Self-Interactions of Strands and Sheets
Self-Interactions of Strands and Sheets
复制标题
线材和片材的自相互作用
DOI：
10.1023/a:1021010526495
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发表时间：
2003
影响因子：
1.6
通讯作者：
A. Maritan
中科院分区：
文献类型：
--
作者：
J. Banavar;Oscar Gonzalez;J. Maddocks;A. Maritan
可以建模为嵌入三维的曲线或曲面的物理线或片在自然界中无处不在，并且在数学、物理、生物学和工程学中具有根本重要性。通常，物理解释表明应在连续体模型中强制执行自回避，即有限能量配置不应自相交。当前具有自我回避功能的连续体模型经常采用成对排斥势，这必然是奇异的。此外，势不具有适合对物理系统的有限厚度进行建模的固有长度尺度。在这里，我们开发了一个用于建模自回避线材和片材的框架，该框架避免了奇点，并提供了引入厚度长度尺度的方法。在我们的方法中，成对相互作用势被涉及三个或更多点以及某些相关圆或球体的半径的多体势所取代。基于这些多体势的自相互作用能量可用于描述有限厚度的自相互作用股线和片材的统计力学。
Physical strands or sheets that can be modelled as curves or surfaces embedded in three dimensions are ubiquitous in nature, and are of fundamental importance in mathematics, physics, biology, and engineering. Often the physical interpretation dictates that self-avoidance should be enforced in the continuum model, i.e., finite energy configurations should not self-intersect. Current continuum models with self-avoidance frequently employ pairwise repulsive potentials, which are of necessity singular. Moreover the potentials do not have an intrinsic length scale appropriate for modelling the finite thickness of the physical systems. Here we develop a framework for modelling self-avoiding strands and sheets which avoids singularities, and which provides a way to introduce a thickness length scale. In our approach pairwise interaction potentials are replaced by many-body potentials involving three or more points, and the radii of certain associated circles or spheres. Self-interaction energies based on these many-body potentials can be used to describe the statistical mechanics of self-interacting strands and sheets of finite thickness.