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Residual stress determination in a C-C composite consisting of a carbonized elastomer matrix filled with graphite, carbon black and short carbon fibers 碳化弹性体基体填充石墨、碳黑和短碳纤维组成的 C-C 复合材料中残余应力的测定
IF 3.1 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-07-23 DOI: 10.3389/fphy.2024.1407517
Eugene S. Statnik, Semen D. Ignatyev, Alexey I. Salimon, Andrey A. Stepashkin, Alexander M. Korsunsky
In this study, composites obtained through low-temperature carbonization of elastomeric matrix highly filled with graphite, carbon black and short carbon fibers were studied for the purpose of determining residual stresses at different scales using a combination of several complementary methods. The state-of-the-art techniques included X-ray stress analysis using the sin2ψ method, the micro-ring-core technique via Focused Ion Beam milling and Digital Image Correlation (FIB-DIC), the contour method, the strain gauge method, and the hole drilling technique with digital laser speckle pattern interferometry (DLSPI). It was found that the contour method could not be used implemented for residual stress evaluation due to the low electrical conductivity of composite. Moreover, the DLSPI hole drilling method did not reveal any fringes indicating significant residual stress level exceeding a few MPa. The strain gauge method also revealed a narrow residual stress distribution with an average value of approximately zero. In contrast, the X-ray sin2ψ method as well as FIB-DIC technique both returned values of about 150–250 MPa. A hierarchical model of the composite is proposed based on the Davidenkov Type I–II–III stress classification that provides an explanation of these observations.
在这项研究中,为了确定不同尺度上的残余应力,研究人员结合使用了几种互补方法,研究了通过对石墨、碳黑和短碳纤维高度填充的弹性基体进行低温碳化而获得的复合材料。最先进的技术包括使用 sin2ψ 法进行 X 射线应力分析、通过聚焦离子束铣削和数字图像相关性(FIB-DIC)进行微环芯技术、等值线法、应变计法以及使用数字激光斑点模式干涉仪(DLSPI)进行钻孔技术。结果发现,由于复合材料的导电率较低,等值线法无法用于残余应力评估。此外,DLSPI 钻孔法也没有发现任何表明残余应力水平超过几兆帕斯卡的显著条纹。应变计方法也显示出平均值约为零的狭窄残余应力分布。相比之下,X 射线 sin2ψ 法和 FIB-DIC 技术都显示出约 150-250 兆帕的残余应力值。根据 Davidenkov I-II-III 型应力分类,提出了复合材料的分层模型,为这些观察结果提供了解释。
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引用次数: 0
An efficient algorithm for resource optimization in TWDM passive optical network using a C-RAN 使用 C-RAN 的 TWDM 无源光网络资源优化的高效算法
IF 3.1 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-07-23 DOI: 10.3389/fphy.2024.1429750
Jun Jiat Tiang, Hee Chan Chung, Jaeyoung Choi, Imran Khan, Asma Alshehri, Pi-Chung Wang, Ibrahim A. Hameed
The traditional base station in C-RAN is divided into three parts: a pool of centralized baseband units (BBUs), a fronthaul network that links the BBUs and remote radio units (RRUs), and RRUs. This paper proposes a novel cooperative algorithm for resource optimization in a time-wavelength division multiplexed (TWDM) passive optical network (PON) incorporating a cloud radio access network (C-RAN). First, a joint collaborative strategy is deployed to optimize cooperative caching and transmission in the wireless and optical domains. Then, the quality of experience (QoE) is improved by bandwidth configuration and caching. Simulation results show that the average throughput of the proposed QoE-aware video cooperative caching and transmission mechanism (QACCTM) algorithm is approximately 30% higher than that of other algorithms. Compared with the relative average residual clutter power (RARCP) and quality-aware wireless edge caching (QAWEC) algorithms, the proposed QACCTM algorithm reduces the access delay by approximately 27.1% and 15.9%, respectively.
C-RAN 中的传统基站分为三个部分:集中基带单元(BBU)池、连接 BBU 和远程无线单元(RRU)的前传网络以及 RRU。本文提出了一种新的合作算法,用于结合云无线接入网(C-RAN)的时分复用(TWDM)无源光网络(PON)中的资源优化。首先,采用联合协作策略来优化无线和光域中的合作缓存和传输。然后,通过带宽配置和缓存改善体验质量(QoE)。仿真结果表明,所提出的 QoE 感知视频合作缓存和传输机制(QACCTM)算法的平均吞吐量比其他算法高出约 30%。与相对平均残余杂波功率(RARCP)和质量感知无线边缘缓存(QAWEC)算法相比,所提出的 QACCTM 算法分别减少了约 27.1% 和 15.9% 的接入延迟。
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引用次数: 0
Insight into the thermal transport by considering the modified Buongiorno model during the silicon oil-based hybrid nanofluid flow: probed by artificial intelligence 通过人工智能探测硅油基混合纳米流体流动过程中的热传输:考虑修改后的布昂奥尔诺模型
IF 3.1 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-07-23 DOI: 10.3389/fphy.2024.1372675
Asad Ullah, Hongxing Yao, Farid Ullah, Haifa Alqahtani, Emad A. A. Ismail, Fuad A. Awwad, Abeer A. Shaaban
This work aims to analyze the impacts of the magnetic field, activation of energy, thermal radiation, thermophoresis, and Brownian effects on the hybrid nanofluid (HNF) (Ag++silicon oil) flow past a porous spinning disk. The pressure loss due to porosity is constituted by the Darcy–Forchheimer relation. The modified Buongiorno model is considered for simulating the flow field into a mathematical form. The modeled problem is further simplified with the new group of dimensionless variables and further transformed into a first-order system of equations. The reduced system is further analyzed with the Levenberg–Marquardt algorithm using a trained artificial neural network (ANN) with a tolerance, step size of 0.001, and 1,000 epochs. The state variables under the impacts of the pertinent parameters are assessed with graphs and tables. It has been observed that when the magnetic parameter increases, the velocity gradient of mono and hybrid nanofluids (NFs) decreases. As the input of the Darcy–Forchheimer parameter increases, the velocity profiles decrease. The result shows that as the thermophoresis parameter increases, temperature and concentration increase as well. When the activation energy parameter increases, the concentration profile becomes higher. For a deep insight into the analysis of the problem, a statistical approach for data fitting in the form of regression lines and error histograms for NF and HNF is presented. The regression lines show that 100% of the data is used in curve fitting, while the error histograms depict the minimal zero error 7.1e6 for the increasing values of Nt. Furthermore, the mean square error and performance validation for each varying parameter are presented. For validation, the present results are compared with the available literature in the form of a table, where the current results show great agreement with the existing one.
这项工作旨在分析磁场、能量活化、热辐射、热泳和布朗效应对流经多孔旋转盘的混合纳米流体(HNF)(银++硅油)的影响。多孔性导致的压力损失由达西-福克海默关系构成。为了以数学形式模拟流场,考虑了改进的 Buongiorno 模型。利用新的无量纲变量组进一步简化了模型问题,并将其转化为一阶方程系统。利用训练有素的人工神经网络(ANN),以公差、步长 0.001 和 1,000 个历元的 Levenberg-Marquardt 算法对简化后的系统进行进一步分析。通过图形和表格对相关参数影响下的状态变量进行了评估。据观察,当磁性参数增加时,单纳米流体和混合纳米流体(NFs)的速度梯度会减小。随着达西-福克海默参数输入的增加,速度曲线也随之减小。结果表明,随着热泳参数的增加,温度和浓度也随之增加。当活化能参数增加时,浓度曲线变高。为了深入分析问题,本文介绍了以回归线和误差直方图形式对 NF 和 HNF 进行数据拟合的统计方法。回归线显示,在曲线拟合中使用了 100% 的数据,而误差直方图显示,随着 Nt 值的增加,最小零误差为 -7.1e6。此外,还显示了每个变化参数的均方误差和性能验证。在验证方面,以表格的形式将当前结果与现有文献进行了比较,结果显示当前结果与现有文献非常一致。
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引用次数: 0
Frontiers | Unfolding experimental distortions in beta spectrometry 前沿 | 揭开贝塔光谱仪中的实验畸变
IF 3.1 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-07-22 DOI: 10.3389/fphy.2024.1435615
Gaël Craveiro, Sylvain Leblond, Xavier Mougeot, Matthieu Vivier
The distortions of measured beta spectra are addressed by means of unfolding algorithms. Two different approaches, the Maximum-Likelihood Expectation-Maximization and the Tikhonov regularization, are tested on various simulated spectra, for which the initial spectrum to retrieve is known, and on a 99Tc spectrum measured with our dedicated setup. Statistical uncertainties of distorted measured spectra are propagated by determining the covariance matrices. Both algorithms provide satisfactory results but Tikhonov performs overall better for most of the studied radionuclides. Highlight is made on the necessity to employ at least two independent methods to ensure the accuracy of the unfolded spectra and to estimate the internal bias of each algorithm.
通过展开算法解决了测量到的β光谱失真问题。最大似然期望最大化和提霍诺夫正则化这两种不同的方法在各种已知初始光谱的模拟光谱上进行了测试,并在利用我们的专用装置测量的 99Tc 光谱上进行了测试。通过确定协方差矩阵来传播扭曲测量光谱的统计不确定性。这两种算法都能提供令人满意的结果,但对于所研究的大多数放射性核素而言,Tikhonov 算法的总体性能更好。突出强调了至少采用两种独立方法的必要性,以确保展开光谱的准确性,并估计每种算法的内部偏差。
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引用次数: 0
Z-ACA allotrope: a topological carbon material with obstructed Wannier charge center, real topology, and hinge states Z-ACA 同素异形体:一种具有受阻万尼尔电荷中心、真实拓扑结构和铰链态的拓扑碳材料
IF 3.1 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-07-19 DOI: 10.3389/fphy.2024.1437146
Lunsheng Wu, Yang Li
As the most prevalent element on our planet, carbon manifests a wide variety of allotropic phases, significantly contributing to its complex physical properties. Recently, several carbon allotropes have been reported to possess abundant topological phases in theory and experiment. This work focuses on a sp3 carbon allotrope, Z-ACA allotrope, which consists of 5-6-7-type Z-ACA carbon rings. This allotrope has been reported previously as a superhard material comparable to diamond. In this study, we report that it is a candidate for both an obstructed atomic insulator and a real Chern insulator. It is worth mentioning that Z-ACA exhibits an unconventional bulk-boundary correspondence due to its hinge boundary state manifestation. Our current research indicates that Z-ACA is a suitable carbon phase platform for studying the real topology and second-order bulk-boundary correspondence.
作为地球上最普遍的元素,碳表现出多种多样的同素异形相,极大地促进了其复杂的物理特性。最近,有报道称几种碳同素异形体在理论和实验中具有丰富的拓扑相。这项研究的重点是由 5-6-7 型 Z-ACA 碳环组成的 sp3 碳同素异形体 Z-ACA 同素异形体。据报道,这种同素异形体是一种可与金刚石媲美的超硬材料。在这项研究中,我们发现它既是受阻原子绝缘体,也是真正的切尔恩绝缘体。值得一提的是,Z-ACA 因其铰链边界态表现而呈现出非常规的体界对应关系。我们目前的研究表明,Z-ACA 是研究真实拓扑和二阶体界对应关系的合适碳相平台。
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引用次数: 0
The closed-form solution by the exponential rational function method for the nonlinear variable-order fractional differential equations 指数有理函数法对非线性变阶分数微分方程的闭式求解
IF 3.1 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-07-19 DOI: 10.3389/fphy.2024.1347636
Mashael M. ALBaidani, Umair Ali, Abdul Hamid Ganie
The symmetry features of fractional differential equations allow effective explanation of physical and biological phenomena in nature. The generalized form of the fractional differential equations is the variable-order fractional differential equations that describe the physical and biological applications. This paper discusses the closed-form traveling wave solutions for the nonlinear space–time variable-order fractional modified Kawahara and (2 + 1)-dimensional Burger hierarchy equations. The variable-order fractional differential equation has a derivative operator in the Caputo sense that is converted into the integer-order ordinary differential equation (ODE) by fractional transformation. The obtained ODE is solved by the exponential rational function method, and as a result, new exact solutions are constructed. Two problems are proposed to confirm the solutions of the space-time variable-order fractional differential equations.
分数微分方程的对称性特征可以有效解释自然界中的物理和生物现象。分数微分方程的广义形式是描述物理和生物应用的变阶分数微分方程。本文讨论了非线性时空变阶分数修正川原方程和(2 + 1)维伯格层次方程的闭式行波解。变阶分数微分方程有一个卡普托意义上的导数算子,通过分数变换转换成整数阶常微分方程(ODE)。用指数有理函数法求解得到的 ODE,并由此构建了新的精确解。提出了两个问题来确认时空变阶分数微分方程的解。
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引用次数: 0
Impact of carboxylic acid structure on α-hemihydrate gypsum crystal morphology and mechanical strength 羧酸结构对 α-半水石膏晶体形态和机械强度的影响
IF 3.1 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-07-18 DOI: 10.3389/fphy.2024.1420138
Guo-gang Li, Jin-e Liu, Liang Ma, Hao-lei Gong, Su-hong Yin
This study investigated the synthesis of α-hemihydrate gypsum (α-HH) through semi-liquid autoclaving of phosphogypsum (PG) using various carboxylic acids as modifying agents. The impact of carboxyl group spatial location, auxiliary functional group type, and the number of carboxyl groups within the carboxylic acid modifiers on the mechanical strength and crystal morphology of α-HH was analyzed using scanning electron microscopy (SEM), strength testing, and molecular dynamics simulations. The results revealed a significant influence of the carboxylic acid molecular structure on the α-HH crystal morphology. Monocarboxylic acids and dicarboxylic acids with a long carbon chain length between carboxyl groups exhibited preferential adsorption on the (200), (110), and (−110) crystal planes, promoting crystal growth along the c-axis. In contrast, hydroxyl groups and cis double bonds in the modifier structure induced selective adsorption on the (001) plane, hindering growth along the c-axis. Conversely, trans double bonds favored adsorption on the (200), (110), and (−110) planes, enhancing growth along the c-axis. Based on these observations, screening principles for carboxylic acid modifiers were established, suggesting that: 1) the number of carboxyl groups should exceed 2; 2) the optimal carbon atom spacing between carboxyl groups is 3; and 3) auxiliary functional groups such as hydroxyl groups and cis double bonds should be introduced. Modifiers like citric acid, ethylene diamine tetraacetic acid (EDTA), and pyromellitic acid, within concentration ranges of 0.05%–0.1%, 0.1%–0.15%, and 0.05%–0.1%, respectively, yielded α-HH with flexural strengths exceeding 4 MPa and compressive strengths greater than 35 MPa, demonstrating the validity of these principles.
本研究探讨了以各种羧酸为改性剂,通过对磷石膏(PG)进行半液体高压蒸煮合成α-半水石膏(α-HH)的过程。利用扫描电子显微镜(SEM)、强度测试和分子动力学模拟分析了羧基的空间位置、辅助官能团类型以及羧酸改性剂中羧基的数量对 α-HH 的机械强度和晶体形态的影响。结果表明,羧酸分子结构对 α-HH 晶体形态有显著影响。羧基之间碳链长度较长的一羧酸和二羧酸会优先吸附在 (200)、(110) 和 (-110) 晶面上,促进晶体沿 c 轴生长。与此相反,改性剂结构中的羟基和顺式双键会选择性地吸附在(001)平面上,阻碍晶体沿 c 轴生长。相反,反式双键有利于吸附在 (200)、(110) 和 (-110) 平面上,从而促进沿 c 轴的生长。根据这些观察结果,我们建立了羧酸改性剂的筛选原则,即:1:1) 羧基的数量应超过 2 个;2) 羧基之间的最佳碳原子间距为 3 个;3) 应引入羟基和顺式双键等辅助官能团。柠檬酸、乙二胺四乙酸(EDTA)和吡咯烷酮酸等改性剂的浓度范围分别为 0.05%-0.1%、0.1%-0.15% 和 0.05%-0.1%,它们产生的 α-HH 抗折强度超过 4 兆帕,抗压强度超过 35 兆帕,证明了这些原则的正确性。
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引用次数: 0
Research on the suitability and spatial and temporal evolution of innovation environment niche suitability of regional innovation ecosystem under digitalization 数字化条件下区域创新生态系统创新环境利基适宜性及时空演化研究
IF 3.1 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-07-18 DOI: 10.3389/fphy.2024.1425130
Zitong He, Haijun Wang, Xiaolin Ma, Yuhan Hu, Huiyan Zhao
Regional innovation ecosystems (RIEs) are a new paradigm in innovation research, and the development of RIEs under digitization is constrained by the development of innovation environments. The study of ecological niche suitability of regional innovation environment provides the basis for the government to create an innovation environment suitable for the development of a regional innovation ecosystem. This paper conducts an empirical analysis based on panel data from 29 provinces (autonomous regions) in China from 2012 to 2021. The paper analyzes the suitability of the ecological niche of the innovation environment as well as the spatio-temporal evolution pattern of the regional innovation ecosystem under digitalization in China. The results of the study show that: (1) The innovation environment of regional innovation ecosystems under digitization in China has become increasingly suitable during the sample period. (2) From the perspective of evolution in time, the suitability of the ecological niche of the regional innovation environment has always maintained an evolutionary trend of rolling forward in the echelon. (3) From the perspective of spatial evolution, the center line of the curve of the development level of the suitability of the regional innovation environment shows a rightward shifting evolution.
区域创新生态系统(RIE)是创新研究的一种新范式,数字化条件下区域创新生态系统的发展受到创新环境发展的制约。区域创新环境的生态位适宜性研究为政府营造适合区域创新生态系统发展的创新环境提供了依据。本文基于中国 29 个省(自治区)2012-2021 年的面板数据进行了实证分析。本文分析了中国数字化下创新环境生态位的适宜性以及区域创新生态系统的时空演化模式。研究结果表明(1)样本期内,中国数字化背景下区域创新生态系统的创新环境适宜度不断提高。(2)从时间演进的角度看,区域创新环境生态位适宜度始终保持梯队滚动向前的演进趋势。(3)从空间演化角度看,区域创新环境适宜度发展水平曲线中心线呈右移演化趋势。
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引用次数: 0
Game-theory based truck platoon avoidance modes selection near the highway off-ramp in mixed traffic environment 混合交通环境下高速公路匝道附近基于博弈论的卡车排避模式选择
IF 3.1 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-07-18 DOI: 10.3389/fphy.2024.1371233
Yi Li, Lan Wang, Zhaoze Xuan, Wenzhe Shen
Introduction: The rise of autonomous vehicles has brought about a transformative shift in transportation, witnessing the coexistence of human-driven and autonomous vehicles on highways in the United States, Europe, and China. This coexistence poses challenges to traffic operations, particularly in intricate scenarios like highway ramps. The interaction between autonomous truck platoons, displaying heightened maneuverability, and human-driven vehicles has emerged as a critical concern. Consequently, this research aims to propose and investigate three avoidance modes (overall, gap and cross) employed by truck platoons, evaluating their comprehensive impact on human-driven vehicles.Methods: Multiple scenarios are simulated utilizing the Simulation of Urban Mobility (SUMO) software, collecting data on three distinctive avoidance modes concerning Travel Time (TT) and Time to Collision (TTC). Employing principles of game theory, a comprehensive assessment is undertaken to evaluate the traffic efficiency and safety of each mode. Comparative analyses against a no-avoidance baseline are conducted, offering a holistic evaluation of each mode’s applicability across diverse scenarios.Results: The findings highlight the commendable performance of gap mode and overall mode in enhancing traffic efficiency, while cross mode excels in fortifying traffic safety. Overall, the gap mode emerges as the optimal choice among the three.Discussion: This study introduces a game-theoretic approach to managing human-machine mixed traffic flow, establishing a foundational framework for theoretical research in decision-making for emerging mixed traffic environments. It considers safety and efficiency perspectives across different types of traffic entities. The insights gained contribute to the evolving discourse on the integration of autonomous vehicles into existing traffic systems, addressing the intricate challenges posed by the coexistence of various vehicle types on highways.
引言自动驾驶汽车的兴起给交通带来了变革,在美国、欧洲和中国的高速公路上,人类驾驶汽车和自动驾驶汽车共存。这种共存给交通运营带来了挑战,尤其是在高速公路匝道等复杂场景中。自动驾驶卡车队显示出更高的机动性,与人类驾驶车辆之间的互动已成为一个关键问题。因此,本研究旨在提出并研究卡车排采用的三种避让模式(整体、间隙和交叉),评估它们对人类驾驶车辆的综合影响:方法:利用城市交通仿真(SUMO)软件模拟多种场景,收集三种不同避让模式在行驶时间(TT)和碰撞时间(TTC)方面的数据。利用博弈论原理,对每种模式的交通效率和安全性进行综合评估。与不避让基线进行比较分析,全面评估了每种模式在不同场景下的适用性:结果:研究结果表明,间隙模式和整体模式在提高交通效率方面的表现值得称赞,而交叉模式则在加强交通安全方面表现出色。总体而言,间隙模式是三种模式中的最佳选择:本研究引入了一种博弈论方法来管理人机混合交通流,为新兴混合交通环境的决策理论研究建立了一个基础框架。它从安全和效率的角度考虑了不同类型的交通实体。所获得的见解有助于将自动驾驶车辆融入现有交通系统的讨论,解决高速公路上各种类型车辆共存所带来的复杂挑战。
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引用次数: 0
Introducing a new approach for modeling stock market prices using the combination of jump-drift processes 利用跳跃-漂移过程组合引入股市价格建模新方法
IF 3.1 3区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-07-18 DOI: 10.3389/fphy.2024.1402593
Ali Asghar Movahed, Houshyar Noshad
The stock price data are sampled at discrete times (e.g., hourly, daily, weekly, etc). When data are sampled at discrete times, they appear as a sequence of discontinuous jump events, even if they have been sampled from a continuous process. On the other hand, distinguishing between discontinuities due to finite sampling of the continuous stochastic process and real jump discontinuities in the sample path is often a challenging task. Such considerations, led us to the question: Can discrete data (e.g., stock price) be modeled using only jump-drift processes, regardless of whether the sampled time series originally belongs to the class of continuous processes or discontinuous processes? To answer this question, we built a stochastic dynamical equation in the general form <jats:inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>d</mml:mi><mml:mi>y</mml:mi><mml:mrow><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:mfenced></mml:mrow><mml:mo>=</mml:mo><mml:mover accent="true"><mml:mi>μ</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mi>d</mml:mi><mml:mi>t</mml:mi><mml:mo>+</mml:mo><mml:mrow><mml:msubsup><mml:mo>∑</mml:mo><mml:mrow><mml:mi>i</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mi>N</mml:mi></mml:msubsup><mml:mrow><mml:msub><mml:mi>ξ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mi>d</mml:mi><mml:msub><mml:mi>J</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mrow><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mrow></mml:mrow></mml:mrow></mml:math></jats:inline-formula>, which includes a deterministic drift term (<jats:inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mover accent="true"><mml:mi>μ</mml:mi><mml:mo>¯</mml:mo></mml:mover><mml:mi>d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:math></jats:inline-formula>) and a combination of stochastic terms with jumpy behaviors (<jats:inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>ξ</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mi>d</mml:mi><mml:msub><mml:mi>J</mml:mi><mml:mi>i</mml:mi></mml:msub><mml:mrow><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mrow></mml:math></jats:inline-formula>), and used it to model the log-price time series <jats:inline-formula><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>y</mml:mi><mml:mrow><mml:mfenced open="(" close=")" separators="|"><mml:mrow><mml:mi>t</mml:mi></mml:mrow></mml:mfenced></mml:mrow></mml:mrow></mml:math></jats:inline-formula>. In this article, we first introduce this equation in its simplest form, including a drift term and a stochastic term, and show that such a jump-drift equation is capable of reconstructing stock prices in Black-Scholes diffusion markets. Afterwards, we extend the equation by considering two jump
股价数据的采样时间是离散的(如每小时、每天、每周等)。当数据按离散时间采样时,即使它们是从连续过程中采样的,也会表现为一连串不连续的跳跃事件。另一方面,区分连续随机过程的有限采样导致的不连续性和采样路径中真正的跳跃不连续性往往是一项具有挑战性的任务。基于这些考虑,我们提出了一个问题:离散数据(如股票价格)能否只用跳跃漂移过程来建模,而不管采样的时间序列原本属于连续过程还是不连续过程?为了回答这个问题,我们建立了一个一般形式的随机动力学方程 dyt=μ¯dt+∑i=1NξidJit,其中包括一个确定性漂移项(μ¯dt)和一个具有跳跃行为的随机项组合(ξidJit),并用它来模拟对数价格时间序列 yt。在本文中,我们首先介绍该方程的最简单形式,包括一个漂移项和一个随机项,并证明这种跳跃-漂移方程能够重构布莱克-斯科尔斯扩散市场中的股票价格。之后,我们通过考虑两个跳跃过程来扩展该方程,并证明这种漂移-跳跃-跳跃方程能让我们比旧的跳跃-扩散模型更准确地重建跳跃-扩散市场中的股票价格。为了证明所提方法的实际应用,我们分析了现实世界的数据,包括两种不同股票的每日股价和两种不同时间跨度(每小时和每周)的黄金价格数据。我们的分析支持该方法的实际应用性。值得注意的是,所提出的方法是可扩展的,甚至可用于非金融研究领域。
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Frontiers in Physics
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