基于流形学习的航空影像匹配方法研究

提出了一种基于流形学习的航空影像匹配方法。该方法利用同一幅影像中特征点之间的空间结构和不同影像中特征点之间的相似性作为特征点映射的约束条件,利用流形学习方法对影像的特征点进行映射,将所有影像的特征点映射到同一空间后采用最小距离方法进行特征点的匹配。利用实际的航空影像进行实验,与SIFT方法、SVD-LLE方法进行综合分析,结果表明本文方法在匹配性能方面具有明显的优越性,并且能够同时获得多幅影像之间的匹配关系。     

Modeling progressive failures in rock slopes with non‐persistent joints using the numerical manifold method

Rock slope failure is a complex process that usually involves both opening/sliding along pre‐existing discontinuities as well as fracturing of intact rock bridges. Discontinuity persistence is an important factor governing rock slope instabilities. However, traditional slope failure analysis assumes persistent discontinuities, and rock slope fails along a predefined persistent continuous potential failure surface because of the limitations of the analysis tools. This paper proposes the numerical manifold method (NMM) incorporated with a Mohr–Coulomb criterion‐based fracturing algorithm to simulate the progressive failure of rock slopes with non‐persistent joints. Detailed fracturing algorithm is first presented. Then, the NMM enabling fracturing is calibrated through simulating an edge‐cracked plate and the Brazilian test. Lastly, the developed code is applied to investigate the failure process of rock slopes involving non‐persistent joints. Numerical results indicate that the proposed method can capture the opening/sliding along existing discontinuities, the fracturing in intact rock bridges and the final kinematic release. Progressive slope failure is well exhibited. Copyright © 2013 John Wiley & Sons, Ltd.     

数值流形法的T样条局部加密算法

在岩土工程分析中求解精度控制常常是必需的,在数值流形法中可以通过控制数学覆盖网格的稀疏和覆盖位移的阶数来达到精度的要求。提出了基于等几何分析的数值流形方法,定义了相应的数学覆盖的构造形式,推导了基于二次B样条的9节点数值流形方法分析格式;针对基于Lagrange插值函数的4节点数值流形方法提出了基于T样条思想的数学覆盖网格的局部加密方法。算例计算结果表明,相对于4节点的数值流形方法,基于非均匀有理B样条的9节点数值流形方法具有更高的精度;基于T样条思想的加密网格在保持计算精度的前提下降低了自由度的数量,表明T样条加密是一种自然的局部加密算法。     

数值流形法中“质量守恒”的探讨

数值流形法是至少包含流形法(NMM)、有限元法(FEM)和非连续变形分析(DDA)的数值方法体系。将数值流形法中物理单元与数学单元完全重合,去掉接触理论,流形元能够回归到有限元,将通过简单的板压缩数值试验验证这一点。在以前的数值流形法法中,质量守恒问题一直被忽视,物理单元的质量会随着单元体积改变,计算结果存在一定的误差。通过改变计算过程中单元密度实现计算过程中的"质量守恒",完善了现有数值流形法的理论基础。     

Bianchi type-V cosmological model with perfect fluid using negative constant deceleration parameter in a scalar tensor theory based on Lyra Manifold

An exact Bianchi type-V perfect fluid cosmological model is obtained in a scalar tensor theory proposed by Sen (Z. Phys. 149:311, 1957) based on Lyra Manifold in case of β is a constant and it is shown that this cosmological model exists only in the case of Radiation Universe (ρ=3p) if β is a function of ‘t’ using negative constant deceleration parameter. Some physical and geometrical properties of these models are discussed.     

多场耦合作用下岩体裂隙扩展演化关键问题研究

裂隙岩体热-水-应力（THM）耦合是目前研究的热点和难点。首先总结了裂隙岩体多场耦合的机制、模型、方法及研究内容,并通过分析裂隙对THM耦合的重要控制作用,提出了在THM耦合中考虑裂隙网络扩展演化及模拟的关键问题,同时指出了研究的3个关键点：（1）建立考虑裂隙网络演化的耦合模型;（2）裂隙扩展的数值模拟方法;（3）THM耦合及岩体变形、失稳全过程的数值模拟算法。随后通过对模拟多场耦合和裂隙扩展数值方法的归类比较,重点论述了目前适用于模拟多场耦合下裂隙扩展模拟的各种数值方法（包括有限单元法、无单元法、单位分解法、离散单元法、岩石破裂过程分析方法和数值流形方法）的优缺点,并通过对比研究,推荐采用数值流形方法（NMM）来实现对关键问题的模拟研究。最后,对研究思路和难点进行了初步探讨。     

开挖模拟在数值流形方法中的实现

针对数值流形方法特有的覆盖剖分方式,提出了一种模拟岩土工程中开挖过程的算法。该算法采取某种措施,在覆盖剖分过程中将开挖面视为特殊的不连续面,这种不连续面将其所在的数学网格剖分成不同的流形单元,但却不对所在的数学覆盖作剖分。这样,开挖面两侧虽分属不同的流形单元,但开挖面两侧同一数学网格内的流形单元却具有相同的物理覆盖。采用该算法,无需对开挖面处的单元进行特殊处理,可在整个分析域采用统一的网格形式;同时,打破了原有数值流形方法的限制,将开挖面的位置完全当作连续介质来处理,避免了因将其视为不连续面而产生的误差。验证了算法的可靠性后,将其应用于某假想隧道的开挖模拟,计算结果表明该算法具有一定的应用前景。     

广义相对论的时空及参照系的数学模型

本之运用拓朴学及流形几何的概念,给出一般时空应具备的几个数学条件,结合相应的物理含义加以说明,并给出了参照系的数学定义及物理意义.     

The Tetrahedral 4‐Body Problem with Rotation

We consider four bodies in space with same masses forming two binaries, each one symmetric with respect to a fixed axis and moving under Newtonian gravitation in opposite directions about this axis. It is given a direct proof that all singularities of this model are due to collisions, and it is proved that the singularities due to simultaneous double collisions are regularizable. The set of equilibrium points on the total collision manifold is studied as well as the possible connections among them. We show that the set of initial conditions on a given energy surface going to quadruple collision is a union of twenty submanifolds: twelve of them have dimension 2 and the others have dimension 3. Similarly for ejection orbits from quadruple collision. This revised version was published online in July 2006 with corrections to the Cover Date.