Former Ambassador Marie Yovanovitch, Key Figure In Impeachment Trial, Retires

Former U.S. Ambassador to Ukraine Marie Yovanovitch testifies before the House Intelligence Committee on Capitol Hill in Washington, on Nov. 15, 2019.

The career diplomat, who served as ambassador to Ukraine, became a key figure in the impeachment of President Trump, was forced out of her post in May.

(Image credit: Andrew Harnik/AP)

News : NPR https://ift.tt/31feIsn February 01, 2020 at 03:10AM

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Solving Van der Pol equation with ivp_solve

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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