Lattice Boltzmann simulation for the energy and entropy of excitable systems

doi:10.1088/1674-1056/20/2/020510

Abstract The internal energy and the spatiotemporal entropy of excitable systems are investigated with the lattice Boltzmann method. The numerical results show that the breakup of spiral wave is attributed to the inadequate supply of energy, i.e., the internal energy of system is smaller than the energy of self-sustained spiral wave. It is observed that the average internal energy of a regular wave state reduces with its spatiotemporal entropy decreasing. Interestingly, although the energy difference between two regular wave states is very small, the different states can be distinguished obviously due to the large difference between their spatiotemporal entropies. In addition, when the unstable spiral wave converts into the spatiotemporal chaos, the internal energy of system decreases, while the spatiotemporal entropy increases, which behaves as the thermodynamic entropy in an isolated system.

Keywords: lattice Boltzmann method energy entropy spiral wave

Received: 01 March 2010
Revised: 21 October 2010
Accepted manuscript online:

PACS:	05.50.+q	(Lattice theory and statistics)
	05.10.-a	(Computational methods in statistical physics and nonlinear dynamics)
	05.45.-a	(Nonlinear dynamics and chaos)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 10765002, 10562001 and 81060307).

Cite this article:

Deng Min-Yi(邓敏艺), Tang Guo-Ning(唐国宁), Kong Ling-Jiang(孔令江), and Liu Mu-Ren(刘慕仁) Lattice Boltzmann simulation for the energy and entropy of excitable systems 2011 Chin. Phys. B 20 020510

[1]	Kim D T, Kwan Y, Lee J L, Ikeda T, Uchida T, Kamjoo K, Kim Y H, Ong J J C, Athill C A, Wu T J, Czer L, Karagueuzian H S and Chen P S 1998 Chaos 8 137
[2]	Ouyang Q 2001 Physics 30 30 (in Chinese)
[3]	Dai Y, Wei H M and Tang G N 2010 Acta Phys. Sin. 59 5979 (in Chinese)
[4]	Pincus S M 1991 Proc. Natl. Acad. Sci. USA 88 2279
[5]	Jun P 2000 Phys. Rev. E 61 2095
[6]	Qian Y H, d'Humi'eres D and Lallemand P 1992 Europhys. Lett. 17 479
[7]	Chen S Y, Chen H D, Martnez D and Matthaeus W 1991 Phys. Rev. Lett. 67 3776
[8]	Li H B, Yi H H, Shan X W and Fang H P 2008 Europhys. Lett. 81 54002
[9]	Yi H H, Chen Y Y and Li H B 2007 Chin. Phys. 16 2444
[10]	Meng J, Qian Y, Li X and Dai S 2008 Phys. Rev. E 77 036108
[11]	Ran Z 2009 Chin. Phys. B 18 2159
[12]	Yu X M and Shi B C 2006 Appl. Math. Comput. 181 958
[13]	Deng M Y, Shi J, Li H B, Kong L J and Liu M R 2007 Acta Phys. Sin. 56 2012 (in Chinese)
[14]	Deng M Y, Shi J, Chen R X, Kong L J and Liu M R 2007 Commun. Theor. Phys. 48 725
[15]	Deng M Y, Tang G N, Kong L J and Liu M R 2010 Acta Phys. Sin. 59 139 (in Chinese)
[16]	Dutt A K 2005 J. Phys. Chem. B 109 17679
[17]	Boon J P, Dab D, Kapral R and Lawniczak A 1996 Phys. Rep. 273 55
[18]	Guo Z L and Zheng C G 2009 Theory and Applications of Lattice Boltzmann Method (Beijing: Science Press) p. 115 (in Chinese)
[19]	C E Shannon 1948 Bell Syst. Tech. J. 27 379
[20]	C E Shannon 1948 Bell Syst. Tech. J. 27 623

[1]	A 4H-SiC trench IGBT with controllable hole-extracting path for low loss Lijuan Wu(吴丽娟), Heng Liu(刘恒), Xuanting Song(宋宣廷), Xing Chen(陈星), Jinsheng Zeng(曾金胜), Tao Qiu(邱滔), and Banghui Zhang(张帮会). Chin. Phys. B, 2023, 32(4): 048503.
[2]	Diffusive field coupling-induced synchronization between neural circuits under energy balance Ya Wang(王亚), Guoping Sun(孙国平), and Guodong Ren(任国栋). Chin. Phys. B, 2023, 32(4): 040504.
[3]	Suppression and compensation effect of oxygen on the behavior of heavily boron-doped diamond films Li-Cai Hao(郝礼才), Zi-Ang Chen(陈子昂), Dong-Yang Liu(刘东阳), Wei-Kang Zhao(赵伟康),Ming Zhang(张鸣), Kun Tang(汤琨), Shun-Ming Zhu(朱顺明), Jian-Dong Ye(叶建东),Rong Zhang(张荣), You-Dou Zheng(郑有炓), and Shu-Lin Gu(顾书林). Chin. Phys. B, 2023, 32(3): 038101.
[4]	Asymmetric image encryption algorithm based ona new three-dimensional improved logistic chaotic map Guo-Dong Ye(叶国栋), Hui-Shan Wu(吴惠山), Xiao-Ling Huang(黄小玲), and Syh-Yuan Tan. Chin. Phys. B, 2023, 32(3): 030504.
[5]	Coexisting lattice contractions and expansions with decreasing thicknesses of Cu (100) nano-films Simin An(安思敏), Xingyu Gao(高兴誉), Xian Zhang(张弦), Xin Chen(陈欣), Jiawei Xian(咸家伟), Yu Liu(刘瑜), Bo Sun(孙博), Haifeng Liu(刘海风), and Haifeng Song(宋海峰). Chin. Phys. B, 2023, 32(3): 036804.
[6]	Ridge regression energy levels calculation of neutral ytterbium (Z = 70) Yushu Yu(余雨姝), Chen Yang(杨晨), and Gang Jiang(蒋刚). Chin. Phys. B, 2023, 32(3): 033101.
[7]	Analysis of cut vertex in the control of complex networks Jie Zhou(周洁), Cheng Yuan(袁诚), Zu-Yu Qian(钱祖燏), Bing-Hong Wang(汪秉宏), and Sen Nie(聂森). Chin. Phys. B, 2023, 32(2): 028902.
[8]	Charge-mediated voltage modulation of magnetism in Hf_0.5Zr_0.5O₂/Co multiferroic heterojunction Jia Chen(陈佳), Peiyue Yu(于沛玥), Lei Zhao(赵磊), Yanru Li(李彦如), Meiyin Yang(杨美音), Jing Xu(许静), Jianfeng Gao(高建峰), Weibing Liu(刘卫兵), Junfeng Li(李俊峰), Wenwu Wang(王文武), Jin Kang(康劲), Weihai Bu(卜伟海), Kai Zheng(郑凯), Bingjun Yang(杨秉君), Lei Yue(岳磊), Chao Zuo(左超), Yan Cui(崔岩), and Jun Luo(罗军). Chin. Phys. B, 2023, 32(2): 027504.
[9]	Quantum properties of nonclassical states generated by an optomechanical system with catalytic quantum scissors Heng-Mei Li(李恒梅), Bao-Hua Yang(杨保华), Hong-Chun Yuan(袁洪春), and Ye-Jun Xu(许业军). Chin. Phys. B, 2023, 32(1): 014202.
[10]	Anionic redox reaction mechanism in Na-ion batteries Xueyan Hou(侯雪妍), Xiaohui Rong(容晓晖), Yaxiang Lu(陆雅翔), and Yong-Sheng Hu(胡勇胜). Chin. Phys. B, 2022, 31(9): 098801.
[11]	Efficiently enhanced energy storage performance of Ba₂Bi₄Ti₅O₁₈ film by co-doping Fe³⁺ and Ta⁵⁺ ion with larger radius Qiong Wu(吴琼), Lei Zhao(赵雷), Xinghao Chen(陈兴豪), and Shifeng Zhao(赵世峰)^†. Chin. Phys. B, 2022, 31(9): 097701.
[12]	Configurational entropy-induced phase transition in spinel LiMn₂O₄ Wei Hu(胡伟), Wen-Wei Luo(罗文崴), Mu-Sheng Wu(吴木生), Bo Xu(徐波), and Chu-Ying Ouyang(欧阳楚英). Chin. Phys. B, 2022, 31(9): 098202.
[13]	Energy levels and magnetic dipole transition parameters for the nitrogen isoelectronic sequence Mu-Hong Hu(胡木宏), Nan Wang(王楠), Pin-Jun Ouyang(欧阳品均),Xin-Jie Feng(冯新杰), Yang Yang(杨扬), and Chen-Sheng Wu(武晨晟). Chin. Phys. B, 2022, 31(9): 093101.
[14]	Physical aspects of magnetized Jeffrey nanomaterial flow with irreversibility analysis Fazal Haq, Muhammad Ijaz Khan, Sami Ullah Khan, Khadijah M Abualnaja, and M A El-Shorbagy. Chin. Phys. B, 2022, 31(8): 084703.
[15]	A 45-μJ, 10-kHz, burst-mode picosecond optical parametric oscillator synchronously pumped at a second harmonic cavity Chao Ma(马超), Ke Liu(刘可), Yong Bo(薄勇), Zhi-Min Wang(王志敏), Da-Fu Cui(崔大复), and Qin-Jun Peng(彭钦军). Chin. Phys. B, 2022, 31(8): 084206.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Lattice Boltzmann simulation for the energy and entropy of excitable systems

Cite this article:

Online attention