搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

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

引用本文:
Citation:

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

Correlated noise induced non-equilibrium phase transition in surface catalytic reaction model

Liu Rui-Fen, Hui Zhi-Xin, Xiong Ke-Zhao, Zeng Chun-Hua
PDF
导出引用
  • 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.
    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.
      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.
      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).
    [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 物理学报 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 物理学报 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

  • [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 物理学报 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 物理学报 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

  • [1] 李诗尧, 于明. 固体炸药爆轰的一种考虑热学非平衡的反应流动模型. 物理学报, 2018, 67(21): 214704. doi: 10.7498/aps.67.20172501
    [2] 申雅君, 郭永峰, 袭蓓. 关联高斯与非高斯噪声激励的FHN神经元系统的稳态分析. 物理学报, 2016, 65(12): 120501. doi: 10.7498/aps.65.120501
    [3] 靳艳飞, 李贝. 色关联的乘性和加性色噪声激励下分段非线性模型的随机共振. 物理学报, 2014, 63(21): 210501. doi: 10.7498/aps.63.210501
    [4] 李贝, 靳艳飞. 色关联的色噪声驱动的分段非线性模型的平均首次穿越时间. 物理学报, 2013, 62(15): 150503. doi: 10.7498/aps.62.150503
    [5] 王国威, 徐大海, 程庆华. 色关联噪声对林木Logistic生长模型的影响. 物理学报, 2013, 62(22): 224208. doi: 10.7498/aps.62.224208
    [6] 马靖杰, 夏辉, 唐刚. 含关联噪声的空间分数阶随机生长方程的动力学标度行为研究. 物理学报, 2013, 62(2): 020501. doi: 10.7498/aps.62.020501
    [7] 何亮, 杜磊, 黄晓君, 陈华, 陈文豪, 孙鹏, 韩亮. 金属互连电迁移噪声的非高斯性模型研究. 物理学报, 2012, 61(20): 206601. doi: 10.7498/aps.61.206601
    [8] 王兵, 吴秀清. 双色噪声驱动光学双稳系统的弛豫时间研究. 物理学报, 2011, 60(7): 074214. doi: 10.7498/aps.60.074214
    [9] 刘志宏, 周玉荣, 张安英, 庞小峰. 色关联噪声驱动下非线性神经元模型的相干共振. 物理学报, 2010, 59(2): 699-704. doi: 10.7498/aps.59.699
    [10] 何成娣, 徐伟, 岳晓乐. 非关联噪声驱动的单稳系统的平均首次穿越时间. 物理学报, 2010, 59(8): 5276-5280. doi: 10.7498/aps.59.5276
    [11] 吕翎, 李岩. 不确定自催化反应扩散时空混沌系统的延时同步. 物理学报, 2009, 58(1): 131-138. doi: 10.7498/aps.58.131
    [12] 郭永峰, 徐 伟. 关联白噪声驱动的具有时间延迟的Logistic系统. 物理学报, 2008, 57(10): 6081-6085. doi: 10.7498/aps.57.6081
    [13] 董小娟. 含关联噪声与时滞项的非对称双稳系统的随机共振. 物理学报, 2007, 56(10): 5618-5622. doi: 10.7498/aps.56.5618
    [14] 邵元智, 钟伟荣, 卢华权, 雷石付. Ising自旋体系的非平衡动态相变. 物理学报, 2006, 55(4): 2057-2063. doi: 10.7498/aps.55.2057
    [15] 牟宗信, 李国卿, 车德良, 黄开玉, 柳 翠. 非平衡磁控溅射沉积系统伏安特性模型研究. 物理学报, 2004, 53(6): 1994-1999. doi: 10.7498/aps.53.1994
    [16] 张良英, 曹 力, 吴大进. 具有色关联的色噪声驱动下单模激光线性模型的随机共振. 物理学报, 2003, 52(5): 1174-1178. doi: 10.7498/aps.52.1174
    [17] 唐刚, 马本堃. 含时空关联噪声的非局域及各向异性Kardar-Parisi -Zhang方程的直接标度分析. 物理学报, 2002, 51(5): 994-998. doi: 10.7498/aps.51.994
    [18] 闫桂沈, 李贺军, 郝志彪. 热解碳化学气相沉积中的多重定态和非平衡相变的研究. 物理学报, 2002, 51(2): 326-331. doi: 10.7498/aps.51.326
    [19] 邵元智, 蓝图, 林光明. 三维动态Ising模型中的非平衡相变:三临界点的存在. 物理学报, 2001, 50(5): 942-947. doi: 10.7498/aps.50.942
    [20] 李富斌. 用细胞自动机方法构造非平衡相变模型. 物理学报, 1992, 41(11): 1837-1841. doi: 10.7498/aps.41.1837
计量
  • 文章访问数:  4898
  • PDF下载量:  90
  • 被引次数: 0
出版历程
  • 收稿日期:  2018-02-01
  • 修回日期:  2018-05-17
  • 刊出日期:  2019-08-20

/

返回文章
返回