15 Sept 2016 : Adil Mughal

Phyllotaxis, disk packing and Fibonacci numbers

Speaker : Dr Adil Mughal – Aberystwyth University, Wales

Venue    : Thu 15 Sept 2016, 3pm (Murdoch University, Senate Room)

Phyllotaxis (the arrangement of buds or branches on a stem, or  flowerets on a flower) has long been debated [1, 2], particularly in regard to the widespread occurrence of spiral structures that are related to the Fibonacci sequence [3-7]. Over the years hundreds of papers, and several books, have attempted to provide explanations of this phenomenon using models of varying complexity, sophistication and ad hoc inventiveness.

Here we off er a theoretical model which relates the problem to disk packings, extending previous work [8, 9] that seeks explanations in that way. Our method
is to adapt the closely related problem of the dense packing of hard disks on a cylinder [10{12], where helical symmetry arises naturally, to the present case of
buds on a gradually enlarging stem.

The figure shows the evolving arrangement of buds on a “bullet shaped” surface (i.e. the stem) at an initial time T1, and subsequent times T2 and T3. Towards the top the arrangement is characterised in phyllotactic notation [l = m+n; m; n] by the structure [1; 1; 0]. With increasing diameter this structure evolves into more complex arrangements – i.e. [2; 1; 1] followed by [3; 2; 1]. This is precisely the rule of progression in the Fibonacci sequence. The images on the left show the pattern “rolled out” onto the plane while the corresponding figures on the right show the arrangement wrapped seamlessly onto the stem.

Buds are introduced at the top of a “bullet-shaped” surface – roughly representative of a plant stem, see Fig (1) – and migrate downwards, while conforming to three principles: dense packing, homogeneity and continuity. Typical results are presented in a video. We show that spiral structures characterised by the Fibonacci sequence (1,1,2,3,5,8,13…), as well as related structures, occur naturally under such rules.

A. M. acknowledges fi nancial support through Aberystwyth University Research Fund.

[1] H. Airy, Proceedings of the Royal Society of London 21, 176 (1872).
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[11] A. Mughal, H. Chan, D. Weaire, and S. Hutzler, Physical Review E 85, 051305 (2012).
[12] A. Mughal and D. Weaire, Physical Review E (2014).

2 Sept 2016 : David Henry

Soil Water Repellence: A Molecular Dynamics Study of Amphiphilic Compounds on Mineral Surfaces

Speaker : Dr David Henry – Murdoch University

Venue    : Fri 2 Sept 2016 @ 3pm (Murdoch University, Senate Room)

This talk describes joint work with Nicholas Daniel, S. M. Mijan Uddin, Richard. J. Harper from the School of Veterinary and Life Sciences, Murdoch University, 90 South Street, Murdoch WA. 6150 Australia.

Hydrophobic soils have been observed around the world, under different climates and land uses1. It is estimated that southern Australia alone has between two and five million hectares affected by hydrophobic soils2. Non-wettable soils cause both environmental and economic problems including increased surface runoff, enhanced erosion rates and chemical leaching, decreased nutrient storage and plant-available water and reduced crop yields.3 This hydrophobicity is caused by amphiphilic organic compounds deposited in the soil that originate from plant materials.4 Our experimental investigation of this phenomenon is complemented by computer modelling of the structuring and interaction of organic species, on different soil types, to identify key driving forces. This study examines intermolecular interactions of monolayers of hexadecanol (CH3(CH2)15OH) and hexadecanoic acid (CH3(CH2)14COOH) on quartz, silica and kaolinite as a function of surface density, using classical molecular dynamics simulations. The computer simulations clearly indicate quite different packing and interfacial interactions between wax molecules on sand/quartz (Fig. 1a) and clay/kaolinite surfaces (Fig. 1b), respectively.5 Consequently, higher levels of wax material are required to render clay particles hydrophobic compared with sand particles.

Figure 1. Alignment of CH3(CH2)15OH on (a) Quartz and (b) Kaolinite

Analysis of the trajectories also reveals that acid mobility is greatest on the quartz surface, and lowest on the silica surface. While the interactions between the surface and acid chains are of primary interest, the interactions between acid chains are also important in determining the structure of the layers formed. Hydrogen-bonding is dominant between the acidic hydrogen and carbonyl oxygen atoms of the neighbouring acid chains. The structuring of water around the functional groups of the surfaces and the waxes also provides insight into the susceptibility of different surfaces to develop water repellence.


1 S. H. Doerr, C. J. Ritsema, L. W. Dekker, D. F. Scott, D. Cater, D. Hydrological Procs. 2007, 21, 2223-2228.

2 R. J. Harper, I. McKissock, R. J. Gilkes, D. J. Carter, P. S. Blackwell, J. Hydrology 2000, 231-232, 371-383.

3 S. H. Doerr, R. A. Shakesby, R. P. D. Walsh, Earth-Sci. Revs. 2000, 51, 33-65.

4 F. A. Hansel, C. T. Aoki, C. M. B. F. Maia, A. Cunha Jr, R. A. Dedecek, R.A. Geoderma 2008, 148, 167-172.

5 L. Walden, R. Harper, D. Mendham, D. Henry, J. Fontaine, Soil Res. 2015, 53, 168-177.