Xiaobing Li — Page 3

arXiv2021

Critical properties of various sizes of cluster in the Ising percolation transition

It is proposed that the $O(n)$ spin and geometrical percolation models can help to study the QCD phase diagram due to the universality properties of the phase transition. In this paper, correlations and fluctuations of various sizes of cluster in the Ising model are systematically studied. With a finite size system, we demonstrate how to use the finite size scaling and fixed point behavior to search for critical point. At critical point, the independency of system size is found from skewness and kurtosis of the maximum, second and third largest cluster and their correlations. It is similar to the Binder-ratio, which has provided a remarkable identification of the critical point. Through an explanation of the universal characteristic of skewness and kurtosis of the order parameter, a possible application to the relativistic heavy-ion collisions is also discussed.

hep-ph↗

arXiv2018

Development of Safety Performance Functions: Incorporating Unobserved Heterogeneity and Functional Form Analysis

To improve transportation safety, this study applies Highway Safety Manual (HSM) procedures to roadways while accounting for unobserved heterogeneity and exploring alternative functional forms for Safety Performance Functions (SPFs). Specifically, several functional forms are considered in Poisson and Poisson-gamma modeling frameworks. Using five years (2011-2015) of crash, traffic, and road inventory data for two-way, two-lane roads in Tennessee, fixed- and random-parameter count data models are calibrated. The models account for important methodological concerns of unobserved heterogeneity and omitted variable bias. With a validation dataset, the calibrated and uncalibrated HSM SPFs and eight new Tennessee-specific SPFs are compared for prediction accuracy. The results show that the statewide calibration factor is 2.48, suggesting rural two-lane, two-way road segment crashes are at least 1.48 times greater than what HSM SPF predicts. Significant variation in four different regions in Tennessee is observed with calibration factors ranging between 2.02 and 2.77. Among all the SPFs considered, fully specified Tennessee-specific random parameter Poisson SPF outperformed all competing SPFs in predicting out-of-sample crashes on these road segments. The best-fit random parameter SPF specification for crash frequency includes the following variables: annual average daily traffic, segment length, shoulder width, lane width, speed limit, and the presence of passing lanes. Significant heterogeneity is observed in the effects of traffic exposure-related variables on crash frequency. The study shows how heterogeneity-based models can be specified and used by practitioners for obtaining accurate crash predictions.

stat.AP↗