{'fraction_non_alphanumeric': 0.016587677725118485, 'fraction_numerical': 0.002369668246445498, 'mean_word_length': 4.787671232876712, '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}}
A Retrospective on Early Analysis and Simulation of Freeze and Thaw Dynamics

This paper recapitulates certain studies of cycles of freezing and thawing in the ground sponsored by the US Corps of Engineers and begun over 45 years ago by the writer and H.P. Aldrich, Jr. Because the latent heat of the soil moisture renders such problems nonlinear, these two MIT professors, together with R.F. Scott and other students, pioneered the use of digital and analog computers for such research. This involved the construction of unique hydraulic and electronic analog devices which have long since become CRREL museum pieces. However, a more lasting contribution was the provision of a new formula for computing the frost depth in temperate climates as well as annual thaw in permafrost zones. This Modified Berggren Formula remains in wide use today.