2,431 research outputs found
Quantifying Spatiotemporal Chaos in Rayleigh-B\'enard Convection
Using large-scale parallel numerical simulations we explore spatiotemporal
chaos in Rayleigh-B\'enard convection in a cylindrical domain with
experimentally relevant boundary conditions. We use the variation of the
spectrum of Lyapunov exponents and the leading order Lyapunov vector with
system parameters to quantify states of high-dimensional chaos in fluid
convection. We explore the relationship between the time dynamics of the
spectrum of Lyapunov exponents and the pattern dynamics. For chaotic dynamics
we find that all of the Lyapunov exponents are positively correlated with the
leading order Lyapunov exponent and we quantify the details of their response
to the dynamics of defects. The leading order Lyapunov vector is used to
identify topological features of the fluid patterns that contribute
significantly to the chaotic dynamics. Our results show a transition from
boundary dominated dynamics to bulk dominated dynamics as the system size is
increased. The spectrum of Lyapunov exponents is used to compute the variation
of the fractal dimension with system parameters to quantify how the underlying
high-dimensional strange attractor accommodates a range of different chaotic
dynamics
Transverse spectral functions and Dzyaloshinskii-Moriya interactions in XXZ spin chains
Recently much progress has been made in applying field theory methods, first
developed to study X-ray edge singularities, to interacting one dimensional
systems in order to include band curvature effects and study edge singularities
at arbitrary momentum. Finding experimental confirmations of this theory
remains an open challenge. Here we point out that spin chains with uniform
Dzyaloshinskii-Moriya (DM) interactions provide an opportunity to test these
theories since these interactions may be exactly eliminated by a gauge
transformation which shifts the momentum. However, this requires an extension
of these X-ray edge methods to the transverse spectral function of the xxz spin
chain in a magnetic field, which we provide
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