r 2 − P)2 )A mQuadratic nonlinearitye i ∫ l mdr−imα e i ∫ l ndr−inα → e i ∫ (l m+l n)dr−i(m+n)α+τ(m, n, m + n)A ∗ nA m+nCubic Saturation (e.g. elastic foundation response)−γA m (|A m | 2 + ∑ δ ms |A s | 2 )Alan C. Newell, Zhiying Sun, Patrick D. Shipman<strong>Phyllotaxis</strong> <strong>and</strong> <strong>patterns</strong> on plants
Page 1 and 2: Phyllotaxis <stron
Page 4 and 5: More Examples of Patterns on Plants
Page 6: Diagrams of phylla formationAlan C.
Page 9 and 10: Diagrams of phylla formationAlan C.
Page 11 and 12: Mechanisms and mod
Page 13 and 14: Biochemical factorsReinhardt (2000)
Page 15 and 16: Biochemical factorsReinhardt (2000)
Page 17 and 18: Mechanical FactorsFvKD Equation(Des
Page 19: Patterns arising from the governing
Page 23 and 24: OutcomeTheorem: The amplitude equat
Page 25 and 26: PDE SimulationFront propagating out
Page 45 and 46: PDE SimulationAlan C. Newell, Zhiyi
Page 47: TransitionsHow are transitions achi

Phyllotaxis and patterns on plants

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?