Computed Probability Density Functions of the Radii of Gyration of Long Randomhyphen;Flight Chains

摘要

Probability density functions for the orthogonal components of the radius of gyration,Si, of a randomhyphen;flight chain were computed using an indirect numerical integration algorithm which was based upon a multiple convolution proposed by Forsman and Hughes. Computations were performed for relatively long chains of 100ndash;1000 statistical segmentst. By using a reduced radius of gyrationxgr;ithinsp;equals;thinsp;lpar;pgr;thinsp;sol;thinsp;23rpar; Silang;Si2rang;minus;1thinsp;sol;thinsp;2the distributions converged to a limiting function at abouttthinsp;equals;thinsp;500, except for extremely small radii,xgr;ithinsp;le;thinsp;lsqb;10lpar;2trpar;1sol;2rsqb;minus;1. Additional computations using the onehyphen;dimensional distributions yielded the corresponding probability densities for both the twohyphen; and threehyphen;dimensional (polar) radii. The computed functions were in excellent agreement with all their limiting properties previously determined by analytical methods.