Causes and Effects of Chaos
Abstract
Chaos was first discovered in turbulent fluid flow, considered 'the' unsolved problem in classical physics. Fluid flow turns from smooth (laminar) to turbulent as its velocity increases. The classic explanation for this was that new frequencies appeared, one at a time, in the velocity and density profiles. In the early 1960s, a meteorology professor at MIT named Edward Lorenz simulated the actions of an air mass between warm ground and cool clouds, modeled by a simplified version of the Navier-Stokes equations for fluid flow. Mathematically, the definition of chaotic behavior requires: sensitive dependence upon initial conditions topological transitivity and dense periodic points in the Poincare section of the system's state space. Sensitive dependence is illustrated by Smale's horseshoe, the nonlinear transformation.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1990
- Accession Number
- ADA241157
Entities
People
- Elizabeth Bradley
Organizations
- Massachusetts Institute of Technology