Modeling repulsive forces on fibres via knot energies
Modeling repulsive forces on fibres via knot energies
复制标题
通过结能量模拟纤维上的排斥力
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
P. Reiter
中科院分区：
文献类型：
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作者：
S. Blatt;P. Reiter
排斥力的建模对于理解某些生物物理过程，特别是DNA分子的运动是必不可少的。这些现象似乎是由某种“能量”驱动的，这种“能量”特别阻止了分子的强烈弯曲和形成自交。受物理玩具模型的启发，在过去的25年里，许多功能被定义为旨在模拟自我回避。一般的想法是产生“纠缠”的曲线，在远链之间有特别大的距离。在这个调查中，我们提出了这些所谓的结能的几个族。从分析的角度来看，它们是非常相似的。我们着重证明了每一类结的自我回避和最小化的存在性。对于这些能量的一个合适的亚族，我们给出了如何证明这些极小值甚至是无限可微的。
Abstract Modeling of repulsive forces is essential to the understanding of certain bio-physical processes, especially for the motion of DNA molecules. These kinds of phenomena seem to be driven by some sort of “energy” which especially prevents the molecules from strongly bending and forming self-intersections. Inspired by a physical toy model, numerous functionals have been defined during the past twenty-five years that aim at modeling self-avoidance. The general idea is to produce “detangled” curves having particularly large distances between distant strands. In this survey we present several families of these so-called knot energies. It turns out that they are quite similar from an analytical viewpoint. We focus on proving self-avoidance and existence of minimizers in every knot class. For a suitable subfamily of these energies we show how to prove that these minimizers are even infinitely differentiable.