ENERGETIC APPROACH TO PHYLLOTAXIS

被引：57

作者：

LEVITOV, LS ^{[1
]}

机构：

[1] CNRS,CTR ETUD CHIM MET,F-94407 VITRY,FRANCE

来源：

EUROPHYSICS LETTERS | 1991年 / 14卷 / 06期

关键词：

D O I：

10.1209/0295-5075/14/6/006

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

Soft lattices subjected to strong compression are studied. Their equilibrium states form a hierarchial system of quasi-bifurcations. Underlying SL(2,Z)XZ2 symmetry of the problem is revealed. The deterministic << principle >> of maximal denominator for quasi-bifurcations is proven analytically, thus explaining the universality of the appearance of Fibonacci numbers for dynamically accessible lattices. The symmetry provides the relation between the hierarchical structure and the Cayley tree with branching number 3 found by Koch and Rothen.

引用

页码：533 / 539

页数：7

共 8 条

[1]

KOCH AJ, 1989, J PHYS I, V50, P1603

[2]

LEVITOV LS, UNPUB PHYLLOTAXIS FL

[3]

Rivier N., 1988, Modern Physics Letters B, V2, P953, DOI 10.1142/S0217984988000758

[4] STRUCTURE OF BENARD CONVECTION CELLS, PHYLLOTAXIS AND CRYSTALLOGRAPHY IN CYLINDRICAL SYMMETRY. [J].

Rivier, N. ;

Occelli, R. ;

Pantaloni, J. ;

Lissowski, A. .

Journal de physique Paris, 1984, 45 (01) :49-63

[5]

RIVIER N, STRUCTURE DYNAMICS P

[6] PHYLLOTAXIS, OR THE PROPERTIES OF SPIRAL LATTICES .1. SHAPE INVARIANCE UNDER COMPRESSION [J].

ROTHEN, F ;

KOCH, AJ .

JOURNAL DE PHYSIQUE, 1989, 50 (06) :633-657

[7]

Thompson dArcy W., 1942, GROWTH FORM, V2

[8]

Weyl Hermann, 1952, SYMMETRY

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