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Analysis of nonlinear fractional-order Fisher equation using two reliable techniques 利用两种可靠技术分析非线性分数阶费雪方程
IF 1.9 4区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-05-11 DOI: 10.1515/phys-2023-0185
Hijaz Ahmad, Muhammad Farooq, Ibrar Khan, Rashid Nawaz, Nicholas Fewster-Young, Sameh Askar
In this article, the solution to the time-fractional Fisher equation is determined using two well-known analytical techniques. The suggested approaches are the new iterative method and the optimal auxiliary function method, with the fractional derivative handled in the Caputo sense. The obtained results demonstrate that the suggested approaches are efficient and simple to use for solving fractional-order differential equations. The approximate and exact solutions of the partial fractional differential equations for integer order were compared. Additionally, the fractional-order and integer-order results are contrasted using simple tables. It has been confirmed that the solution produced using the provided methods converges to the exact solution at the appropriate rate. The primary advantage of the suggested method is the small number of computations needed. Moreover, it may be used to address fractional-order physical problems in a number of fields.
本文利用两种著名的分析技术确定了时间分数费雪方程的解。所建议的方法是新迭代法和最优辅助函数法,并在 Caputo 意义上处理分数导数。所得结果表明,所建议的方法在求解分数阶微分方程时既高效又简单。比较了整数阶分数偏微分方程的近似解和精确解。此外,还使用简单的表格对比了分数阶和整数阶的结果。结果证实,使用所提供的方法得出的解能以适当的速度收敛到精确解。建议方法的主要优点是所需计算量少。此外,它还可用于解决多个领域的分数阶物理问题。
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引用次数: 0
Influence of variable viscosity on existing sheet thickness in the calendering of non-isothermal viscoelastic materials 非等温粘弹性材料压延过程中粘度变化对现有板材厚度的影响
IF 1.9 4区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-05-10 DOI: 10.1515/phys-2024-0023
Muhammad Zahid, Fateh Ali, Basma Souayeh, Muhammad Tahir Khan
The calendering process is pivotal in enhancing various materials’ surface properties and characteristics, making them indispensable for achieving desired product quality and performance. Also, this process holds significant relevance in various industrial applications, such as polymer processing, food production, and the manufacturing of composite materials. So, the aim of this study is to theoretically examine the calendering process applied to third-grade materials. It specifically explores how temperature variations impact material behavior during passage through two counter-rotating heated rolls. Particular consideration is given to the influence of temperature-dependent viscosity via Reynold’s model. The complexities of mass, momentum, and energy balance equations are reduced through the application of the Lubrication approximation theory. Solutions to these equations for variables such as velocity, flow rate, and temperature fields are accomplished by combining perturbation and numerical techniques. In relation to the calendering process, the thickness of the exiting sheet is specifically explored. Furthermore, this study quantifies substantial engineering parameters such as roll-separating force, pressure distribution, and power transferal from the rolls to the fluid. The governing equations belong to three key dimensionless parameters, namely, the Brinkman number, which is a product of Eckert number and Prandtl number, the temperature-dependent consistency index μ mu , and a parameter η eta correlating to non-Newtonian behavior. The outcomes of this study are presented both graphically and in tabular form. It has been observed that a rise in the third-grade parameter decreases detachment point and sheet thickness due to increased material rigidity. Furthermore, established results in the literature regarding the calendering of Newtonian fluids are validated.
压延工艺在提高各种材料的表面性能和特性方面起着关键作用,是实现理想产品质量和性能所不可或缺的。此外,该工艺在聚合物加工、食品生产和复合材料制造等各种工业应用中也具有重要意义。因此,本研究旨在从理论上研究应用于第三级材料的压延工艺。它特别探讨了温度变化如何影响材料在通过两个反向旋转的加热辊时的行为。通过雷诺模型,特别考虑了与温度相关的粘度的影响。通过应用润滑近似理论,降低了质量、动量和能量平衡方程的复杂性。速度、流速和温度场等变量方程的解决方案是通过结合扰动和数值技术来实现的。在压光过程中,还特别探讨了流出板材的厚度。此外,这项研究还量化了重要的工程参数,如轧辊分离力、压力分布以及从轧辊到流体的功率传递。控制方程属于三个关键的无量纲参数,即布林克曼数(它是埃克特数和普朗特数的乘积)、与温度相关的稠度指数 μ mu 以及与非牛顿行为相关的参数 η eta 。研究结果以图表形式呈现。研究发现,由于材料刚度增加,第三级参数的增加会降低脱离点和板材厚度。此外,文献中有关牛顿流体压延的既定结果也得到了验证。
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引用次数: 0
Transformer-based intelligent fault diagnosis methods of mechanical equipment: A survey 基于变压器的机械设备智能故障诊断方法:调查
IF 1.9 4区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-05-10 DOI: 10.1515/phys-2024-0015
Rongcai Wang, Enzhi Dong, Zhonghua Cheng, Zichang Liu, Xisheng Jia
Transformer is extensively employed in natural language processing, and computer vision (CV), with the self-attention structure. Due to its outstanding long-range dependency modeling and parallel computing capability, some leading researchers have recently attempted to apply Transformer to intelligent fault diagnosis tasks for mechanical equipment, and have achieved remarkable results. Physical phenomena such as changes in vibration, sound, and heat play a crucial role in the research of mechanical equipment fault diagnosis, which directly reflects the operational status and potential faults of mechanical equipment. Currently, intelligent fault diagnosis of mechanical equipment based on monitoring signals such as vibration, sound, and temperature using Transformer-based models remains a popular research topic. While some review literature has explored the related principles and application scenarios of Transformer, there is still a lack of research on its application in intelligent fault diagnosis tasks for mechanical equipment. Therefore, this work begins by examining the current research status of fault diagnosis methods for mechanical equipment. This study first provides a brief overview of the development history of Transformer, outlines its basic structure and principles, and analyzes the characteristics and advantages of its model structure. Next it focuses on three model variants of Transformer that have generated a significant impact in the field of CV. Following that, the research progress and current challenges of Transformer-based intelligent fault diagnosis methods for mechanical equipment are discussed. Finally, the future development direction of Transformer in the field of mechanical equipment fault diagnosis is proposed.
Transformer 具有自注意结构,在自然语言处理和计算机视觉(CV)中得到广泛应用。由于其出色的远距离依赖建模和并行计算能力,最近一些领先的研究人员尝试将 Transformer 应用于机械设备的智能故障诊断任务,并取得了显著的成果。振动、声音、热量等物理现象的变化在机械设备故障诊断研究中起着至关重要的作用,它直接反映了机械设备的运行状态和潜在故障。目前,利用基于变压器的模型,基于振动、声音和温度等监测信号的机械设备智能故障诊断仍是一个热门研究课题。虽然一些综述性文献探讨了变压器的相关原理和应用场景,但对其在机械设备智能故障诊断任务中的应用仍缺乏研究。因此,本研究首先探讨了机械设备故障诊断方法的研究现状。本研究首先简要介绍了变压器的发展历史,概述了其基本结构和原理,分析了其模型结构的特点和优势。接着,重点介绍了在 CV 领域产生重大影响的三种变压器模型变体。随后,讨论了基于变压器的机械设备智能故障诊断方法的研究进展和当前面临的挑战。最后,提出了 Transformer 在机械设备故障诊断领域的未来发展方向。
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引用次数: 0
Numerical study on bionic airfoil fins used in printed circuit plate heat exchanger 关于印刷电路板热交换器中使用的仿生翼翅的数值研究
IF 1.9 4区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-05-10 DOI: 10.1515/phys-2023-0200
Chulin Yu, Binfeng Liu, Yulin Cui, Wenqing Wang, Yuxi Yang
Airfoil printed circuit heat exchangers (PCHEs) possess exceptional comprehensive performance. In recent years, extensive research has been conducted on the layout and structure optimization of airfoil fins. As biomimetic technologies gradually mature, bionics has achieved numerous outcomes in optimizing airfoil aerodynamic characteristic. Inspired by the sailfish geometry, four types of bionic airfoils are proposed based on the NACA 0015 airfoil, to enhance the thermal-hydraulic performance of the airfoil PCHEs. The results show that while the four types of sailfish airfoils are effective in terms of drag reduction, their overall performance at the same pumping power is suboptimal, with only one type providing an advantage at the low Re region. Moreover, airfoils with concave head curves further increase the weakening of heat transfer by the velocity boundary layer.
机翼印制电路热交换器(PCHE)具有优异的综合性能。近年来,人们对机翼翅片的布局和结构优化进行了广泛的研究。随着仿生技术的逐渐成熟,仿生学在优化机翼气动特性方面取得了众多成果。受旗鱼几何形状的启发,研究人员在 NACA 0015 机翼的基础上提出了四种仿生机翼,以提高机翼 PCHE 的热液压性能。结果表明,虽然四种类型的旗鱼翼面都能有效减少阻力,但在相同抽气功率下,它们的整体性能并不理想,只有一种类型的翼面在低 Re 区域具有优势。此外,具有凹形头部曲线的机翼会进一步加剧速度边界层对热传递的削弱。
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引用次数: 0
Analytical and numerical investigation for viscoelastic fluid with heat transfer analysis during rollover-web coating phenomena 带热传导分析的粘弹性流体在翻转网状涂层现象中的分析和数值研究
IF 1.9 4区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-05-07 DOI: 10.1515/phys-2024-0024
Fateh Ali, Muhammad Zahid, Basma Souayeh, Farwa Asmat, Chinedu Nwaigwe
The current study theoretically and computationally analyses the viscoelastic Sisko fluids during the non-isothermal rollover web phenomenon. The mathematical modeling produces a system of partial differential equations, which we further simplify into ordinary differential equations through appropriate transformations. We have formulated the problem based on the lubrication approximation theory. The solution has been obtained with the perturbation method, and the outcomes are found in mathematical, tabular, and graphical forms that highlight the influence of pertinent parameters on velocity profiles, pressure gradients, flow rates per unit width, Nusselt number, pressure profile, temperature distributions, and other significant engineering quantities. Further, A comparative analysis between analytic and numerical solutions, utilizing the middefer method in the Maple environment, demonstrates reasonable agreement. Also, we observe that the fluid parameter significantly influences both velocity and temperature profiles. Moreover, the determination of a separation point 2.5000, accompanied by the observation of a maximum coating thickness of 0.6960. The enhancement in fluid heat transfer rate is approximately 5% compared to non-Newtonian fluid parameter values, with potential for further improvement by increasing the non-Newtonian parameter values. This comprehensive investigation offers valuable insights for practical implementation and future scholarly endeavors, with zero-order findings showcasing enhanced precision.
本研究从理论和计算角度分析了非等温翻滚网现象中的粘弹性西斯科流体。数学建模产生了一个偏微分方程系,我们通过适当的变换将其进一步简化为常微分方程。我们根据润滑近似理论对问题进行了表述。结果以数学、表格和图形的形式呈现,突出了相关参数对速度剖面、压力梯度、单位宽度流速、努塞尔特数、压力剖面、温度分布和其他重要工程量的影响。此外,利用 Maple 环境中的 middefer 方法,对解析解和数值解进行了比较分析,结果表明两者之间存在合理的一致性。同时,我们还发现流体参数对速度和温度曲线都有显著影响。此外,我们还确定了分离点 2.5000,并观察到最大涂层厚度为 0.6960。与非牛顿流体参数值相比,流体传热速率提高了约 5%,通过增加非牛顿流体参数值,有可能进一步提高传热速率。这项全面的研究为实际应用和未来的学术研究提供了宝贵的见解,零阶研究结果表明精度得到了提高。
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引用次数: 0
Numerical analysis of the MHD Williamson nanofluid flow over a nonlinear stretching sheet through a Darcy porous medium: Modeling and simulation 通过达西多孔介质对非线性拉伸片上的 MHD 威廉姆森纳米流体流动进行数值分析:建模与模拟
IF 1.9 4区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-05-04 DOI: 10.1515/phys-2024-0016
Mohamed M. Khader, Hijaz Ahmad, Mohamed Adel, Ahmed M. Megahed
In the current study, we delve into examining the movement of a nanofluid within a Williamson boundary layer, focusing on the analysis of heat and mass transfer (HMT) processes. This particular flow occurs over a sheet that undergoes nonlinear stretching. A significant facet of this investigation involves the incorporation of both the magnetic field and the influence of viscous dissipation within the model. The sheet is situated within a porous medium, and this medium conforms to the Darcy model. Since more precise outcomes are still required, the model assumes that both fluid conductivity and viscosity change with temperature. In this research, we encounter a system of extremely nonlinear ordinary differential equations that are treated through a numerical technique, specifically by employing the spectral collocation method. Graphical representations are used to illustrate how the relevant parameters impact the nanoparticle volume fraction, velocity, and temperature profiles. The study involves the computation and analysis of the effect of physical parameters on the local Sherwood number, skin friction coefficient, and local Nusselt number. Specific significant findings emerging from the present study highlight that the rate of mass transfer is particularly influenced by the thermophoresis factor, porous parameter, and Williamson parameter, showing heightened effects, while conversely, the Brownian motion parameter demonstrates an opposing pattern. The results were computed and subjected to a comparison with earlier research, indicating a notable degree of conformity and accord.
在当前的研究中,我们深入研究了纳米流体在威廉姆森边界层内的运动,重点分析了热量和质量传递(HMT)过程。这种特殊的流动发生在经历非线性拉伸的薄片上。这项研究的一个重要方面是在模型中加入磁场和粘性耗散的影响。薄片位于多孔介质中,该介质符合达西模型。由于还需要更精确的结果,该模型假定流体的导电性和粘度都会随温度变化。在这项研究中,我们遇到了一个极其非线性的常微分方程系统,该系统通过数值技术进行处理,特别是采用了谱配位法。使用图形表示法来说明相关参数如何影响纳米粒子的体积分数、速度和温度曲线。研究包括计算和分析物理参数对局部舍伍德数、皮肤摩擦系数和局部努塞尔特数的影响。本研究得出的具体重要发现突出表明,热泳系数、多孔参数和威廉姆森参数对传质速率的影响尤为明显,显示出更高的效应,而反之,布朗运动参数则显示出相反的模式。对结果进行了计算,并与之前的研究进行了比较,结果表明两者在很大程度上是一致的。
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引用次数: 0
Prediction of COVID-19 spread with models in different patterns: A case study of Russia 利用不同模式的模型预测 COVID-19 的传播:俄罗斯案例研究
IF 1.9 4区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-04-29 DOI: 10.1515/phys-2024-0009
Mehmet Akif Cetin, Seda Igret Araz
This study deals with a mathematical model that examines the spread of Coronavirus disease (COVID-19). This model has been handled with different processes such as deterministic, stochastic, and deterministic–stochastic. First of all, a detailed analysis is presented for the deterministic model, which includes the positivity of the solution, the basic reproduction number, the disease, and endemic equilibrium points. Then, for the stochastic model, we investigate under which conditions, the solution exists and is unique. Later, model is reconsidered with the help of the piecewise derivative, which can combine deterministic and stochastic processes. Numerical simulations are presented for all these processes. Finally, the model has been modified with the rate indicator function. The model presenting these four different situations is compared with the real data in Russia. According to the results obtained from these situations, the model that is obtained by adding the rate indicator function predicts the COVID-19 outbreak in Russia more accurately. Thus, it is concluded that the model with the rate indicator function presents more realistic approach than the previous ones.
本研究涉及一个研究冠状病毒病(COVID-19)传播的数学模型。该模型采用了不同的过程,如确定性过程、随机过程和确定性-随机过程。首先,对确定性模型进行了详细分析,包括解的正向性、基本繁殖数、疾病和流行平衡点。然后,对于随机模型,我们研究了在哪些条件下解法存在且是唯一的。之后,在片断导数的帮助下对模型进行了重新考虑,这可以将确定性过程和随机过程结合起来。对所有这些过程都进行了数值模拟。最后,利用速率指示函数对模型进行了修改。将呈现这四种不同情况的模型与俄罗斯的实际数据进行了比较。根据这些情况得出的结果,加入速率指标函数后得到的模型能更准确地预测俄罗斯 COVID-19 的爆发。因此,可以得出结论,与之前的模型相比,带有速率指标函数的模型更符合实际情况。
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引用次数: 0
Study of ultrasonic influence on heat transfer and resistance performance of round tube with twisted belt 研究超声波对扭带圆管传热和阻力性能的影响
IF 1.9 4区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-04-26 DOI: 10.1515/phys-2023-0183
Yuxi Yang, Hongyan Liu, Chulin Yu, Wenqing Wang, Xiaohan Lv, Haiqing Zhang
In this study, ultrasonic technology is combined with twisted belts to explore the comprehensive performance, and this study also investigated the effect of different Reynolds numbers, ultrasonic frequencies, and number of transducers on the performance of circular and twisted band tubes. It was found that ultrasonic waves applied on the tube plate enhanced the heat transfer performance of the heat exchanger tubes, reduced the flow resistance, and improved the overall performance, and the lower the ultrasonic frequency, the better the heat transfer and resistance reduction ability, and at the experimental condition frequency of 21 kHz, the maximum increase of Nu is 19.06%. With the increase of Reynolds number, the better the ultrasonic enhancement heat transfer performance, but the worse the resistance reduction performance. For different heat exchanger tube structures, the synergistic enhanced heat transfer effect of ultrasonic waves with the twisted belt is better than round tubes, and the synergistic drag reduction effect with the round tube is better than the twisted tape round tube. When the installed ultrasonic transducers are two, the heat transfer performance of the heat exchanger tube is the best, and the maximum increase in the value of Nu was 28.06%.
本研究将超声波技术与扭曲带相结合,探索其综合性能,本研究还考察了不同雷诺数、超声波频率和换能器数量对圆形管和扭曲带管性能的影响。研究发现,在管板上施加超声波可增强换热管的传热性能,降低流动阻力,改善综合性能,且超声波频率越低,传热和降阻能力越强,在实验条件频率为 21 kHz 时,Nu 的最大增幅为 19.06%。随着雷诺数的增加,超声波增强传热性能越好,但减阻性能越差。对于不同的换热管结构,超声波与扭曲带的协同强化传热效果优于圆管,与圆管的协同减阻效果优于扭曲带圆管。当安装的超声波换能器为两个时,换热管的传热性能最好,Nu 值的最大增幅为 28.06%。
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引用次数: 0
A comparative analysis of shielding effectiveness in glass and concrete containers 玻璃容器和混凝土容器屏蔽效果的比较分析
IF 1.9 4区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-04-25 DOI: 10.1515/phys-2024-0019
Ghada ALMisned, Duygu Sen Baykal, Wiam Elshami, Gulfem Susoy, Gokhan Kilic, Huseyin Ozan Tekin
Nuclear waste control and related equipment play a vital role in safeguarding human health and the environment from the potential dangers of radioactive waste. This study addresses the critical challenge of enhancing the shielding effectiveness of container materials for nuclear waste management, with a focus on comparing the attenuation properties of glass and concrete composites. Our analysis revealed that the copper oxide-reinforced borosilicate glass container demonstrated a significant transmission factor (TF) value decrease by approximately 15% compared to steel–magnetite concrete at 1.3325 MeV, with a standard deviation of ±1.5%, indicating its lower protective characteristics. Nonetheless, it exhibited a 10% higher TF reduction compared to the cement–bitumen mix at the same energy level, with a precision error of ±1.2%. In addition, the half-value layer for this glass was determined to be 2.5 cm for 1.3325 MeV gamma rays, showing moderate shielding capacity. The study demonstrates that optimizing the oxide content in the borosilicate glass matrix significantly enhances its shielding effectiveness. This advancement in nuclear waste management materials is justified by our comprehensive evaluation, highlighting the potential of optimized glass materials to outperform traditional concrete in certain scenarios, thus contributing to the development of more effective nuclear waste containment solutions.
核废料控制及相关设备在保护人类健康和环境免受放射性废物潜在危险方面发挥着至关重要的作用。本研究探讨了如何提高核废料管理容器材料的屏蔽效果这一重大挑战,重点是比较玻璃和混凝土复合材料的衰减特性。我们的分析表明,与钢磁铁矿混凝土相比,氧化铜增强的硼硅酸盐玻璃容器在 1.3325 MeV 下的透射系数 (TF) 值显著降低了约 15%,标准偏差为 ±1.5%,表明其防护特性较低。不过,在相同的能量水平下,与水泥-沥青混合料相比,其 TF 值降低了 10%,精度误差为 ±1.2%。此外,对于 1.3325 MeV 伽马射线,这种玻璃的半值层被确定为 2.5 厘米,显示出中等的屏蔽能力。研究表明,优化硼硅玻璃基体中的氧化物含量可显著提高其屏蔽效果。我们的综合评估证明了核废料管理材料的这一进步,强调了优化玻璃材料在某些情况下优于传统混凝土的潜力,从而有助于开发更有效的核废料封隔解决方案。
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引用次数: 0
Numerical simulations for fractional Hirota–Satsuma coupled Korteweg–de Vries systems 分数 Hirota-Satsuma 耦合 Korteweg-de Vries 系统的数值模拟
IF 1.9 4区 物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY Pub Date : 2024-04-23 DOI: 10.1515/phys-2024-0008
Abdul Hamid Ganie, Saima Noor, Maryam Al Huwayz, Ahmad Shafee, Samir A. El-Tantawy
In this investigation, the fractional Hirota–Satsuma coupled Korteweg–de Vries (KdV) problem is solved using two modern semi-analytic techniques known as the Aboodh residual power series method (ARPSM) and Aboodh transform iteration method (ATIM). The two suggested approaches are briefly explained, along with how to use them to solve the fractional Hirota–Satsuma coupled KdV problem. Some analytical approximate solutions for the current problem are derived using the proposed techniques until the second-order approximation. To ensure high accuracy of the derived approximation, they are analyzed numerically and graphically and compared with the exact solutions of the integer cases. The offered techniques demonstrate more accuracy in their outcomes compared to other alternatives. The numerical results show that ARPSM and ATIM are highly accurate, practical, and beneficial for solving nonlinear equation systems. The current results are expected to help many physics researchers in modeling their different physical problems, especially those interested in plasma physics.
在本研究中,使用了两种现代半解析技术,即阿布德残差幂级数法(ARPSM)和阿布德变换迭代法(ATIM),解决了分数广田-萨摩耦合 Korteweg-de Vries(KdV)问题。本文简要介绍了这两种建议的方法,以及如何使用它们求解分数 Hirota-Satsuma 耦合 KdV 问题。使用所建议的技术推导出了当前问题的一些分析近似解,直到二阶近似。为确保推导近似解的高精度,对其进行了数值和图形分析,并与整数情况下的精确解进行了比较。与其他替代方法相比,所提供的技术在结果上表现出更高的准确性。数值结果表明,ARPSM 和 ATIM 在求解非线性方程系统方面具有很高的准确性、实用性和效益。目前的研究成果有望帮助许多物理研究人员,尤其是对等离子体物理感兴趣的研究人员,对不同的物理问题进行建模。
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引用次数: 0
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Open Physics
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