{'fraction_non_alphanumeric': 0.026004728132387706, 'fraction_numerical': 0.004728132387706856, 'mean_word_length': 5.515384615384615, 'pattern_counts': {'":': 0, '<': 3, '<?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}}
Dielectric Spectra of Grainy High-Permittivity Materials

Dielectric response of grainy systems is described proposing the generalized brick model, in which the shape of grains (separated by grain boundaries or cracks) is characterized by the depolarizing factor n=xg (0<n<1), where g<1 is a geometrical factor, x ≪ 1 is the volume fraction of grain boundaries. The standard mixing formulas (series or parallel capacities, Hashin-Shtrikman formula) can be obtained by an appropriate choice of the g value. Considering both the classical three parameter and generalized four parameter models for the polar phonon contribution to the permittivity, the effective dielectric response is analytically calculated. It is shown that the effective frequency of each phonon mode increases linearly with the concentration x and with its dielectric strength.