溶蚀岩体三维随机洞体数学模型的设计

溶蚀岩体是地质体中一种特定的岩体 ,它在水流等自然因素作用下 ,生成了许多溶蚀洞体 ,本文首先对作为其载体的三维地质体进行数学描述和显示 ,然后对如何确定椭球洞体形状和大小、复杂洞体的生成、三维随机洞体的数学模型以及确定性洞体的数学描述和计算机显示进行了详尽的阐述。本文提出的溶蚀岩体三维随机洞体的数学模型为溶蚀岩体的溶蚀率和渗透特性的研究提供了可视化手段 ,能够有力地指导溶蚀岩体三维随机洞体的计算机显示的编程实践     

Brownian dynamics simulations for suspension of ellipsoids in liquid crystalline phase under simple shear flows

Brownian dynamics simulations of shear flows are carried out for various suspensions of ellipsoids interacting via the Gay-Berne potential. In this simulation all the systems of the suspension are in a liquid crystalline phase at rest. In a shear flow they exhibit various motions of the director depending on the shear rate: the continuous rotation, the intermittent rotation, the wagging-like oscillation, and the aligning. The director is almost always out of the vorticity plane when it rotates, that is the kayaking. The number density of the system and the inter-particle potential intensity significantly affect the shear rate dependence of orientation. In particular, the continuous rotation of director is maintained to higher shear rates for the system with a stronger potential. Furthermore, the rheological properties are examined. The shear-thinning in viscosity is observed, but the negative first normal difference is not obtained.     

Interval,ellipsoidal, and super-ellipsoidal calculi for experimental and theoretical treatment of uncertainty: Which one ought to be preferred?

In this study we compare three calculi listed in the title for analysis of structures involving uncertainty. The main idea is based on the consideration that the maximum structural response predicted by the preferred theory ought to be minimal, and the minimum structural response predicted by the preferred theory ought to be maximal, to constitute a lower overestimation. We present analytic results that allow one to calculate the structural response via the interval, ellipsoidal or super-ellipsoidal calculus. We provide several examples of truss structures and illustrate that in different situations, depending on the available data, one of these calculi ought to be preferred. Conclusion is made on the preferable approach to be the super-ellipsoidal calculus.     

Influence of aspect ratio and arrangement direction on the shear behavior of ellipsoids

This work studies the macroscopic and microscopic behaviors of ellipsoids under triaxial tests using 3D discrete element method (DEM) simulation. To avoid the boundary effect, a novel stress servo-controlled periodic boundary condition is proposed to maintain the confining pressure of samples during testing. The shape features of ellipsoids are investigated, including the aspect ratio of elongated/oblate ellipsoids and the initial arrangement directions of ellipsoids. The macroscopic properties of ellipsoidal particle samples, such as the deviatoric stress, volumetric strain, internal friction angle, as well as dilatancy angles are explored. Elongated and oblate ellipsoids with varying aspect ratios are investigated for the occurrence of stick-slips. In addition, it is demonstrated that the initial arrangement direction has a significant impact on the coordination number and contact force chains. The corresponding anisotropy coefficients of the entire contact network are analyzed to probe the microscopic roots of macroscopic behavior.     

Confinement Induced Ordering in Fluid of Hard Ellipsoids

The ordering configurations of a fluid of anisotropic ellipsoids under the confinement of two apposing impenetrable walls are studied by Monte Carlo simulations. The excess adsorption of the fluid on the walls with respect to the aspect ratio has a maximum at the critical aspect ratio of 2.9 in high-density ellipsoid fluids, indicating an orientational ordering in the adjacent region of the walls, which is confirmed by probing into the density configurations and the orientational order parameter in the adjacent region of the walls for varying aspect ratios. In addition, the orientational order parameter in the bulk fluid at the same density is calculated, and it indicates an isotropic state as the bulk density is still below the bulk isotropic-to-nematic transition. Therefore, it can be concluded that the anisotropic ordering near the walls in the ellipsoid fluid that exhibits isotropic in the bulk is induced by the confinement effect of the walls.     

受限导致硬椭球液体的取向有序

Monte Carlo模拟研究了两平行硬墙受限下各向异相的硬椭球液体形成的有序结构. 墙壁对椭球粒子的过量吸附和椭球的长短径之比有关;对于高密度的椭球液体,它在一个临界的长短径之比 a/b=2.9处达到最大值,表明在墙表面附近发生了取向有序. 墙表面附近的密度分布和取向序参量进一步证实这结论. 相同密度条件下体相中的取向序参量计算表明体相结构均为各向同性,这是由于体系的密度依然低于各向同性相向相列向转变的临界密度. 该受限椭球液体中墙表面的取向有序是由墙面的几何受限所导致的.     

Veiled assonance between geodesics on ellipsoid and billiard in its focal ellipse

We introduce new special ellipsoidal confocal coordinates in ⁿ (n ≥ 3) and apply them to the geodesic problem on a triaxial ellipsoid in ³ as well as the billiard problem in its focal ellipse.

Using such appropriate coordinates we show that these different dynamical systems have the same common analytic first integral. This fact is not evident because there exists a geometrical spatial gap between the geodesic and billiard flows under consideration, and this separating gap just “veils” the resemblance of the two systems.

In short, a geodesic on the ellipsoid and a billiard trajectory inside its focal ellipse are in a “veiled assonance”—under the same initial data they will be tangent to the same confocal hyperboloid. But this assonance is rather incomplete: the dynamical systems in question differ by their intrinsic action angle-variables, thereby the different dynamics arise on the same phase space (i.e. the same phase curves in the same phase space bear quite different rotation numbers).

Some results of this work have been published before in Russian (Tabanov, 1993) and presented to the International Geometrical Colloquium (Moscow, May 10–14, 1993) and the International Symposium on Classical and Quantum Billiards (Ascona, Switzerland, July 25–30, 1994).     

A polynomial time algorithm for solving the fermat-weber location problem with mixed norms

This paper discusses the Fermat-Weber location problem, manages to apply the ellipsoid method to this problem and proves the ellipsoid method can be terminated at an approximately optimal location in polynomial time, verifies the ellipsoid method is robust for the lower dimensional location problem     

Ellipsoid projection method in matrix games

A problem of calculating a solution of a zero-sum matrix game is considered in the paper The problem of search of a solution is reduced to a constrained convex minimization problem for which an ellipsoid projection algorithm is used. The algorithm generates an ?-optimal solution of the game in a polynomial time