论文标题
确切的最小停车库的建造：最佳包装层状结构中的非线性螺旋图案
Construction of exact minimal parking garages: nonlinear helical motifs in optimally packed lamellar structures
论文作者
论文摘要
最小的表面是流体膜的能量最小化，因此在多种生物系统中发现。内质网的紧密层状结构和植物类囊体由这样的最小表面组成，其中左右左手的螺旋基序嵌入了石学计量中，表明全球倾斜平衡。到目前为止，对最小表面中螺旋基序的分析处理仅限于小斜率近似，在小斜率近似中，基序由谐波函数图表示。但是，在大多数生物学和物理相关的方案中，间距间的分离与其音高相当，因此该近似失败。在这里，我们提出了一种配方，用于构建具有螺旋基序的任意分布的精确最小表面，表明任何谐波图只能通过利用侧向位移来将任何谐波图形变为最小表面。我们详细分析了相似和相反的依据的基序，以及具有相似或交替的手工的相同基序链。最后，我们研究了具有渐近螺旋结构的螺旋基序的功能的第二个变化，并表明，在这种最小表面稳定性的子类中，稳定性的稳定性要求集合的收集是平衡的。
Minimal surfaces arise as energy minimizers for fluid membranes and are thus found in a variety of biological systems. The tight lamellar structures of the endoplasmic reticulum and plant thylakoids are composed of such minimal surfaces in which right and left handed helical motifs are embedded in stoichiometry suggesting global pitch balance. So far, the analytical treatment of helical motifs in minimal surfaces was limited to the small-slope approximation where motifs are represented by the graph of harmonic functions. However, in most biologically and physically relevant regimes the inter-motif separation is comparable with its pitch, and thus this approximation fails. Here, we present a recipe for constructing exact minimal surfaces with an arbitrary distribution of helical motifs, showing that any harmonic graph can be deformed into a minimal surface by exploiting lateral displacements only. We analyze in detail pairs of motifs of the similar and of opposite handedness and also an infinite chain of identical motifs with similar or alternating handedness. Last, we study the second variation of the area functional for collections of helical motifs with asymptotic helicoidal structure and show that in this subclass of minimal surfaces stability requires that the collection of motifs is pitch balanced.
