{'fraction_non_alphanumeric': 0.040632054176072234, 'fraction_numerical': 0.007900677200902935, 'mean_word_length': 4.993243243243243, '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}}
Viscous attractor for the Galton board.

We analyze the Galton Board [or periodic "Lorentz Gas"] with a point mass scattered by elastic disks of diameter sigma, using a constant driving field g and a constant-viscosity linear drag force -p/tau, where p is the point-mass momentum. This combination leads to a nonequilibrium steady state which depends only upon the dimensionless ratio gtau(2)/sigma. The long-time-averaged trajectory leads to multifractal phase-space structures closely resembling those we found earlier using isokinetic equations of motion derived from Gauss' Principle of Least Constraint. A highly damped [small tau] creeping-flow limit describes our results for gtau(2)/sigma less than about 0.2. The lightly damped Green-Kubo linear-response limit for the model provides an accurate description of the dissipative dynamics for gtau(2)/sigma greater than about 2.0.