Wavelet Phase Synchronization of Fractional-Order Chaotic Systems *

ISSN: 0256-307X 中国物理快报 Chinese Physics Letters

Volume 29 Number 7 July 2012 A Series Journal of the Chinese Physical Society Distributed by IOP Publishing Online: http://iopscience.iop.org/cpl http://cpl.iphy.ac.cn

C HINESE P HYSICAL S OCIETY

CHIN. PHYS. LETT. Vol. 29, No. 7 (2012) 070501 Wavelet Phase Synchronization of Fractional-Order Chaotic Systems *

CHEN Feng(陈枫)1, XIA Lei(夏雷)2, LI Chun-Guang(李春光)3** 1School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu 610054 2Xi’an Institute of Electromechanical Information Technology, Xi’an 710065 3 Department of Information Science and Electronic Engineering, Zhejiang University, Hangzhou 310027

(Received 21 March 2012) Nowadays, fractional-order systems are attracting more and more attention. There are several ways available for analyzing fractional-order systems, among which wavelet transform is an efficient method for analyzing system dynamics in both time and frequency domains. We investigate the wavelet phase synchronization employing wavelet transform to explore the phase synchronization behaviors of fractional-order chaotic oscillators. We analyze in detail the synchronization behaviors with changes to the coupling strength, the central frequency Ω 0, and the time scale of the wavelet.

PACS: 05.45.-a, 05.45.Xt DOI: 10.1088/0256-307X/29/7/070501

The chaotic dynamics of fractional order sys- edge, wavelet phase synchronization in fractional or- tems began to attract more and more attention re- der chaotic systems has not been discussed yet. In cently. Fractional calculus has a history of more this Letter, we address it in detail. than 300 years,[1] the applications of which to physics In Refs. [23-26] the researchers proposed to use a and engineering are just a recent focus of interest. wavelet approach to investigate the synchronization Many systems are known to display fractional-order of chaotic systems. It was approved that synchroniza- dynamics, such as viscoelastic systems,[2] dielectric tion can be detected by introducing a complex wavelet polarization,[3] electrode-electrolyte polarization,[4] transform, as demonstrated in Ref. [23], 푊 (푎, 푡) = and electromagnetic waves.[5] Many investigations |푊 (푎, 푡)| exp(푖휙(푎, 푡)), where 휙(푎, 푡) is the phase de- were devoted to dynamics[6−15] of fractional-order sys- fined. The corresponding condition for the synchro- tems. Specifically, in Ref. [6] chaos and hyperchaos in nization between chaotic systems with phases 휙1(푎, 푡) the fractional order Rössler equations were studied, in and 휙2(푎, 푡) on a time scale 푎 is |휙1(푎, 푡) − 휙2(푎, 푡)| < which we showed that chaos can exist in the fractional const. In the present study, this wavelet approach order Rössler equation with order as low as 2.4, and is applied to the coupled fractional-order chaotic sys- hyperchaos can exist in the fractional order Rössler tems. As in many studies of phase synchronization, hyperchaos equation with order as low as 3.8. the chaotic system is selected as the Rössler oscilla- In the study of chaotic systems, synchronization is tor. a focus of interest.[16−18] Besides the identical (com- First, let us build the system. Our system con- plete) synchronization of chaotic systems, some other sists of two coupled fractional-order Rössler oscilla- types of synchronization also have very interesting tors. There are several definitions of fractional deriva- cooperative behaviors of chaotic systems, including tives in the literature.[1] The best known may be the phase synchronization,[19,20] lag synchronization,[21] Riemann–Liouville definition, which is given by projective synchronization,[22] and wavelet phase 푑 푓(푡) 1 푑푛 ∫︁ 푡 푓(휏) synchronization/time-scale synchronization of chaotic 훼 훼 = 푛 훼−푛+1 푑휏, (1) oscillators.[23−26] 푑푡 Γ (푛 − 훼) 푑푡 0 (푡 − 휏) In Ref. [27] we have studied the synchronization of where Γ is the gamma function and 푛 − 1 ≤ 훼 < 푛. fractional order chaotic systems, and since then, the Upon considering all the initial conditions to be zero, synchronization of fractional order chaotic systems has the Laplace transform of the Riemann–Liouville frac- 훼 푑 푓(푡) 훼 begun to attract the attention of some researchers, see tional derivative is 퐿{ 푑푡훼 } = 푠 퐿{푓(푡)}. Thus, the e.g. Ref. [28]. However, in the literature, the authors fractional integral operator of order 훼 can be repre- are mostly concerned with the identical synchroniza- sented by the transfer function 퐹 (푠) = 1/푠훼 in the tion of fractional order chaotic systems. In Ref. [29] frequency domain. The standard definition of frac- we studied the phase and lag synchronization of cou- tional differintegral does not allow direct implementa- pled fractional order chaotic oscillators. In Ref. [30] tion of the fractional operators in time-domain simula- we investigated the projective synchronization of frac- tions. An efficient method to circumvent this problem tional order chaotic systems. However, to our knowl- is to approximate fractional operators by using stan-

*Supported by the National Natural Science Foundation of China under Grant Nos 61171153 and 61101045, the Foundation for the Author of National Excellent Doctoral Dissertation of China under Grant No 2007B42, the Zhejiang Provincial Natural Science Foundation under Grant No LR12F01001, and the Scientific Research Foundation for the Returned Overseas Chinese Scholars. **Corresponding author. Email: [email protected] © 2012 Chinese Physical Society and IOP Publishing Ltd 070501-1 CHIN. PHYS. LETT. Vol. 29, No. 7 (2012) 070501 dard integer order operators. In the following simu- not grow with time, i.e. |휙1(푎, 푡) − 휙2(푎, 푡)| < const, lations, we use the approximation method proposed thus the phase synchronization condition is satisfied. in Ref. [31], which was also adopted in many studies. In Table1 of Ref. [7], the authors presented the ap- 40 Ω π proximations for 1/푠푞 with 푞 = 0.1 − 0.9 in steps 0.1 0=0.5 30 | with errors of approximately 2 dB. We will mainly use 2 Ω0=1π 20 - φ these approximations in the following simulations. In 1 our model, the conventional derivative is replaced by | φ 10 Ω =1.5π a fractional derivative as follows: 0 0 Ω0=2π 훼 0 200 400 600 800 1000 1200 1400 1600 1800 푑 푥1,2 = −휔 푦 − 푧 + 휀(푥 − 푥 ), Time 푑푡푎 1,2 1,2 1,2 2,1 1,2 훼 Fig. 2. Phase differences calculated for different central- 푑 푦1,2 = 휔 푥 + 푏푦 , frequency values. 푑푡푎 1,2 1,2 1,2 훼 푑 푧1,2 30 푎 = 0.2 + 푧1,2(푥1,2 − 10), (2) (a) 푑푡 25 | where 훼 is the fractional-order, 푏 is a constant, and 2 20

- φ 15 ε=0.05 휔1,2 are system parameters for the oscillators 1 and 2, 1 | φ which control the frequency. The parameter 휀 is the 10 ε=0.1 coupling strength between the two oscillators. From 5 0 Ref. [6], we set 훼 = 0.9, 푏 = 0.35, and 휔 ≈ 1, then ε=0.5 1,2 −5 the chaotic behavior is found. The chaotic attractor 0 200 400 600 800 1000 1200 1400 1600 1800 Time is shown in Fig. 1. 3 (b) 2.5 25 20 2

15 2 1.5 Α z 10 5 1 0 0.5 20 10 15 20 0 0 5 10 y −10 −5 0 0 0.5 1 1.5 2 2.5 3 −20 −15 −10 x Α1

Fig. 1. Chaotic attractor of the fractional-order Rössler Fig. 3. (a) Phase differences of the coupled fractional- oscillator. order Rössler equations at time scale 푎 = 5. (b) The Next, let us consider to use the continuous Morlet- correlation between the amplitude 퐴1, 퐴2. Here 푎 = 5, 휀 = 0.5. wavelet to obtain the wavelet transform of chaotic time series,[23,24] so that we can analyze the wavelet In our simulation, the time series used for wavelet phase synchronization of this coupled system. transform are generated by the two coupled Rössler equations. In Ref. [24] the authors proved that only ∫︁ +∞ at a certain time scale are the two integer-order os- 푊 (푎, 푡 ) = 푥(푡)휓* (푡)푑푡, (3) 0 푎,푡0 −∞ cillators synchronized with each other. We set the time scale 푎 = 5 for the wavelet function, and set where 휓푎,푡0 (푡) is the wavelet function related to the 휔1,2 = 1.03 and 0.97 for the two oscillators. For √1 푡−푡0 mother-wavelet 휓0(푡) as 휓푎,푡0 (푡) = 푠 휓0( 푠 ). The an integer order chaotic system, it was mentioned time scale 푎 corresponds to the width of the wavelet in Ref. [25] that there will be no phase synchroniza- function 휓푎,푡0 (푡), and 푡0 is the time shift of the tion if the central frequency Ω0 is lower than a cer- wavelet. The Morlet-wavelet[32] tain critical value. In Ref. [26], the author adopted an interesting method to investigate the influence of 1 −휂2 휓 (휂) = √ exp(푗Ω 휂) exp( ) (4) the central frequency Ω0 on the phase synchroniza- 0 4 0 휋 2 tion. Now, we study the impact of the central fre- is regarded as a mother-wavelet function. The wavelet quency Ω0 on phase synchronization in the fractional- surface function is order chaotic system. We set the coupling parameter 휀 = 0.5. The simulation result is shown in Fig. 2. We 푊 (푎, 푡) = |푊 (푎, 푡)| exp(푖휙(푎, 푡)). (5) can see that the phase difference increases with time when Ω0 = 0.5휋, 휋 and remains bounded if Ω0 > 1.5휋. The phase 휙(푎, 푡) = arg 푊 (푎, 푡). Thus, in the fractional-order chaotic system, the cen- We define the mean frequency difference as ∆Ω = tral frequency Ω0 is also important for determining ˙ ˙ [19] ⟨휑1(푎, 푡) − 휑2(푎, 푡)⟩, where ⟨·⟩ denotes the average the phase synchronization. With the above parame- over time. When ∆Ω ≈ 0, the phase difference does ter setting, the phase synchronization threshold lies 070501-2 CHIN. PHYS. LETT. Vol. 29, No. 7 (2012) 070501 somewhere between 휋 and 1.5휋. 304 J. Appl. Mech. 51 In the following, we set the central frequency Ω0 = Koeller R C 1984 299 2휋 for the wavelet function to study the effect of cou- Koeller R C 1986 Acta Mech. 58 251 [3] Sun H H, Abdelwahad A A and Onaral B 1984 IEEE Trans. pling strength on phase synchronization. We still set Autom. Control 29 441 the time scale 푎 = 5. The simulation results are [4] Ichise M, Nagayanagi Y and Kojima T 1971 J. Electroanal. shown in Fig. 3. As we can see from Fig. 3(a), when Chem. 33 253 we change the value of the coupling parameter 휀, the [5] Heaviside O 1971 Electromagnetic Theory (New York: Chelsea) phase difference decreases with the increasing of the [6] Li C G and Chen G 2004 Physica A 341 55 coupling parameter 휀. When 휀 = 0.05 and 0.1, the [7] Hartley T T, Lorenzo C F and Qammer H K 1995 IEEE phase difference increases with time. When 휀 = 0.5, Trans. CAS-I 42 485 Pro- the phase difference does not increase with time at all [8] Arena P, Caponetto R, Fortuna L and Porto D 1997 ceedings of the ECCTD (Budapest) 1259 and |휙1(푎, 푡) − 휙2(푎, 푡)| < const, thus the phase syn- [9] Ahmad W, El-Khazali R, El-Wakil A 2001 Electron. Lett. chronization is achieved for this time scale. In the last 37 1110 [10] Ahmad W M and Sprott J C 2003 Chaos Solitons Fractals case, the amplitudes of 푊1 and 푊2 remain chaotic and 16 339 their correlation are pretty small as shown in Fig. 3(b), [11] Ahmad W M and Harb W M 2003 Chaos Solitons Fractals although the phases are locked. 18 693 [12] Grigorenko I and Grigorenko E 2003 Phys. Rev. Lett. 91 034101 0.025 [13] Arena P, Caponetto R, Fortuna L and Porto D 1998 Int. J. 0.02 Bifur. Chaos 7 1527 0.015 ∆Ω 0.01 Arena P, Fortuna L, Porto D 2000 Phys. Rev. E 61 776 0.005 Chaos Solitons Fractals 22 0 [14] Li C G and Chen G 2004 549 0.2 0 0.4 [15] Zhou P and Chen Y M 2009 Chin. Phys. Lett. 26 120503 0 1 2 3 0.6 4 5 6 7 8 9 10 0.8 ε Yang Y Q and Chen Y 2009 Chin. Phys. Lett. 26 100501 Time scale a Zhong Q S, Bao J F, Yu Y B and Liao X F 2008 Chin. Phys. Lett. 25 Fig. 4. The mean frequency differences of the coupled 2812 Chin. Phys. Lett. 29 fractional-order Rössler equations. Wang S and Yu G Y 2012 020505 [16] Pecora L M and Carroll T L 1990 Phys. Rev. Lett. 64 821 In the above simulation, we show that for a specific [17] Boccaletti S, Kurths J, Osipov G, Valladares D L and Zhou C S 2002 Phys. Rep. 366 1 time scale, if the central frequency Ω0 is above a cer- [18] Zhang J B, Liu Z R and Li Y 2007 Chin. Phys. Lett. 24 tain critical value, the wavelet phase synchronization 1494 can be achieved. Next, we systematically investigate Guo R W 2011 Chin. Phys. Lett. 28 040205 the dependence of the phase synchronization on differ- Lee Tae H and Park Ju H 2009 Chin. Phys. Lett. 26 090507 ent coupling strength 휀 and different time scale 푎. The Miao Q Y, Fang J A, Tang Y and Dong A H 2009 Chin. Phys. Lett. 26 050501 coupling parameter ranges from 0 to 0.8, and the time Al-sawalha M M and Noorani M S M 2011 Chin. Phys. Lett. scale 푎 ranges from 0 to 10. The simulation results are 28 110507 shown in Fig. 4. We find that with the increasing cou- Zheng Z G, Hu G and Hu Bambi 2001 Chin. Phys. Lett. 18 pling strength 휀, the mean frequency difference ∆Ω 874 Zhan M, Hu G and Wang X G 2000 Chin. Phys. Lett. 17 for the coupled systems decreases at all time scales, 332 but approaches zero only at certain time scales. [19] Rosenblum M, Pikovsky A and Kurtz J 1996 Phys. Rev. In summary, we have built a coupled fractional- Lett. 76 1804 Phys- order Rössler system and investigated the phase syn- [20] Pikovsky A, Rosenlum M, Osipov G and Kurtz J 1997 ica D 104 219 chronization behaviors with the approach of complex [21] Rosenblum M, Pikovsky A S and Kurths J 1997 Phys. Rev. Morlet-wavelet transform. For other factional-order Lett. 78 4193 chaotic systems, as long as we can define the phase [22] Mainieri R and Rehacek J 1999 Phys. Rev. Lett. 82 3042 [23] Hramov A E and Koronovskii A A 2004 JETP Lett. 79 316 appropriately, we can also use the above-mentioned [24] Hramov A E and Koronovskii A A 2005 Physica D 206 252 method to investigate the phase synchronization. [25] Postnikov E B 2007 J. Exp. Theor. Phys. 105 652 The study is useful for enhancing our understand- [26] Postnikov E B 2009 Phys. Rev. E 80 057201 ing of the phase synchronization of fractional-order [27] Li C G, Liao X F and Yu J 2003 Phys. Rev. E 68 067203 [28] Deng W H and Li C P 2005 J. Phys. Soc. Jpn. 74 1645 chaotic systems. Developing some analysis methods Lu J G 2005 Chaos Solitons Fractals 26 1125 for fractional-order systems and synchronization in Gao X and Yu J B 2005 Chaos Solitons Fractals 26 141 fractional-order systems is an interesting topic for fu- Lu J G 2006 Chaos Solitons Fractals 27 519 ture research. Zhang H, Li C G and Chen G 2005 Int. J. Mod. Phys. C 16 815 Deng W H and Li C P 2005 Physica A 353 61 [29] Li C G 2007 Int. J. Mod. Phys. B 21 5159 References [30] Li C G 2006 Prog. Theor. Phys. 115 661 [31] Charef A, Sun H H, Tsao Y Y and Onaral B 1992 IEEE [1] Podlubny I 1999 Fractional Differential Equations (New Trans. Autom. Control 37 1465 York: Academic Press) [32] Grossman A and Morlet J 1984 SIAM J. Math. Anal. 15 [2] Bagley R L and Calico R A 1991 J. Guid. Contr. Dyn. 14 723

070501-3 Chinese Physics Letters Volume 29 Number 7 July 2012

EXPRESS LETTERS 074216 Nonlocal Imaging by Conditional Averaging of Random Reference Measurements LUO Kai-Hong, HUANG Bo-Qiang, ZHENG Wei-Mou, WU Ling-An 074501 Breakdown of Energy Equipartition in Vibro-Fluidized Granular Media in Micro-Gravity CHEN Yan-Pei, Pierre Evesque, HOU Mei-Ying

GENERAL 070301 Symmetry Groups and Gauss Kernels of the Schr¨odingerEquations with Potential Functions KANG Jing, QU Chang-Zheng 070302 Discontinuity of the Measurement-Induced Nonlocality Evolution XU Guo-Fu, TONG Dian-Min 070303 Exact Solutions to the Two-Dimensional Spatially Inhomogeneous Cubic-Quintic Nonlinear Schr¨odingerEquation with an External Potential CHEN Jun-Chao, ZHANG Xiao-Fei, LI Biao, CHEN Yong 070304 Quasi-exactly Solvable Cases of the N-Dimensional Symmetric Quartic Anharmonic Oscillator PAN Feng, XIE Ming-Xia, SHI Chang-Liang, J. P. DRAAYER 070305 Multi-particle Entanglement Generation Using Quantum-Dot Spin and Optical Microcavity System ZHANG Chuan-Lin, WANG Chuan, CAO Cong, ZHANG Ru 070306 Testing Quantum Entanglement with Local Measurement XIE Qing, WU Xian-Xin, DING Xiang-Mao, YANG Wen-Li, YUE Rui-Hong, FAN Heng 070401 Thermodynamics of the Bardeen Regular Black Hole M. Akbar, Nema Salem, S. A. Hussein 070501 Wavelet Phase Synchronization of Fractional-Order Chaotic Systems CHEN Feng, XIA Lei, LI Chun-Guang 070601 A Novel Super-High Resolution Phase Comparison Approach YU Jian-Guo, ZHOU Wei, DU Bao-Qiang, DONG Shao-Feng, FAN Qiao-Yan

070701 Enhanced Gas Sensing Properties of Aligned Porous SnO2 Nanofibers ZHAO Yan, HE Xiu-Li, LI Jian-Ping, JIA Jian, GAO Xiao-Guang 070702 Label-Free and Real-Time Detection of Antigen-Antibody Capture Processes Using the Oblique-Incidence Reflectivity Difference Technique HE Li-Ping, DAI Jun, SUN Yue, WANG Jing-Yi, LU¨ Hui-Bin, WANG Shu-Fang, JIN Kui-Juan, ZHOU Yue-Liang, YANG Guo-Zhen 070703 Lateral Resolution and Signal to Noise Ratio in Electrostatic Force Detection Based on Scanning Probe Microscopy ZHANG Dong-Dong, WANG Xiao-Wei, WANG Rui, WANG Sheng-Nan, CHENG Zhi-Hai, QIU Xiao-Hui

THE PHYSICS OF ELEMENTARY PARTICLES AND FIELDS 071201 Pair Production in an Intense Laser Pulse: The Eﬀect of Pulse Length REN Na, WANG Jia-Xiang, LI An-Kang, WANG Ping-Xiao + − 071301 Radiative Dileptonic Decays Bs → l l γ in the TC2 Model ZHANG Jiao, YUE Chong-Xing

071401 Weak Decays of First Radial Excited Dq(2S) and Bq(2S) States WANG Zhi-Hui, WANG Guo-Li, ZHANG Jin-Mei, WANG Tian-Hong NUCLEAR PHYSICS 072101 Transition from Electric Rotation to Chiral Mode in 135Nd QI Bin, LI Jian, WANG Shou-Yu, ZHANG Jing, ZHANG Shuang-Quan 072301 Methodological Study on Change in Half Life of 210Po Embedded in a Metallic Medium at Ultra-Low Temperature DONG Ke-Jun, JIANG Shan, HE Ming, HE Xian-Wen, RUAN Xiang-Dong, GUAN Yong-Jing, LIN De-Yu, YUAN Jian, WU Shao-Yong √ 072501 Dependence of Elliptic Flow on Transverse Momentum in s = 200 GeV Au-Au and √ NN sNN = 2.76 TeV Pb-Pb Collisions LI Bao-Chun, FU Yuan-Yuan, WANG Li-Li, WANG Er-Qin, WEN Xin-Jian, LIU Fu-Hu

ATOMIC AND MOLECULAR PHYSICS 073101 Angle-Dependent Irradiation of C4 in Femtosecond Laser Pulses WANG Zhi-Ping ZHANG Feng-Shou, ZHU Yun, XIE Guan-Hao 2 2 073102 Energy-Crossing and Its Eﬀect on Lifetime of the 4s 4p P3/2 Level for Highly Charged Ga-Like Ions FAN Jian-Zhong, ZHANG Deng-Hong, CHANG Zhi-Wei, SHI Ying-Long, DONG Chen-Zhong 073201 Detached Electron Spectra from H− near a Partially Reﬂecting Spherical Surface Muhammad Haneef, Saleh Mohammad, Jehan Akbar, Suneela Arif, Muhammad Zahir, Humayun Khan 073202 Superradiant Laser with Ultra-Narrow Linewidth Based on 40Ca WANG Yan-Fei, CHEN Jing-Biao 073203 Coherent Control of Lithium Atom by Adiabatic Rapid Passage with Chirped Microwave Pulses JIANG Li-Juan, ZHANG Xian-Zhou, MA Huan-Qiang, XIA Li-Hua, JIA Guang-Rui 073401 Exact Quantum-Scattering Study of the D(2S)+DS(2Π ) Reaction LV Shuang-Jiang, ZHANG Pei-Yu, HE Guo-Zhong

FUNDAMENTAL AREAS OF PHENOMENOLOGY(INCLUDING APPLICATIONS) 074201 Comparison of Small-Scale Actively and Passively Q-Switched Eye-Safe Intracavity Optical Parametric Oscillators at 1.57 µm MIAO Jie-Guang, PAN Yu-Zhai, QU Shi-Liang 074202 Numerical Approximations to the Solution of Ray Tracing through the Crystalline Lens A. Yildirim, A. G¨okdo˘gan,M. Merdan, V. Lakshminarayanan 074203 Controllable Dual-Wavelength Fiber Laser LI Zhen, ZHOU Jun, HE Bing, LIU Hou-Kang, LIU Chi, WEI Yun-Rong, DONG Jing-Xing, LOU Qi-Hong 074204 Numerical Study of Plasmonic Modes in Hexagonally Arranged Metal Nanowire Array YAN Hao-Zhe, PENG Jing-Gang, LI Jin-Yan, YANG L-Yun 074205 Dual-Peak Bragg Gratings Inscribed in an All-Solid Photonic Bandgap Fiber for Sensing Applications ZHANG Ji-Huang, LIU Ning-Liang, WANG Ying, JI Ling-Ling, LU Pei-Xiang 074206 A Compact Setup of Saturated Absorption Spectroscopy for Diode Laser Frequency Stabilization ZHANG Xian, HUANG Kai-Kai, XU Hao, XU Zhou-Xiang, LI Nan, LU Xuan-Hui

074207 Application of Optical Kerr Gate with SrTiO3 Crystal in Acquisition of Gated Spectra from a Supercontinuum YAN Li-He, JIA Sen, SI Jin-Hai, MATSUO Shigeki, CHEN Feng, HOU Xun 074208 Experimental Realization of a Magnetically Tunable Cavity in a Gyromagnetic Photonic Crystal LIAN Jin, FU Jin-Xin, GAN Lin, LI Zhi-Yuan 074209 Enhanced and Tunable Spin Hall Effect of Light upon Reflection of One-Dimensional Photonic Crystal with a Defect Layer LING Xiao-Hui, LUO Hai-Lu, TANG Ming, WEN Shuang-Chun 074210 Electromagnetic Wave Propagation over Oil-Covered Sea Surface YANG Chao, JIN Wei, GUO Li-Xin 074211 Resonance Cavities in Parallel-Hetero Perturbation Photonic Crystal Waveguide Structures WANG Chen, LI Zhi-Yuan 074212 Resolution for Forward and Phase-Conjugate Degenerate Four-Wave Mixing in Hot Atomic Media CHENG Xue-Mei, CHEN Hao-Wei, WANG Jian, MIAO Yi-Zhu, YIN Xun-Li, REN Zhao-Yu, BAI Jin-Tao 074213 Evolution of Slow Dual Steady-State Optical Solitons in a Cold Three-State Medium SUN Jian-Qiang, LI Hao-Chen, GU Xiao-Yan 074214 Estimation of the Maximum Output Power of Double-Clad Photonic Crystal Fiber Laser CHEN Yue-E, WANG Yong, QU Xi-Long 074215 High-Power High-Temperature Continuous-Wave Operation of Quantum Cascade Laser at λ∼4.6 µm without Lateral Regrowth LIANG Ping, LIU Feng-Qi, ZHANG Jin-Chuan, WANG Li-Jun, LIU Jun-Qi, WANG Zhan-Guo 074216 Nonlocal Imaging by Conditional Averaging of Random Reference Measurements LUO Kai-Hong, HUANG Bo-Qiang, ZHENG Wei-Mou, WU Ling-An 074401 Enhancement Effect of Patterning Resolution Induced by an Aluminum Thermal Conduction Layer with AgInSbTe as a Laser Thermal Lithography Film LI Hao, WANG Rui, GENG Yong-You, WU Yi-Qun, WEI Jing-Song 074501 Breakdown of Energy Equipartition in Vibro-Fluidized Granular Media in Micro-Gravity CHEN Yan-Pei, Pierre Evesque, HOU Mei-Ying 074701 Aspherical Oscillation of Two Interacting Bubbles in an Ultrasound Field LIANG Jin-Fu, CHEN Wei-Zhong, SHAO Wei-Hang, QI Shui-Bao 074702 Marangoni Bifurcation Flow in a Microchannel T-Junction and Its Micropumping Effect: A Computational Study PAN Zhen-Hai, WANG Hao, YANG Zhen 074703 Dynamics Evolution Investigation of Mack Mode Instability in a Hypersonic Boundary Layer by Bicoherence Spectrum Analysis HAN Jian, JIANG Nan 074704 Numerical Simulation of Thermocapillary-Buoyant Convection in an Annular Pool under Various Gravity Levels ZHOU Xiao-Ming, HUANG Hu-Lin

PHYSICS OF GASES, PLASMAS, AND ELECTRIC DISCHARGES 075201 Usage of Displaced Current in Langmuir Probe Measurement MING Zhang-Jian, LI Hong, CHEN Zhi-Peng, LUO Chen, XIE Jin-Lin, LAN Tao, LIU A-Di, LIU Wan-Dong 075202 Eﬀects of an Electric Field on the Cylindrical Dust Acoustic Wave in Magnetized Complex Plasmas B. Farokhi, M. Eghbali 075203 Deactivation of Enterococcus Faecalis Bacteria by an Atmospheric Cold Plasma Brush CHEN Wei, HUANG Jun, DU Ning, LIU Xiao-Di, LV Guo-Hua, WANG Xing-Quan, ZHANG Guo-Ping, GUO Li-Hong, YANG Si-Ze 075204 Study on the Resistive Wall Instability Driven by Plasma Flow LI Li, LIU Yue

CONDENSED MATTER: STRUCTURE, MECHANICAL AND THERMAL PROPERTIES 076101 Collision Energy Dependence of Defect Formation in Graphene MAO Fei, ZHANG Chao, ZHANG Yan-Wen, ZHANG Feng-Shou 076401 Unsteady Cavitating Flow around a Hydrofoil Simulated Using the Partially-Averaged Navier–Stokes Model JI Bin, LUO Xian-Wu, WU Yu-Lin, XU Hong-Yuan 076501 Growth, Mechanical and Thermal Properties of Bi4Si3O12 Single Crystals SHEN Hui, XU Jia-Yue, PING Wei-Jie, HE Qing-Bo, ZHANG Yan, JIN Min, JIANG Guo-Jian 076801 Metalorganic Chemical Vapor Deposition Growth of InAs/GaSb Superlattices on GaAs Substrates and Doping Studies of P-GaSb and N-InAs LI Li-Gong, LIU Shu-Man, LUO Shuai, YANG Tao, WANG Li-Jun, LIU Feng-Qi, YE Xiao-Ling, XU Bo, WANG Zhan-Guo

CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES 077101 Optimal Electron Density Mechanism for Hydrogen on the Surface and at a Vacancy in Tungsten LIU Yue-Lin, GAO An-Yuan, LU Wei, ZHOU Hong-Bo, ZHANG Ying 077102 Diﬀerent Roles of a Boron Substitute for Carbon and Silicon in β-SiC ZHOU Yan, WANG Kun, FANG Xiao-Yong, HOU Zhi-Ling, JIN Hai-Bo, CAO Mao-Sheng 077301 Low Bias Negative Diﬀerential Resistance with Large Peak-to-Valley Ratio in a BDC60 Junction REN Hua, LIANG Wei, ZHAO Peng, LIU De-Sheng 077302 Controllable Excitation of Surface Plasmons in End-to-Trunk Coupled Silver Nanowire Structures ZHU Yin, WEI Hong, YANG Peng-Fei, XU Hong-Xing

077303 Alternating-Current Transport Properties in Nd0.7Sr0.3MnO3 Ceramic with Secondary Phases CHEN Shun-Sheng, YANG Chang-Ping, LUO Xiao-Jing, Medvedeva I V 077304 Influence of Temperature and Frequency on Dielectric Permittivity and ac Conductivity of Au/SnO2/n-Si (MOS) Structures R. Ertu˘grul,A. Tataro˘glu 077305 Controllable Negative Differential Resistance Behavior of an Azobenzene Molecular Device Induced by Different Molecule-Electrode Distances FAN Zhi-Qiang, ZHANG Zhen-Hua, QIU Ming, DENG Xiao-Qing, TANG Gui-Ping 077306 Synthesis of ITO Nanoparticles Prepared by the Degradation of Sulfide Method Majid. Farahmandjou 077307 Electron Transport through Magnetic Superlattices with Asymmetric Double-Barrier Units in Graphene HUO Qiu-Hong, WANG Ru-Zhi, YAN Hui 077308 Polarization-Selective Collimation Effect with a Reflective Plasmonic Cavity MAO Fei-Long, XIE Jin-Jin, FAN Qing-Yan, ZHANG Li-Jian, AN Zheng-Hua 077701 First Principle Study of the Electronic Properties of 3C-SiC Doped with Different Amounts of Ni DOU Yan-Kun, QI Xin, JIN Hai-Bo, CAO Mao-Sheng, Usman Zahid, HOU Zhi-Ling 077801 Can Hydrogen be Incorporated inside Silicon Nanocrystals? NI Zhen-Yi, PI Xiao-Dong, YANG De-Ren 077802 Abnormal Temperature Dependence of Coercivity in Cobalt Nanowires FAN Xiu-Xiu, HU Hai-Ning, ZHOU Shi-Ming, YANG Mao, DU Jun, SHI Zhong 077803 Growth-induced Stacking Faults of ZnO Nanorods Probed by Spatial Resolved Cathodoluminescence XIE Yong, JIE Wan-Qi, WANG Tao, WIEDENMANN Michael, NEUSCHL Benjamin, MADEL Manfred, WANG Ya-Bin, FENEBERG Martin, THONKE Klaus

CROSS-DISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY 078101 Ultrathin Carbon Films Prepared by Negative Cluster-Beam Technology ZHANG Zao-Di, WANG Ze-Song, WANG Shi-Xu, FU De-Jun 078102 Betavoltaic Battery Conversion Efficiency Improvement Based on Interlayer Structures LI Da-Rang, JIANG Lan, YIN Jian-Hua, TAN Yuan-Yuan, LIN Nai 078103 Effect of Grain Boundary on Spinodal Decomposition Using the Phase Field Crystal Method YANG Tao, CHEN Zheng, ZHANG Jing, DONG Wei-Ping, WU Lin 078501 Influence of Dry Etching Damage on the Internal Quantum Efficiency of Nanorod InGaN/GaN Multiple Quantum Wells YU Zhi-Guo, CHEN Peng YANG Guo-Feng, LIU Bin, XIE Zi-Li, XIU Xiang-Qian, WU Zhen-Long, XU Feng, XU Zhou, HUA Xue-Mei, HAN Ping, SHI Yi ZHANG Rong, ZHENG You-Dou 078502 Gate-Recessed AlGaN/GaN MOSHEMTs with the Maximum Oscillation Frequency Exceeding 120 GHz on Sapphire Substrates KONG Xin, WEI Ke, LIU Guo-Guo, LIU Xin-Yu 078701 Thermoluminescence Response of Germanium-Doped Optical Fibers to X-Ray Irradiation M. A. Saeed, N. A. Fauzia, I. Hossain, A. T. Ramli, B. A. Tahir 078801 A Poly-(3-Hexylthiophene) (P3HT)/[6,6]-Phenyl-C61-Butyric Acid Methyl Ester (PCBM) Bilayer Organic Solar Cell Fabricated by Airbrush Spray Deposition CHEN Zheng, DENG Zhen-Bo, ZHOU Mao-Yang, LU¨ Zhao-Yue, DU Hai-Liang, ZOU Ye, YIN Yue-Hong, LUN Jian-Chao 078901 Response Surface Analysis of Crowd Dynamics during Tawaf Zarita Zainuddin, Lim Eng Aik

GEOPHYSICS, ASTRONOMY, AND ASTROPHYSICS 079501 Laser Interferometer Used for Satellite–Satellite Tracking: an On-Ground Methodological Demonstration LI Yu-Qiong, LUO Zi-Ren, LIU He-Shan, DONG Yu-Hui, JIN Gang 079801 Cosmological Constant Dominated Transit Universe from the Early Deceleration Phase to the Current Acceleration Phase in Bianchi-V Spacetime YADAV Anil Kumar