Signed Chord Length Distribution. II

TL;DR

This paper extends the study of signed chord length distributions, exploring their relation to transfer integrals and geometrical distributions for unions of bodies, especially nonconvex objects, with implications for correlation functions and distributions.

Contribution

It provides new insights into the mathematical relations between transfer integrals and geometrical distributions for unions of bodies, including nonconvex cases, building on prior work.

Findings

Relation between transfer integrals and geometrical distributions established

Derivatives of correlation functions can produce negative densities for nonconvex unions

Many equations are direct extensions from Part I

Abstract

This paper continues description of applications of signed chord length distribution started in part I (arXiv:0711.4734). It is shown simple relation between equation for some transfer integrals with source and target bodies and different geometrical distributions for union of this bodies. The union of disjoint bodies is always nonconvex object and for such a case derivatives of correlation function (used for definition of signed radii and chord lengths distributions) always produce (quasi)densities with negative values. Many equations used in this part are direct consequences of analogue formulas in part I.