Numerical manifold method for thermo-mechanical coupling simulation of fractured rock mass

As a calculation method based on the Galerkin variation,the numerical manifold method(NMM)adopts a double covering system,which can easily deal with discontinuous deformation problems and has a high calculation accuracy.Aiming at the thermo-mechanical(TM)coupling problem of fractured rock masses,this study uses the NMM to simulate the processes of crack initiation and propagation in a rock mass under the influence of temperature field,deduces related system equations,and proposes a penalty function method to deal with boundary conditions.Numerical examples are employed to confirm the effectiveness and high accuracy of this method.By the thermal stress analysis of a thick-walled cylinder(TWC),the simulation of cracking in the TWC under heating and cooling conditions,and the simulation of thermal cracking of the SwedishÄspöPillar Stability Experiment(APSE)rock column,the thermal stress,and TM coupling are obtained.The numerical simulation results are in good agreement with the test data and other numerical results,thus verifying the effectiveness of the NMM in dealing with thermal stress and crack propagation problems of fractured rock masses.

Delineating homogeneous domains of fractured rocks using topological manifolds and deep learning

Determining homogeneous domains statistically is helpful for engineering geological modeling and rock mass stability evaluation.In this text,a technique that can integrate lithology,geotechnical and structural information is proposed to delineate homogeneous domains.This technique is then applied to a high and steep slope along a road.First,geological and geotechnical domains were described based on lithology,faults,and shear zones.Next,topological manifolds were used to eliminate the incompatibility between orientations and other parameters(i.e.trace length and roughness)so that the data concerning various properties of each discontinuity can be matched and characterized in the same Euclidean space.Thus,the influence of implicit combined effect in between parameter sequences on the homogeneous domains could be considered.Deep learning technique was employed to quantify abstract features of the characterization images of discontinuity properties,and to assess the similarity of rock mass structures.The results show that the technique can effectively distinguish structural variations and outperform conventional methods.It can handle multisource engineering geological information and multiple discontinuity parameters.This technique can also minimize the interference of human factors and delineate homogeneous domains based on orientations or multi-parameter with arbitrary distributions to satisfy different engineering requirements.

A STABILITY RESULT FOR TRANSLATINGSPACELIKE GRAPHS IN LORENTZ MANIFOLDS

In this paper,we investigate spacelike graphs defined over a domain Ω⊂M^(n) in the Lorentz manifold M^(n)×ℝ with the metric−ds^(2)+σ,where M^(n) is a complete Riemannian n-manifold with the metricσ,Ωhas piecewise smooth boundary,and ℝ denotes the Euclidean 1-space.We prove an interesting stability result for translating spacelike graphs in M^(n)×ℝ under a conformal transformation.

Galerkin-based quasi-smooth manifold element(QSME)method for anisotropic heat conduction problems in composites with complex geometry

The accurate and efficient analysis of anisotropic heat conduction problems in complex composites is crucial for structural design and performance evaluation. Traditional numerical methods, such as the finite element method(FEM), often face a trade-off between calculation accuracy and efficiency. In this paper, we propose a quasi-smooth manifold element(QSME) method to address this challenge, and provide the accurate and efficient analysis of two-dimensional(2D) anisotropic heat conduction problems in composites with complex geometry. The QSME approach achieves high calculation precision by a high-order local approximation that ensures the first-order derivative continuity.The results demonstrate that the QSME method is robust and stable, offering both high accuracy and efficiency in the heat conduction analysis. With the same degrees of freedom(DOFs), the QSME method can achieve at least an order of magnitude higher calculation accuracy than the traditional FEM. Additionally, under the same level of calculation error, the QSME method requires 10 times fewer DOFs than the traditional FEM. The versatility of the proposed QSME method extends beyond anisotropic heat conduction problems in complex composites. The proposed QSME method can also be applied to other problems, including fluid flows, mechanical analyses, and other multi-field coupled problems, providing accurate and efficient numerical simulations.

Isometric Immersions of Lightlike Warped Product Manifolds

In this paper, we deal with isommetric immersions of globally null warped product manifolds into Lorentzian manifolds with constant curvature c in codimension k≥3. Under the assumptions that the globally null warped product manifold has no points with the same constant sectional curvature c as the Lorentzian ambient, we show that such isometric immersion splits into warped product of isometric immersions.

Singular Points, Closed Orbits, Stable Manifolds and Unstable Manifolds of Second Order Autonomous Birkhoff Systems

Aim To study singular points, closed orbits, stable manifolds and unstable manifolds of a second order autonomous Birkhoff system. Methods Qualitative methods of ordinary differential equation were used. Results and Conclusion The criteria for singular points, closed orbits and hyperbolic equilibrium points of a second order autonomous Birkhoff system are given. Moreover the stability of equilibria, stable manifolds and unstable manifolds are obtained.

基于Manifold Ranking和结合前景背景特征的显著性检测

针对基于图和流形排序(Manifold Ranking)的显著性检测算法(MR算法)过度依赖边界节点的背景特征的问题,提出一种改进的结合前景背景特征的显著性检测算法。首先,对图像进行超像素分割,建立闭环图模型;然后利用流形排序算法根据图像前景特征和背景特征分别得出前景种子和背景种子;再通过亮度和颜色特征对两类种子进行结合,筛选出更为准确的查询节点;最后再利用流形排序算法进行显著值计算,得到最终的显著图。实验表明,改进方法与MR算法相比在精确率、召回率、F值等多个评价指标上均有明显提升,得到的显著图更接近真值。

CR-submanifolds in Almost Hermitian Manifold

Studies are made of the cohomology of CR_ submanifolds and integrability of the distribution D of CR_submanifolds. When dim D⊥】1, the totally umbilical non-trival CR-submanifold i n nea r Kaehler manifold is totally geodesic. In the end, we get:If is n ear Kaehler manifold with B】0, then is not permitt ed to have fixed foliate non-trival CR-submanifold.

On the Comparison Theorems for the Volume of Tubes in Kahlerian Manifolds

In this note we give some comparison theorems for the volume of tubes around a complex submanifold in a Kahlerian monifold.

Biharmonic product maps between doubly warped product manifolds

The biharmonicity of the product map Φ2=φ×ψ and the two generalized projections φ-and ψ-are analyzed. Some results are obtained, that is, Φ2 is a proper biharmonic map if and only if b is a non-constant solution of -1/f2 Jφ（dφ（grad（lnb）））＋n/2 grad｜dφ（grad（lnb））｜2=0 and f is a non-constant solution of -1/b2Jψ（dψ（grad（lnf）））＋m/2grad｜dψ（grad（lnf））｜2=0, and Φ2=φ×ψ is a proper biharmonic map if and only if φ-and ψ-are proper biharmonic maps.

Submanifolds with Parallel Mean Curvacture

In this paper, we consider a class of submanifolds with parallel mean curvacture vector fields. We obitain the suffitient conditions that the above submanifolds is of tatall umbilical and that its codimension is decrease.

Principal Manifolds and Nonlinear Dimensionality Reduction via Tangent Space Alignment

We present a new algorithm for manifold learning and nonlinear dimensionality reduction. Based on a set of unorganized data points sampled with noise from a parameterized manifold, the local geometry of the manifold is learned by constructing an approximation for the tangent space at each point, and those tangent spaces are then aligned to give the global coordinates of the data points with respect to the underlying manifold. We also present an error analysis of our algorithm showing that reconstruction errors can be quite small in some cases. We illustrate our algorithm using curves and surfaces both in 2D/3D Euclidean spaces and higher dimensional Euclidean spaces. We also address several theoretical and algorithmic issues for further research and improvements.

2D numerical manifold method based on quartic uniform B-spline interpolation and its application in thin plate bending

A new numerical manifold （NMM） method is derived on the basis of quartic uniform B-spline interpolation. The analysis shows that the new interpolation function possesses higher-order continuity and polynomial consistency compared with the conven- tional NMM. The stiffness matrix of the new element is well-conditioned. The proposed method is applied for the numerical example of thin plate bending. Based on the prin- ciple of minimum potential energy, the manifold matrices and equilibrium equation are deduced. Numerical results reveal that the NMM has high interpolation accuracy and rapid convergence for the global cover function and its higher-order partial derivatives.

Gating system optimization of low pressure casting A356 aluminum alloy intake manifold based on numerical simulation

To eliminate the shrinkage porosity in low pressure casting of an A356 aluminum alloy intake manifold casting, numerical simulation on fi lling and solidifi cation processes of the casting was carried out using the ProCAST software. The gating system of the casting is optimized according to the simulation results. Results show that when the gating system consists of only one sprue, the fi lling of the molten metal is not stable; and the casting does not follow the sequence solidifi cation, and many shrinkage porosities are observed through the casting. After the gating system is improved by adding one runner and two in-gates, the fi lling time is prolonged from 4.0 s to 4.5 s, the fi lling of molten metal becomes stable, but this casting does not follow the sequence solidifi cation either. Some shrinkage porosity is also observed in the hot spots of the casting. When the gating system was further improved by adding risers and chill to the hot spots of the casting, the shrinkage porosity defects were eliminated completely. Finally, by using the optimized gating system the A356 aluminum alloy intake manifold casting with integrated shape and smooth surface as well as dense microstructure was successfully produced.

OPTIMIZATION DESIGN OF HYDRAULIC MANIFOLD BLOCKS BASED ON HUMAN-COMPUTER COOPERATIVE GENETIC ALGORITHM

Optimization design of hydraulic manifold blocks (HMB) is studied as acomplex solid spatial layout problem. Based on comprehensive research into structure features anddesign rules of HMB, an optimal mathematical model for this problem is presented. Usinghuman-computer cooperative genetic algorithm (GA) and its hybrid optitation strategies, integratedlayout and connection design schemes of HMB can be automatically optimized. An example is given totestify it.

Modeling and simulation of turbofan engine based on equilibrium manifold

Because the normal operation of the engine is located near the equilibrium manifold, the method of equilibrium mani fold nonlinear dynamic modeling is adopted for turbofan engine more than the local train modeling. The method studies the sys tem characteristics near the equilibrium manifold. The modeling method can be realized through dynamic and static twostep, and for the specific parameter modeling steps and algorithm are given. The output of the test data is compared with the model output through numerical simulation, to check the model with an additional set of test data. The simulation results show that the model has reached the requirements of engineering accuracy.

SOME RESULTS ON PRODUCT COMPLEX FINSLER MANIFOLDS

Let （M, F ） be the product complex Finsler manifold of two strongly pseudoconvex complex Finsler manifolds （M 1 , F 1 ） and （M 2 , F 2 ）. In this paper, we obtain the relationship between the Chern Finsler connection coefficients Γ i ; k associated to F and the Chern Finsler connection coefficients Γ a ; c , Γα ; γ associated to F 1 , F 2 , respectively. As applications we prove that, if both （M 1 , F 1 ） and （M 2 , F 2 ） are strongly Ka¨hler Finsler （complex Berwald, or locally complex Minkowski, respectively） manifolds, so does （M, F ）. Furthermore, we prove that the holomorphic curvature K F = 0 if and only if K F1 = 0 and K F2 = 0.

Stability for manifolds of equilibrium states of generalized Birkhoff system

Stability for the manifolds of equilibrium states of a generalized Birkhoff system is studied. A theorem for the stability of the manifolds of equilibrium states of the general autonomous system is used to the generalized BirkhoiYian system and two propositions on the stability of the manifolds of equilibrium states of the system are obtained. An example is given to illustrate the application of the results.

A supervised multimanifold method with locality preserving for face recognition using single sample per person

Although real-world experiences show that preparing one image per person is more convenient, most of the appearance-based face recognition methods degrade or fail to work if there is only a single sample per person(SSPP). In this work, we introduce a novel supervised learning method called supervised locality preserving multimanifold(SLPMM) for face recognition with SSPP. In SLPMM, two graphs: within-manifold graph and between-manifold graph are made to represent the information inside every manifold and the information among different manifolds, respectively. SLPMM simultaneously maximizes the between-manifold scatter and minimizes the within-manifold scatter which leads to discriminant space by adopting locality preserving projection(LPP) concept. Experimental results on two widely used face databases FERET and AR face database are presented to prove the efficacy of the proposed approach.

Turbulent combustion modeling using a flamelet generated manifold approach——a validation study in Open FOAM

An OpenFOAM based turbulence combustion solver with flamelet generated manifolds (FGMs) is presented in this paper. A series of flamelets, representative for turbulent flames, are calculated first by a one-dimensional (1D) detailed chemistry solver with the consideration of both transport and stretch/curvature contributions. The flame structure is then parameterized as a function of multiple reaction control variables. A manifold, which collects the 1D flame properties, is built from the 1D flame solutions. The control variables of the mixture fraction and the progress variable are solved from the corresponding transport equations. During the calculation, the scalar variables, e.g., temperature and species concentration, are retrieved from the manifolds by interpolation. A transport equation for NO is solved to improve its prediction accuracy. To verify the ability to deal with the enthalpy loss effect, the temperature retrieved directly from the manifolds is compared with the temperature solved from a transport equation of absolute enthalpy. The resulting FGM-computational fluid dynamics (CFD) coupled code has three significant features, i.e., accurate NO prediction, the ability to treat the heat loss effect and the adoption at the turbulence level, and high quality prediction within practical industrial configurations. The proposed method is validated against the Sandia flame D, and good agreement with the experimental data is obtained.