A little over a decade ago, Brooklyn-born billionaire Jeffrey Epstein got caught running what the Miami Herald describes as a "sexual pyramid scheme" on the backs of underage girls, allegedly committing multiple acts of pedophilia and engaging in child sex trafficking. The evidence against him appeared damning, but until now it's been kept largely out of the public eye, thanks to the efforts and missteps of prosecutors at the federal and state level—including President Donald Trump's current Labor Secretary and a prosecutor in Manhattan District Attorney Cy Vance's office. [ more › ] Gothamist https://ift.tt/2Aw7xPo November 29, 2018 at 11:21PM
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 ...
Comments
Post a Comment