{'fraction_non_alphanumeric': 0.009164969450101833, 'fraction_numerical': 0.0, 'mean_word_length': 5.922535211267606, '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}}
Velocity shifts and reflection coefficients for periodic interdigital transducers: a demonstration of the equivalence of three methods

Previous methods of determining reflection coefficients and velocity shifts in surface acoustic wave devices mechanically loaded by a periodic grating have included boundary condition matching, perturbation theory, and the variational principle. The variational and perturbative treatments for piezoelectric substrates and arbitrary overlay materials were not however in good agreement for those cases in which the substrate and overlay material differed. With the use of an improved trial function for the variational treatment, the variational and perturbative approaches are shown to yield identical results for both isotropic and anisotropic media. The boundary matching method has also been generalized to allow for fingers of an arbitrary overlay material, and it is shown that for isotropic media all three methods are formally equivalent.