# Rainey Lyons

## Research

I am broadly interested in applied mathematics, but I have specific interests in mathematical modeling, differential equations, measure valued PDEs, numerical analysis, dynamical systems, optimization, etc.

I will gladly work on any interesting mathematical problem with applications to the natural sciences.

## Teaching

I have taught the following courses:

- College Algebra (University of Louisiana at Lafayette (UL)),
- Precalculus Algebra (UL),
- Precalculus Trigonometry (UL),
- Survey of Calculus (UL),
- Elementary Linear Algebra (UL).

## Collaboration

My main collaborator at this time is **Adrian Muntean** here at Karlstad University. Some other collaborators include:

**Sander Hille**(Leiden University),**Emilio N. M. Cirillo**(Sapienza University of Rome),**Andrea Muntean**(Karlstad University),**Azmy S. Ackleh**(University of Louisiana at Lafayette),**Nicolas Saintier**(University of Buenos Aires),**Annette M Ostling**(University of Texas at Austin),**Ursula Trigos-Raczkowski**(University of Michigan).

## Bio

Originally from New Orleans, Louisiana, I attended the University of Louisiana at Lafayette for my Bachelor of Science in Mathematics (2016), Master's of Science in mathematics (2019), and Doctor of Philosophy in Mathematics (2021).

## Selected publications

**R.Lyons**, S. A. Muntean, E. N. M. Cirillo, , A. Muntean, A Continuum Model for Morphology Formation from Interacting Ternary Mixtures: Simulation Study of the Formation and Growth of Patterns, preprint.

A. S. Ackleh, **R. Lyons**, and N. Saintier, Finite difference schemes for a size structured coagulation-fragmentation model in the space of Radon measures, *IMA Journal of Numerical Analysis*, 2022; https://doi.org/10.1093/imanum/drac071

A. S. Ackleh, **R. Lyons**, and N. Saintier, Structured Coagulation-Fragmentation Equation in the Space of Radon Measures: Unifying Discrete and Continuous Models, *ESAIM: Mathematical Modelling and Numerical Analysis*, 2021;

https://doi.org/10.1051/m2an/2021061 |

## Other

During my time here as a postdoctoral fellow, I am supported by The Carl Trygger Foundation for Scientific Research.

## Publications

- Rainey Lyons, Stela Andrea Muntean, Emilio N.M. Cirillo, Adrian Muntean, 2023
- Azmy S. Ackleh, Rainey Lyons, Nicolas Saintier, 2023