10th International Aerosol Conference September 2 - September 7, 2018 America's Center Convention Complex St. Louis, Missouri, USA
Abstract View
Interpreting the Kinetics of Ballistic-to-Diffusive Transition Using Directional Statistics
PAI LIU, William Heinson, Benjamin Sumlin, Rajan K. Chakrabarty, Washington University in St. Louis
Abstract Number: 823 Working Group: Aerosol Physics
Abstract We demonstrate a new method to interpret the rate of ballistic-to-diffusive (BD) transition in stochastic motion commonly observed in many physical systems. The correlation between successive steps of the motion is parametrized using a wrapped Cauchy distribution (WCD) that governs the probability distribution of the tracer’s turning angle. With increasing timescale, the distribution evolves from a delta function to a uniform distribution, marked by a decrease in the shape factor of WCD. This trend agrees with BD transition behavior revealed from the scaling law between the mean-squared displacement and time. We next propose an analytical solution to the decrease in the shape factor which accurately predicts the transition rates. We conclude this work with simple mathematical equations that relate three parameters of the motion: time, exponent of the spatial-temporal scaling power-law, and the shape factor of WCD.