Empirical Method for Assessing the Chirality of Objects in the Material World: From Molecular to Galactic Scales
摘要
A new algorithm is proposed for calculating a functional that characterizes the empirical chirality of an examined object. Empirical chirality is calculated as the normalized scalar product of a vector connecting the first and last reference points with the sum of the vector products of vectors connecting adjacent reference points. The system of reference points is constructed based on experimental data and characterizes the object with the given precision. The sign of the empirical chirality indicates the object’s twist direction (positive for right-handed, negative for left-handed). The chirality modulus, equal to zero, corresponds to an achiral object, while a modulus of one represents a maximally twisted object. Using the elongation of the object as a secondary coordinate allows for its representation as a point on a two-dimensional chirality map. The empirical chirality of biological macromolecules shows good agreement with the existing structural representations. The proposed algorithm is used to study the chirality of technical objects, and the found estimates of the chirality of the two stairs of the Leaning Tower of Pisa correspond to their design. Analyzing the Orion Arm in the vicinity of the Solar System required calculating reference points based on the averaged coordinates of multiple stars. It is found that the Orion Arm has a left-handed twist. The proposed method enables the calculation of empirical chirality, characterizing the geometric properties of objects across a wide range of scales, and facilitates their representation on a general map of chirality.