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Approach to zigzag and checkerboard patterns in spatially extended systems

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  • Warambhe, Manoj C.
  • Gade, Prashant M.

Abstract

Zigzag patterns in one dimension or checkerboard patterns in two dimensions occur in a variety of pattern-forming systems. We introduce an order parameter ‘phase defect’ to identify this transition and help to recognize the associated universality class on a discrete lattice. In one dimension, if xi(t) is a variable value at site i at time t. We assign spin si(t)=1 for xi(t)>xi−1(t), si(t)=−1 if xi(t)

Suggested Citation

  • Warambhe, Manoj C. & Gade, Prashant M., 2023. "Approach to zigzag and checkerboard patterns in spatially extended systems," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    • Handle: RePEc:eee:chsofr:v:172:y:2023:i:c:s0960077923004113
    DOI: 10.1016/j.chaos.2023.113510
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    References listed on IDEAS

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    1. Rajvaidya, Bhakti Parag & Deshmukh, Ankosh D. & Gade, Prashant M. & Sahasrabudhe, Girish G., 2020. "Transition to coarse-grained order in coupled logistic maps: Effect of delay and asymmetry," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    2. Walter, J.-C. & Barkema, G.T., 2015. "An introduction to Monte Carlo methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 418(C), pages 78-87.
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    Cited by:

    1. Kong, Chao & Li, Jinqing & Tang, Xinyi & Li, Xuli & Jiao, Ju & Cao, Jun & Deng, Haiming, 2024. "Composite solitary vortices of three-wave mixing in quasi-phase-matched photonic crystals," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).

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