{'fraction_non_alphanumeric': 0.029508196721311476, 'fraction_numerical': 0.013114754098360656, 'mean_word_length': 5.542857142857143, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
Electromagnetic radiation and scattering from elliptical torus knots

A mathematically rigorous approach for combining knot theory with Maxwell's theory of electromagnetism was reported by Werner (see IEEE Antennas and Propagation Society International Symposium Digest, vol.2, p.1468-71, Montreal, Canada, 1997). This analysis methodology was initially used to investigate the electromagnetic characteristics of a special class of knots, known as (p,q)-torus knots. A convenient set of parametric representations was developed by Werner for this particular family of knots by making use of the fact that they may be constructed on the surface of a standard circular torus in R/sup 3/. These parameterizations were then used in combination with Maxwell's equations to derive vector potential and field expressions which describe the radiation and scattering of electromagnetic waves from circular (p,q)-torus knots.