Research
As an applied mathematics PhD student I have worked on building numerical methods for two phase-field problems.
First, for nematic liquid crystals using the Landau-de Gennes Q-tensor theory. This uses a mean-field approach to model the phase transitions of materials through intermediate phases between isotropic liquid and crystalline solid. Additionally, I have also developed methods for studying cholesteric and blue phase liquid crystals.
Second, for the Cahn-Hilliard equation. I have worked on developing a model for mixtures of three (or more) phases or components using a modified Cahn-Hillard system.
Numerical schemes for such problems are often designed to balance accuracy with efficiency, and to preserve some property of the continuous PDE problem at the discrete level. For example, it is desirable that the discrete solution will have similar energy dissipation as the true solution.
These problems are challenging since there are often several unknowns coupled through nonlinear terms in a large system of equations. Creating models which can accurately model dynamics in three dimensions efficiently is valuable to researchers in materials science to help explain their laboratory experiments.
Topic Summaries:Publications
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Linear Numerical Schemes for a Q-Tensor System for Nematic Liquid Crystals
Justin Swain and Giordano Tierra
Comp. Methods in App. Mechanics and Engineering
doi: 10.1016/j.cma.2024.117190 -
Dynamic Motions of Topological Defects in Nematic Liquid Crystals under Spatial Confinement
Tejal Pawale, Justin Swain, Mohammad Reza Hashemi, Giordano Tierra, and Xiao Li
Advanced Materials Interfaces
doi: 10.1002/admi.202300136 -
Genome Sequences of Streptomyces Phages Amela and Verse
Layton, S. R., Hemenway, R. M., Munyoki, C. M., Barnes, E. B., Barnett, S. E., Bond, A. M., Narvaez, J. M., Sirisakd, C. D., Smith, B. R., Swain, J., Syed, O., Bowman, C. A., Russell, D. A., Bhuiyan, S., Donegan-Quick, R., Benjamin, R. C., & Hughes, L. E.
Genome announcements
doi: 10.1128/genomeA.01589-15
Conference Presentations
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Linear Numerical Schemes for a Q-Tensor Model of Nematic Liquid Crystals
Mini-symposium talk at SIAM TX-LA Sectional Meeting
Lafyette LA, November 2023 -
Energy Stable Numerical Schemes for Nematic Liquid Crystals
Poster presentation at SIAM Annual Meeting
Pittsburgh PA, July 2022 -
New Numerical Schemes for the Q-Tensor Model of Nematic Liquid Crystals
Poster presentation at SIAM TX-LA Sectional Meeting
Houston TX, November 2022
Efficient and Unconditionally Energy Stable Numerical Schemes for a Ternary Cahn-Hilliard System
Mini-symposium talk at SIAM TX-LA Sectional Meeting
Waco TX, October 2024
Efficient and Unconditionally Energy Stable Numerical Scheme for a Ternary Cahn-Hilliard Model
Poster presentation at UNT Research Day 2024
Denton TX, October 2024
