气体放电系统螺旋波斑图数值模拟

doi:10.3969/j.issn.1000-1565.2026.04.004

摘要/Abstract

摘要： 利用Ginzburg-Landau方程模拟了螺旋波斑图的动力学行为,研究了初始条件、边界条件和边界形状对斑图的影响.模拟结果显示:初始条件和控制参数决定斑图的类型;边界条件引入了环境与系统的相互作用.当边界条件的对称性与力场的对称性不同时,系统状态是2种不同对称性相互作用的结果,即边界条件对斑图形态进行一定的调制,区域尺度越小,边界作用越明显,模拟结果与实验结果相符.该研究对于深入理解及控制螺旋波斑图具有重要参考意义.

关键词: 螺旋波, 斑图, 数值模拟, 气体放电

Abstract: Dynamics of spiral patterns has been simulated using the Ginzburg-Landau equation. The influences of initial condition, boundary perturbation and boundary shape have been simulated. The simulation result shows that the initial condition and the parameters control the type of pattern; boundary condition incorporates the interplay between the environment and the system. When the symmetry of the boundary conditions is different from the symmetry of the force field, the system state is the result of the two different symmetries interacting. That is the boundary conditions modulate the pattern morphology to some extent. The smaller the area scale, the more obvious the boundary effect.The simulated results match the experiment results. This work is of importance for understanding and controlling spiral patterns.

Key words: spiral wave, pattern, numerical simulation, gas discharge

中图分类号:

O461

杨帆,刘书华. 气体放电系统螺旋波斑图数值模拟[J]. 河北大学学报(自然科学版), 2026, 46(4): 367-373.

YANG Fan, LIU Shuhua. Numerical simulation on spiral patterns in gas discharge system[J]. Journal of Hebei University(Natural Science Edition), 2026, 46(4): 367-373.

参考文献

[1] Von K A, Huhn F, Munuzuri A P, et al. Measurement of large spiral and target waves in chemical reaction-diffusion-advection systems: turbulent diffusion enhances pattern formation[J]. Phys Rev Lett, 2013, 110(8): 088302. DOI:10.1103/physrevlett.110.088302.
[2] Bansagi T J, Vanag V K, Epstein I R. Tomography of reaction-diffusion microemulsions reveals three-dimensional turing patterns[J]. Science, 2011, 331(6022):1309-1312. DOI:10.1126/science.1200815.
[3] Fan W L, Deng T K, Liu S, et al. Spatiotemporal patterns in coupled reaction-diffusion systems with nonidentical kinetics[J]. Phys Rev E, 2025, 111:024210. DOI:10.1103/PhysRevE.111.024210.
[4] Perkins A C, Grigoriev R O, Schatz M F. Modal spectra extracted from nonequilibrium fluid patterns in laboratory experiments on Rayleigh-Bénard convection[J]. Phys Rev Lett, 2011, 107(6): 064501. DOI:10.1103/physrevlett.107.064501.
[5] Cominotti R, Berti A, Farolfi A, et al. Observation of massless and massive collective excitations with faraday patterns in a two-component superfluid[J]. Phys Rev Lett, 2022, 128(21): 210401. DOI:10.1103/physrevlett.128.210401.
[6] Kiyashko S V, Korzinov L N, Rabinovich M I, et al. Rotating spirals in a faraday experiment[J]. Phys Rev E, 1996, 54(5): 5037-5040. DOI:10.1103/physreve.54.5037.
[7] Rogers J L, Schatz M F, Brausch O, et al. Superlattice patterns in vertically oscillated Rayleigh-Bénard convection[J]. Phys Rev Lett, 2000, 85(20): 4281-4284. DOI:10.1103/physrevlett.85.4281.
[8] Fenton F H, Cherry E M, Hastings H M, et al. Multiple mechanisms of spiral wave breakup in a model of cardiac electrical activity[J]. Chaos Interdiscip J Nonlinear Sci, 2002, 12(3): 852-892. DOI:10.1063/1.1504242.
[9] Davidsen J, Glass L, Kapral R. Topological constraints on spiral wave dynamics in spherical geometries with inhomogeneous excitability[J]. Phys Rev E, 2004, 70(5): 056203. DOI:10.1103/physreve.70.056203.
[10] Fan W, Wang Q, Li R, et al. Manipulation of rotation for triangular plasma photonic crystals in dielectric barrier discharge[J]. Appl Phys Lett, 2024, 124: 121703. DOI:10.1063/5.0201378.
[11] 刘靖楠,冉俊霞,吴凯玥,等.双气隙介质阻挡放电中3种 C_4v 对称性的斑图及其时空相关性[J].河北大学学报(自然科学版), 2024, 44(1): 27-33. DOI:10.3969/j.issn.1000 1565.2024.01.004.
[12] 李雪辰,陈俊宇,贾鹏英,等.外加电压参数对大气压等离子体射流形貌的影响[J].河北大学学报(自然科学版), 2021,41(5):495-502. DOI:10.3969/j.issn.1000 1565.2021.05.006.
[13] Callegari T, Bernecker B, Boeuf J P. Pattern formation and dynamics of plasma filaments in dielectric barrier discharges[J]. Plasma Sources Sci Technol, 2014, 23(5): 054003. DOI:10.1088/0963-0252/23/5/054003.
[14] Breazeal W, Flynn K M, Gwinn E G. Static and dynamic two-dimensional patterns in self-extinguishing discharge avalanches[J]. Phys Rev E, 1995, 52(2): 1503-1515. DOI:10.1103/physreve.52.1503.
[15] Gurevich E L, Astrov Y A, Purwins H G. Pattern formation in planar dc-driven semiconductor-gas discharge devices: two mechanisms[J]. J Phys D: Appl Phys, 2005, 38(3): 468-476. DOI:10.1088/0022-3727/38/3/019.
[16] Dong L F, Liu B B, Li C X, et al. Formation of kagome-white-eye-honeycomb hexagonal superlattice pattern in dielectric barrier discharge[J]. Phys Rev E, 2019, 100(6): 063201. DOI:10.1103/physreve.100.063201.
[17] 冉俊霞,张寒,陈沁怡,等.环-点阵-同心环斑图的放电演化机理及光谱诊断研究[J].物理学报, 2025, 74(18): 198-206. DOI:10.7498/aps.74.20250737.
[18] 田爽,张寒,张喜,等.双气隙下介质阻挡放电斑图的放电特性与参数诊断[J].物理学报, 2025, 74(11): 212-219. DOI:10.7498/aps.74.20250111.
[19] 李耀华,燕兆赫,闫志浩,等.介质阻挡放电中类蜂窝超点阵斑图[J].物理学报, 2025, 74(22): 225201. DOI: 10.7498/aps.74.20250952.
[20] 李骋,闫志浩,齐晓秀,等.条纹水电极介质阻挡放电中 D_2h 超点阵斑图[J].物理学报, 2025, 74(22): 225202. DOI: 10.7498/aps.74.20250985.
[21] 董丽芳,陈浩然,孙凤霞,等.双气隙介质阻挡放电中具有C_6v对称性的三维斑图[J].中国科学: 物理学力学天文学, 2026, 56: 235211. DOI: 10.1360/SSPMA-2025-0026.
[22] Dong L F, Zhang L J, He Y N, et al. Patterned discharges for material localized treatment in dielectric barrier discharge with modulated gas gap[J]. Appl Phys Lett, 2024, 125: 104101. DOI: 10.1063/5.0219136.
[23] Ipsen M, Kramer L, Sorensen P G. Amplitude equations for description of chemical reaction-diffusion systems[J]. Phys Rep, 2000, 337(1/2): 193-235. DOI:10.1016/S0370-1573(00)00062-4.
[24] Yang L F, Epstein I R. Symmetric, asymmetric, and antiphase Turing patterns in a model system with two identical coupled layers[J]. Phys Rev E, 2004, 69(2): 026211. DOI:10.1103/physreve.69.026211. (