Tomadakis M M, Sotirchos S V
Department of Chemical Engineering, University of Rochester, New York 14627-1066.
Radiat Res. 1993 Sep;135(3):302-11.
Distributions associated with random tracks in bodies are important to understanding the effects of radiation on objects and their response to it. Results of computer simulations are presented for the distribution densities, average lengths, and relative frequencies of the various types of random tracks resulting from the traversal of random arrays of cylinders by random lines. We consider arrays consisting of freely overlapping long circular cylinders distributed randomly with their axes parallel to a line or a plane, or oriented randomly in the three-dimensional space. The problem of random tracks lying outside the cylinders (external random tracks) is treated analytically, while the distributions of random tracks found within the cylinders (internal random tracks) are determined using a simulation procedure based on a discrete step-by-step random walk mechanism applied in finite samples of the arrays. The numerical results are used to validate various general analytical results for the distribution densities and average lengths of random tracks in structures of arbitrary shape. It is found that the distributions of internal random tracks exhibit strong dependence on the cylinder volume fraction, while the external random tracks are distributed independently of the cylinder volume fraction for all three cases of orientation distribution. At the limit of high cylinder volume fraction, the internal random track distributions approach the distributions of the external random tracks, while at the other extreme, they become, as expected, identical to those determined analytically for a single infinite cylinder.
与物体中随机轨迹相关的分布对于理解辐射对物体的影响及其对辐射的响应非常重要。本文给出了计算机模拟结果，涉及随机线穿过随机圆柱阵列时产生的各种类型随机轨迹的分布密度、平均长度和相对频率。我们考虑由自由重叠的长圆形圆柱组成的阵列，这些圆柱的轴平行于一条线或一个平面随机分布，或者在三维空间中随机定向。对于位于圆柱外部的随机轨迹（外部随机轨迹）问题进行了分析处理，而对于圆柱内部发现的随机轨迹（内部随机轨迹）的分布，则使用基于离散逐步随机游走机制的模拟程序来确定，该机制应用于阵列的有限样本。数值结果用于验证关于任意形状结构中随机轨迹的分布密度和平均长度的各种一般分析结果。结果发现，内部随机轨迹的分布强烈依赖于圆柱体积分数，而对于所有三种取向分布情况，外部随机轨迹的分布与圆柱体积分数无关。在高圆柱体积分数的极限情况下，内部随机轨迹分布接近外部随机轨迹分布，而在另一个极端情况下，正如预期的那样，它们变得与针对单个无限圆柱解析确定的分布相同。
