Presentation by Mansi Mahajan

Title : Spectral Finite Elements for Electromagnetic Metamaterial Models

Abstract: Metamaterials are artificially structured materials designed to exhibit electromagnetic properties not found in naturally occurring materials. This talk begins with a brief overview of electromagnetic metamaterials and their applications, such as cloaking, negative refraction, and superlensing. I will then introduce spectral finite element methods for modeling wave propagation in such media, with a focus on dispersive models like the Drude model and the use of edge (Nédélec) elements for accurate discretization of Maxwell’s equations. The talk will also touch on dispersion relations arising from the discretized system and their relevance to wave behavior in metamaterials.

Presentation by Nicholas Slugg

Title: Modeling Hysteresis in Permafrost Thaw Using Neural Networks

Abstract: Modeling permafrost thaw is an important task due to the importance of permafrost on the local landscape and global climate. Permafrost presents several modeling challenges due to its heterogeneity leading to several physical processes being coupled together. In particular the incorporation of phase changes presents a significant challenge. We consider modeling permafrost with a hysteretic phase change, where the relationship between the temperature and unfrozen water content has memory dependence. We discuss the calibration of Preisach hysteresis models using feedforward NN in order to avoid issues faced with other methods of calibration. Finally, we consider implementation with a coupled heat transfer model and present numerical solutions.