The bone-chilling polar vortex that has transformed much of the Midwest into a dangerous freeze box is now coming for New York City, with temperatures set to plummet tonight and remain in the single digits for much of the next two days. If you're an apartment-dwelling New Yorker whose home isn't sufficiently warm, the city's housing department has promised to hold your landlord accountable. But for the tens of thousands of NYCHA residents who've already gone without heat and hot water this winter, there's little option but to wait and see. [ more › ] Gothamist http://bit.ly/2FZgVjx January 30, 2019 at 10:39PM
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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