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Applied and Computational Math Seminar

From materials science to computational topology: interaction networks in particulate matter

Lou Kondic (New Jersey Institute of Technology)

Location:  Hill 705
Date & time: Tuesday, 07 March 2023 at 11:00AM - 12:00PM

We will discuss interaction networks that spontaneously form in particulate-based systems. These networks, most commonly known as `force chains' in granular systems, are dynamic structures which are by now known to be of fundamental importance for the purpose of revealing the underlying physical causes of a number of physical phenomena involved in statics and dynamics of particulate-based systems. The presentation will focus on applications of algebraic topology, and in particular of persistent homology (PH) to analysis of such networks found in both simulations and experiments. PH allows for a simplified representation of complex interaction field in both two and three spatial dimensions in terms of persistent diagrams (PDs)that are essentially point clouds. These point clouds could be compared in a meaningful manner, meaning that they allow for the analysis of both static and dynamic properties of the underlying systems. It is important to point out that such representation is robust with respect to small perturbations, which is crucial in particular when applying the method to the analysis of experimental data. In the second part of the talk, we will focus on interaction networks in both simulated and experimental systems experiencing stick-slip, intermittent type of dynamics, with focus on exploring predictability potential of the considered topological measures.  

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