利用拟概率分布将Dirac弦方法推广到非凸集情形
Extension of Dirac's chord method to the case of a nonconvex set by use of quasi-probability distributions
摘要：
狄拉克弦法可以适用于物理学的不同领域，用于使用弦长分布的概率密度来表示凸体的某些六维积分。对于在具有相同性质的介质中具有非凸体的齐次模型，如果使用所谓的广义弦分布，则可以得到狄拉克弦方法的类似物。该函数被定义为自相关函数的归一化二阶导数。对于非凸体，该二阶导数可能具有负值，并且不能与概率密度直接相关。被认为是这样一个功能的解释使用交替的概率密度的总和。这种准概率分布可用于Monte Carlo计算的一些积分为一个单一的机构的任意形状和系统的两个或两个以上的对象和这样的应用程序也讨论了这项工作。
英文摘要：
The Dirac's chord method may be suitable in different areas of physics for the representation of certain six-dimensional integrals for a convex body using the probability density of the chord length distribution. For a homogeneous model with a nonconvex body inside a medium with identical properties an analogue of the Dirac's chord method may be obtained, if to use so-called generalized chord distribution. The function is defined as normalized second derivative of the autocorrelation function. For nonconvex bodies this second derivative may have negative values and could not be directly related with a probability density. An interpretation of such a function using alternating sums of probability densities is considered. Such quasi-probability distributions may be used for Monte Carlo calculations of some integrals for a single body of arbitrary shape and for systems with two or more objects and such applications are also discussed in this work.
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