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Study of several probability distribution functions for the Klein–Kramers equation 克莱因-克拉默方程的几种概率分布函数研究
Pub Date : 2024-02-09 DOI: 10.1142/s0217984924502129
Yaxi Li, Yue Kai
In this paper, we take variable separation method to study Klein–Kramers (KK) equation. By choosing different eigenvalues and noise functions, we can get different probability density functions (PDFs) of KK equation. These PDFs contain not only normal distributions but also other distributions that correspond to anomalous diffusion phenomena. For example, power-law distribution, truncated Cauchy–Lorentz distribution, Weibull distribution, log-logistic distribution, Gamma distribution. We also show the 3D and 2D profiles of these PDFs to analyze the corresponding dynamic properties and illustrate the possible practical applications of these results. In addition, we also find some exact solutions that are not PDFs. They are also listed to ensure the completeness of the results and to illustrate the potential applications of these exact solutions.
本文采用变量分离法研究克莱因-克拉默斯(KK)方程。通过选择不同的特征值和噪声函数,我们可以得到 KK 方程的不同概率密度函数(PDF)。这些 PDF 不仅包含正态分布,还包含与异常扩散现象相对应的其他分布。例如,幂律分布、截断考奇-洛伦兹分布、威布尔分布、对数-逻辑分布、伽马分布。我们还展示了这些分布的三维和二维剖面,以分析相应的动态特性,并说明这些结果可能的实际应用。此外,我们还发现了一些非 PDF 的精确解。为了确保结果的完整性,并说明这些精确解的潜在应用,我们也列出了这些精确解。
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引用次数: 0
Study of several probability distribution functions for the Klein–Kramers equation 克莱因-克拉默方程的几种概率分布函数研究
Pub Date : 2024-02-09 DOI: 10.1142/s0217984924502129
Yaxi Li, Yue Kai
In this paper, we take variable separation method to study Klein–Kramers (KK) equation. By choosing different eigenvalues and noise functions, we can get different probability density functions (PDFs) of KK equation. These PDFs contain not only normal distributions but also other distributions that correspond to anomalous diffusion phenomena. For example, power-law distribution, truncated Cauchy–Lorentz distribution, Weibull distribution, log-logistic distribution, Gamma distribution. We also show the 3D and 2D profiles of these PDFs to analyze the corresponding dynamic properties and illustrate the possible practical applications of these results. In addition, we also find some exact solutions that are not PDFs. They are also listed to ensure the completeness of the results and to illustrate the potential applications of these exact solutions.
本文采用变量分离法研究克莱因-克拉默斯(KK)方程。通过选择不同的特征值和噪声函数,我们可以得到 KK 方程的不同概率密度函数(PDF)。这些 PDF 不仅包含正态分布,还包含与异常扩散现象相对应的其他分布。例如,幂律分布、截断考奇-洛伦兹分布、威布尔分布、对数-逻辑分布、伽马分布。我们还展示了这些分布的三维和二维剖面,以分析相应的动态特性,并说明这些结果可能的实际应用。此外,我们还发现了一些非 PDF 的精确解。为了确保结果的完整性,并说明这些精确解的潜在应用,我们也列出了这些精确解。
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引用次数: 0
First-principles study on the effects of Zr doping and interstitial H and O vacancy on the optoelectronic properties of β-Ga2O3 掺杂 Zr 以及间隙 H 和 O 空位对 β-Ga2O3 光电特性影响的第一性原理研究
Pub Date : 2024-02-09 DOI: 10.1142/s0217984924501999
Ding‐Du Chen, Shu‐Min Wen, Xin‐Ya Yang, Xia Liu, Er-Jun Zhao, Chun Ying
In this work, the electronic structure and optical properties of Zr-doped [Formula: see text]-Ga2O3 with interstitial H and O vacancies were studied by using first-principles generalized gradient approximation combined with the Hubbard U method based on density functional theory. The energy band structure, density of states, absorption spectrum, effective mass, mobility and conductivity of the doped system were calculated and analyzed. Results showed that the doped system was more stable under the Ga-rich condition than under the O-rich condition. With the increase in Zr doping concentration, the bandgap of the [Formula: see text]-Ga2O3 system gradually narrowed and the absorption spectrum of the system blue-shifted in the wavelength range of 162–275[Formula: see text]nm. System conductivity was enhanced by Zr doping, decreased by O vacancies and greatly improved by interstitial H. Therefore, doping Zr into the [Formula: see text]-Ga2O3 system is important for improving material properties and preparing electronic and optical devices.
本研究采用基于密度泛函理论的第一原理广义梯度近似和哈伯德 U 方法,研究了掺杂 Zr [式中:见正文] -Ga2O3 的电子结构和光学性质。计算并分析了掺杂体系的能带结构、态密度、吸收光谱、有效质量、迁移率和电导率。结果表明,掺杂体系在富含 Ga 的条件下比富含 O 的条件下更稳定。随着掺杂Zr浓度的增加,[式中:见正文]-Ga2O3体系的带隙逐渐变窄,体系的吸收光谱在波长162-275[式中:见正文]nm范围内发生蓝移。因此,在[式:见正文]-Ga2O3 体系中掺杂 Zr 对改善材料性能和制备电子及光学器件具有重要意义。
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引用次数: 0
Evidence for Vogel Fulcher behavior of the 50K-relaxation in (Tm+Ta) co-doped TiO2 ceramics 掺杂(Tm+Ta)的二氧化钛陶瓷中 50K 弛豫的沃格尔-富彻尔行为证据
Pub Date : 2024-02-09 DOI: 10.1142/s0217984924501987
Tianyu Li, W. Cao, Yingtang Zhang, Chunchang Wang
There is still no consensus about the relaxation behavior of the so-called 50[Formula: see text]K-relaxation in acceptor and donor co-doped TiO2 system. Herein, the relaxation behavior of the 50[Formula: see text]K-relaxation was investigated in (Tm[Formula: see text][Formula: see text][Formula: see text]Ta) co-doped rutile TiO2 ceramics. Dielectric properties of the sample were studied in the temperature range of 2–300[Formula: see text]K under 100 frequencies in the range of 102–106[Formula: see text]Hz. The sample shows a pronounced 50[Formula: see text]K-relaxation. Various relaxation behaviors of Arrhenius, Mott’s variable range hopping, and Vogel Fulcher laws were tried to describe the relaxation. The result indisputably evidences that the 50[Formula: see text]K-relaxation follows the Vogel Fulcher law. This work provides a heuristic hint to understand the fundamental physics underlying the colossal permittivity behavior in the acceptor and donor co-doped TiO2 ceramics system.
关于受体和供体共掺杂 TiO2 体系中所谓 50[式:见正文]K-弛豫的弛豫行为,目前仍未达成共识。本文研究了 50[式:见正文]K-弛豫在(Tm[式:见正文][式:见正文][式:见正文]Ta)共掺杂金红石型 TiO2 陶瓷中的弛豫行为。在 102-106[式:见正文]赫兹的 100 频率下,研究了样品在 2-300[式:见正文]K温度范围内的介电性能。样品显示出明显的 50[式:见正文]K-弛豫。我们尝试用阿伦尼乌斯、莫特变程跳变和沃格尔-富尔赫定律等各种弛豫行为来描述这种弛豫。结果无可争议地证明,50[公式:见正文]K-松弛遵循沃格尔-富尔赫定律。这项工作为理解受体和供体共掺杂 TiO2 陶瓷体系中巨大介电常数行为的基本物理原理提供了启发式提示。
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引用次数: 0
Evidence for Vogel Fulcher behavior of the 50K-relaxation in (Tm+Ta) co-doped TiO2 ceramics 掺杂(Tm+Ta)的二氧化钛陶瓷中 50K 弛豫的沃格尔-富彻尔行为证据
Pub Date : 2024-02-09 DOI: 10.1142/s0217984924501987
Tianyu Li, W. Cao, Yingtang Zhang, Chunchang Wang
There is still no consensus about the relaxation behavior of the so-called 50[Formula: see text]K-relaxation in acceptor and donor co-doped TiO2 system. Herein, the relaxation behavior of the 50[Formula: see text]K-relaxation was investigated in (Tm[Formula: see text][Formula: see text][Formula: see text]Ta) co-doped rutile TiO2 ceramics. Dielectric properties of the sample were studied in the temperature range of 2–300[Formula: see text]K under 100 frequencies in the range of 102–106[Formula: see text]Hz. The sample shows a pronounced 50[Formula: see text]K-relaxation. Various relaxation behaviors of Arrhenius, Mott’s variable range hopping, and Vogel Fulcher laws were tried to describe the relaxation. The result indisputably evidences that the 50[Formula: see text]K-relaxation follows the Vogel Fulcher law. This work provides a heuristic hint to understand the fundamental physics underlying the colossal permittivity behavior in the acceptor and donor co-doped TiO2 ceramics system.
关于受体和供体共掺杂 TiO2 体系中所谓 50[式:见正文]K-弛豫的弛豫行为,目前仍未达成共识。本文研究了 50[式:见正文]K-弛豫在(Tm[式:见正文][式:见正文][式:见正文]Ta)共掺杂金红石型 TiO2 陶瓷中的弛豫行为。在 102-106[式:见正文]赫兹的 100 频率下,研究了样品在 2-300[式:见正文]K温度范围内的介电性能。样品显示出明显的 50[式:见正文]K-弛豫。我们尝试用阿伦尼乌斯、莫特变程跳变和沃格尔-富尔赫定律等各种弛豫行为来描述这种弛豫。结果无可争议地证明,50[公式:见正文]K-松弛遵循沃格尔-富尔赫定律。这项工作为理解受体和供体共掺杂 TiO2 陶瓷体系中巨大介电常数行为的基本物理原理提供了启发式提示。
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引用次数: 0
First-principles study on the effects of Zr doping and interstitial H and O vacancy on the optoelectronic properties of β-Ga2O3 掺杂 Zr 以及间隙 H 和 O 空位对 β-Ga2O3 光电特性影响的第一性原理研究
Pub Date : 2024-02-09 DOI: 10.1142/s0217984924501999
Ding‐Du Chen, Shu‐Min Wen, Xin‐Ya Yang, Xia Liu, Er-Jun Zhao, Chun Ying
In this work, the electronic structure and optical properties of Zr-doped [Formula: see text]-Ga2O3 with interstitial H and O vacancies were studied by using first-principles generalized gradient approximation combined with the Hubbard U method based on density functional theory. The energy band structure, density of states, absorption spectrum, effective mass, mobility and conductivity of the doped system were calculated and analyzed. Results showed that the doped system was more stable under the Ga-rich condition than under the O-rich condition. With the increase in Zr doping concentration, the bandgap of the [Formula: see text]-Ga2O3 system gradually narrowed and the absorption spectrum of the system blue-shifted in the wavelength range of 162–275[Formula: see text]nm. System conductivity was enhanced by Zr doping, decreased by O vacancies and greatly improved by interstitial H. Therefore, doping Zr into the [Formula: see text]-Ga2O3 system is important for improving material properties and preparing electronic and optical devices.
本研究采用基于密度泛函理论的第一原理广义梯度近似和哈伯德 U 方法,研究了掺杂 Zr [式中:见正文] -Ga2O3 的电子结构和光学性质。计算并分析了掺杂体系的能带结构、态密度、吸收光谱、有效质量、迁移率和电导率。结果表明,掺杂体系在富含 Ga 的条件下比富含 O 的条件下更稳定。随着掺杂Zr浓度的增加,[式中:见正文]-Ga2O3体系的带隙逐渐变窄,体系的吸收光谱在波长162-275[式中:见正文]nm范围内发生蓝移。因此,在[式:见正文]-Ga2O3 体系中掺杂 Zr 对改善材料性能和制备电子及光学器件具有重要意义。
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引用次数: 0
Results validation by using finite volume method for the blood flow with magnetohydrodynamics and hybrid nanofluids 利用有限体积法对磁流体动力学和混合纳米流体的血流进行结果验证
Pub Date : 2024-02-09 DOI: 10.1142/s0217984924502087
J. A. Haider, Shahbaz Ahmad, H. A. Ghazwani, Mohamed Hussien, M. Almusawa, Emad A. Az-Zo’bi
This paper conducts an extensive comparative analysis of numerical methods employed in modeling blood flow through arteries with Magnetohydrodynamics (MHD) and hybrid nanofluids. The study investigates the effectiveness and precision of distinct numerical approaches: Akbari Ganji’s Method (AGM), Fourth-Order Runge–Kutta (RK4), Finite Volume Method (FVM), and the Finite Element Method (FEM). These methods are essential for comprehending the intricate fluid dynamics that arise in the presence of magnetic fields and hybrid nanofluids a phenomenon relevant in numerous medical applications. Blood flow is subjected to a homogeneous magnetic field in a radial direction while the magneto-hemodynamics effect is taken into account. A variety of medical, physiological, and surgical procedures, as well as the regulation of blood pressure, heat distribution, wound healing, diagnostic imaging, and drug discovery, depend on blood flow through arteries to carry out vital functions such as oxygen and nutrition delivery, organ maintenance, and wound healing. Our findings highlight that while each method has strengths, their applicability varies based on the problem’s characteristics and computational resource constraints. This analysis aids researchers and practitioners in selecting the most suitable method for their modeling requirements, advancing numerical techniques for complex fluid dynamics involving MHD and hybrid nanofluids.
本文对利用磁流体动力学(MHD)和混合纳米流体对流经动脉的血流进行建模时所采用的数值方法进行了广泛的比较分析。研究调查了不同数值方法的有效性和精确性:Akbari Ganji 方法 (AGM)、四阶 Runge-Kutta (RK4)、有限体积法 (FVM) 和有限元方法 (FEM)。这些方法对于理解磁场和混合纳米流体存在时产生的错综复杂的流体动力学是必不可少的。血流在径向方向上受到均匀磁场的作用,同时考虑到磁流体动力学效应。各种医疗、生理和外科手术,以及血压调节、热分布、伤口愈合、诊断成像和药物研发,都依赖于动脉血流来实现氧气和营养输送、器官维护和伤口愈合等重要功能。我们的研究结果突出表明,虽然每种方法都有其优势,但根据问题的特点和计算资源的限制,它们的适用性各不相同。这项分析有助于研究人员和从业人员根据建模要求选择最合适的方法,推动涉及 MHD 和混合纳米流体的复杂流体动力学数值技术的发展。
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引用次数: 0
Photoelectric properties of monolayer 1T-CrS2 modified by doping non-metal atoms under strains 掺杂非金属原子修饰的单层 1T-CrS2 在应变条件下的光电特性
Pub Date : 2024-02-02 DOI: 10.1142/s0217984924502026
Huaidong Liu, Lu Yang, Shihang Sun, Yanshen Zhao, Xingbin Wei
Based on the first principle, the change of photoelectric properties of non-metal-doped CrS2 under biaxial tension was studied. The formation energy indicates that the doping system is stable. Studies have shown that the partial doping system achieves a semiconductor metal phase transition. The strain opens the bandgap of the F-doped system, and the system changes from metal to n-type semiconductor. The Te-doped system realizes the transition from indirect bandgap to direct bandgap under the adjustment of 2% strain. The O and Se doping systems realize the reverse regulation of the bandgap under strain, and the conductivity gradually increases with the increase of strain. The absorption efficiency of Te doping under a certain strain is significantly enhanced, the static dielectric properties of the F doping system are increased by more than two times, the absorption spectrum response range is increased, and the absorption capacity of the system is enhanced. This lays a foundation for applying monolayer CrS2 in microelectronics and optoelectronics.
基于第一原理,研究了非金属掺杂的 CrS2 在双轴拉力作用下的光电特性变化。形成能表明掺杂体系是稳定的。研究表明,部分掺杂体系实现了半导体金属相变。应变打开了掺杂 F 的体系的带隙,体系从金属转变为 n 型半导体。掺杂 Te 的体系在 2% 的应变调节下实现了从间接带隙到直接带隙的转变。O 和 Se 掺杂体系在应变作用下实现了带隙的反向调节,电导率随应变的增加而逐渐增大。在一定应变下,Te 掺杂的吸收效率显著提高,F 掺杂体系的静态介电性能提高了两倍以上,吸收光谱响应范围增大,体系的吸收能力增强。这为单层 CrS2 在微电子学和光电子学中的应用奠定了基础。
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引用次数: 0
Photoelectric properties of monolayer 1T-CrS2 modified by doping non-metal atoms under strains 掺杂非金属原子修饰的单层 1T-CrS2 在应变条件下的光电特性
Pub Date : 2024-02-02 DOI: 10.1142/s0217984924502026
Huaidong Liu, Lu Yang, Shihang Sun, Yanshen Zhao, Xingbin Wei
Based on the first principle, the change of photoelectric properties of non-metal-doped CrS2 under biaxial tension was studied. The formation energy indicates that the doping system is stable. Studies have shown that the partial doping system achieves a semiconductor metal phase transition. The strain opens the bandgap of the F-doped system, and the system changes from metal to n-type semiconductor. The Te-doped system realizes the transition from indirect bandgap to direct bandgap under the adjustment of 2% strain. The O and Se doping systems realize the reverse regulation of the bandgap under strain, and the conductivity gradually increases with the increase of strain. The absorption efficiency of Te doping under a certain strain is significantly enhanced, the static dielectric properties of the F doping system are increased by more than two times, the absorption spectrum response range is increased, and the absorption capacity of the system is enhanced. This lays a foundation for applying monolayer CrS2 in microelectronics and optoelectronics.
基于第一原理,研究了非金属掺杂的 CrS2 在双轴拉力作用下的光电特性变化。形成能表明掺杂体系是稳定的。研究表明,部分掺杂体系实现了半导体金属相变。应变打开了掺杂 F 的体系的带隙,体系从金属转变为 n 型半导体。掺杂 Te 的体系在 2% 的应变调节下实现了从间接带隙到直接带隙的转变。O 和 Se 掺杂体系在应变作用下实现了带隙的反向调节,电导率随应变的增加而逐渐增大。在一定应变下,Te 掺杂的吸收效率显著提高,F 掺杂体系的静态介电性能提高了两倍以上,吸收光谱响应范围增大,体系的吸收能力增强。这为单层 CrS2 在微电子学和光电子学中的应用奠定了基础。
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引用次数: 0
Electronic and optical properties of strain-regulated O-doped monolayer MoS2 应变调节 O 掺杂单层 MoS2 的电子和光学特性
Pub Date : 2024-02-02 DOI: 10.1142/s0217984924502002
Xuewen Gao, Ying Wang, Qing Su, Yan Su, Mengmeng Zhao, Yilin Wang, Guili Liu, Guoying Zhang
The effect of biaxial strain on O-doped monolayers MoS2 has been systematically studied by the first-principles calculations. It is shown that the strain decreases the structural stability of O-doped monolayer MoS2. Between 0% and 12% tensile strains, the bandgap steadily narrows. At different compression strains, the bandgap increases and then decreases. The optical properties analysis shows that the strain causes the peaks of both the real and imaginary parts of the dielectric function to appear in the low energy region. And it affects the absorption and reflection peaks of the doping system so that it has a strong absorption of photons in the ultraviolet region. The doping system shows resonance in the range of 0–10[Formula: see text]eV. The results of this study verify that strain can properly regulate the electronic and optical properties of O-doped monolayer MoS2, and provide a theoretical reference for the implementation of MoS2 in optoelectronic devices.
通过第一性原理计算,系统地研究了双轴应变对掺杂 O 的单层 MoS2 的影响。结果表明,应变会降低掺杂 O 的单层 MoS2 的结构稳定性。在 0% 到 12% 的拉伸应变之间,带隙逐渐变窄。在不同的压缩应变下,带隙先增大后减小。光学特性分析表明,应变会导致介电函数的实部和虚部的峰值出现在低能区。应变还影响了掺杂系统的吸收峰和反射峰,使其在紫外区对光子有很强的吸收。掺杂体系在 0-10[式中:见正文]eV 范围内出现共振。该研究结果验证了应变可以适当调节 O 掺杂单层 MoS2 的电子和光学特性,为 MoS2 在光电器件中的应用提供了理论参考。
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引用次数: 0
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Modern Physics Letters B
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