Related Experiment Video
Updated: Jul 23, 2026

Perceptual and Category Processing of the Uncanny Valley Hypothesis' Dimension of Human Likeness: Some Methodological Issues
Published on: June 3, 2013
Are continuum predictions of clustering chaotic?
William D Fullmer1, Christine M Hrenya1
1Department of Chemical and Biological Engineering, University of Colorado, Boulder, Colorado 80309, USA.
Abstract:
Gas-solid multiphase flows are prone to develop an instability known as clustering. Two-fluid models, which treat the particulate phase as a continuum, are known to reproduce the qualitative features of this instability, producing highly-dynamic, spatiotemporal patterns. However, it is unknown whether such simulations are truly aperiodic or a type of complex periodic behavior. By showing that the system possesses a sensitive dependence on initial conditions and a positive largest Lyapunov exponent, λ1≈1/τ, we provide a tentative answer: continuum predictions of clustering are chaotic. We further demonstrate that the chaotic behavior is dimensionally dependent, a conclusion which unifies previous results and strongly suggests that the chaotic behavior is not a direct consequence of the fundamental kinematic instability, but requires a secondary (inherently multidimensional) instability.
Related Concept Videos
Entropy Change in Reversible Processes
The statement can be further generalized to prove that entropy is a state function. Take a cyclic process between any two points on a p-V diagram.
Uncertainty: Overview
The Entropy as a State Function
Entropy Changes Accompanying Specific Processes
BIBO stability of continuous and discrete -time systems
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.
Continuity for Functions of Multiple Variables

