Random matrices and the New York City subway system.

We analyze subway arrival times in the New York City subway system. We find regimes where the gaps between trains are well modeled by (unitarily invariant) random matrix statistics and Poisson statistics. The departure from random matrix statistics is captured by the value of the Coulomb potential along the subway route.

Universality in numerical computations with random data.

The authors present evidence for universality in numerical computations with random data. Given a (possibly stochastic) numerical algorithm with random input data, the time (or number of iterations) to convergence (within a given tolerance) is a random variable, called the halting time. Two-component universality is observed for the fluctuations of the halting time--i.

Neck instability of bright solitons in normally dispersive Kerr media.

The neck instability of bright solitons of the hyperbolic nonlinear Shrödinger equation is investigated. It is shown that this instability originates from a four-wave mixing interaction that links on-axis to off-axis radiation at opposite frequency bands. Our experiment supports this interpretation.

Experimental demonstration of the oscillatory snake instability of the bright soliton of the (2+1)D hyperbolic nonlinear Schrödinger equation.

The transition between the standard snake instability of bright solitons of the hyperbolic nonlinear Schrödinger equation and the recently theoretically predicted oscillatory snake instability is experimentally demonstrated. The existence of this transition is proven on the basis of spatiotemporal spectral features of bright soliton laser beams propagating in normally dispersive Kerr-type nonlinear planar waveguides.