Bücher der Reihe Institute for Nonlinear Science

The volume that you have before you is the result of a growing realization that fluctuations in nonequilibrium systems playa much more important role than was 1 first believed.

The volume that you have before you is the result of a growing realization that fluctuations in nonequilibrium systems playa much more important role than was 1 first believed.

This book provides a summary of the research conducted at UCLA, Stanford University, and UCSD over the last ?ve years in the area of nonlinear dyn- ics and chaos as applied to digital communications.

Intended for graduates and researchers in physics, chemistry, biology, and applied mathematics, this book provides an up-to-date introduction to current research in fluctuations in spatially extended systems.

This text describes the statistcal behavior of complex systems and shows how the fractional calculus can be used to model the behavior. The book gives general strategies for understanding wave propagation through random media, the nonlinear response of complex materials, and the fluctuations of heat transport in heterogeneous materials.

The chapters were prepared by the invited speakers as didactic reviews of their subjects but also include the structure, mechanical properties, and function of the heart and the myocardium, electrical activity of the heart and myocardium, and mathematical models of heart function.

When I encountered the idea of chaotic behavior in deterministic dynami- cal systems, it gave me both great pause and great relief. The origin of the great relief was work I had done earlier on renormalization group properties of homogeneous, isotropic fluid turbulence. At the time I worked on that, it was customary to ascribe the apparently stochastic nature of turbulent flows to some kind of stochastic driving of the fluid at large scales. It was simply not imagined that with purely deterministic driving the fluid could be turbulent from its own chaotic motion. I recall a colleague remarking that there was something fundamentally unsettling about requiring a fluid to be driven stochastically to have even the semblance of complex motion in the velocity and pressure fields. I certainly agreed with him, but neither of us were able to provide any other reasonable suggestion for the observed, apparently stochastic motions of the turbulent fluid. So it was with relief that chaos in nonlinear systems, namely, complex evolution, indistinguish- able from stochastic motions using standard tools such as Fourier analysis, appeared in my bag of physics notions. It enabled me to have a physi- cally reasonable conceptual framework in which to expect deterministic, yet stochastic looking, motions. The great pause came from not knowing what to make of chaos in non- linear systems.