量化三维网格模型复杂度的Fractal Dimension^(+)方法

对三维网格模型复杂度的评估及应用进行研究,提出基于Fractal Dimension^(+)方法量化三维网格模型复杂度。该方法利用分形几何学的分形维度来确定三维网格模型的不规则性;为了全面量化复杂度并且提高量化的准确性和可信度,在分形维度算法中添加孔隙比和亏格数的概念,全面考虑介质内部空间分布和几何结构的连接性以及孔洞分布的信息。对大量三维网格模型进行实验,结果表明Fractal Dimension^(+)方法可以有效计算出准确的复杂度。

分形维数(Fractal dimension)及其测量方法

给出了相似维数、容量维数、盒子维数、信息维数、关联维数、广义维数分形维数等 6种分形维数的定义方式 ,并讨论了它们的应用范围。在此基础上 ,概括出改变粗视化程度求维数、根据测度关系求维数、根据关联函数求维数、根据分布函数求维数、根据波谱求维数等 5种测量维数的方法 ,为不同领域的科研人员应用维数测量提供了有力工具。

加快建设优势学科的多维思考

学科是人才培养、科技创新和服务经济社会发展的重要载体。进入新发展阶段,面向世界科技前沿、面向经济主战场、面向国家重大需求、面向人民生命健康,以改革创新为驱动,加快建设一批中国特色、世界一流的优势学科,是扎实迈进高等教育强国的重要举措。优势学科概念内涵、文化背景、精神追求、建设路径等方面均体现着高质量发展阶段加快建设高等教育强国的战略布局。为此,在厘清优势学科的内涵、特征及生成机制的前提下,我们应从价值逻辑、经济逻辑、实践逻辑、政策逻辑等维度进一步探明优势学科建设的逻辑向度,在此基础上,以完善顶层设计为引领力,以善用数字技术为牵引力,可持续推进优势学科高质量建设。

新课标视域下中学历史课程“四维融合”教学模式的探索

在中学历史教学中,把握历史课程的特征,树立“述史、释史、论史、评史”四个维度的学习方式极为重要,有助于历史知识的有效掌握。述史是对基本历史知识、历史过程的叙述;释史是对知识重难点的深入阐释;论史是引导学生“以史为据”“论从史出”,参与历史讨论;评史是使用唯物史观对基本历史现象、事件和人物的客观评价。通过“四维融合”的模式,引导授课对象全过程的参与课堂学习,从而通过深度学习,促进学生形成正确的历史观,实现学生对历史知识的深度学习与掌握,实现中学历史课程教学目标的深度达成。

煤矿掘进机机电设备故障诊断与维护

针对煤矿掘进机机电设备传统故障诊断方法效率较低、故障识别较为困难、潜在故障无法及时发现等问题,本文对煤矿掘进机机电设备故障诊断与维护技术进行研究。在分析了掘进机关键结构常见故障和监测方法的基础上,提出了煤矿掘进机故障监测与智能诊断系统,完成硬件系统选型和软件控制系统设计,实现了对掘进机机电设备运行状态实时监控和远程运维,转被动维护为主动维护,提高了设备运行可靠性,降低了设备维护成本,提高了机电设备故障诊断效率。经安装调试后表明:当掘进机关键部位出现异常现象时可准确识别,并且故障响应时间仅为1.28 s,故障发现率达97.8%,对潜在故障准确识别和判断,智能诊断系统极大提高了设备故障诊断效率,故障排除时间降低为97.3%。

Hausdorff Dimension of Range and Graph for General Markov Processes

We establish the Hausdorff dimension of the graph of general Markov processes on Rd based on some probability estimates of the processes staying or leaving small balls in small time.In particular,our results indicate that,for symmetric diffusion processes(withα=2)or symmetricα-stable-like processes(withα∈(0,2))on Rd,it holds almost surely that dimH GrX([0,1])=1{α<1}+(2−1/α)1{α≥1,d=1}+(d∧α)1{α≥1,d≥2}.We also systematically prove the corresponding results about the Hausdorff dimension of the range of the processes.

Dimension by Dimension Finite Volume HWENO Method for Hyperbolic Conservation Laws

In this paper,we propose a finite volume Hermite weighted essentially non-oscillatory(HWENO)method based on the dimension by dimension framework to solve hyperbolic conservation laws.It can maintain the high accuracy in the smooth region and obtain the high resolution solution when the discontinuity appears,and it is compact which will be good for giving the numerical boundary conditions.Furthermore,it avoids complicated least square procedure when we implement the genuine two dimensional(2D)finite volume HWENO reconstruction,and it can be regarded as a generalization of the one dimensional(1D)HWENO method.Extensive numerical tests are performed to verify the high resolution and high accuracy of the scheme.

Scalable Temporal Dimension Preserved Tensor Completion for Missing Traffic Data Imputation With Orthogonal Initialization

Dear Editor,This letter puts forward a novel scalable temporal dimension preserved tensor completion model based on orthogonal initialization for missing traffic data(MTD)imputation.The MTD imputation acts directly on accessing the traffic state,and affects the traffic management.

Publisher’s Note:“Benchmark simulations of radiative transfer in participating binary stochastic mixtures in two dimensions”[Matter Radiat.Extremes 9, 067802 (2024)]

This article was originally published online on 30 August 2024.Due to a production error,as originally published the author list was not in its intended order.All online versions of this article were corrected on 9 September 2024 and it appears correctly in print.AIP Publishing apologizes for this error.

Benchmark simulations of radiative transfer in participating binary stochastic mixtures in two dimensions

We study radiative transfer in participating binary stochastic mixtures in two dimensions(2D)by developing an accurate and efficient simulation tool.For two different sets of physical parameters,2D benchmark results are presented,and it is found that the influence of the stochastic mixture on radiative transfer is clearly parameter-dependent.Our results confirm that previous multidimensional results obtained in different studies are basically consistent,which is interpreted in terms of the relationship between the photon mean free path l_(p)and the system size L.Nonlinear effects,including those due to scattering and radiation-material coupling,are also discussed.To further understand the particle size effect,we employ a dimensionless parameter l_(p)/L,from which a critical particle size can be derived.On the basis of further 2D simulations,we find that an inhomogeneous mix is obtained for l_(p)/L>0.1.Furthermore,2D material temperature distributions reveal that self-shielding and particle-particle shielding of radiation occur,and are enhanced when l_(p)/L is increased.Our work is expected to provide benchmark results to verify proposed homogenized models and/or other codes for stochastic radiative transfer in realistic physical scenarios.

An Exploration of the Three Dimensions and Epochal Strengths of Building a Human Community With a Shared Future

The idea of a human community with a shared future was proposed by the Communist Party of China(CPC)Central Committee with Comrade Xi Jinping at its core for the future development of human beings to face up to the most important question in today's world:“What is happening to the world and what should we do?”It profoundly answers the question of the world,history,and the times.The theory of a human community with a shared future is an innovative theory with a multidimensional formation logic that guides humanity toward continually seeking common interests and values.This paper dives into the profound motivations behind building a human community with a shared future from historical,cultural,and practical dimensions and analyzes its epochal value from both domestic and international perspectives.This not only helps exert China's role in the international community,contributing Chinese strength to the construction of a peaceful,stable,and prosperous human society,but also enhances the influence of the idea of a human community with a shared future in the international community,accelerating the building of a human community with a shared future that considers the legitimate concerns of all countries,and aiding in solving the crises facing the world.

Mean Dimension for Non-autonomous Iterated Function Systems

In this paper we introduce the notions of mean dimension and metric mean dimension for non-autonomous iterated function systems(NAIFSs for short)on countably infinite alphabets which can be regarded as generalizations of the mean dimension and the Lindenstrauss metric mean dimension for non-autonomous iterated function systems.We also show the relationship between the mean topological dimension and the metric mean dimension.

Fractal analysis of major faults and fractal dimension of lineaments in the Indo-Gangetic Plain on a regional scale

The Indo-Gangetic Plain(IGP)is one of the most seismically vulnerable areas due to its proximity to the Himalayas.Geographic information system(GIS)-based seismic characterization of the IGP was performed based on the degree of deformation and fractal dimension.The zone between the Main Boundary Thrust(MBT)and the Main Central Thrust(MCT)in the Himalayan Mountain Range(HMR)experienced large variations in earthquake magnitude,which were identified by Number-Size(NS)fractal modeling.The central IGP zone experienced only moderate to low mainshock levels.Fractal analysis of earthquake epicenters reveals a large scattering of earthquake epicenters in the HMR and central IGP zones.Similarly,the fault fractal analysis identifies the HMR,central IGP,and south-western IGP zones as having more faults.Overall,the seismicity of the study region is strong in the central IGP,south-western IGP,and HMR zones,moderate in the western and southern IGP,and low in the northern,eastern,and south-eastern IGP zones.

A Dynamical System-Based Framework for Dimension Reduction

We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems,which we call the dynamical dimension reduction(DDR).In the DDR model,each point is evolved via a nonlinear flow towards a lower-dimensional subspace;the projection onto the subspace gives the low-dimensional embedding.Training the model involves identifying the nonlinear flow and the subspace.Following the equation discovery method,we represent the vector field that defines the flow using a linear combination of dictionary elements,where each element is a pre-specified linear/nonlinear candidate function.A regularization term for the average total kinetic energy is also introduced and motivated by the optimal transport theory.We prove that the resulting optimization problem is well-posed and establish several properties of the DDR method.We also show how the DDR method can be trained using a gradient-based optimization method,where the gradients are computed using the adjoint method from the optimal control theory.The DDR method is implemented and compared on synthetic and example data sets to other dimension reduction methods,including the PCA,t-SNE,and Umap.

Experimental investigation of methane explosion fracturing in bedding shales:Load characteristics and three-dimensional fracture propagation

Methane in-situ explosion fracturing(MISEF)enhances permeability in shale reservoirs by detonating desorbed methane to generate detonation waves in perforations.Fracture propagation in bedding shale under varying explosion loads remains unclear.In this study,prefabricated perforated shale samples with parallel and vertical bedding are fractured under five distinct explosion loads using a MISEF experimental setup.High-frequency explosion pressure-time curves were monitored within an equivalent perforation,and computed tomography scanning along with three-dimensional reconstruction techniques were used to investigate fracture propagation patterns.Additionally,the formation mechanism and influencing factors of explosion crack-generated fines(CGF)were clarified by analyzing the morphology and statistics of explosion debris particles.The results indicate that methane explosion generated oscillating-pulse loads within perforations.Explosion characteristic parameters increase with increasing initial pressure.Explosion load and bedding orientation significantly influence fracture propagation patterns.As initial pressure increases,the fracture mode transitions from bi-wing to 4–5 radial fractures.In parallel bedding shale,radial fractures noticeably deflect along the bedding surface.Vertical bedding facilitates the development of transverse fractures oriented parallel to the cross-section.Bifurcation-merging of explosioninduced fractures generated CGF.CGF mass and fractal dimension increase,while average particle size decreases with increasing explosion load.This study provides valuable insights into MISEF technology.

A novel box-counting method for quantitative fractal analysis of threedimensional pore characteristics in sandstone

Fractal theory offers a powerful tool for the precise description and quantification of the complex pore structures in reservoir rocks,crucial for understanding the storage and migration characteristics of media within these rocks.Faced with the challenge of calculating the three-dimensional fractal dimensions of rock porosity,this study proposes an innovative computational process that directly calculates the three-dimensional fractal dimensions from a geometric perspective.By employing a composite denoising approach that integrates Fourier transform(FT)and wavelet transform(WT),coupled with multimodal pore extraction techniques such as threshold segmentation,top-hat transformation,and membrane enhancement,we successfully crafted accurate digital rock models.The improved box-counting method was then applied to analyze the voxel data of these digital rocks,accurately calculating the fractal dimensions of the rock pore distribution.Further numerical simulations of permeability experiments were conducted to explore the physical correlations between the rock pore fractal dimensions,porosity,and absolute permeability.The results reveal that rocks with higher fractal dimensions exhibit more complex pore connectivity pathways and a wider,more uneven pore distribution,suggesting that the ideal rock samples should possess lower fractal dimensions and higher effective porosity rates to achieve optimal fluid transmission properties.The methodology and conclusions of this study provide new tools and insights for the quantitative analysis of complex pores in rocks and contribute to the exploration of the fractal transport properties of media within rocks.

VA族元素修饰对二维AlN电磁性质调控的理论研究

采用基于密度泛函理论的第一性原理计算方法,研究了VA族元素(N、P、As、Sb、Bi)对二维AlN电磁性质的影响.研究发现,VA族元素修饰后,二维AlN的能带结构发生显著劈裂,表明体系转变为磁性材料.同时,导带底部向低能量区域移动,使得二维AlN的吸收阈值从紫外线区域扩展至可见光区域.因此,VA族元素的修饰显著调控了二维AlN的电子结构和磁性,为实现可见光响应的光电子和自旋电子器件提供了新思路和可能性.

The Global Attractor and Its Dimension Estimation of Generalized Kolmogorov-Petrovlkii-Piskunov Equation

In this paper, the initial boundary value problem of a class of nonlinear generalized Kolmogorov-Petrovlkii-Piskunov equations is studied. The existence and uniqueness of the solution and the bounded absorption set are proved by the prior estimation and the Galerkin finite element method, thus the existence of the global attractor is proved and the upper bound estimate of the global attractor is obtained.

Lax-Oleinik-Type Formulas and Efficient Algorithms for Certain High-Dimensional Optimal Control Problems

Two of the main challenges in optimal control are solving problems with state-dependent running costs and developing efficient numerical solvers that are computationally tractable in high dimensions.In this paper,we provide analytical solutions to certain optimal control problems whose running cost depends on the state variable and with constraints on the control.We also provide Lax-Oleinik-type representation formulas for the corresponding Hamilton-Jacobi partial differential equations with state-dependent Hamiltonians.Additionally,we present an efficient,grid-free numerical solver based on our representation formulas,which is shown to scale linearly with the state dimension,and thus,to overcome the curse of dimensionality.Using existing optimization methods and the min-plus technique,we extend our numerical solvers to address more general classes of convex and nonconvex initial costs.We demonstrate the capabilities of our numerical solvers using implementations on a central processing unit(CPU)and a field-programmable gate array(FPGA).In several cases,our FPGA implementation obtains over a 10 times speedup compared to the CPU,which demonstrates the promising performance boosts FPGAs can achieve.Our numerical results show that our solvers have the potential to serve as a building block for solving broader classes of high-dimensional optimal control problems in real-time.

Computational Quantification of Map Projection Distortion by Fractal Dimension of Coastlines

Maps, essential tools for portraying the Earth’s surface, inherently introduce distortions to geographical features. While various quantification methods exist for assessing these distortions, they often fall short when evaluating actual geographic features. In our study, we took a novel approach by analyzing map projection distortion from a geometric perspective. We computed the fractal dimensions of different stretches of coastline before and after projection using the divide-and-conquer algorithm and image processing. Our findings revealed that map projections, even when preserving basic shapes, inevitably stretch and compress coastlines in diverse directions. This analysis method provides a more realistic and practical way to measure map-induced distortions, with significant implications for cartography, geographic information systems (GIS), and geomorphology. By bridging the gap between theoretical analysis and real-world features, this method greatly enhances accuracy and practicality when evaluating map projections.