{'fraction_non_alphanumeric': 0.01997780244173141, 'fraction_numerical': 0.0011098779134295228, 'mean_word_length': 4.895424836601308, '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}}
Numerical Simulations of N Point Vortices on Bounded Domains

Behavior of vortices is core to the understanding of phenomenons in nature, such as Jupiter’s red spot. The simplification to point vortices provides us with an easier way to model behaviors of large numbers of vortices. Although we know from statistical mechanics that there exists a time invariant measure, it is unclear whether the measure derived from the Mean Field Equation (MFE) reflects the true behavior in nature. We explore the point vortex model on the 2 dimensional disk and test for the convergence to the Mean Field distribution using Kolmogorov-Smirinov test (K-S test). Due to the pairwise interaction of the vortices, we use the Fast Multipole Method (FMM) to decrease the calculations required. We hope that the observed behavior on the disk imply a general result on all simply connected domains via conformal mappings.