Characterization and Modeling of Spatiotemporal Behaviors in Corals, Elastic Metamaterials and Origami

Abstract

Spatiotemporal behaviors have been widely found in natural and artificial systems, indicating the movement and dynamics that occur in both space and time. These behaviors have significant impact on numerous fields, including ecology, finance, transportation and mechanical engineering. Some examples of spatiotemporal behaviors in these fields include the movement of animals, human behaviors, traffic flow, and vibrations. Understanding spatiotemporal behaviors is essential for developing effective management strategies and gaining insights into the underlying physical mechanisms that motivate these behaviors. Coral reef ecosystems harbor a vast range of species and biological activities, but they are facing a severe crisis caused by the increasingly intensive anthropogenic activities and climate change. To better understand the impact of these challenges on coral reef survival and fitness, it is essential to comprehend the behaviors of corals in a timely manner. Coral motion, encompassing the movements of tissues, polyps, and tentacles, is a fundamental behavioral trait of the coral holobiont that plays a critical role in feeding, competition, reproduction, and ultimately survival. As a result, characterizing coral behaviors through motion analysis can aid our understanding in basic biological and physical functions. Nevertheless, characterization and modeling of coral motion are challenging and largely unexplored, given the complexity of the biological system and the inherent spatiotemporal multi-scale features of these movements. Apart from the corals, artificial systems such as elastic metamaterials and origami structures also possess spatiotemporal behaviors such as elastic wave propagation and structural dynamics. However, the lack of corresponding data-driven analysis and nonlinear nature of origami structures result in the research voids. To address these challenges in characterization and modeling of spatiotemporal behaviors, in terms of coral motions, we have implemented a range of approaches, including observation techniques, imaging processing techniques, and theoretical/data-driven modeling. Specifically, we have employed several techniques used in the engineering fields such as digital image correlation, motion magnification and object tracking, as well as modeling methods such as the Langevin equation and dynamic mode decomposition. These methods have been proven effective in characterizing and modeling the motion of coral tissues, polyps and tentacles. By combining these different approaches, we aim to better understand the underlying biophysics of corals and to develop new tools and methodologies for managing the impact of climate change on coral reef ecosystems. Furthermore, in terms of elastic metamaterials and origami, we use theoretical modeling and dynamic mode decomposition(and its variants) to characterize and model the corresponding systems. Our approaches provide insights into the underlying physics in wave dynamics and structural dynamics, and develop models for predicting the future responses under external stimuli. Our work has not only resulted in unparalleled understanding of coral biophysical behaviors in terms of motions, providing a useful toolkit for the coral research community to face the challenges in the future climate change, but also paved the way in characterizing and modeling elastic wave propagation and origami dynamics using theoretical/data-driven methods. We anticipate that our methods, particularly the data-driven approach of dynamic mode decomposition, will be applicable to solve problems of dynamics in a variety of complex systems in the future research.