bluuebunny/crossref_metadata_2025_split huggingface dataset:
Calculus of a kind of improper integral
Authors: Pan Yuefeng , Shi Menghan , Shen Tianle 
Published: September 2021

Abstract
The calculation of improper integral is of great importance. In this paper, we consider a kind of real improper integral using the method of complex analysis and prove the equation

∫
0
∞

x
α

(
1
+

x
β

)
x

d
x

=

π

β

sin

α
π

β

. Firstly we give the condition for the convergence of the improper integral

∫
0
∞

x
α

(
1
+

x
β

)
x

d
x

when

0
<
α
<
β

, so we can see the integrand as a complex function. This function is defined on a simply connected set not containing zero to ensure that the function is holomorphic. We use three methods to prove the equation. In the first method, we choose a certain closed path as the boundary of the simply connected set, compute the integral along the path by the Residue Formula according to Cauchy’s Theorem, and obtain the value of the real improper integral. In the second method, we use Mellin transform, while the idea is similar to that of the Residue Formula. In the third method, we find that the path we choose becomes simpler by a variable substitution. The function that is integrated along the new path does not have the problem of multivaluedness, so we do not have to define it on a simply connect set. Moreover, using the method of complex analysis, we prove that the equation holds when α, β are complex numbers, and the condition is about the real parts of α and β, i.e.,

0
<
ℜ
α
<
ℜ
β

. The real improper integral is just a particular case where α, β are real numbers. We compute the value of such kind of complex improper integral by some calculation and simplification, which is exactly

π

β

sin

α
π

β

. We find the relationship between this integral and gamma function. The equation can prove a property of gamma function. We prove that the equation holds when α, β are complex numbers, and the condition becomes

0
<
ℜ
α
<
ℜ
β

. We hope that this can be used in the research of more properties of the gamma function. The proof of the equation reminds us of a way of calculating such kinds of real improper integrals.
Finite difference method based on polynomial interpolation for solving Helmholtz equation
Authors: Zhang Zihan , Fang Silong 
Published: September 2021

Abstract
The generalized finite difference formula plays an important role in the meshless method for solving differential equations. The main purpose of this paper is to find the numerical solution of Helmholtz equation, an elliptic partial differential equation describing electromagnetic waves in physics, by using the generalized finite difference formula. Firstly, this paper introduces a simple and practical nodal distribution, which not only guarantees the uniqueness of multivariate polynomial interpolation, but also makes the matrix triangular, so that the constructed basic polynomials can be transformed into Lagrange basis polynomials. Secondly, the generalized finite difference formula is created by polynomial interpolation. Finally, a numerical example of Helmholtz equation under general boundary conditions is given.
Numerical simulation of nozzle flow based on Euler equation
Authors: Li Qiaoxin , Qin Xu , Qu Ruixin , Wang Jiaqi 
Published: September 2021

Abstract
In this paper, the Euler-based numerical simulation method is employed to investigate the flow characteristics inside the Laval nozzle. In detail, the central difference method is used to discretize the flow field of the nozzle. And two kinds of flow conditions are simulated numerically: the isentropic flow from subsonic to supersonic, and the isentropic flow at full subsonic speed. The results show that the velocity increases and then decreases slowly, reaching the peak point near the nozzle throat. The pressure decreases non-linearly, and the density increases at first and then drops, following by a sharp rise later. The shock wave oscillation also appears in the flow from subsonic to supersonic, and this is because the artificial viscous term is not enough in discrete solution. Then we analyze the law of change of physical quantity by changing the shape of the nozzle. The results demonstrate that the larger the nozzle’s curvature, the faster the change rate of a physical quantity is. And the velocity at the nozzle inlet approaches zero when the area at the inlet and outlet approaches infinity.
Accelerated GPU simulation of the gaseous detonation cell structure
Authors: Yang Ruixin , Wang Chun 
Published: September 2021

Abstract
The aim of the present paper is to report on our recent results for GPU accelerated simulations of the gaseous detonation structure. Reactive Euler equations with a one-step Arrhenius chemistry model have been used for numerical simulation. And the NND space discretization scheme combined with Steger-Warming split method has been used. For time discretization we have applied the explicit third order Runge-Kutta method. We have obtained a speedup of 8 times ( in comparison to 30 threads openmp program) for the gaseous detonation simulation on a structure grid of 320 million points.
A short proof on the Plancherel formula
Authors: Zhou Ganling , Zhao Qiyuan 
Published: September 2021

Abstract
Fourier transform is a linear transform that applicants in the field of engineering and physics. The main goal of this research study is to give a self-contained study of the Fourier transform. As a modern analysis tool, the Fourier Transform has multiple applications in many fields, from the study of partial differential equations to dynamical systems. Fourier transformation has played a key role in many research fields. In this paper, we summarize the basic computational properties of the Fourier transformation and give proof of the Plancherel formula.
Analysis of Theoretical and Experimental Research on Bubble Parameters and Gas-liquid Interaction in Bubble Flow
Authors: Yin Jun 
Published: September 2021

Abstract
Bubble flow is a phenomenon in which gas flows with liquid in the form of bubbles, which widely exists in production and life. As an important part of fluid mechanics, bubble flow also has a certain impact on the actual production process. This work briefly summarizes the development of research on bubble flow in recent years. Firstly, a brief introduction to the development process and current situation of bubble flow in chronological order is presented, and the main difficulties related to the research and development of bubble flow are also pointed out, including the complicated gas-liquid distribution pattern and the exchange of materials and energy between gas and liquid phases, which slow down scholars’ research progress. Then, several theoretical models for bubble flow research are introduced. These models take bubble parameters into account, including the ultimate velocity of bubble rising, the transfer of energy and matter in the coalescence, and rupture of the bubble, the phase distribution of the bubble in the tube, and the interaction between the bubble and the liquid (the shear stress produced by bubbles affecting the turbulence field). This work briefly explains the ideas of each model and the results obtained, compares and analyzes their advantages, disadvantages and limitations, and predicts the theoretical and technical means required for subsequent theoretical model construction. Finally, part of the experimental research is summarized, along with the process and technical means of each experiment as well as the relationship between the experimental results and the theoretical research. It is hoped that this work could help to have a preliminary understanding of the research process and research methods of bubble flow, and provide some perspectives for incorporating bubble flow hydrodynamic theory into industrial applications and real life.
Recent Advances of Lattice Boltzmann Method in Microfluidic numerical Simulation
Authors: Xu Zeyu , Zhao Zilong , Xiao Yi 
Published: September 2021

Abstract
The technology of microfluidics is widely adopted in various fields such as biomedicine, microanalysis, and microelectronics. For example, pharmaceutical scientists often use microfluidics as a tool for drug delivery or cell separation. The LBM (Lattice Boltzmann method) is a commonly used numerical simulation in microfluidic researches. LBM is used extensively for simulations containing complicated boundary conditions and multiphase interfaces as it needs relatively low computing power compared to other numerical simulation methods in complex situations. The brilliant capability in parallelism also allows it to have a high multitasking performance, increasing overall efficiency. In this paper, we reviewed several typical applications of LBM in the following three fields: (1) particle regulation; (2) flow control; (3) drug delivery. We concluded defects in current studies and proposed potential improvements to be investigated in the future.
Euler and Small Disturbance Equation-based Simulation of a Nozzle Flow
Authors: Huang Kuihao 
Published: September 2021

Abstract
The de Laval nozzle has been widely studied and used in many industries ranging from the aerospace to the dairy industry. This study investigated two numerical methods used to simulate nozzle flow, namely one-dimensional Euler equations and the small disturbance equations (SDE) based simulation. The simulation results reveal that the SDE method accurately captured the shock bubbles in the nozzle flow. However, the one-dimensional Euler method is not sufficient to handle two-dimensional nozzle flow simulation because at any particular nozzle location, a mix of subsonic and supersonic flow can occur. This research allows an informed choice between Euler and SDE method.
Research progress in numerical simulation of Laval nozzle
Authors: Huang Congchi , Wang Tianyue , Zhang Zongyu 
Published: September 2021

Abstract
The Laval nozzle is a very widely used device that has made great contributions due to its invention in aerospace, mechanical engineering, applied chemistry etc. The development of many modern technologies relies on the establishment of nozzles. In this paper, the current research advances on the numerical simulation methods of the nozzle flow and nozzle-related investigation or applications in different fields are reviewed. For example, the analytical and numerical simulation of nozzles in subsonic and supersonic modes are mentioned in this article. In summary, although the applications for various fields of nozzles are now very mature, the solution of the Navier-Stokes equation for nozzles is still a future direction where science and mathematics need to be strongly developed.
Evaluating the solution accuracy of the heat equation by a posteriori error estimation
Authors: Han Feng , Yan Hui , Fu Meiyan , Lei Yu , Yan Kai 
Published: September 2021

Abstract
A produce based on a guaranteed posterior error estimates is proposed to estimate the accuracy of solution of the time-dependent heat equation. The time-dependent heat equation is discretized by the backward Euler scheme in time and conforming finite elements in space. The error between the exact solution and the numeric solution in space is bounded by a guaranteed posterior error estimates which is calculated at every time step. Numerical results demonstrate that the produce can be used to evaluate the accuracy of numerical solutions.
A short proof of two identities using techniques of complex numbers
Authors: Qingjing Ji 
Published: September 2021

Abstract
The sweeping development of mathematics is largely due to the introduction of complex numbers. Although complex numbers are just absurd notations for most people, complex numbers play essential roles in engineering fields. When mathematicians began to take an investigation of complex numbers, human beings enter a marvelous world. Complex numbers convince scientists that our world is magical, full of wonderful insights and even miraculous. In this paper, I first review several basic properties of complex numbers. The set of complex numbers is a group not only under the operation of the multiplication but under the operation of addition. Then, I show a visualisation of complex numbers through building a bijective connection between complex numbers and points on the complex plane. I also give several alternative expression forms of complex numbers, namely the trigonometric form and the general form. By invoking the arithmetic properties of complex numbers, I prove two trigonometric identities.
Numerical Simulation for Hypersonic Flow with High Temperature Thermochemical Nonequilibrium Effect
Authors: Pan Sha , Cao Guo , Guo Hongshuo , Long Dibing 
Published: September 2021

Abstract
Numerical simulations were conducted for calorically perfect gas and high temperature thermochemical nonequilibrium gas by CFD methods. Hypersonic Flow with High Temperature Thermochemical Nonequilibrium Effect was studied. The results showed that high temperature effects change the flow field and reduce heat transfer observably. For high temperature flow the kinetic energy associated with hypervelocity flight is converted into increasing the temperature of the air and endothermic reactions including dissociation and ionization of the air past shock. Thus, temperature in the shock layer dramatically decreases. All these works build foundations for further hypersonic aerodynamical computations and engineering applications.
Analysis of Water Quality of Guangzhou Waterworks Based on Grey Correlation Method
Authors: Chen Cang , Zhao Zhiqin , He Suizhi 
Published: September 2021

Abstract
The quality of urban drinking water has a great influence on the life and work of the residents. Only when the water quality reaches the National Standard, the safety of the residents and the development of society and economy can be guaranteed. In order to study the water quality of tap water in Guangzhou, 42 indicators from 8 water plants in Guangzhou were selected as sample data, and the grey correlation method was used to analyze and evaluate the indicators. The results showed that the water quality of each waterworks met the national sanitary standard for drinking water, among which the water quality of D, G and H waterworks was better than that of E and F waterworks. Based on the comparative analysis of the test indexes, some suggestions for improving the water quality of the factory are put forward. The grey correlation method can be used to evaluate the water quality of waterworks, which can not only make full use of the original data, but also be easy to calculate and the evaluation result is objective, it’s very practical.
Stellar-mass Black Hole Spin Measurements and its Implementation
Authors: Ji Ziming 
Published: September 2021

Abstract
The spin of the black hole is one of the deterministic qualities for itself, providing us with the knowledge of its birth and evolution. In this review, I described two kinds of the spin measurements, respectively based upon electromagnetic waves and gravitational waves, and discuss the meaning for the black hole spin evolution indicated by the spin results measured by these methods. We find that for X-ray binaries, the spin results are much bigger than those results for natal spin, and for binary black holes the spin result are much smaller than those in X-ray binaries, which may be resulted from their different evolutions. For binary black holes detected through gravitational waves, formation channels of the binary systems are essential for interpreting spin results in these binary systems.
Contribution of supernova remnants to the cosmic-ray electron AMS-02 data
Authors: Liu Jingbo 
Published: September 2021

Abstract
The Alpha Magnetic Spectrometer (AMS-02) experiment on board of the International Space Station is revolutionizing our understanding of cosmic rays. AMS-02 Collaboration has released the most precise data for several cosmic-ray species ever. Electrons are among the rarest cosmic particles and have been measured between 0.5 and 1000 GeV by AMS-02 with very high precision. This paper explores the possibility that the origin of cosmic-ray electrons is associated with the acceleration of particles from supernova remnants. In this paper we calculate the flux of cosmic electrons from two nearby and radio bright sources in our Galaxies: Vela and Cygnus supernova remnants. We concluded that they contribute at the few percent level at 1 TeV. Finally, we calculate the flux of other bright sources taken from radio catalog of supernova remnants, finding that their cumulative contribution is about 10% at 1 TeV. Further exploration of the AMS-02 data could lead to the conclusion that supernova remnants are among the important accelerators of cosmic-ray electrons in the galaxy.
Distribution probability of galaxies in Local Group
Authors: Yan Shaomin , Wu Guang 
Published: September 2021

Abstract
The evolution of galaxies is a very important topic for understanding of the evolution of Universe, and this evolution results in that galaxies are not evenly distributed in space. The probability of distribution of galaxies in space can be computed according to probabilistic models. Although the evolution of galaxies has been studied from various angles, the probability of distribution of galaxies in space has yet to be studied with respect to their positions over time. Of galaxies, the positions of galaxies in Local Group have been studied more thoroughly. In this study, we computed the distribution probabilities of galaxies in Local Group, i.e. the distribution probabilities of galaxies at present and previous positions, and the probability for an even distribution of galaxies in space. The results show that galaxies in Local Group have an extremely small chance to distribute evenly, and the distribution probability of galaxies in Local Group increases from the past to the present. The implication is that the accelerating expansion of the universe is increasing the distribution probability of galaxies, i.e. the accelerating expansion of the universe is a probabilistically probable event.
Advancements in Applications of Quantum Entanglement
Authors: Yu Yue 
Published: September 2021

Abstract
Quantum entanglement, an unknown “spooky action” that confused scientists like Einstein, has become one of the research hotspots in quantum mechanics. Based on the technique, applications distributed among diverse fields have appeared, e.g., cryptography, computer science, distant communication, etc, which has attracted interest from researchers in varied fields. This article reviews the basics of manifestations of quantum entanglement, namely quantum key distribution, quantum computation, and quantum teleportation. An overview of milestones is presented, e.g., Bennett-Brassard 1984 protocol, entanglement-based quantum computers, Shor’s and Grover’s algorithm as well as the process of transporting quantum states at an unprecedented speed. Moreover, the implementations of quantum entanglement are demonstrated, evolving these technologies to higher levels. Finally, a brief conclusion and expectations for future developments on entanglement are given.
Expected sensitivity to test of standard solar models with future solar CNO neutrino flux measurement
Authors: Zhou Tianhong 
Published: September 2021

Abstract
Standard solar models built from spectroscopy and from the helioseismology predicted inconsistent solar metallicity. Solar neutrino fluxes can be used to test two models. Hypothesis test was performed using 7Be, 8B CNO neutrino fluxes. Current experimental results already disfavored the low metallicity standard solar model at a significance of 2.1 σ. Considering new experiments that can improve the precision of the measured CNO neutrino flux are being planned, it is important to study their potentiality to discriminating two standard solar models. We evaluated the expected significance to reject the low metallicity solar model where the assumed central value and uncertainty of the measured CNO neutrino flux vary within the range of 3.5 × 108 -- 8 × 108 s−1cm−2 and 1%--20%, respectively. It was found that the potentiality of future experiments to reject the low metallicity standard solar model strongly depends on the central value of the CNO neutrino flux measurement. When the central value is the same as the value measured by Borexino in 2020, the required precision to reach 3 σ and 5 σ are 20% and 8%, respectively, which are both achievable.
The principals, detection schemes and experimental progress for three types of dark matter: supersymmetry, axions and neutrinos
Authors: Peng Zhenyu , Wang Kaiwen , Jia Zichen 
Published: September 2021

Abstract
The theory of dark matter (DM) has been perfected developments throughout the past ten decades. Although DM are still not being detected nowadays, plenty of models were proposed in detail. This paper focus on supersymmetry, axions, and neutrinos, which are three typical models of DM. Specifically, the basic descriptions of these kinds of DM are introduced, including definition, principals, detections, etc. Besides, the importance and latest studies/proposals are discussed. These results will offer a guideline for further research in DM.
Relation between the Density of States in Different Cases and the Corresponding Examples
Authors: Xu Yubo 
Published: September 2021

Abstract
The study of particle system is inevitable to study its statistical law, and understanding the distribution of particles is fundamental and important. In this paper, the author points out the relation between the number of states of free particles in the relativistic and non-relativistic cases, and gives formulae for each case. Furthermore, the author enumerates some popular and basic particle systems, as well as classifies them in terms of relativistic and non-relativistic cases, also their basic formulae are deduced and enumerated in this paper. These particle systems are applicable to different formulae for the density of states for relativistic or non-relativistic cases. It is concluded that the different densities of states in different cases are related to each other through the de Broglie relation and the energy formula.
Development of a Python Program Simulating Motions of Celestial Bodies
Authors: Yan Jin 
Published: September 2021

Abstract
While the research of the celestial body is essential to understand the universe, it requires considerable costs in time and equipment. However, the computation methods can be used to analyze the astrophysics process in a simple approach. In this paper, a model of computing the motion of solar system based on Euler’s method is established. The model divided the process into infinite small time steps, and iteration is used to represent integration and update the position of planets over the process. The NumPy and matplotlib are used to visualize the motion. By the analysis of momentum and energy through the process and the application in the 2-body situation, the model is proved to be valid and accurate.
Primordial black holes’ relevancy with dark matter
Authors: Liu Qiyuan , Li Kuntong , Xu Sixing 
Published: September 2021

Abstract
Primordial black holes (PBHs) are probable candidates of dark matter (DM). In this review, we gathered data, evidence, and opinions from previous literatures to support the theory that PBHs are a form of DM. Besides, the formation of PBHs is introduced as well to give a more comprehensive description of PBHs. According to the results, the PBHs could assemble DM, or be DM itself, or generates DM, or influence DM. On the other hand, DM could have the similar influence on PBHs. Different relationships are discussed between PBHs and DM, including entropy, microlensing, distribution, growth rate, mass, and different detections (e.g., gammy ray). These results offer a guideline for future studies of PBHs.