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11.
利用多相场模型对液-固两相体系中固相颗粒的粗化过程进行了三维模拟,对粗化过程中的界面形状分布进行了统计分析,研究了不同固相体积分数下颗粒连接状态对界面形状演化及粗化速率的影响.模拟结果表明:当颗粒间存在大量连接时,粗化速率随固相分数的变化速率比颗粒无连接时变缓,且随着粗化进行,高曲率的双曲形界面所占比例不断降低,低曲率的椭球形界面所占比例逐渐增多;无论固相颗粒间是否发生连接,界面形状演化经历一定阶段后,三维界面形状分布均呈现自相似性,但随着固相体积分数的增加,界面形状分布呈现自相似性所需的时间延长. 相似文献
12.
13.
Guo-lian~Xu ChandrajitL.Bajaj 《计算数学(英文版)》2003,21(5):681-688
In this paper, we provide simple and explicit formulas for computing Riemannian curvatures, mean curvature vectors, principal curvatures and principal directions for a 2-dimensional Riemannian manifold embedded in IR^k with k ≥ 3. 相似文献
14.
A. R. Veeravalli 《Commentarii Mathematici Helvetici》2001,76(1):155-160
For a closed hypersurface in a space form, this work provides some sharp upper bounds for its first positive Laplacian eigenvalue. These bounds are extrinsic as they rely on the mean curvatures and center(s) of gravity of the hypersurface. Received: May 22, 2000 相似文献
15.
We prove anisotropic Reilly-type upper bounds for divergence-type operators on hypersurfaces of the Euclidean space in presence of a weighted measure. 相似文献
16.
Wenxiong Chen & Ruobing Zhang 《数学研究》2020,53(4):436-470
In this paper, we will explore the geometric effects of conformally covariantoperators and the induced nonlinear curvature equations in certain nonlocal nature.Mainly, we will prove some regularity and rigidity results for the distributional solutions to those equations. 相似文献
17.
18.
Ricardo Uribe-Vargas 《Bulletin of the Brazilian Mathematical Society》2005,36(3):285-307
The focal curve of an immersed smooth curve γ : θ ↦ γ (θ), in Euclidean space ℝm+1, consists of the centres of its osculating hyperspheres. This curve may be parametrised in terms of the Frenet frame of γ (t, n1, . . . , nm), as Cγ (θ) = (γ +c1n1+ c2n2 + • • • + cmnm)(θ), where the coefficients c1, . . . , cm-1 are smooth functions that we call the focal curvatures of γ . We discovered a remarkable formula relating the Euclidean curvatures κi , i = 1, . . . ,m, of γ with its focal curvatures. We show that the focal curvatures satisfy a system of Frenet equations (not vectorial, but scalar!).
We use the properties of the focal curvatures in order to give, for ℓ = 1, . . . ,m, necessary and sufficient conditions for the radius of the osculating ℓ-dimensional sphere to be critical. We also give necessary
and sufficient conditions for a point of γ to be a vertex. Finally, we show explicitly the relations of the Frenet frame and the Euclidean curvatures of γ with the Frenet frame and the Euclidean curvatures of its focal curve Cγ. 相似文献
19.
Hsiao‐Fan Tseng Ming‐Hsiang Cheng Kai‐Sheng Jeng Jia‐Wei Li Jiun‐Tai Chen 《Macromolecular rapid communications》2016,37(22):1825-1831
Anisotropic polymer particles such as Janus particles have attracted significant attention in recent years because of their unique properties and unusual self‐assembly behavior. Most anisotropic polymer particles synthesized so far, however, only have different chemical regions compartmentalized on the particles. It remains a great challenge to fabricate anisotropic polymer particles with different shapes within a single particle. A novel approach is developed to prepare anisotropic polymer particles that contain two hemispheres with different curvatures by annealing polystyrene microspheres on poly(vinyl alcohol) films. During the annealing process, the polymer microspheres gradually sink into the polymer films and transform to asymmetric polymer particles, driven by the surface and interfacial tensions of the polymers. Selective removal techniques are also used to confirm the morphologies of the asymmetric particles.
20.
We study hypersurfaces in Euclidean space
whose position vector x satisfies the condition L
k
x = Ax + b, where L
k
is the linearized operator of the (k + 1)th mean curvature of the hypersurface for a fixed
,
is a constant matrix and
is a constant vector. For every k, we prove that the only hypersurfaces satisfying that condition are hypersurfaces with zero (k + 1)th mean curvature and open pieces of round hyperspheres and generalized right spherical cylinders of the form
, with
. This extends a previous classification for hypersurfaces in
satisfying
, where
is the Laplacian operator of the hypersurface, given independently by Hasanis and Vlachos [J. Austral. Math. Soc. Ser. A
53, 377–384 (1991) and Chen and Petrovic [Bull. Austral. Math. Soc. 44, 117–129 (1991)].
相似文献