Where were you when the great snow squall swallowed the city back in January 2019? It feels like it was only 15 minutes ago that we were engulfed in a full-blown snow squall micro-blizzard that made New York City VANISH in a shroud of white. How young we were back then! How many dreams we had! It's now been over 30 minutes since the storm that rocked the city. Below, we take a fond look back at the historic event, and the people whose lives were forever changed. [ more › ] Gothamist http://bit.ly/2G9Nafi January 31, 2019 at 12:52AM
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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