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Relaxation Oscillator

April 20, 2017 Leave a comment

Professor Strogatz Cornell course video lectures on “Nonlinear Dynamics and Chaos” are now online. This post pays homage to lecture 10 on analysis of the  Van der Pol equaltion:

\ddot{x}+x+\mu \dot{x}(x^2-1)=0

In the following the case for \mu =2,\mu =10 and the examination of the \mu >>1. It nicely illustrates the two time scales referred to, the slow then fast parts of the oscillation.

The phase portrait is the x, y plane where y is the the Lienard transformed and rescaled version of the equation.

So the system is:
\dot{x}=\mu(y-(x^3/3-x))
\dot{y}=-x/\mu

msevdp

msevdp2

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Milestone

April 4, 2017 Leave a comment

mserep_001

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Double Pendulum

March 31, 2017 Leave a comment

doublependulumin

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Chronic Mitral Regurgitation Misconception

March 29, 2017 Leave a comment

Gaasch et al report an interesting study looking at the commonly expressed “low impedance” retrograde regurgitant volume. This graphic uses the mathematical model in the paper:

mrimpedance.png

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Pi By Any Other Name

March 23, 2017 Leave a comment

coprimepiThis post is motivated by this video by standupmath (Matt Parker).

This simulates the procedure in the video (different upper bounds of integers and sample sizes):

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Ask a Dead Salmon

March 6, 2017 Leave a comment

I found this on “Calling Bullshit”. It is no doubt a wonderful illustration of spurious correlation. It made me laugh out loud.

 

deadsalmon

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More Hypocycloid Fun

February 27, 2017 Leave a comment

The generalization of hypocycloid in hypocycloid. In this case 5,11:

 

msehcmusing.gif

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