A method is described for the manufacture of pivoting colloidal assemblies comprising rotating diamond and rotating triangle geometries that show tunable folding and unfolding by thermal fluctuations and actuation by magnetic attractions.
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Poincaré half-space model. Take the open upper half-space \[\mathbb{H}^n := \{(x_1,\dots,x_n)\in\mathbb{R}^n \mid x_n 0\}\] equipped with the Riemannian metric whose components on the coordinate tangent vectors are \[g_{ij}(p) \;=\; g_p\!\left(\frac{\partial}{\partial x_i}\bigg|_p,\; \frac{\partial}{\partial x_j}\bigg|_p\right) \;=\; \frac{1}{p_n^2}\,\delta_{ij}.\] Geodesics are semicircles (or rays) orthogonal to the boundary hyperplane \(\{x_n = 0\}\).
[+-] Kvaesitso replaced Niagra for my launcher. The extra customization options were appreciated and it's FOSS. [4]，这一点在谷歌浏览器【最新下载地址】中也有详细论述