The Lorenz system still fascinates many people because of the simplicity of the equations that generate such complicated dynamics on the famous butterfly attractor. This paper addresses the role of the global stable and unstable manifolds in organising the dynamics. More precisely, for the standard system parameters, the origin has a two-dimensional stable manifold and the other two equilibria ...

Submitted for the MAR13 Meeting of The American Physical Society Beyond the constant Lorenz number for separating thermal conductivities of electrons and phonons: A DFT study1 MINGXING CHEN, Department of Physics, University of Wisconsin-Milwaukee, RAIMUND PODLOUCKY, Department of Physical Chemistry, University of Vienna, Austria — Lorenz number is an important quantity for separating thermal c...

A class of stochastic differential equations given by dx(t) = f(x(t))dt + g(x(t))dW(t),  x(t 0) = x 0,  t 0 ≤ t ≤ T < +∞, are investigated. Upon making some suitable assumptions, the existence and uniqueness of solution for the equations are obtained. Moreover, the existence and uniqueness of solution for stochastic Lorenz system, which is illustrated by example, are in good agreement with the ...

A tabletop waterwheel, designed and built by Prof. Willem Malkus (Math. Dept., MIT), is used to demonstrate chaos in a mechanical analog of the Lorenz equations. The waterwheel’s rotational damping rate can be adjusted by tightening or loosening a brake. When the brake is not too tight, the wheel settles into a steady rotation. Either direction of rotation is possible. When the brake was tighte...