17th International Conference on Fundamental and Applied Aspects of Physical Chemistry (Proceedings, Volume I) (2024) [PL-09, pp. 35]
AUTHOR(S) / АУТОР(И): Giulio Facchini 
, Marcello Budroni , Gabor Schuszter , Fabian Brau , Anne De Wit
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DOI: 10.46793/Phys.Chem24I.035F
ABSTRACT / САЖЕТАК:
Phyllotactic patterns, i.e. regular arrangements of leaves or flowers around a plant stem, are beautiful and fascinating examples of regular complex structures encountered in Nature. In botany, their specific symmetries develop when a new primordium periodically grows in the largest gap left between the previous primordium and the apex [1]. Experiments using ferrofluid droplets have also shown that phyllotactic patterns spontaneously form when identical elements repulsing each other are periodically released at a given distance from an injection center and are advected radially at a constant speed [2]. A central issue in phyllotaxis is to understand whether other self-organized mechanisms can generate such patterns. We show that phyllotactic patterns can also develop in the large class of spatial symmetry-breaking systems giving spotted structures with an intrinsic wavelength in the case of radial growth. The constraint of maintaining a fixed wavelength between spots while expanding radially either diffusively or advectively generalizes the concept of successive release of repulsing agents in botany or ferrofluids to new classes of systems. We evidence this numerically on two different models describing reaction-driven phase transitions [3] and self- organized spatial Turing patterns [4], respectively. We further confirm it experimentally with phyllotactic patterns obtained within a radial flow using a precipitation reaction, similar to mineralization reactions important for CO2 sequestration [5]. A generalized method for the construction of this new family of phyllotactic structures is presented. Revealing the genericity of the simple conditions needed to obtain such new phyllotactic arrangements paves the way to discover them in large classes of systems ranging from spinodal decomposition [3], chemical [6], biological [7] or optical [8] Turing structures, and ecological [9] or Liesegang [10] patterns, to name a few.
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REFERENCES / ЛИТЕРАТУРА:
- V. Jean, Phyllotaxis, (Cambridge University Press, 2010).
- Douady, & Y. Couder, Phys. Rev. Lett., 68 (1992) 2098
- W. Cahn & J.E. Hilliard, The Journal of Chemical Physics, 28 (1958) 258.
- Turing, Philos Trans R Soc Lond B. 237 (1952) 37.
- Schuszter, F. Brau, & A. De Wit, Environ. Sci. Technol. Lett. 3 (2016) 156.
- Castets, et al., Phys. Rev. Lett. 64 (1990) 2953.
- Kondo & Asai, Pomacanthus, Nature 376 (1995) 765.
- Staliunas. Phys. Rev. Lett. 81 (1998) 81.
- Lefever & O. Lejeune, Bull. Math. Biol. 59 (1997) 263.
- M. Dayeh, M. Ammar, and M. Al-Ghoul, RSC Adv. 4 (2014) 60034.