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Instabilities in Reaction-Diffusion Systems
Here I want to provide a very brief introduction to instabilities in some generic spatial equations, and in particular reaction-diffusion systems on continuous and discrete (network) domains. Turing instabilities in such systems provide a way to generate spatially heterogeneous states … Continue reading
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Quotes about Mathematical Modelling
Below is a list of quotes I have come across related to modelling, widely interpreted. I will try and update this as I come across interesting statements. Please do send me things I have missed here (errors, quotes to consider, … Continue reading
Posted in Pedagogy, Perspectives, Uncategorized
Tagged mathematical modelling, quotes, theory
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Dynamical Phase Portraits
So this is a short tale about how stumbling upon two curious ideas led me to a cathartic afternoon of making some pretty videos. Skip to the bottom for some pretty animations unless you’re keen to see where the ideas … Continue reading
Posted in Expository, Mathematical, Uncategorized
Tagged Chebfun, complex variables, polynomials
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Theodicy
“Do not be daunted by the enormity of the world’s grief. Walk humbly now. Do justly now. Love mercy now. You are not expected to complete the work, but neither are you free to abandon it.” -various religious sources including … Continue reading
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An Interesting Year
This year has been an exceptionally productive one, partly due to many things from the previous few years accumulating, and partly because it was a long year of hard work. I formally completed my DPhil at Oxford (though my Thesis was … Continue reading
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Numerically Approximating Conformal Maps with the Zipper Algorithm
Update: A commenter points out some errors in the terminology used. Additionally, there are now much better codes available for zipper-like algorithms in Matlab, as well as Julia implementations. Additionally there are codes for the circle packing algorithm which someone may find … Continue reading
Posted in Expository, Mathematical, Uncategorized
Tagged complex analysis, conformal maps
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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
Posted in Expository, Mathematical, My Research, Uncategorized
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Fluid Dynamics and Mechanobiology
Today I want to discuss some of the mathematics I’ve been doing, and mention where I hope my research goes. My doctoral research hasn’t exactly narrowed down on a particular question yet, as we are asking around to find experimental … Continue reading
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Empathic Dynamics 