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Department of Mathematics and Philosophy

Events

Colloquium

Thursday, April 18, 2024
4:00 p.m. (refreshments served at 3:30)
Morgan Hall 204
Zoom:

Generation of High-Order Meshes for Biomedical Simulations. Dr. Suzanne Shontz, University of Kansas

Abstract: High-quality meshes are required when numerically solving partial differential equations (PDEs) on biomedical models to ensure sufficient accuracy. Such meshes are needed when simulating the heart’s bioelectricity or blood flow, for example. There are several challenges when generating high-quality meshes on anatomical models, such as cardiac anatomies, due to the complex geometry of the heart, its curvature, and its motion. Computational modeling of anatomical models bounded by curved surfaces can benefit from the use of high-order curved meshes. Using such meshes ensures that the curvature is captured correctly in the corresponding mesh. In addition, the use of high-order meshes in combination with a high-order PDE solver leads to greater computational efficiency. Such meshes also help prevent instabilities when used in dynamic simulations. In this talk, we first present our advancing front-based method for generating high-order tetrahedral meshes. While most high-order mesh generation methods represent the boundary surface using a computer-aided design (CAD) model, our method is more general. It can employ a high-order surface mesh which was generated from medical image segmentation masks or a CAD model. Our method then directly generates a highorder volume mesh and optimizes its quality. Second, we present our method for generating dynamic high-order tetrahedral meshes. Our method is based on a finite element formulation for hyperelastic materials. This allows us to apply the algorithm to study time-dependent deformations of organs and tissues in the human body, such as those present in cardiac applications. We use these methods to generate several high-order tetrahedral meshes of anatomical models obtained from medical images and CAD models and apply several time-dependent deformations. This talk represents joint work with Fariba Mohammadi, University of Michigan, and Cristian Linte, Rochester Institute of Technology.

Student Colloquium

Thursday, March 28, 2024
3:30 p.m. (refreshments served at 3:15)
Morgan Hall 204
Zoom:

Are we there yet? Predicting the global peak of an infection with COVID-19 as a case study. Harsha Induruwage.

Abstract: While a pandemic progresses, it is quite difficult to predict the day of the global peak or the number of infections until the peak. Using COVID-19 data, we demonstrate how one could utilize Ito stochastic differential equations with a gamma distribution correction to estimate disease transmission parameters as functions of time to predict the dynamics. This research is a collaborative effort between Dr. Dinesh Ekanayake, Dr. Elizabeth Hansen, and Harsha lduruwage.

Colloquium

Wednesday, March 27, 2024
4:00 p.m. (refreshments served at 3:30)
Morgan Hall 204
Zoom:

A Microgenetic Learning Analysis of Contextuality in Reasoning about Exponential Modeling. Elahe Allahyari.

Abstract: Exponential functions are a difficult, yet important, mathematical concept that plays an important role in the study of advanced mathematics (Weber, 2002). There is an essential need to explore students’ understanding of different topics at the college level, especially those topics that students find difficult such as exponential functions. This study found that undergraduate students’ understanding of exponential functions and modeling is highly context sensitive. Educators need to have a better understanding of students’ perception of contextual variation and its influence on students’ thinking and reasoning (Wagner, 2006; 2010). In this presentation, I will describe how we may utilize a conceptual change theory to understand better what features of contextual tasks students notice and how this impacts their reasoning patterns. I will present the results of this study that draws on the Knowledge in Pieces epistemological perspective (diSessa, 1993; 2018) to better understand the knowledge resources that students activate coming to discern the appropriateness of exponential models. This study investigates how students’ reasoning patterns shift as they engage with a sequence of tasks designed to help them link their prior experience with linear modeling to exponential modeling. Some examples of data analysis and students’ cognitive patterns will be presented, and I will discuss potential implications of the result of this study.