A few weeks ago, we had the pleasure of getting to know Dan Smith, the somewhat mysterious NYC icon who has spent the last 25 years plastering every laundromat window, pizzeria and bodega door in the city with his now iconic flyers—and also, of course, teaching people to play guitar. While Smith certainly has a sense of humor about his public persona, he is very sincere and very serious about what he does—especially about how learning to play guitar can teach you something much bigger: how to live. But that's because he's done the seemingly impossible: he turned what for most people would be a hobby into a lifelong profession [ more › ] Gothamist https://ift.tt/2YsiCMF March 28, 2019 at 10:15PM
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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