Math Colloquia | College of Sciences

Fall 2026 Mathematics Colloquia Schedule

Colloquium Date	Colloquium Presenter
September 25, 2026	Dr. Panayotis Panayotaros Mode Interactions of Surface Gravity Waves in Triangular Domains September 25 abstract We present a model of nonlinear mode interactions of 2-D gravity surface water waves in a domain with inclined lateral boundaries, assuming free surface potential flow. We consider an isosceles triangular domain with known linear modes and frequencies, and describe a preliminary analysis of the lowest nonlinear mode using normal forms. We also discuss theoretical and numerical work in progress on linear waves in more general domains. This is joint work with Eddaly Guerra Velasco, Boris A. Percino Figueroa, and Rosa M. Vargas Magaña. 4:30–5:30 pm \| FLN 2.01.02
October 2, 2026	Dr. Rayanne Luke Mathematical Models of Contact Lens Drug Delivery: Blinking and Lens Design October 2 abstract Drug-eluting contact lenses are an ophthalmic drug delivery alternative to eye drops. Such lenses can significantly increase drug residence time and therefore effectiveness. We design models of contact lens drug delivery to align with experimental systems and consider blinking and lens design. Our approach couples partial differential equations for linear diffusion of drug inside the contact lens with compartment models for the pre- and post-lens tear films and the eyelid region. To study blinking, we model the effect of a blink on the pre- and post-lens tear film drug concentrations, investigating mechanisms such as partial or full sweep out of drug by the eyelid, and squeezing or sliding of the lens. The most likely scenario is identified by comparing to model eye data. To study lens design, we model drug-polymer films encapsulated in hydrogel lenses, where the drug-laden region appears as an annulus in a top-down view. We investigate the dependence of drug release time on lens material and geometric properties and identify drug delivery transport mechanisms by comparing to in vivo data. In both cases, we recover drug cumulative release profiles from experimental systems, and determine the effects of blinking and lens design properties on cumulative release. This can inform our understanding of the mechanics of contact lens drug delivery and predict targeted tissue transport of drug. This is joint work with Dan Anderson (GMU). 2:50–4 pm \| BSB 3.03.02

Colloquium Date

Colloquium Presenter

September 25, 2026

Dr. Panayotis Panayotaros
Mode Interactions of Surface Gravity Waves in Triangular Domains
September 25 abstract

We present a model of nonlinear mode interactions of 2-D gravity surface water waves in a domain with inclined lateral boundaries, assuming free surface potential flow. We consider an isosceles triangular domain with known linear modes and frequencies, and describe a preliminary analysis of the lowest nonlinear mode using normal forms. We also discuss theoretical and numerical work in progress on linear waves in more general domains. This is joint work with Eddaly Guerra Velasco, Boris A. Percino Figueroa, and Rosa M. Vargas Magaña.

4:30–5:30 pm | FLN 2.01.02

October 2, 2026

Dr. Rayanne Luke
Mathematical Models of Contact Lens Drug Delivery: Blinking and Lens Design
October 2 abstract

Drug-eluting contact lenses are an ophthalmic drug delivery alternative to eye drops. Such lenses can significantly increase drug residence time and therefore effectiveness. We design models of contact lens drug delivery to align with experimental systems and consider blinking and lens design. Our approach couples partial differential equations for linear diffusion of drug inside the contact lens with compartment models for the pre- and post-lens tear films and the eyelid region. To study blinking, we model the effect of a blink on the pre- and post-lens tear film drug concentrations, investigating mechanisms such as partial or full sweep out of drug by the eyelid, and squeezing or sliding of the lens. The most likely scenario is identified by comparing to model eye data. To study lens design, we model drug-polymer films encapsulated in hydrogel lenses, where the drug-laden region appears as an annulus in a top-down view. We investigate the dependence of drug release time on lens material and geometric properties and identify drug delivery transport mechanisms by comparing to in vivo data. In both cases, we recover drug cumulative release profiles from experimental systems, and determine the effects of blinking and lens design properties on cumulative release. This can inform our understanding of the mechanics of contact lens drug delivery and predict targeted tissue transport of drug. This is joint work with Dan Anderson (GMU).

2:50–4 pm | BSB 3.03.02

Mathematics Colloquia

Fall 2026 Mathematics Colloquia Schedule

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