Experimental nonlinear dynamics

Abstract

Although it is difficult to point to a definite origin of the field of nonlinear dynamics, it evolved in part from attempts to understand two fundamentally different types of deterministic systems-very simple systems with as few as three variables on the one side that generate erratic non-periodic dynamics, exemplified by the three-body problem; and nearly infinite dimensional systems, such as fluids, that transition from very well-behaved dynamics through a range of increasingly complex space and time-varying dynamics, exemplified by the transitions from laminar to turbulent hydrodynamic flows.By the 1980s, the nonlinear dynamics community fitted roughly into two camps, those looking at and harnessing low-dimensional chaos-the emergence of complex unpredictable behaviour from systems with few degrees of freedom; and those looking at pattern formation-or the emergence of order, or coherentstructured dynamics in space and time-from systems with infinite degrees of freedom. The classic experimental systems for the study of, and application of, chaos were circuits and pendulums, lasers and population dynamics. Pattern formation was studied in fluid flows, crystal growth dynamics, chemical reactions and biology. Often, there was cross-pollination between these camps in developed theoretical tools, computational hardware, data analysis and visualization technology and experimental approach. The objectives overall were to both understand the origins of the phenomena and provide insight into how to harness the origins of complexity, exemplified in the 1990s by the development of chaos control techniques.The current issue is a cross-sectional sampling of the broad experimental applications now addressed in the nonlinear dynamics community. It starts with a solution to a classic hydrodynamic problem in Metcalfe et al. (2010). The challenge addressed is how to optimally mix fluids-critical, for example, in chemical reactors and heat exchangers-with simple laminar, low-energy, flows. Efficient mixing brings arbitrary pairs of fluid particles together. The simplest of such flows does not have the mixture of convergent and divergent points needed to do so. But, as the authors demonstrate, super-positions of such flow patterns, achieved by alternating between boundary conditions, yield highly chaotic fluid trajectories and therefore ideal mixing.The next two articles address issues and applications in chaotic dynamics. In the 1990s, atomic physics was essentially re-born with the perfection of techniques to greatly cool and trap individual, or small numbers of, atoms (Letokhov et al. 1995). Such systems then allow for real experimental systems Networks abound both in nature and in our man-made world. Understanding the underlying structure of such networks, how the individual elements' dynamics determines and is modulated by the group dynamics, how information is processed and transmitted through such networks and how robust they are to changes in connections is currently a major undertaking. Kocarev et al. (2010) address one ...