Bounds for minimum step number of knots confined to tubes in the simple cubic lattice
Bounds for minimum step number of knots confined to tubes in the simple cubic lattice
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DOI：
10.1088/1751-8121/aa6a4f
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发表时间：
2012-02
期刊：
影响因子：
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通讯作者：
K. Ishihara;Maxime Pouokam;Atsumi Suzuki;R. Scharein;M. Vázquez;J. Arsuaga;K. Shimokawa
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文献类型：
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作者：
K. Ishihara;Maxime Pouokam;Atsumi Suzuki;R. Scharein;M. Vázquez;J. Arsuaga;K. Shimokawa
结在自然界中普遍存在，它们的分析在包括流体动力学、材料科学以及分子和结构生物学在内的各种领域都具有重要意义。在许多系统中，粒子是在拥挤的环境中发现的，因此很自然地要严格地描述有限体积中结点的性质。在这项工作中，我们结合联合收割机的分析和数值计算工作的简单立方晶格，以确定最小的晶格步骤，最小的步骤数，需要使一个结内的管状区域。我们的互补方法帮助我们建立一个详细的枚举最小的结的长度和/或构象的结在管状区域。分析结果表征了可以嵌入管状区域的结和链接的类型，并确定了在（2×1）管中构建所有2桥结和链接多达10个交叉点所需的最少步骤数。另一方面，模拟结果估计了最小步数，并为更宽的管状区域提供了多达八个交叉点的所有结类型的精确轨迹。这些研究结果不仅确定了什么样的结和链接可以建立在一个高度封闭的体积，但也提供了进一步的证据，实现一个结类型所需的最小步骤数增加与封闭体积。
Knots are ubiquitous in nature and their analysis has important implications in a wide variety of fields including fluid dynamics, material science and molecular and structural biology. In many systems particles are found in crowded environments hence it is natural to rigorously characterize the properties of knots in confined volumes. In this work we combine analytical and numerical work on the simple cubic lattice to determine the minimal number of lattice steps, minimum step number, needed to make a knot inside a tubular region. Our complementary approaches help us establish a detailed enumeration of minimal knot lengths and/or conformations of knots in tubular regions. Analytical results characterize the types of knots and links that can be embedded in a tubular regions and determines the minimum number of steps required to construct all 2-bridge knots and links up to ten crossings in the (2×1)-tube. Simulation results, on the other hand, estimate the minimum step number and provide exact trajectories of all knot types up to eight crossings for wider tubular regions. These findings not only determine what knots and links can be built in a highly confined volume but also provide further evidence that the minimum step number required to realize a knot type increases with confining volume.