Engineering topics

Yorke, J. A.

Publications and source records attributed to Yorke, J. A..

2 records

NASA NTRS1985

Exterior dimension of fat fractals

Geometric scaling properties of fat fractal sets (fractals with finite volume) are discussed and characterized via the introduction of a new dimension-like quantity which is called the exterior dimension. In addition, it is shown that the exterior dimension is related to the 'uncertainty exponent' previously used in studies of fractal basin boundaries, and it is shown how this connection can be exploited to determine the exterior dimension. Three illustrative applications are described, two in nonlinear dynamics and one dealing with blood flow in the body. Possible relevance to porous materials and ballistic driven aggregation is also noted.

Grebogi, C.↗

NASA NTRS1981

Chaotic behavior and fluid dynamics

It is shown that while fluids are very complicated systems having many degrees of freedom, the basic mechanism underlying the observed chaotic behavior of fluid turbulence may not require the consideration of many degrees of freedom. Simple dynamical systems display erratic and chaotic behavior reminiscent of turbulence, the key to which is the 'sensitivity to initial conditions' introduced by Ruelle (1978). Simple models which are sensitive to initial data and have permitted workers to study chaotic behavior are described, with attention to the Lorenz equations, Landau's idea of a continuous transition to turbulence via an infinite cascade of bifurcations, and one-dimensional maps.

Yorke, J. A.↗