表面催化反应模型中关联噪声诱导非平衡相变

刘瑞芬; 惠治鑫; 熊科诏; 曾春华

doi:10.7498/aps.67.20180250

摘要

建立含有关联噪声的双分子-单分子（DM）表面催化反应延迟反馈模型，该模型能同时显示一级和二级非平衡动力学相变，即在一级和二级非平衡动力学相变之间的反应窗口展现.讨论双分子在DM延迟反馈模型中两种吸附机制，即局域和随机吸附模型.研究结果表明：1）外部噪声及两噪声关联性致使反应窗口的宽度收缩；2）内部噪声对非平衡动力学相变行为的影响依赖两噪声关联性，即当两噪声负关联，内部噪声致使反应窗口的宽度变宽；而当两噪声正关联时，内部噪声致使反应窗口的宽度收缩；3）关联噪声致使反应窗口变化对DM模型中一级和二级非平衡动力学相变研究具有重要的科学意义.

关键词:

Abstract

In recent years, with the development of chemical study of complex systems, such as surface catalytic system, etc. the research of nonlinear dynamics problem of complex system has received much attention. These systems have high-degree complexity, and they are inevitably affected by intrinsic and extrinsic fluctuations (noise) and time delay. The combination of noise and time delay is ubiquitous in nature, and often changes fundamentally dynamical behavior of the system, and thus making the system produce more richer and complex dynamical behaviors. At present, in the theoretical studies of the nonlinear dynamic properties, the macroeconomic deterministic or stochastic dynamic equation is adopted most, and the time delay factor, especially the influences of combination of noise and time delay on complex system are rarely taken into account. Thus, the study of the character, mechanism and application has important realistic significance and scientific value. In this paper, we first introduce the Dimer-Monomer reaction model (DM model), where various dimer adsorption mechanisms in catalyst surface, namely, the local and random adsorption surface catalytic reaction models are considered. Then we use the stochastic delayed theory involved in this paper and its extension, including the analytical approximation and numerical simulation of complex systems under the action of noise and time delay. In this paper, we consider the effects of noise and time-delayed feedback in the surface catalytic reaction model, and construct a delayed monomer-dimer surface reaction model including correlated noise. According to the Langevin equation, applying small delay approximation, we obtain the delayed Fokker-Planck equation for calculating characteristic parameters of the non-equilibrium phase transition behavior (the extreme of the steady state probability distribution), analyzing the effect mechanism of noise and its correlation with the non-equilibrium phase transition. The MD model exhibits the first- and second-order phase transition, namely, the reactive window between first- and second-order phase transition. The MD models for various dimer adsorption mechanisms (namely, local and random adsorption models) are discussed. The results are indicated as follows. (1) The external noise and correlation between two noise signals cause the reactive window width to contract. (2) The influence of the internal noise on the behavior of non-equilibrium dynamical phase transition depends on the noise correlation, i.e., when the two noise signals are negatively correlated, the internal noise causes the reactive window width to expand. However when the two noise signals are positively correlated, the internal noise causes the reactive window width to contract. (3) The noise-caused changes of reaction window have important scientific significance in the first- and second-order phase transition of the MD surface reaction model.

Keywords:

作者及机构信息

1.
昆明理工大学理学院/物理与工程科学研究院, 昆明 650500;

2.
宁夏师范学院物理与电子信息工程学院, 固原 756000;

3.
华东师范大学物理系, 上海 200062

通信作者: 曾春华, zchh2009@126.com

基金项目: 国家自然科学基金（批准号：11665014）、云南省自然科学基金（批准号：2017FB003）、云南省中青年科学技术后备人才项目（批准号：2015HB025）、宁夏自然科学基金项目（批准号：NZ17255）和宁夏高等学校科学研究项目（批准号：NGY2016194）资助的课题.

Authors and contacts

1.
Institute of Physical and Engineering Science, Kunming University of Science and Technology, Kunming 650500, China;

2.
School of Physics and Electronic Information Engineering, Ningxia Normal University, Guyuan 756000, China;

3.
Department of Physics, East China Normal University, Shanghai 200062, China

Corresponding author: Zeng Chun-Hua, zchh2009@126.com

Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11665014), the Natural Science Foundation of Yunnan Province, China (Grant No. 2017FB003), the Candidate Talents Training Fund of Yunnan Province, China (Grant No. 2015HB025), the Natural Science Foundation of Ningxia, China (Grant No. NZ17255), and the Scientific Research Foundation of the Higher Education Institutions of Ningxia, China (Grant No. NGY2016194).

参考文献

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[29]	Zeng C, Zhou X, Tao S 2009 J. Phys. A: Math. Theor. 42 495002
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[31]	Zeng C, Gong A, Tian Y 2010 Physica A 389 1971
[32]	Zeng C H, Wang H, Nie L R 2012 Chaos 22 033125
[33]	Zeng C H, Wang H, Nie L R 2012 Chaos 22 039901
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[35]	Zhang X D, Yang X Q, Tao Y 2011 Plos One 6 17104
[36]	Ghosh S, Banerjee S, Bose I 2012 Eur. Phys. J. E 35 11
[37]	Zeng C, Han Q L, Yang T, Wang H, Jia Z L 2013 J. Stat. Mech. 2013 P10017
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[40]	Zeng C, Wang H 2012 Chem. Phys. 402 1
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[51]	Berdichevsky V, Gitterman M 1999 Phys. Rev. E 60 1494

施引文献

[1]	Xin H W, Hou Z H 2009 Nonlinear Chemistry (Hefei: University of Science and Technology of China Press) pp1-10 (in Chinese) [辛厚文, 候中怀 2009 非线性化学 (合肥: 中国科学技术大学出版社) 第1–10页]
[2]	Zeng C H 2014 Ph. D. Dissertation (Kunming: Kunming University of Science and Technology) (in Chinese) [曾春华 2014 博士学位论文(昆明: 昆明理工大学)]
[3]	Hu G, Ditzinger T, Ning C Z, Haken H 1993 Phys. Rev. Lett. 71 807
[4]	Bao J D, Zhuo Y Z 2003 Phys. Rev. Lett. 91 138107
[5]	Glansdorff P, Prigogine I 1971 Thermodynamic Theory of Structure, Stability and Fluctuations (New York: Wiley-Interscience) pp21-50
[6]	Yu W, Zhang J, Tang J 2017 Acta Phys. Sin. 66 200201 (in Chinese) [于文婷, 张娟, 唐军 2017 66 200201]
[7]	Jia Y, Li J R 1997 Phys. Rev. Lett. 78 994
[8]	Ai B Q, Wang X J, Liu GT, et al. 2003 Phys. Rev. E 67 022903
[9]	Hou Z, Xin H 2003 J. Chem. Phys. 119 11508
[10]	Hou Z, Yang L, Xin H 1998 Surface Sci. 399 L332
[11]	Suchorski Y, Beben J, James E W, et al. 1999 Phys. Rev. Lett. 82 1907
[12]	Sachs C, Hildebrand M, Volkening S, et al. 2001 Science 293 1635
[13]	Peskov N V, Slinko M M, Jaeger N I 2002 J. Chem. Phys. 116 2098
[14]	Zhao G, Hou Z H, Xin H W 2005 J. Phys. Chem. A 109 8515
[15]	Zhao N, Luo J 2001 J. Chem. Phys. 114 7761
[16]	Luo J, Zhao N, Hu B 2002 Phys. Chem. Chem. Phys. 4 4149
[17]	Hayase Y, Wehner S, Kuppers J, Brand H R 2004 Phys. Rev. E 69 021609
[18]	Pineda M, Imbihl R, Schimansky-Geier L 2007 Phys. Rev. E 75 061107
[19]	Pineda M, Toral R 2009 J. Chem. Phys. 130 124707
[20]	Pineda M, Imbihl R, Schimansky-Geier L 2010 Physica A 389 1178
[21]	Cisternas J, Lecaros R, Wehner S 2011 Eur. Phys. J. D 62 91
[22]	Fulinski A, Telejko T 1991 Phys. Lett. A 152 11
[23]	Zhou R W, Li J C, Dong Z W, et al. 2017 Acta Phys. Sin. 66 040501 (in Chinese) [周若微, 李江城, 董志伟, 等 2017 66 040501]
[24]	Madureira A J R, Hänggi P, Wio H S 1996 Phys. Lett. A 217 248
[25]	Zeng C, Zeng J, Liu F, Wang H 2016 Sci. Reports 6 19591
[26]	Shit A, Chattopadhyay S, Banik S K, Chaudhuri J R 2010 Chaos 20 023130
[27]	Tessone C J, Wio H S, Hänggi P 2000 Phys. Rev. E 62 4623
[28]	Jia Y, Yu S N, Li J R 2000 Phys. Rev. E 62 1869
[29]	Zeng C, Zhou X, Tao S 2009 J. Phys. A: Math. Theor. 42 495002
[30]	Zeng C, Wang H 2010 J. Stat. Phys. 141 889
[31]	Zeng C, Gong A, Tian Y 2010 Physica A 389 1971
[32]	Zeng C H, Wang H, Nie L R 2012 Chaos 22 033125
[33]	Zeng C H, Wang H, Nie L R 2012 Chaos 22 039901
[34]	Liu Q, Jia Y 2004 Phys. Rev. E 70 041907
[35]	Zhang X D, Yang X Q, Tao Y 2011 Plos One 6 17104
[36]	Ghosh S, Banerjee S, Bose I 2012 Eur. Phys. J. E 35 11
[37]	Zeng C, Han Q L, Yang T, Wang H, Jia Z L 2013 J. Stat. Mech. 2013 P10017
[38]	Duan W, Zeng C 2017 Appl. Math. Comput. 292 400
[39]	Duan W, Zeng C 2017 Appl. Math. Comput. 293 611
[40]	Zeng C, Wang H 2012 Chem. Phys. 402 1
[41]	Zeng C, Wang H, Yang T, et al. 2014 Eur. Phys. J. B 87 137
[42]	Ziff R M, Gulari E, Barshad Y 1986 Phys. Rev. Lett. 56 2553
[43]	Dickman R 1986 Phys. Rev. A 34 4246
[44]	Tammaro M, Evans J W 1995 Phys. Rev. E 52 2310
[45]	Turanyi T, Tomlin A, Pilling M 1993 J. Phys. Chem. 97 1674
[46]	Bennett M R, Volfson D, Tsimring L, Hasty J 2007 Biphys. J. 92 3501
[47]	Pineda M, Toral R 2009 J. Chem. Phys. 130 124707
[48]	Frank T D 2005 Phys. Rev. E 71 031106
[49]	Frank T D 2005 Phys. Rev. E 72 011112
[50]	Gitterman M 1999 J. Phys. A 32 L293
[51]	Berdichevsky V, Gitterman M 1999 Phys. Rev. E 60 1494

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