Turing/Turing-like patterns: Products of random aggregation of spatial components
Jian Gao(高见)1,2,†, Xin Wang(王欣)1,2, Xinshuang Liu(刘心爽)1,2, and Chuansheng Shen(申传胜)1,2
1 International Joint Research Center of Simulation and Control for Population Ecology of Yangtze River in Anhui, Anqing Normal University, Anqing 246011, China; 2 School of Mathematics and Physics, Anqing Normal University, Anqing 246011, China
Abstract Turing patterns are typical spatiotemporal ordered structures in various systems driven far from thermodynamic equilibrium. Turing's reaction-diffusion theory, containing a long-range inhibiting agent and a local catalytic agent, has provided an explanation for the formation of some patterns in nature. Numerical, experimental and theoretical studies about Turing/Turing-like patterns have been generally focused on systems driven far from thermodynamic equilibrium. The local dynamics of these systems are commonly very complex, which brings great difficulties to understanding of formation of patterns. Here, we investigate a type of Turing-like patterns in a near-equilibrium thermodynamic system experimentally and theoretically, and put forward a new formation mechanism and a quantitative method for Turing/Turing-like patterns. Specifically, we observe a type of Turing-like patterns in starch solutions, and study the effect of concentration on the structure of patterns. The experimental results show that, with the increase of concentration, patterns change from spots to inverse spots, and labyrinthine stripe patterns appear in the region of intermediate concentration. We analyze and model the formation mechanism of these patterns observed in experiments, and the simulation results agree with the experimental results. Our conclusion indicates that the random aggregation of spatial components leads to formation of these patterns, and the proportion of spatial components determines the structures. Our findings shed light on the formation mechanism for Turing/Turing-like patterns.
Received: 17 January 2023
Revised: 28 February 2023
Accepted manuscript online: 03 March 2023
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 12205006 and 11975025), the Excellent Youth Scientific Research Project of Anhui Province (Grant No. 2022AH030107), the Natural Science Foundation of Anhui Higher Education Institutions of China (Grant No. KJ2020A0504), and the International Joint Research Center of Simulation and Control for Population Ecology of Yangtze River in Anhui (Grant No. 12011530158).
Jian Gao(高见), Xin Wang(王欣), Xinshuang Liu(刘心爽), and Chuansheng Shen(申传胜) Turing/Turing-like patterns: Products of random aggregation of spatial components 2023 Chin. Phys. B 32 070503
[1] Cross M C and Hohenberg P C 1993 Rev. Mod. Phys.65 851 [2] Turing A M 1952 Phil. Trans. R. Soc. Lond. B237 37 [3] Kondo S and Miura T 2010 Science329 1616 [4] Green J B A and Sharpe J 2015 Development142 1203 [5] Economou A D, Ohazama A, Porntaveetus T et al. 2012 Nat. Genet.44 348 [6] Onimaru K, Marcon L, Musy M, Tanaka M and Sharpe J 2016 Nat. Commun.7 11582 [7] Koch A J and Meinhardt H 1994 Rev. Mod. Phys.66 1481 [8] Yuan X J, Shao X, Liao H M and Ouyang Q 2009 Chin. Phys. Lett.26 024702 [9] Castets V, Dulos E, Boissonade J and De-Kepper P 1990 Phys. Rev. Lett.64 2953 [10] Ouyang Q and Swinney H L 1991 Nature352 610 [11] Kyoung J L, McCormick W D, Ouyang Q and Swinney H L 1993 Science261 192 [12] Horváth J, Szalai I and De-Kepper P 2009 Science324 772 [13] Kondo S and Asai R 1995 Nature376 765 [14] Meinhardt H 2009 The Algorithmic Beauty of Sea Shells (Springer-Verlag) [15] Boettiger A, Ermentrout B and Oster G 2009 Proc. Natl. Acad. Sci. USA106 6837 [16] Dziekan P, Hansen J S and Nowakowski B 2014 J. Chem. Phys.141 124106 [17] Tan Z, Chen S, Peng X, Zhang L and Gao C 2018 Science360 518 [18] Fuseya Y, Katsuno H, Behnia K and Kapitulnik A 2021 Nat. Phys.17 1031 [19] Bénard H 1900 Rev. Gen. Sci. Pures Appl.11 1271 [20] Rayleigh L 1917 Proc. Roy. Soc. Lond. A93 148 [21] Berge L I, Ahlers G and Cannell D S 1993 Phys. Rev. E48 R3236 [22] Pena B. and Perez-Garcia C 2001 Phys. Rev. E64 056213 [23] Weiss S, Seiden G and Bodenschatz E 2012 New J. Phys.14 053010 [24] Astrov Y A, Müller I, Ammelt E et al. 1998 Phys. Rev. Lett.80 5341 [25] Ammelt E, Astrov Y and Purwins H G 1998 Phys. Rev. E58 7109 [26] Purwins H G, Bödeker H U and Liehr A W 2004 AIP Conf. Proc.742 289 [27] Wang Y, Zhang R, Wang Z and Han Z 2019 Chin. Phys. B28 050503 [28] Karig D, Martini K M, Lu T, DeLateur N A, Goldenfeld N and Weiss R 2018 Proc. Natl. Acad. Sci. USA115 6572 [29] Zincenko A, Petrovskii S, Volpert V and Banerjee M 2021 J. R. Soc. Interface18 20210034 [30] Cooper R L, Thiery A P, Fletcher A G, Delbarre D J, Rasch L J and Fraser G J 2018 Sci. Adv.4 eaau5484 [31] Miyazawa S, Okamoto M and Kondo S 2010 Nat. Commun.1 66 [32] Henyey L G and Grasberger W 1955 Astrophys. J.122 498 [33] Vilar J M G and Rubi J M 2001 Proc. Natl. Acad. Sci. USA98 11081 [34] Kleidon A 2010 Phil. Trans. R. Soc. B365 1303 [35] Ross J, Hunt K L C and Hunt P M 1988 J. Chem. Phys.88 2719 [36] Prigogine I and Stengers I 1979 The New Alliance (Paris: Gallimard) [37] Wang W M, Liu H Y, Cai Y L and Li Z Q 2011 Chin. Phys. B20 074702 [38] He Y F, Liu F C, Fan W L and Dong L F 2012 Chin. Phys. B21 034701
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