基于格子Boltzmann方法研究扩散作用对螺旋波的影响
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摘要
基于格子玻尔兹曼方法的D2Q9模型,研究激发系统中扩散作用对螺旋波演化行为的影响.数值计算结果显示:保持系统其它参数不变,改变快变量的扩散系数D_y,系统中的螺旋波由圆形向方形转变且波臂变粗,系统能量随D_y的增大而逐渐减少,但总量仍然足以维持系统螺旋波稳定;保持系统其它参数不变,改变慢变量的扩散系数D_x,系统中可以演化出稳定螺旋波、小螺旋波和混沌态3种斑图,系统能量随D_x的增大急剧减少;当D_x=0.24时,可观察到系统中长臂螺旋波排斥短臂螺旋波现象,D_x增大到一定值时,系统将由激发系统向振荡系统转变.
Based on the D2 Q9 model of the lattice Boltzmann method, the influence of the diffusion effect on the evolution behavior of the spiral wave in the excitation system was researched. The numerical results show that changing the diffusion coefficient of the fast variable with other parameters maintained, the spiral wave in the system varies from circular to square with thicker wave arm and the system energy decreases with the increase of D_y. However, the total amount is still sufficient to maintain the stability of the spiral wave of the system. Changing the diffusion coefficient of the slow variable with other parameters maintained, three patterns of stable spiral wave, small spiral wave and chaotic state are able to be evolved in the system with sharply decrease of system energy. When D_x=0.24, it is observed that the long-arm spiral wave repels the short-arm spiral wave phenomenon in the system. When D_x increases to a certain value, the system will change from the excitation system to the oscillation system.
Based on the D2 Q9 model of the lattice Boltzmann method, the influence of the diffusion effect on the evolution behavior of the spiral wave in the excitation system was researched. The numerical results show that changing the diffusion coefficient of the fast variable with other parameters maintained, the spiral wave in the system varies from circular to square with thicker wave arm and the system energy decreases with the increase of D_y. However, the total amount is still sufficient to maintain the stability of the spiral wave of the system. Changing the diffusion coefficient of the slow variable with other parameters maintained, three patterns of stable spiral wave, small spiral wave and chaotic state are able to be evolved in the system with sharply decrease of system energy. When D_x=0.24, it is observed that the long-arm spiral wave repels the short-arm spiral wave phenomenon in the system. When D_x increases to a certain value, the system will change from the excitation system to the oscillation system.
引文
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[3] ZHOU L Q,ZHANG C X,OUYANG Q.Spiral instabilities in a reaction-diffusion system[J].Journal of Physical Chemistry A,2001,105(1):112-118.
[4] 戴瑜,韦海明,唐国宁.非均匀激发介质中螺旋波的演化[J].物理学报,2010,59(9):5979-5984.DAI Y,WEI H M,TANG G N.The evolution of spiral waves in inhomogeneous excitable media[J].Acta Physica Sinica,2010,59(9):5979-5984.(Ch).
[5] WITKOWSKI F X,LEON L J,PENKOSKE P A,et al.Spatiotemporal evolution of ventricular fibrillation[J].Nature,1998,392(6671):78-82.
[6] 邓敏艺,唐国宁,孔令江,等.激发介质中螺旋波失稳的微观机理研究[J].物理学报,2010,59(4):2339-2344 DENG M Y,TANG G N,KONG L J,et al.Microcosmic mechanism of spiral wave’s instability in excitable medium[J].Acta Physica Sinica,2010,59(4):2339-2344(Ch)
[7] PETER J,WANG J CH,RENATE W,et al.Coherent structure analysis of spatiotemporal chaos[J].Phys Rev E,2000,61(2):2095-2098
[8] 钟敏,唐国宁.用钙离子通道激动剂抑制心脏组织中的螺旋波和时空混沌[J].物理学报,2010,59(5):3070-3076.ZHONG M,TANG G N.Suppressing spiral waves and spatiotemporal chaos in cardiac tissue by using calcium channel agonist[J].Acta Physica Sinica,2010,59(5):3070-3076.(Ch).
[9] 高加振,谢玲玲,谢伟苗,等.Fitz Hugh-Nagumo系统中螺旋波的控制[J].物理学报,2011,60(8):59-67.GAO J Z,XIE L L,XIE W M,et al.Control of spiral waves in Fitz Hugh-Nagumo systems[J].Acta Physica Sinica,2011,60(8):59-67.(Ch).
[10] 韦海明,唐国宁.交替行为对螺旋波影响的数值模拟研究[J].物理学报,2011,60(4):66-71.WEI H M,TANG G N.Numerical simulation study on effects of alternans behavior on spiral waves[J].Acta Physica Sinica,2011,60(4):66-71.(Ch).
[11] 郭照立,郑楚光.格子Boltzmann方法的原理及应用[M].北京:科学出版社,2009:8-10.GUO ZH L,ZHENG CH G.Theory and Applications of Lattice Boltzmann Method[M].Beijing:Science Press,2009:8-10.(Ch).
[12] DUTT A K.Wavenumber distribution in Hopf-wave instability:the reversible selkov model of glycolytic oscillation [J].Phy Chem B,2005,109(37):17679-17682.
[13] 邓敏艺,施娟,李华兵,等.用晶格玻尔兹曼方法研究螺旋波的产生机制和演化行为[J].物理学报,2007,56(4):2012-2017.DENG M Y,SHI J,LI H B,et al.Lattice Boltzmann method for the production and evolution of spiral waves[J].Acta Physica Sinica,2007,56(4):2012-2017.(Ch).
[14] 郭照立,郑楚光.格子Boltzmann方法的原理及应用[M].北京:科学出版社,2009:48-49.GUO ZH L,ZHENG CH G.Theory and Applications of Lattice Boltzmann Method[M].Beijing:Science Press,2009:48-49.(Ch).
[15] 张晓明.耦合混沌振子系统中的自组织现象及心肌组织中螺旋波和破碎螺旋波的控制[D].北京:北京师范大学,2007.ZHANG X M.Self-organization in Coupled Chaotic Oscillator System and Control of Broken Spiral Wave in Myocardium[D].Beijing:Beijing Normal University,2007.(Ch).