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缺陷致非线性电路孤子非对称传输

刘昊华 王少华 李波波 李桦林

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缺陷致非线性电路孤子非对称传输

刘昊华, 王少华, 李波波, 李桦林

Defect induced asymmetric soliton transmission in the nonlinear circuit

Liu Hao-Hua, Wang Shao-Hua, Li Bo-Bo, Li Hua-Lin
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  • 设计了一种有缺陷的非线性电感-电容(LC)电路,简单方便地实现了电路能量非对称传输,且其能量的载体是非线性波孤子.在LC电路中,当缺陷靠近驱动时,驱动频率接近缺陷本振频率,缺陷共振致电路导通.远离驱动时,电路不导通.缺陷的引入改变电路的均一性,实现小驱动振幅下孤子的单向释放,提高驱动能量转化为孤子能量的效率.对非线性LC电路的传输能量、缺陷系数和驱动振幅三者的关系进行了讨论.
    Electrical diode, the first device to rectify the current flux, has significantly revolutionized fundamental science and advanced technology in various aspects of our routine life. Motivated by the one-way rectification effect, considerable effort has been dedicated to the study of the unidirectional transmission in other physical systems for the potential applications, such as the acoustic diode, thermal diode, etc. The nonlinear LC circuit, which has unique advantages in the measurement of energy with which the voltage and current can be achieved by digital oscilloscope conveniently, provides a simple and effective way of studying the nonlinear wave propagation in a dispersive medium. In this paper, we design a defective LC nonlinear circuit deliberately to realize asymmetric transmission of energy, and the energy carrier is nonlinear wave which is so-called soliton, instead of the linear wave in the pass band. The defect-induced localized wave is a kind of intrinsic bound-state wave mode that is evanescent away from the defect site but vibrates around the site with an intrinsic frequency fr. In the LC circuit, when the defect is close to the driver, with the frequency of driven signal in the forbidden band of system approaching to the intrinsic resonance frequency fr of the defect, the resonance induced by the defect enables the circuit to turn on, which is relevant to but somewhat different from what was uncovered by Leon et al. about the intrinsic instability of evanescent waves stirred up directly by a boundary drive. On the other hand, the system acts like an insulator, for the defect is far away from the drive. The defect changes the homogeneity of the line, which allows the soliton to be released in one direction by the local resonance, with the driver being at a lower amplitude. As a result, the introducing of defects significantly improves conversion efficiency from the driver energy into the soliton. To further understand this phenomenon in the defective LC nonlinear circuit, we numerically investigate the relationship among transmission energy, defect coefficient and driver amplitude. Finally, the combined defects are also considered to further adjust the LC nonlinear circuit.
      通信作者: 王少华, shitoucheng_w@sina.com
    • 基金项目: 国家自然科学基金(批准号:11174140,11574149)资助的课题.
      Corresponding author: Wang Shao-Hua, shitoucheng_w@sina.com
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11174140, 11574149).
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    Liang B, Yuan B, Cheng J C 2009 Phys. Rev. Lett. 103 104301

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    Li B, Wang L, Casati G 2004 Phys. Rev. Lett. 93 184301

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    Hu B, Yang L, Zhang Y 2006 Phys. Rev. Lett. 97 124302

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    Konotop V V, Kuzmiak V 2002 Phys. Rev. B 66 235208

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    Wang J W, Yuan B G, Cheng Y, Liu X J 2015 Sci. China: Phys. Mech. Astron. 58 1

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    Tao F, Chen W, Xu W, Pan J T, Du S D 2011 Phys. Rev. E 83 056605

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    Tao F, Chen W Z, Xu W, Du S D 2012 Acta Phys. Sin. 61 134103 (in Chinese) [陶峰, 陈伟中, 许文, 都思丹 2012 物理学报 61 134103]

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    Hirota R, Suzuki K 1970 J. Phys. Soc. Jpn. 28 1366

    [11]

    Motcheyo A B T, Tchawoua C, Siewe M S, Tchameu J D T 2013 Commu. Nonlinear Sci. Numer.Simulat. 18 946

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    Leon J 2003 Phys. Lett. A 319 130

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    Marquie P, Bilbault J M, Remoissenet M 1994 Phys. Rev. E 49 828

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    Kuusela T 1995 Chaos Solut Fract. 5 2419

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    Haus H A, Wong W S 1996 Rev. Mod. Phys. 68 423

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    Yu G K, Wang X L, Tao Z 2011 Phys. Rev. E 83 026605

    [17]

    Liu C, Du Z, Sun Z, Gao H J, Guo X 2015 Phys. Rev. Appl. 3 064014

    [18]

    Remoissenet M 1999 Waves Called Solitons: Concepts and Experiments (2nd Ed.) (Berlin: Springer-Verlag) pp37-97

    [19]

    Koon K T V, Leon J, Marquie P, Dinda P T 2007 Phys. Rev. E 75 066604

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    Nagahama K, Yajima N 1989 J. Phys. Soc. Jpn. 58 1539

    [21]

    Pan J T, Chen W Z, Tao F, Xu W 2011 Phys. Rev. E 83 016601

  • [1]

    Li X F, Ni X, Feng L, Lu M H, He C, Chen Y F 2011 Phys. Rev. Lett. 106 084301

    [2]

    Liang B, Yuan B, Cheng J C 2009 Phys. Rev. Lett. 103 104301

    [3]

    Li B, Wang L, Casati G 2004 Phys. Rev. Lett. 93 184301

    [4]

    Hu B, Yang L, Zhang Y 2006 Phys. Rev. Lett. 97 124302

    [5]

    Konotop V V, Kuzmiak V 2002 Phys. Rev. B 66 235208

    [6]

    Wang J W, Yuan B G, Cheng Y, Liu X J 2015 Sci. China: Phys. Mech. Astron. 58 1

    [7]

    Boechler N, Theocharis G, Daraio C 2011 Nature Mater. 10 665

    [8]

    Tao F, Chen W, Xu W, Pan J T, Du S D 2011 Phys. Rev. E 83 056605

    [9]

    Tao F, Chen W Z, Xu W, Du S D 2012 Acta Phys. Sin. 61 134103 (in Chinese) [陶峰, 陈伟中, 许文, 都思丹 2012 物理学报 61 134103]

    [10]

    Hirota R, Suzuki K 1970 J. Phys. Soc. Jpn. 28 1366

    [11]

    Motcheyo A B T, Tchawoua C, Siewe M S, Tchameu J D T 2013 Commu. Nonlinear Sci. Numer.Simulat. 18 946

    [12]

    Leon J 2003 Phys. Lett. A 319 130

    [13]

    Marquie P, Bilbault J M, Remoissenet M 1994 Phys. Rev. E 49 828

    [14]

    Kuusela T 1995 Chaos Solut Fract. 5 2419

    [15]

    Haus H A, Wong W S 1996 Rev. Mod. Phys. 68 423

    [16]

    Yu G K, Wang X L, Tao Z 2011 Phys. Rev. E 83 026605

    [17]

    Liu C, Du Z, Sun Z, Gao H J, Guo X 2015 Phys. Rev. Appl. 3 064014

    [18]

    Remoissenet M 1999 Waves Called Solitons: Concepts and Experiments (2nd Ed.) (Berlin: Springer-Verlag) pp37-97

    [19]

    Koon K T V, Leon J, Marquie P, Dinda P T 2007 Phys. Rev. E 75 066604

    [20]

    Nagahama K, Yajima N 1989 J. Phys. Soc. Jpn. 58 1539

    [21]

    Pan J T, Chen W Z, Tao F, Xu W 2011 Phys. Rev. E 83 016601

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出版历程
  • 收稿日期:  2016-11-08
  • 修回日期:  2017-03-02
  • 刊出日期:  2017-05-05

缺陷致非线性电路孤子非对称传输

  • 1. 南京大学声学研究所, 近代声学教育部重点实验室, 南京 210093
  • 通信作者: 王少华, shitoucheng_w@sina.com
    基金项目: 国家自然科学基金(批准号:11174140,11574149)资助的课题.

摘要: 设计了一种有缺陷的非线性电感-电容(LC)电路,简单方便地实现了电路能量非对称传输,且其能量的载体是非线性波孤子.在LC电路中,当缺陷靠近驱动时,驱动频率接近缺陷本振频率,缺陷共振致电路导通.远离驱动时,电路不导通.缺陷的引入改变电路的均一性,实现小驱动振幅下孤子的单向释放,提高驱动能量转化为孤子能量的效率.对非线性LC电路的传输能量、缺陷系数和驱动振幅三者的关系进行了讨论.

English Abstract

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