I remember feeling both enraged and terrified when I first heard the story of James Byrd, Jr. — the black man who was chained to the back of a pickup truck and dragged to his death by three avowed white supremacists in Jasper, Texas. The year was 1998 and at the time I lived alone in Brooklyn, a good 45 minutes from my office on the Upper East Side of Manhattan, where I worked as a television producer for a talk show on PBS. Even as Byrd lived in the deep South, where deep-seated racism continued in open acts of violence and terror, I’d never heard of anything this horrific, and after that, I started looking over my shoulder more when I walked home from the subway. [ more › ] Gothamist http://bit.ly/2FXUnjb January 30, 2019 at 12:21AM
Van der Pol’s differential equation is The equation describes a system with nonlinear damping, the degree of damping given by μ. If μ = 0 the system is linear and undamped, but for positive μ the system is nonlinear and damped. We will plot the phase portrait for the solution to Van der Pol’s equation in Python using SciPy’s new ODE solver ivp_solve . The function ivp_solve does not solve second-order systems of equations directly. It solves systems of first-order equations, but a second-order differential equation can be recast as a pair of first-order equations by introducing the first derivative as a new variable. Since y is the derivative of x , the phase portrait is just the plot of ( x , y ). If μ = 0, we have a simple harmonic oscillator and the phase portrait is simply a circle. For larger values of μ the solutions enter limiting cycles, but the cycles are more complicated than just circles. Here’s the Python code that made the plot. from scipy import linspace from ...
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