Elucidation of Relaxation Dynamics Beyond Equilibrium Through AI-informed X-ray Photon Correlation Spectroscopy

Understanding and interpreting dynamics of functional materials \textit{in situ} is a grand challenge in physics and materials science due to the difficulty of experimentally probing materials at varied length and time scales. X-ray photon correlation spectroscopy (XPCS) is uniquely well-suited for characterizing materials dynamics over wide-ranging time scales, however spatial and temporal heterogeneity in material behavior can make interpretation of experimental XPCS data difficult. In this work we have developed an unsupervised deep learning (DL) framework for automated classification and interpretation of relaxation dynamics from experimental data without requiring any prior physical knowledge of the system behavior. We demonstrate how this method can be used to rapidly explore large datasets to identify samples of interest, and we apply this approach to directly correlate bulk properties of a model system to microscopic dynamics. Importantly, this DL framework is material and process agnostic, marking a concrete step towards autonomous materials discovery

Asymptotic properties of a stochastic Lotka–Volterra model with infinite delay and regime switching

Abstract We investigate the long-term properties of a stochastic Lotka–Volterra model with infinite delay and Markovian chains on a finite state space. We investigate that the stochastic model admits a unique positive global solution which stays in the way of stochastically ultimate boundedness by constructing Lyapunov functions. Furthermore, the main results that the growth of the solution is slower than time under moderate condition and moment estimation in time average with the power p could be controlled are derived, which modified the known ones in recent literatures