碰撞粒子群的稳态尺寸分布：强度依赖于尺寸的解析解
Steady-State Size Distributions for Collisional Populations: Analytical Solution with Size-Dependent Strength
摘要：
由碰撞级联产生的物体的稳定态人口取决于材料强度如何随尺寸变化。我们发现一个简单的表达式的幂律指数的人口，给定一个幂律，描述了材料的强度如何随大小而变化。这一结果被推广到与小行星带和柯伊伯带有关的情况，其中物质强度由两个独立的幂律描述--一个适用于小天体，一个适用于大天体。我们发现小天体总体的幂律指数不受大天体强度定律的影响，反之亦然。简单的解析表达式描述了一个波，由于描述强度的两个幂律之间的过渡，波叠加在大物体上。这些分析结果与碰撞演化的数值模拟结果吻合得很好。这些结果将有助于解释小行星和KBO的观测，并限制这些物体的强度特性。
英文摘要：
The steady-state population of bodies resulting from a collisional cascade depends on how material strength varies with size. We find a simple expression for the power-law index of the population, given a power law that describes how material strength varies with size. This result is extended to the case relevant for the asteroid belt and Kuiper belt, in which the material strength is described by 2 separate power laws--one for small bodies and one for larger bodies. We find that the power-law index of the small body population is unaffected by the strength law for the large bodies, and vice versa. Simple analytical expressions describe a wave that is superimposed on the large body population because of the transition between the two power laws describing the strength. These analytical results yield excellent agreement with a numerical simulation of collisional evolution. These results will help to interpret observations of the asteroids and KBOs, and constrain the strength properties of those objects.
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