Author Archives: Andrew Krause

Some Surprising Things

Below are two surprising mathematical results which I found interesting recently. They kind of demonstrate some really fascinating ‘arbitrarily complex’ behaviours of very simple objects, and are primarily useful for philosophical grounding in terms of understanding tools used in science, … Continue reading

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Some Projects from 2017

This has been an incredibly busy and hectic year, but overall an extraordinarily rewarding one. I will catalogue some of what I did here in case anyone is interested, and point out some of the things that will hopefully happen … Continue reading

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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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