Publication Date

2026

Abstract/Description/Artist Statement

We study the evolution of nematic liquid crystals in two dimensions using the Q-tensor model, a continuum framework that describes the orientational order of rod-like molecules via symmetric, traceless matrices. Focusing on the Landau-de Gennes energy and its associated gradient flow, we consider a reduced two-dimensional formulation in which the Q-tensor is fully described by two scalar functions. This reduction simplifies the system to a nonlinear, coupled PDE for the scalars, while preserving essential physical features. A key question is whether the eigenvalues of the Q-tensor remain within the physically admissible range under this flow. Building on a theoretical result that establishes eigenvalue preservation for smooth solutions, we perform numerical simulations to verify this behavior. Our results confirm the robustness of the eigenvalue constraint across various initial configurations, providing computational support for the physical consistency of the model.

Presenting Author Name/s

Marcel DeGuzman

Faculty Advisor/Mentor

Xiang Xu

Faculty Advisor/Mentor Department

Department of Mathematics and Statistics

College/School Affiliation

College of Sciences

Student Level Group

Undergraduate

Presentation Type

Oral Presentation

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Eigenvalue Bound Preservation: Numerical Experiments on the 2D Q-Tensor Flow

We study the evolution of nematic liquid crystals in two dimensions using the Q-tensor model, a continuum framework that describes the orientational order of rod-like molecules via symmetric, traceless matrices. Focusing on the Landau-de Gennes energy and its associated gradient flow, we consider a reduced two-dimensional formulation in which the Q-tensor is fully described by two scalar functions. This reduction simplifies the system to a nonlinear, coupled PDE for the scalars, while preserving essential physical features. A key question is whether the eigenvalues of the Q-tensor remain within the physically admissible range under this flow. Building on a theoretical result that establishes eigenvalue preservation for smooth solutions, we perform numerical simulations to verify this behavior. Our results confirm the robustness of the eigenvalue constraint across various initial configurations, providing computational support for the physical consistency of the model.