A local pseudo arc-length method for hyperbolic conservation laws

A local pseudo arc-length method（LPALM）for solving hyperbolic conservation laws is presented in this paper.The key idea of this method comes from the original arc-length method,through which the critical points are bypassed by transforming the computational space.The method is based on local changes of physical variables to choose the discontinuous stencil and introduce the pseudo arc-length parameter,and then transform the governing equations from physical space to arc-length space.In order to solve these equations in arc-length coordinate,it is necessary to combine the velocity of mesh points in the moving mesh method,and then convert the physical variable in arclength space back to physical space.Numerical examples have proved the effectiveness and generality of the new approach for linear equation,nonlinear equation and system of equations with discontinuous initial values.Non-oscillation solution can be obtained by adjusting the parameter and the mesh refinement number for problems containing both shock and rarefaction waves.

Identifying influential spreaders in complex networks based on entropy weight method and gravity law

In complex networks,identifying influential spreader is of great significance for improving the reliability of networks and ensuring the safe and effective operation of networks.Nowadays,it is widely used in power networks,aviation networks,computer networks,and social networks,and so on.Traditional centrality methods mainly include degree centrality,closeness centrality,betweenness centrality,eigenvector centrality,k-shell,etc.However,single centrality method is onesided and inaccurate,and sometimes many nodes have the same centrality value,namely the same ranking result,which makes it difficult to distinguish between nodes.According to several classical methods of identifying influential nodes,in this paper we propose a novel method that is more full-scaled and universally applicable.Taken into account in this method are several aspects of node’s properties,including local topological characteristics,central location of nodes,propagation characteristics,and properties of neighbor nodes.In view of the idea of the multi-attribute decision-making,we regard the basic centrality method as node’s attribute and use the entropy weight method to weigh different attributes,and obtain node’s combined centrality.Then,the combined centrality is applied to the gravity law to comprehensively identify influential nodes in networks.Finally,the classical susceptible-infected-recovered(SIR)model is used to simulate the epidemic spreading in six real-society networks.Our proposed method not only considers the four topological properties of nodes,but also emphasizes the influence of neighbor nodes from the aspect of gravity.It is proved that the new method can effectively overcome the disadvantages of single centrality method and increase the accuracy of identifying influential nodes,which is of great significance for monitoring and controlling the complex networks.

SOLUTION OF THE RAYLEIGH PROBLEM FOR A POWER-LAW NON-NEWTONIAN CONDUCTING FLUID VIA GROUP METHOD

An investigation is made of the magnetic Rayleigh problem where a semi_infinite plate is given an impulsive motion and thereafter moves with constant velocity in a non_Newtonian power law fluid of infinite extent. The solution of this highly non_linear problem is obtained by means of the transformation group theoretic approach. The one_parameter group transformation reduces the number of independent variables by one and the governing partial differential equation with the boundary conditions reduce to an ordinary differential equation with the appropriate boundary conditions. Effect of the some parameters on the velocity u(y,t) has been studied and the results are plotted.

SPECTRAL/HP ELEMENT METHOD WITH HIERARCHICAL RECONSTRUCTION FOR SOLVING NONLINEAR HYPERBOLIC CONSERVATION LAWS

The hierarchical reconstruction （HR） [Liu, Shu, Tadmor and Zhang, SINUM ＇07] has been successfully applied to prevent oscillations in solutions computed by finite volume, Runge-Kutta discontinuous Galerkin, spectral volume schemes for solving hyperbolic conservation laws. In this paper, we demonstrate that HR can also be combined with spectral/hp element method for solving hyperbolic conservation laws. An orthogonal spectral basis written in terms of Jacobi polynomials is applied. High computational efficiency is obtained due to such matrix-free algorithm. The formulation is conservative, and essential nomoscillation is enforced by the HR limiter. We show that HR preserves the order of accuracy of the spectral/hp element method for smooth solution problems and generate essentially non-oscillatory solutions profiles for capturing discontinuous solutions without local characteristic decomposition. In addition, we introduce a postprocessing technique to improve HR for limiting high degree numerical solutions.

Godunov＇s method for initial-boundary value problem of scalar conservation laws

This paper is concerned with Godunov＇s scheme for the initial-boundary value problem of scalar conservation laws. A kind of Godunov＇s scheme, which satisfies the boundary entropy condition, was given. By use of the scheme, numerical simulation for the weak entropy solution to the initial-boundary value problem of scalar conservation laws is conducted.

Conservative and Easily Implemented Finite Volume Semi-Lagrangian WENO Methods for 1D and 2D Hyperbolic Conservation Laws

The paper is devised to propose finite volume semi-Lagrange scheme for approximating linear and nonlinear hyperbolic conservation laws. Based on the idea of semi-Lagrangian scheme, we transform the integration of flux in time into the integration in space. Compared with the traditional semi-Lagrange scheme, the scheme devised here tries to directly evaluate the average fluxes along cell edges. It is this difference that makes the scheme in this paper simple to implement and easily extend to nonlinear cases. The procedure of evaluation of the average fluxes only depends on the high-order spatial interpolation. Hence the scheme can be implemented as long as the spatial interpolation is available, and no additional temporal discretization is needed. In this paper, the high-order spatial discretization is chosen to be the classical 5th-order weighted essentially non-oscillatory spatial interpolation. In the end, 1D and 2D numerical results show that this method is rather robust. In addition, to exhibit the numerical resolution and efficiency of the proposed scheme, the numerical solutions of the classical 5th-order WENO scheme combined with the 3rd-order Runge-Kutta temporal discretization (WENOJS) are chosen as the reference. We find that the scheme proposed in the paper generates comparable solutions with that of WENOJS, but with less CPU time.

Numerical Method for Non-Linear Conservation Laws: Inviscid Burgers Equation

This paper deals with the Burgers equation which is the most common model used in the nonlinear conservation laws. Here the theoretical aspect of conservation law is discussed by using inviscid Burgers equation. At first, we introduce the general non-linear conservation law as a partial differential equation and its solution procedure by the method of characteristic. Next, we present the weak solution of the problem with entropy condition. Taking into account shock wave and rarefaction wave, the Riemann problem has also been discussed. Finally, the finite volume method is considered to approximate the numerical solution of the inviscid Burgers equation with continuous and discontinuous initial data. An illustration of the problem is provided by some examples. Moreover, the Godunov method provides a good approximation for the problem.

A Riemann-Solver Free Spacetime Discontinuous Galerkin Method for General Conservation Laws

This paper summarizes a Riemann-solver-free spacetime discontinuous Galerkin method developed for general conservation laws. The method integrates the best features of the spacetime Conservation Element/Solution Element (CE/SE) method and the discontinuous Galerkin (DG) method. The core idea is to construct a staggered spacetime mesh through alternate cell-centered CEs and vertex-centered CEs within each time step. Inside each SE, the solution is approximated using high-order spacetime DG basis polynomials. The spacetime flux conservation is enforced inside each CE using the DG concept. The unknowns are stored at both vertices and cell centroids of the spatial mesh. However, the solutions at vertices and cell centroids are updated at different time levels within each time step in an alternate fashion. Thanks to the staggered spacetime formulation, there are no left and right states for the solution at the spacetime interface. Instead, the solution available to evaluate the flux is continuous across the interface. Therefore, no (approximate) Riemann solvers are needed to provide a unique numerical flux. The current method can be used to solve arbitrary conservation laws including the compressible Euler equations, shallow water equations and magnetohydrodynamics (MHD) equations without the need of any form of Riemann solvers. A set of benchmark problems of various conservation laws are presented to demonstrate the accuracy of the method.

On the Approximation of Fractal-Fractional Differential Equations Using Numerical Inverse Laplace Transform Methods

Laplace transform is one of the powerful tools for solving differential equations in engineering and other science subjects.Using the Laplace transform for solving differential equations,however,sometimes leads to solutions in the Laplace domain that are not readily invertible to the real domain by analyticalmeans.Thus,we need numerical inversionmethods to convert the obtained solution fromLaplace domain to a real domain.In this paper,we propose a numerical scheme based on Laplace transform and numerical inverse Laplace transform for the approximate solution of fractal-fractional differential equations with orderα,β.Our proposed numerical scheme is based on three main steps.First,we convert the given fractal-fractional differential equation to fractional-differential equation in Riemann-Liouville sense,and then into Caputo sense.Secondly,we transformthe fractional differential equation in Caputo sense to an equivalent equation in Laplace space.Then the solution of the transformed equation is obtained in Laplace domain.Finally,the solution is converted into the real domain using numerical inversion of Laplace transform.Three inversion methods are evaluated in this paper,and their convergence is also discussed.Three test problems are used to validate the inversion methods.We demonstrate our results with the help of tables and figures.The obtained results show that Euler’s and Talbot’s methods performed better than Stehfest’s method.

Determination of the Henry’s Law Constant of Hexane in High-Viscosity Polymer Systems

The Henry’s law constant of volatiles in polymer systems is a crucial parameter reflecting the gas-liquid equilibrium,which is very important for devolatilization.In this research,polyolefin elastomer(POE)-cyclohexane and polydimethylsiloxane(PDMS)-hexane systems were studied,and the Henry’s law constant was obtained by measuring the gas phase equilibrium partial pressure when polymer solutions containing different mass fractions of volatiles reached a saturated state.The effects of temperature,type of volatiles,and polymer viscosity on the gas phase equilibrium partial pressure and Henry’s law constant of the volatiles were investigated.The results indicate that,with the increase of temperature and polymer viscosity,the gas phase equilibrium partial pressure and Henry’s law constant of volatiles increase.As temperature increases,the solubility of gas in liquid decreases.The relationship between the Henry’s law constant and temperature is consistent with the Arrhenius law.In the PDMS-hexane system,the gas phase equilibrium partial pressure and Henry’s law constant of n-hexane are higher than those of cyclohexane.The obtained Henry’s law constants can be used as a reference for perfecting the devolatilization process and improving the devolatilization effect.

Spectral Element Viscosity Methods for Nonlinear Conservation Laws on the Semi-Infinite Interval

In this paper we propose a spectral element: vanishing viscosity (SEW) method for the conservation laws on the semi-infinite interval. By using a suitable mapping, the problem is first transformed into a modified conservation law in a bounded interval, then the well-known spectral vanishing viscosity technique is generalized to the multi-domain case in order to approximate this trarsformed equation more efficiently. The construction details and convergence analysis are presented. Under a usual assumption of boundedness of the approximation solutions, it is proven that the solution of the SEW approximation converges to the uniciue entropy solution of the conservation laws. A number of numerical tests is carried out to confirm the theoretical results.

洞桩法地铁车站边桩结构受力机制的模型试验设计

为了方便学生更形象地理解洞桩法地铁车站边桩结构的受力机制,该文以广州地区某洞桩法地铁车站工程为依托,设计了一种简化的洞桩法车站边桩结构模型试验。基于该试验方法,演示分析了边桩结构在洞桩法车站开挖过程中的施工力学行为规律,并对比研究了不同桩型布置参数下的桩后土压力、边桩结构的力学和变形规律。通过该试验,为学生展示了洞桩法边桩结构模型的设计、制作、试验具体操作及数据监测的全过程,从而让学生更好地掌握洞桩法车站边桩结构力学行为演变规律,以及采用不同边桩布置型式的力学行为差异。

信息化时代的法学实践教学方法革新——以家事法教学中运用类案检索方法为例

类案检索是信息化时代法学实践教学方法革新的重要途径和有效方案。以吉林大学法学院和西北政法大学为起始的类案检索教学改革试点经验,证实了该种教学方法在学生法律思维训练、法学分析能力提升、自主学习能力养成方面的效能。但必须承认,类案检索方法在受益于信息时代给予的信息便利的同时,也受制于信息公开的有限范围。跨越这一障碍,不仅需要文书公开制度的开放与包容,更需要法律共同体多机构间的有效合作。

论作为数字行政执法方式的行政行为码

数字信息技术与行政权力的融合为以法治为中心的政府治理带来挑战,而行政行为码作为数字行政执法方式的应用是数治与法治结合的重要体现,并蕴含着整体智治下对行政执法体制一体化塑造的制度逻辑、行政自制论对数字赋能与赋权关系重塑的理论逻辑以及行政效能对行政执法全流程覆盖的实践逻辑。行政行为码以统一赋码、一码关联、一码查询与一码追踪的实践运行机理,兼具政府信息公开与政府数据开放的法律性质,也为拓展应用奠定了理论基础。与此同时作为数字新兴执法方式的行政行为码由于规制理念的不明确、规则体系不健全以及功能应用程度不足,限制其应用场景与空间。在未来,行政行为码应从理念更新、规范控制和功能拓展三个方面进行塑形,推动行政行为码的功能实现与广泛应用。

盾构隧道下穿高铁路基变形影响规律及加固优化研究

为研究盾构隧道下穿高铁路基施工时对路基的影响规律,探究在隧道开挖过程中运用不同加固措施对既有高铁路基的影响程度。以西安市某地铁工程为依托,利用室内模型试验对比分析盾构隧道下穿高铁CFG桩复合路基过程中,无加固、超前管幕工法加固与地表袖阀管注浆加固3种隧道施工条件下,地表沉降值和沉降槽的空间分布规律;采用数值模拟分析验证超前管幕工法加固工况下盾构隧道下穿时,高铁路基、道床的位移变化规律。室内模型试验结果表明:盾构隧道施工中采用管幕工法加固后复合地基正上方的地表沉降最大值减小28.6%,采用袖阀管注浆加固后减小18.0%,并且采用两种加固措施后的CFG桩最大附加轴力均减小20%以上。因此,在隧道掘进过程中采用一定加固措施,可改善围岩稳定性,其中管幕工法加固效果更为显著。数值模拟分析表明:采取管幕工法加固施工与不采取加固措施相比,路基最大沉降量减少33.78%,道床最大沉降量减少45.08%。因此,管幕工法加固能够有效减小对既有高铁路基的影响。

核心价值观融入法治思维培养的内在逻辑与实现机理

在坚持全面依法治国,推进法治中国建设的过程中,针对法治建设后备军的法科学生,有必要进行核心价值观融入法治思维的培养。这不同于意识形态的教育,本质上是法律方法的训练。文章首先分析了核心价值观融入法治思维培养的内在逻辑,进而以法律适用为进路,在教学中通过将核心价值观融入法律规范的选择、法律漏洞的填补、冲突利益的衡量,以教会法科学生在未来的职业活动中运用法治思维,依靠法律方法,将核心价值观融入司法裁判和行政执法之中,从而为践行弘扬核心价值观提供机会和可能。

极高地应力硬岩隧道变形规律及施工优化研究

依托重庆市巫镇高速宝山隧道工程,采用数值模拟方法开展极高地应力无仰拱硬岩隧道的变形规律和施工优化研究,对不同施工工法、施工步距进行了比选。研究表明:1)不同施工工法隧道变形规律基本一致,竖向位移大于水平位移且基底隆起较拱顶沉降更明显,全断面法施工隧道变形收敛速度最快;2)不同施工工法均为基底应力释放程度最大,释放后基底应力仅为初始的55%,且全断面法拱脚处应力集中范围最小;3)隧道周围的岩体以拉伸破坏为主,部分位置存在剪切破坏,施工工法对塑性区的水平影响范围有限;4)该隧道选用全断面法施工可行且较经济。全断面法不同施工步距变形及应力分布基本规律相同,施工步距越大,水平竖向位移越大,拱脚处应力集中越显著,最小主应力值也越大,综合考虑现场施工建设速度、变形收敛情况、应力分布状态,采用1.6 m步距较经济合理。

论我国可分离性标准的重塑

美国法中的可分离性标准是立法政策选择的结果,本质上是一项事实命题。我国司法实践中的可分离性标准借鉴自美国立法,但由于缺乏实体法依据,其被视为思想/表达二分法的自然推论加以适用,这决定了我国的可分离性标准在本质上有别于美国,是一项价值命题。司法实践对这一差异的忽视导致可分离性标准在我国的适用出现了判断困境、逻辑矛盾以及功能异化等问题。对此,应当明确可分离性标准的价值命题属性,并基于著作权法平衡激励创造与保留进入之要求,以公平和效率为价值取向重塑我国的可分离性标准。具体制度构建方面,将可分离性标准定位为权利范围的限定准则,根据实用艺术品艺术性表达部分的可替代程度之高低适用不同类别的保护模式。

体育学法概念辨析——兼与《体育学法论》作者商榷

文章通过对《体育学法论》的分析,明确体育学法概念。《体育学法论》把“体育学法”等同于“体育学习方法”,甚至是体育课堂上学生个别的行为表现,与书中教学生“学会学习”初衷相悖,由于体育学习方法界限具象且狭窄,造成《体育学法论》研究内卷化,教法和学法互为因果,真正的体育学法概念被遮蔽。把体育学法定义为学习体育知识与技能的规律与法则,可以区别体育学法与体育学习方法、学习行为、学习能力等相关概念。文章在学校体育教学中,依从全面深化课程改革要求,尤其是在基础教育阶段,把教学重心从项目教学转移到学法教学,符合发展学生核心素养的现代教学理念,为提升学生适应终身发展和社会发展需要的关键能力赋能。