标题： 聚合物结的空间扭曲与签名 显示英文标题

标题： The space writhes and signatures of polymer knots

摘要： 纽结的空间缠绕数是其三维嵌入的一个属性，其中包含了关于其潜在拓扑的信息，但空间缠绕数与其他拓扑不变量之间的对应关系尚未完全理解。 我们对打结的半刚性聚合物进行了朗之万动力学模拟，并测量了它们的系综平均空间缠绕数。 我们证明，对于所有最多有10个交叉点的纽结，交替纽结和非交替纽结，平均空间缠绕数几乎等于相同纽结最紧致已知构型的空间缠绕数，且差异很小。 利用这种等价性，我们表明，对于最多有38个交叉点的更复杂纽结，平均空间缠绕数与纽结的签名高度相关。 这确立了签名与空间缠绕数之间的联系在更大的交叉点数量上仍然成立。 显示英文摘要

摘要： The space writhe of a knot is a property of its three-dimensional embedding that contains information about its underlying topology, but the correspondence between space writhe and other topological invariants is not fully understood. We perform Langevin dynamics simulations of knotted semiflexible polymers and measure their ensemble average space writhe. We show that for all knots up to 10 crossings, alternating and non-alternating, the average space writhe is almost equal to that of the tightest known configuration of the same knot, with minor differences. Using this equivalence, we show that for more complex knots with up to 38 crossings, the average space writhe is strongly correlated with the signature of the knot. This establishes that the connection between signature and space writhe holds at larger crossing numbers.