Mathematical and Computational Engineering Stream

Topological Data Analysis for the Study of Granular Materials

Faculty: Tejas Murthy (Civil) and Vijay Natarajan (CSA)

Figure 1: A Morse theory-based method produces high quality segmentation of an X-ray CT scan of cemented sand particles. Further, it enables the computation of a network representation of the contacts between individual particles.

Summary: Granular materials (or particulate materials) such as sand, powders, food grains, and tablets are ubiquitous in the infrastructure, mining, pharmaceutical and food industries. They exhibit an array of intriguing properties that are dependent on the interparticle arrangement. An understanding of granular materials is crucial for handling of these systems in the industry. The advent of imaging and image analysis has provided unparalleled insight into the physics and mechanics of such particulate materials.

This project seeks to investigate a framework for understanding particles of various morphologies using image analysis. High resolution tomography data will be used for a detailed understanding of the structure and packing of granular media of various particle morphologies. Further tenets of networks will be suitably adapted for understanding packing of such ensembles.

Topological methods provide powerful concepts for data abstraction that are characterized by their robustness, rigorous guarantees, and multi-scale nature. Methods from topological data analysis (TDA) play an important role for structural data analysis and visualization in many science and engineering disciplines. TDA builds on solid mathematical foundations in Morse theory and their extensions from smooth functions to piecewise linear and discrete data, and algebraic topology [2]. We will explore the development of novel TDA methods for the study of granular media.

Requirement: Applicants should have either

  • a background in mathematics, applied mathematics, computer science, or computational science with a strong interest in physics / engineering
  • a background in materials science / engineering, soft matter physics with strong mathematical and computing skills.

References

  • Karran Pandey, Talha Bin Masood, Saurabh Singh, Ingrid Hotz, Vijay Natarajan, and Tejas G. Murthy. Morse theory-based segmentation and fabric quantification of granular materials. Granular Matter, 24(1), 2022, 27:1-20. https://vgl.csa.iisc.ac.in/paper.php?pid=068
  • Lin Yan, Talha Bin Masood, Raghavendra Sridharamurthy, Farhan Rasheed, Vijay Natarajan, Ingrid Hotz and Bei Wang. Scalar Field Comparison with Topological Descriptors: Properties and Applications for Scientific Visualization. Computer Graphics Forum (EuroVis STAR 2021), 40(3), 2021, 599–633. https://vgl.csa.iisc.ac.in/paper.php?pid=065