准周期激励与应变超晶格的动力学稳定性

罗晓华; 何为; 吴木营; 罗诗裕

doi:10.7498/aps.62.247301

摘要

假设超晶格锯齿形沟道对粒子的作用等效为形状相似的周期场作用. 在经典力学框架内，引入正弦平方势，把粒子运动方程化为具有阻尼项和双频激励项的摆方程. 用Melnikov方法对单频激励系统的分叉与混沌进行分析；用Lyapunov方法对双频激励系统的稳定性进行讨论. 结果表明：在弱非线性情况下，双频激励系统存在局域不稳定，且这种不稳定将向全局扩展，直至混沌的出现；导致混沌的双频激励强度远小于单频激励强度；外加一个适当的超声场可望将这种敏感钝化，使系统的稳定性得到改善.

关键词:

超晶格 /
准周期激励 /
混沌 /
稳定性

Abstract

In this paper, the action exerted by a superlattice sawtooth-shaped channel on the particle is assumed to be equivalent to that exerted by a periodic field with a similar shape. In the framework of classical mechanics, by introducing the sines-quared potential, the particle motion equation is reduced to pendulum equation with a damping term and dual-frequency excitation term. The bifurcation and chaos of single-frequency excitation system are analyzed with the Melnikov method. The stability of dual-frequency excitation system is discussed by using the Lyapunov exponent. The results show that in the case of weak nonlinearity, local instability can be found in the dual frequency excitation system, and it will be expanded globally until chaos appears. The dual excitation intensity leading to chaos is far less than that of single-frequency excitation. The application of an appropriate ultrasonic field is likely to make such a sensitivity passivated, and the stability of the system improved as well.

Keywords:

作者及机构信息

1.
重庆大学电气工程学院, 重庆 400044;

2.
重庆交通大学图书馆, 重庆 400074;

3.
东莞理工学院电子工程学院, 东莞 523808

Authors and contacts

1.
College of Electric Engineering, Chongqing University, Chongqing 400044, China;

2.
Library of Chongqing Jiaotong University, Chongqing 400074, China;

3.
College of Electronic Engineering, Dongguan University of Technology, Dongguan 523808, China

参考文献

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[3]	Kubankin A S, Nasonov N N 2008 J. Surf. Investig. X Ra. 2 317
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[8]	Gennady B S, Bezchastnov V G, Solovyov I A, Korol A V, Greiner W, Solovyov A V 2013 J. Comput. Phys. 252 404
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[10]	Luo S Y, Shao M Z, Luo X H 2010 Acta Phys. Sin. 59 2685 (in Chinese) [罗诗裕, 邵明珠, 罗晓华 2010 59 2685]
[11]	Luo X H, Wu M Y, Li H T, Shao M Z, Xiong J Z, Luo S Y, He W 2011 Chin. J. Solid Mech. 32 440 (in Chinese) [罗晓华, 吴木营, 李洪涛, 邵明珠, 熊金志, 罗诗裕, 何为 2011 固体力学学报 32 440]
[12]	Luo X H, He W, Shao M Z 2008 High Power Laser and Particle Beams 20 675 (in Chinese) [罗晓华, 何为, 邵明珠 2008 强激光与粒子束 20 675]
[13]	Luo S Y, Shao M Z 2005 Chin. J. Seimcond. 26 294 (in Chinese) [罗诗裕, 邵明珠 2005 半导体学报 26 294]
[14]	Li X P, Wang S J, Chen Q, Luo S Y 2013 Seim. Optoelectron. 34 441 (in Chinese) [李秀平, 王善进, 陈琼, 罗诗裕 2013 半导体光电 34 441]
[15]	Luo X H, He W, Wu M Y, Shao M Z, Luo S Y 2013 Chin. Phys. B 22 064210
[16]	Liu H Z, Luo S Y Shao M Z 2013 Chin. Phys. B 22 047807
[17]	Nayfeh A H 1981 Introduction to Peturbation Techniques (London: John Wiley and Sons.) p226
[18]	Grishchenko A D, Vavriv D M 1997 Zh. Tekh. Fiz. 67 1 (in Russia)
[19]	Vavriv D M, Vavriv D D 2008 Proceedings of Ultrawideband and Ultrashort Impulse Signals Sevastopol, Ukraine, September 15–19, 2008 p16
[20]	Wolf A, Swift J B, Vastano J A, Sminney H L 1985 Physica D 16 285

施引文献

[1]	Korol A V, Solovyov A V, Greiner W 2004 Int. J. Mod. Phys. E 13 867
[2]	Korol A V, Solovyov A V, Greiner W 2008 Nucl. Inst. Meth. Phys. Res. B 266 1173
[3]	Kubankin A S, Nasonov N N 2008 J. Surf. Investig. X Ra. 2 317
[4]	Tabrizi M, Korol A V, Solovyov A V 2007 Phys. Rev. Lett. 98 164801
[5]	Korol A V, Solovyov A V, Greiner W 2007 Int. J. Mod. Phys. E 13 867
[6]	Sushko G B, Korol A V, Greiner W, Solov’yov A V 2013 J. Phys.: Conf. Ser. 438 012018
[7]	Korol A V, Solov’yov A V, Greiner W 2013 Channeling and Radiation in Periodically Bent Crystals, Springer Series on Atomic, Optical, and Plasma Physics (Berlin: Splinger) p195
[8]	Gennady B S, Bezchastnov V G, Solovyov I A, Korol A V, Greiner W, Solovyov A V 2013 J. Comput. Phys. 252 404
[9]	Luo S Y, Shao M Z, Luo X H 2010 Sci. China: Phys. Mech. Astron. 40 207 (in Chinese) [罗诗裕, 邵明珠, 罗晓华 2010 中国科学: 物理学, 力学和天文学 40 207]
[10]	Luo S Y, Shao M Z, Luo X H 2010 Acta Phys. Sin. 59 2685 (in Chinese) [罗诗裕, 邵明珠, 罗晓华 2010 59 2685]
[11]	Luo X H, Wu M Y, Li H T, Shao M Z, Xiong J Z, Luo S Y, He W 2011 Chin. J. Solid Mech. 32 440 (in Chinese) [罗晓华, 吴木营, 李洪涛, 邵明珠, 熊金志, 罗诗裕, 何为 2011 固体力学学报 32 440]
[12]	Luo X H, He W, Shao M Z 2008 High Power Laser and Particle Beams 20 675 (in Chinese) [罗晓华, 何为, 邵明珠 2008 强激光与粒子束 20 675]
[13]	Luo S Y, Shao M Z 2005 Chin. J. Seimcond. 26 294 (in Chinese) [罗诗裕, 邵明珠 2005 半导体学报 26 294]
[14]	Li X P, Wang S J, Chen Q, Luo S Y 2013 Seim. Optoelectron. 34 441 (in Chinese) [李秀平, 王善进, 陈琼, 罗诗裕 2013 半导体光电 34 441]
[15]	Luo X H, He W, Wu M Y, Shao M Z, Luo S Y 2013 Chin. Phys. B 22 064210
[16]	Liu H Z, Luo S Y Shao M Z 2013 Chin. Phys. B 22 047807
[17]	Nayfeh A H 1981 Introduction to Peturbation Techniques (London: John Wiley and Sons.) p226
[18]	Grishchenko A D, Vavriv D M 1997 Zh. Tekh. Fiz. 67 1 (in Russia)
[19]	Vavriv D M, Vavriv D D 2008 Proceedings of Ultrawideband and Ultrashort Impulse Signals Sevastopol, Ukraine, September 15–19, 2008 p16
[20]	Wolf A, Swift J B, Vastano J A, Sminney H L 1985 Physica D 16 285

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