Tag Archives: expository

Scientific software workflow

We know the big differences between trying out a calculation on a back of an envelope and writing a rigorous proof. Likewise, there are differences between prototyping in a Matlab script and writing a reliable pre that supports a reproducible research project. In a 15-minute presentation for a introductory workshop on scientific software at UW Madison math department, I showcased my own workflow on a simple example of plotting several solutions to an ODE in Matlab.

Repository for the workshop can be obtained by

git clone https://bitbucket.org/mbudisic/workshopworkflow.git

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Two mode decompositions: POD and DMD

This is a short overview of the Proper Orthogonal and Dynamic/Koopman Mode Decompositions, which are commonly used in analysis of velocity fields of fluid flows. While I worked with the theoretical side of Koopman modes, I never implemented the numerical code myself; I wrote these notes up a I was teaching myself the basics of numerics of these decompositions, and consequently used the notes for two lectures. The notes are based References at the end of the post. Caveat lector: Notes may contain gross oversimplifications — the emphasis was on understanding and not on precision. I welcome your corrections and comments below. (You can always stop by my Van Vleck office if you’re in Madison to discuss any part of this).

UPDATE: I have now posted my own implementation of several algorithms for Koopman mode decompositions. [GitHub]

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Madison Math Circle: Mathematics of epidemics

Last night I had an amazing time at Madison Math Circle, hanging out with a bunch of bright school kids, who were undaunted by either diseases or mathematics. Since I had quite a few questions after the lecture, I decided to post an overview so anyone interested can go over it themselves. For those of you who attended and have further questions, or even wish to explore mathematical dynamics on your own, feel free to leave a comment below or e-mail me at marko@math.wisc.edu and I’ll try to answer all your questions and provide some guidance for future.
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Ergodic quotient in a finite-time, expanding context

I am currently attending 10th AIMS Conference on dynamics in Madrid, where I participated in the session on transport barriers in unsteady fluid flows. One of the talks in the session suggested that the ergodic quotient techniques for detecting coherent sets would not apply to finite-time setting, i.e., when ergodic averages are replaced by finite-time averages. This is, of course, of interest in cases when ergodic averages do not exist, so finite-time average is a potential resolution of this problem. I decided to investigate the potentially-problematic example given (2d linear saddle) using the code I made available at [github]. I found that in that case, ergodic quotient algorithm still works, even away from the asymptotic averaging limit.
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