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My research focuses on the theory and applications of dynamical systems that feature multiple timescales, such as the Koper model from chemical kinetics and the Hodgkin-Huxley equations from mathematical neuroscience. In parallel, I also look into the existence and stability of travelling waves in reaction-diffusion equations with cut-off functions.
My mathematical research is motivated by the need to handle energetic materials (materials with large stores of chemical energy) with care. I develop models to describe a sample's thermo-mechanical response to a given low-energy mechanical insult, focusing on the physics underlying the material's behaviour, so as to inform safety principles. When analysing the models, I tend to opt for pen-and-paper techniques, such as matched asymptotics and PDE methods.
Andrés Miniguano Trujillo