Bifurcation and Pattern Symmetry Selection in Reaction-Diffusion Systems with Kinetic Anisotropy

Gao, Yipeng; Zhang, Yongfeng; Schwen, Daniel; Jiang, Chao; Gan, Jian

doi:10.1038/s41598-019-44303-2

Cited by 6 publications

(5 citation statements)

References 44 publications

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“…When vacancy diffusivity is comparable or even higher than that of SIA, due to the isotropical diffusion of vacancies, the anisotropic effect induced by anisotropic SIA diffusion will become less significant. Different ordering phenomena may occur in such a situation (Gao et al 2019). It should be noted that a much higher SIA diffusivity than that of vacancy has been postulated as a criteria for superlattice formation (Hu and Henager 2009).…”

Section: Discussionmentioning

confidence: 99%

Symmetry breaking during defect self-organization under irradiation

et al. 2020

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One of the most intriguing phenomena under radiation is the self-organization of defects, such as the void superlattices, which have been observed in a list of bcc and fcc metals and alloys when the irradiation conditions fall into certain windows defined by temperature and dose rate. A superlattice features a lattice parameter and a crystal structure. Previously, it has been shown that the superlattice parameter is given by the wavelength of vacancy concentration waves that develop when the uniform concentration field becomes unstable. This instability is driven thermodynamically by vacancy concentration supersaturation and affected by the irradiation condition. However, a theory that predicts the superlattice symmetry, i.e., the selection of superlattice structure, has remained missing decades after the first report of superlattices. By analyzing the nonlinear recombination between vacancies and self-interstitial-atoms (SIAs) in the discrete lattice space, this work establishes the physical connection between symmetry breaking and anisotropic SIA diffusion, allowing for predictions of void ordering during defect self-organization. The results suggest that while the instability is driven thermodynamically by vacancy supersaturation, the symmetry development is kinetically rather than thermodynamically driven. The significance of SIA diffusion anisotropy in affecting superlattice formation under irradiation is also indicated. Various superlattice structures can be predicted based on different SIA diffusion modes, and the predictions are in good agreement with atomistic simulations and previous experimental observations.

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Section: Discussionmentioning

confidence: 99%

Symmetry breaking during defect self-organization under irradiation

et al. 2020

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“…It should be noted that all predictions in Table 4 are based on the assumption that SIA diffuses much faster than vacancy, which is true in most metals. When this assumption is reversed, it has been found that < 111 > 1D SIA diffusion may lead to fcc superlattice instead of bcc (Gao et al, 2019).…”

Section: Figurementioning

confidence: 99%

A review of void and gas bubble superlattices self-organization under irradiation

Zhang

2023

Front. Nucl. Eng.

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Irradiation by high-energy particles has been well known as a destructive force that “damages” crystalline materials by creating lattice defects. One surprising outcome from irradiation is the self-organization of void superlattices and gas bubble superlattices in various materials under irradiation. While these superlattices exhibit crystal structures that mimic atomic lattices, their self-organization takes place in far-from-equilibrium environment. A thermodynamic driving force that entails ordering is either absent or yet to be identified. In the past few decades, extensive research efforts have been made to generate such superlattices and to discern their formation mechanisms. While a consensus is yet to reach, these studies have substantially enriched our understanding on defect evolution and self-organization under irradiation. Appending previous reviews that are mostly done two decades ago, this article presents a comprehensive review of new experimental, theoretical, and simulational studies of void and gas bubble superlattices in the past two decades. An in-depth discussion on the formation mechanisms and their implications on superlattice properties is provided for the purpose of encouraging future studies.

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“…There have been studies of the Turing instability and Turing patterns in the presence of static anisotropic diffusion [13][14][15][16][17][18], and the analysis for static anisotropic diffusion follows similarly to the standard Turing analysis [10]. However, more care is needed when studying time-varying anisotropic diffusion.…”

Section: Turing Instability Under Time-varying Anisotropic Diffusionmentioning

confidence: 99%

“…The investigation of Turing patterns under anisotropic diffusion is often focussed on static anisotropic diffusion tensors in Cartesian coordinates. Busiello et al [14] and Gao et al [13] have carried out the Turing analysis for such cases, with Gao et al [13] relating their results to symmetry selection in Turing patterns. Das [15] has extended this approach to anisotropic diffusion parameters that depend on the concentrations of species.…”

Section: Introductionmentioning

confidence: 99%

“…While the Turing instability is typically analysed in isotropic domains, the work of Hiscock & Megason [11] suggested that anisotropy in diffusion and growth can provide a mechanism for controlling the spacing and orientation of Turing-like patterns. Various chemical and biological phenomena have been linked to anisotropic diffusion, including skin pattern formation of fishes [12], the formation of zebrafish stripes [11], the formation of the void/gas bubble superlattices in crystals under irradiation [13] and periodic patterns in cellular development [11].…”

Section: Introductionmentioning

confidence: 99%

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Modification of Turing patterns through the use of time-varying anisotropic diffusion

Önder,

Van Gorder

2023

Proc. R. Soc. A.

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The Turing mechanism underpinning pattern formation in reaction–diffusion relies on the interplay between diffusion parameters and reaction kinetics. Diffusion is typically assumed isotropic, however anisotropic diffusion is known to arise in both nature and laboratory conditions. We study how the Turing instability and resulting Turing patterns are modified when the underlying diffusion tensor is both anisotropic and time-dependent, modelling, for instance, chemical species reacting and diffusing through time-varying anisotropic media. We show that the set of unstable wavenumber vectors corresponding to Turing modes evolve in a spatially biased manner under this anisotropy, thereby modifying the spatial scale and structure of any resulting Turing patterns differently along each spatial coordinate. We employ this spatial bias to develop control strategies to modify the shape or even structure of Turing patterns over time. We are able to make minor changes to the aspect ratio of Turing patterns, such as morphing circular Schnakenberg spots into elliptical spots, as well as more major changes to the structure of patterns, for instance converting Gierer–Meinhardt spots into stripes or FitzHugh–Nagumo labyrinthine patterns into target patterns. Our results suggest that time-varying anisotropic media may be used as a tool by which to modify and even control Turing patterns.

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Bifurcation and Pattern Symmetry Selection in Reaction-Diffusion Systems with Kinetic Anisotropy

Cited by 6 publications

References 44 publications

Symmetry breaking during defect self-organization under irradiation

Symmetry breaking during defect self-organization under irradiation

A review of void and gas bubble superlattices self-organization under irradiation

Modification of Turing patterns through the use of time-varying anisotropic diffusion

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