从峡谷到山谷：从粘性硬球簇到更平滑的潜力景观的数字延续
From canyons to valleys: Numerically continuing sticky hard sphere clusters to the landscapes of smoother potentials
摘要：
我们研究了具有短程吸引相互作用的粒子的能量景观，随着相互作用范围的增加。从一组局部极小值的$6\leq N\leq12$硬球是“粘性”，即他们只有当他们的表面是完全接触时，他们相互作用，我们使用数值延拓演变的局部极小值（集群）的范围内的潜在的增加，使用两个Lennard-Jones和莫尔斯家族的相互作用势。随着距离的增加，集群合并，直到在长距离上只剩下一个或两个集群。我们比较了不同的潜力，通过延续得到的集群，并发现，对于短期和中期的范围内，高达约30\%的颗粒直径，连续的集群几乎是相同的，无论是内部和跨家庭的潜力。对于更长的范围内的集群变化显着，与家庭之间的变化比家庭内的潜力。我们分析了合并事件背后的机制，发现大多数重排发生在一对非键合粒子进入势的范围内。一个例外发生在非调和的集群，那些有一个零本征值在他们的海森，这经历了一个更全面的重排。
英文摘要：
We study the energy landscapes of particles with short-range attractive interactions as the range of the interactions increases. Starting with the set of local minima for $6\leq N\leq12$ hard spheres that are "sticky", i.e. they interact only when their surfaces are exactly in contact, we use numerical continuation to evolve the local minima (clusters) as the range of the potential increases, using both the Lennard-Jones and Morse families of interaction potentials. As the range increases, clusters merge, until at long ranges only one or two clusters are left. We compare clusters obtained by continuation with different potentials and find that for short and medium ranges, up to about 30\% of particle diameter, the continued clusters are nearly identical, both within and across families of potentials. For longer ranges the clusters vary significantly, with more variation between families of potentials than within a family. We analyze the mechanisms behind the merge events, and find that most rearrangements occur when a pair of non-bonded particles comes within the range of the potential. An exception occurs for nonharmonic clusters, those that have a zero eigenvalue in their Hessian, which undergo a more global rearrangement.
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