Editorial: The pre-history of Chaos—An Interdisciplinary Journal of Nonlinear Science

Published versio

Spin-Peierls transition in the Heisenberg chain with finite-frequency phonons

We study the spin-Peierls transition in a Heisenberg spin chain coupled to optical bond phonons. Quantum Monte Carlo results for systems with up to N=256 spins show unambiguously that the transition occurs only when the spin-phonon coupling α exceeds a critical value α_c. Using sum rules, we show that the phonon spectral function has divergent (for N→∞) weight extending to zero frequency for α<α_c. The phonon correlations decay with distance r as 1/r. This behavior is characteristic for all 0<α<α_c and the q=π phonon does not soften (to zero frequency) at α=α_c.First author draf

Behavior and Breakdown of Higher-Order Fermi-Pasta-Ulam-Tsingou Recurrences

We investigate numerically the existence and stability of higher-order recurrences (HoRs), including super-recurrences, super-super-recurrences, etc., in the alpha and beta Fermi-Pasta-Ulam-Tsingou (FPUT) lattices for initial conditions in the fundamental normal mode. Our results represent a considerable extension of the pioneering work of Tuck and Menzel on super-recurrences. For fixed lattice sizes, we observe and study apparent singularities in the periods of these HoRs, speculated to be caused by nonlinear resonances. Interestingly, these singularities depend very sensitively on the initial energy and the respective nonlinear parameters. Furthermore, we compare the mechanisms by which the super-recurrences in the two model's breakdown as the initial energy and respective nonlinear parameters are increased. The breakdown of super-recurrences in the beta-FPUT lattice is associated with the destruction of the so-called metastable state and hence is associated with relaxation towards equilibrium. For the alpha-FPUT lattice, we find this is not the case and show that the super-recurrences break down while the lattice is still metastable. We close with comments on the generality of our results for different lattice sizes

Method and system for respiration analysis Patent

Respiration analyzing method and apparatus for determining subjects oxygen consumption in aerospace environment

Chaos at Fifty

In 1963 Edward Lorenz revealed deterministic predictability to be an illusion and gave birth to a field that still thrives. This Feature Article discusses Lorenz's discovery and developments that followed from it.Comment: For an animated visualization of the Lorenz attractor, click here http://www.youtube.com/watch?v=iu4RdmBVdp