I am going to guess that roughly 90 percent of the headlines you have seen today have something to do with the extreme cold sweeping much of the country, New York City absolutely included. The panic seems deserved. Yesterday we warned you that the impending ARCTIC BLAST will bring marrow-freezing wind chill and insidious black ice, and all of that still stands. Now, however, I bring you another exciting winter storm ingredient, courtesy of Notify NYC: whiteout conditions. Let's throw that in the mix, why the hell not. [ more › ] Gothamist http://bit.ly/2DJbUJA January 30, 2019 at 08:01PM
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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