Category Archives: Expository

Numerically Approximating Conformal Maps with the Zipper Algorithm

As with the previous post, I want to mention some other work I did related to my DPhil course. This project was about implementing an algorithm to numerically compute conformal maps between simply connected domains and the unit disk. By … Continue reading

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Some Visualizations in Mathematical Physiology

“…the equations we deal with are probably more complicated than even most physical scientists are accustomed to. This is because the phenomena we are attempting to describe are generally more complex than most physical systems, although it may reflect our … Continue reading

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Non-Existence of Patterns in Reaction-Diffusion Systems

In writing up several recent papers I have spent some time reading about Reaction-Diffusion systems and the kinds of behaviour they can have. I will likely blog about these kinds of equations more often, as well as applications of them … Continue reading

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Dissipative Functions and Reaction-Diffusion Equations

I want to review some aspects of dynamical systems theory for a class of dissipative systems which are particularly simple. These are systems that posses a Lyapunov function. Dissipative systems are mathematical objects that evolve in time, but remain in … Continue reading

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Nonlinear Dynamics on Networks

Today I want to talk about dynamical systems on networks. A good review article can be found here. In this post I want to focus on the interplay between the topology of the underlying network, and the asymptotic dynamics of … Continue reading

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A Note on Multiple Scales: Homogenization Theory

As I have mentioned before, many problems in science can be profitably attacked from a large variety of different angles. Today I want to discuss one particular aspect of theoretical work in a technical way, in order to provide a bit more … Continue reading

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The Spectrum of Rigour: PDE Theory, Shocks, and the Devil’s Invention

An overly simplistic (and hence incorrect) view of science is one in which we think all scientists have the same level of certainty in their descriptions of natural phenomena. One might suggest that different scientific fields could be arranged by … Continue reading

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