Phyllotaxis, Pushed Pattern-Forming Fronts, and Optimal Packing

Pennybacker, Matthew; Newell, Alan C.

doi:10.1103/physrevlett.110.248104

Cited by 17 publications

(15 citation statements)

References 22 publications

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“…At a certain point, central cells shift in phase such that they propagate florets or seed from the outside in, ring by ring. There is a defined velocity at the front of this inward propagating dynamic (Pennybacker and Newell, 2013).…”

Section: Convective Processes and Energy Saving Mechanisms Long Timesmentioning

confidence: 99%

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Energy saving mechanisms, collective behavior and the variation range hypothesis in biological systems: A review

Trenchard

Perc

2016

Biosystems

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Energy saving mechanisms are ubiquitous in nature. Aerodynamic and hydrodynamic drafting, vortice uplift, Bernoulli suction, thermoregulatory coupling, path following, physical hooks, synchronization, and cooperation are only some of the better-known examples. While drafting mechanisms also appear in non-biological systems such as sedimentation and particle vortices, the broad spectrum of these mechanisms appears more diversely in biological systems including bacteria, spermatozoa, various aquatic species, birds, land animals, semi-fluid dwellers like turtle hatchlings, as well as human systems. We present the thermodynamic framework for energy saving mechanisms, and we review evidence in favor of the variation range hypothesis. This hypothesis posits that, as an evolutionary process, the variation range between strongest and weakest group members converges on the equivalent energy saving quantity that is generated by the energy saving mechanism. We also review self-organized structures that emerge due to energy saving mechanisms, including convective processes that can be observed in many systems over both short and long time scales, as well as high collective output processes in which a form of collective position locking occurs.

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Section: Convective Processes and Energy Saving Mechanisms Long Timesmentioning

confidence: 99%

“…These fronts comprise two kinds: pulled fronts and pushed fronts (Pennybacker and Newell, 2013). The first is determined by conditions ahead of the front; the second is determined by conditions behind the front and involves speeds greater than pulled fronts.…”

Section: Convective Processes and Energy Saving Mechanisms Long Timesmentioning

confidence: 99%

Energy saving mechanisms, collective behavior and the variation range hypothesis in biological systems: A review

Trenchard

Perc

2016

Biosystems

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“…More precisely, we are interested in systems that exhibit stable or metastable ordered states, such as stripes, or spots arranged in hexagonal lattices. Examples of such systems arise for example in di‐block copolymers , phase‐field models , and other phase separative systems , as well as in phyllotaxis , and reaction–diffusion systems . Throughout, we will focus on a paradigmatic model, the Swift–Hohenberg equation

u_{t} = - {(1 + Δ)}^{2} u + μ u - u^{3},

where

u = u (t, x, y) \in R

false(x, y false) \in {double-struckR}^{2}

t \in R

, subscripts denote partial derivatives, and

Δ u = u_{x x} + u_{y y}

.…”

Section: Introductionmentioning

confidence: 99%

Pattern‐forming fronts in a Swift–Hohenberg equation with directional quenching — parallel and oblique stripes

Goh

Scheel

2018

J. London Math. Soc.

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We study the effect of domain growth on the orientation of striped phases in a Swift–Hohenberg equation. Domain growth is encoded in a step‐like parameter dependence that allows stripe formation in a half plane, and suppresses patterns in the complement, while the boundary of the pattern‐forming region is propagating with fixed normal velocity. We construct front solutions that leave behind stripes in the pattern‐forming region that are parallel to or at a small oblique angle to the boundary. Technically, the construction of stripe formation parallel to the boundary relies on ill‐posed, infinite‐dimensional spatial dynamics. Stripes forming at a small oblique angle are constructed using a functional‐analytic, perturbative approach. Here, the main difficulties are the presence of continuous spectrum and the fact that small oblique angles appear as a singular perturbation in a traveling‐wave problem. We resolve the former difficulty using a farfield‐core decomposition and Fredholm theory in weighted spaces. The singular perturbation problem is resolved using preconditioners and boot‐strapping.

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“…Topological defects in curved two-dimensional (2D) crystal structures arise in many biological and physical processes, 27,28 from plant growth [29][30][31] and assembly of bacterial cell walls, 32,33 viral capsids 34,35 and microtubules 36 to the targeted design of carbon nanotube sensors 37 and microlense fabrication. 38 On closed manifolds, Euler's theorem 39 links the net charge of the topological defects to the genus g of the underlying surface, imposing for example the 12 pentagons on a soccer ball.…”

Section: Introductionmentioning

confidence: 99%

Defect formation dynamics in curved elastic surface crystals

Stoop

Dunkel

2018

Soft Matter

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Topological defects shape the material and transport properties of physical systems. Examples range from vortex lines in quantum superfluids, defect-mediated buckling of graphene, and grain boundaries in ferromagnets and colloidal crystals, to domain structures formed in the early universe. The Kibble-Zurek (KZ) mechanism describes the topological defect formation in continuous non-equilibrium phase transitions with a constant finite quench rate. Universal KZ scaling laws have been verified experimentally and numerically for second-order transitions in planar Euclidean geometries, but their validity for non-thermal transitions in curved and topologically nontrivial systems still poses open questions. Here, we use recent experimentally confirmed theory to investigate topological defect formation in curved elastic surface crystals formed by stress-quenching a bilayer material. For both spherical and toroidal crystals, we find that the defect densities follow KZ-type power laws. Moreover, the nucleation sequences agree with recent experimental observations for spherical colloidal crystals. Our results suggest that curved elastic bilayers provide an experimentally accessible macroscopic system to study universal properties of non-thermal phase transitions in non-planar geometries.

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Phyllotaxis, Pushed Pattern-Forming Fronts, and Optimal Packing

Cited by 17 publications

References 22 publications

Energy saving mechanisms, collective behavior and the variation range hypothesis in biological systems: A review

Energy saving mechanisms, collective behavior and the variation range hypothesis in biological systems: A review

Pattern‐forming fronts in a Swift–Hohenberg equation with directional quenching — parallel and oblique stripes

Defect formation dynamics in curved elastic surface crystals

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