St. Mark's Comics, which has been a mainstay of St. Mark's Place in the East Village for over 36 years, announced on Tuesday evening that it would be closing at the end of February. "Thanks for all your kind words and concern as word has gotten out," the store's account tweeted. "We will be starting our store-emptying #sale [Wednesday] morning @ 11AM." [ more › ] Gothamist http://bit.ly/2UtWZsf January 30, 2019 at 04:52PM
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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