Split-operator technique for propagating phase space functions: Exploring chaotic, dissipative and relativistic dynamics

Gómez E.A.; Thirumuruganandham S.P.; Santana A.

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Split-operator technique for propagating phase space functions: Exploring chaotic, dissipative and relativistic dynamics

机译：用于传播相空间函数的分裂算子技术：探索混沌，耗散和相对论动力学

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We conduct a comprehensive analysis of the split-operator method for propagating phase space distribution functions in different scenarios of classical mechanics. A numerical method based on Fast Fourier Transform allows to propagate almost any sampled or exact localized initial state, as well as the direct calculation of current densities in phase space. In order to demonstrate the potential of the proposed numerical scheme some simulations involving chaotic, dissipative and relativistic dynamics are performed. In the conducted simulations, dynamical functions like autocorrelations as well as the detailed structures in phase space are discussed. We find that the split-operator technique demonstrates the effectiveness for studying time evolution of interacting one-dimensional classical systems.

机译：我们对在经典力学的不同情况下传播相空间分布函数的分裂算子方法进行了全面分析。基于快速傅立叶变换的数值方法可以传播几乎所有采样或精确的局部初始状态，以及在相空间中直接计算电流密度。为了证明所提出的数值方案的潜力，进行了一些涉及混沌，耗散和相对论动力学的模拟。在进行的仿真中，讨论了诸如自相关之类的动力学函数以及相空间中的详细结构。我们发现分裂算子技术证明了研究相互作用的一维经典系统的时间演化的有效性。

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《Computer physics communications》 |2014年第1期|共8页
作者
Gómez E.A.; Thirumuruganandham S.P.; Santana A.;
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正文语种 eng
中图分类计算机的应用;
关键词
Chaotic dynamics; Dissipative dynamics; Liouville equation; Phase space distribution function; Split-operator technique;

机译：混沌动力学;耗散动力学;Liouville方程;相空间分布函数;分裂算子技术;

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1. Split-operator technique for propagating phase space functions: Exploring chaotic, dissipative and relativistic dynamics [J] . Gómez E.A., Thirumuruganandham S.P., Santana A. Computer physics communications . 2014,第1期

机译：用于传播相空间函数的分裂算子技术：探索混沌，耗散和相对论动力学
2. Parallelizable split-operator propagator for treating Coriolis-coupled quantum dynamics [J] . Cvitas MT, Althorpe SC Computer physics communications . 2007,第4期

机译：用于处理科里奥利耦合量子动力学的可并行分裂算子传播器
3. Study of Wavelet Methodology and Chaotic Behavior of Produced Particles in Different Phase Spaces of Relativistic Heavy Ion Collisions [J] . M. Ayaz Ahmad, Vyacheslav V. Lyashenko, Zhanna V. Deineko, Journal of Applied Mathematics and Physics . 2017,第5期

机译：相对论重离子碰撞不同相空间中产生颗粒的小波方法和混沌行为的研究
4. A phase-space approach for propagating field-field correlation functions near stochastic sources [C] . Gabriele Gradoni, Stephen C Creagh, Gregor Tanner 2016 URSI International Symposium on Electromagnetic Theory . 2016

机译：在随机源附近传播场-场相关函数的相空间方法
5. Dynamical Systems: Chaotic Attractors and Synchronization using Time-Averaged Partial Observations of the Phase Space. [D] . Blocher, Jordan Fleming. 2016

机译：动力系统：混沌吸引子和使用相空间的时间平均局部观测进行同步。
6. Exploring Configuration Space and Path Space of Biomolecules Using Enhanced Sampling Techniques—Searching for Mechanism and Kinetics of Biomolecular Functions [O] . Hiroshi Fujisaki, Kei Moritsugu, Yasuhiro Matsunaga 2018

机译：利用增强的采样技术探索生物分子的构型空间和路径空间—寻找生物分子功能的机理和动力学
7. EEG Signal Discrimination using Non-linear Dynamics in the EMD Domain S. M. Shafiul Alam,S. M. Shafiul Alam,Aurangozeb, and Syed TarekShahriar Abstract—An EMD-chaos based approach is proposed todiscriminate EEG signals corresponding to healthy persons,and epileptic patients during seizure-free intervals and seizureattacks. An electroencephalogram (EEG) is first empiricallydecomposed to intrinsic mode functions (IMFs). The nonlineardynamics of these IMFs are quantified in terms of the largestLyapunov exponent (LLE) and correlation dimension (CD).This chaotic analysis in EMD domain is applied to a large groupof EEG signals corresponding to healthy persons as well asepileptic patients (both with and without seizure attacks). It isshown that the values of the obtained LLE and CD exhibitfeatures by which EEG for seizure attacks can be clearlydistinguished from other EEG signals in the EMD domain.Thus, the proposed approach may aid researchers in developingeffective techniques to predict seizure activities. Index Terms—Electroencephalogram (EEG), empiricalmode decomposition (EMD), largest Lyapunov exponent (LLE),correlation dimension (CD), epileptic seizures. The Authors are with the Electrical and Electronic EngineeringDepartment, Bangladesh University of Engineering and Technology,Dhaka-1000, Bangladesh (e-mail: imamul@eee.buet.ac.bd) PDF Cite: S. M. Shafiul Alam,S. M. Shafiul Alam,Aurangozeb, and Syed Tarek Shahriar, "EEG Signal Discrimination using Non-linear Dynamics in the EMD Domain," International Journal of Computer and Electrical Engineering vol. 4, no. 3, pp. 326-330, 2012. PREVIOUS PAPER Perception of Emotions Using Constructive Learningthrough Speech NEXT PAPER Physical Layer Impairments Aware OVPN Connection Selection Mechanisms Copyright © 2008-2013. International Association of Computer Science and Information Technology Press (IACSIT Press) [O] . S. M. Shafiul Alam, Syed TarekShahriar 2012

机译：EEG信号在EMD域S. S. Shafiul Alam，S中的非线性动力学使用非线性动力学。 M. Shafiul Alam，Aurangozeb和Syed Tarekshahriar摘要 - 基于EMD Chaos的方法，提出了对应于健康人的EEG信号，癫痫发作期间的癫痫患者和Seizureattacks。脑电图（EEG）首先被凭经上分解为内在模式功能（IMF）。这些IMF的非线性动力学在最大范围的指数（LLE）和相关尺寸（CD）方面是量化的。本域中的混沌分析应用于与健康人相对应的大型脑电图（Asepileptic患者）（两者都有癫痫发作）。因此，所获得的LLE和CD表展的价值可以从EMD领域的其他EEG信号中清晰地区分脑电图的表达展示。本拟议的方法可以帮助研究人员以预测癫痫发作的癫痫发作技术。索引术语 - 脑电图（EEG），仿真态分解（EMD），最大的Lyapunov指数（LLE），相关维度（CD），癫痫发作。作者与电气电子和电子工程公司，孟加拉国工程和技术大学，孟加拉国达卡 - 1000（电子邮件：imamul@eee.buet.ac.bd）pdf cite：s. m. shafiul Alam，s。 M. Shafiul Alam，Aurangozeb和Syed Tarek Shahriar，“EEG信号歧视在EMD领域的非线性动态，”计算机电气工程卷国际杂志。 4，不。 3，pp。326-330,2012，上一篇论文对情绪的看法，使用建设性的学习言论下一篇论文物理层障碍意识到OVPN连接选择机制版权所有©2008-2013。国际计算机科学与信息技术协会出版社（IACSIT Press）

Split-operator technique for propagating phase space functions: Exploring chaotic, dissipative and relativistic dynamics

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