After announcing this morning that he planned to vote yes on Brett Kavanaugh's confirmation to the Supreme Court, Jeff Flake had some sort of come-to-Jesus moment while sitting in the Senate Judiciary Committee hearing this afternoon. After huddling with Democrats and much palace intrigue, he ultimately announced he would not support final confirmation until the FBI had a week to further investigate the accusations of sexual assault against Kavanaugh. And many people are pointing to two women in particular as responsible for this dramatic twist. [ more › ] Gothamist https://ift.tt/2DDiDH3 September 29, 2018 at 12:32AM
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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