1,396 research outputs found
Quantitative recurrence statistics and convergence to an extreme value distribution for non-uniformly hyperbolic dynamical systems
For non-uniformly hyperbolic dynamical systems we consider the time series of
maxima along typical orbits. Using ideas based upon quantitative recurrence
time statistics we prove convergence of the maxima (under suitable
normalization) to an extreme value distribution, and obtain estimates on the
rate of convergence. We show that our results are applicable to a range of
examples, and include new results for Lorenz maps, certain partially hyperbolic
systems, and non-uniformly expanding systems with sub-exponential decay of
correlations. For applications where analytic results are not readily available
we show how to estimate the rate of convergence to an extreme value
distribution based upon numerical information of the quantitative recurrence
statistics. We envisage that such information will lead to more efficient
statistical parameter estimation schemes based upon the block-maxima method.Comment: This article is a revision of the previous article titled: "On the
convergence to an extreme value distribution for non-uniformly hyperbolic
dynamical systems." Relative to this older version, the revised article
includes new and up to date results and developments (based upon recent
advances in the field
Symmetries in the Lorenz-96 model
The Lorenz-96 model is widely used as a test model for various applications,
such as data assimilation methods. This symmetric model has the forcing
and the dimension as parameters and is
equivariant. In this paper, we unravel its dynamics for
using equivariant bifurcation theory. Symmetry gives rise to invariant
subspaces, that play an important role in this model. We exploit them in order
to generalise results from a low dimension to all multiples of that dimension.
We discuss symmetry for periodic orbits as well.
Our analysis leads to proofs of the existence of pitchfork bifurcations for
in specific dimensions : In all even dimensions, the equilibrium
exhibits a supercritical pitchfork bifurcation. In dimensions
, , a second supercritical pitchfork bifurcation occurs
simultaneously for both equilibria originating from the previous one.
Furthermore, numerical observations reveal that in dimension , where
and is odd, there is a finite cascade of exactly
subsequent pitchfork bifurcations, whose bifurcation values are independent
of . This structure is discussed and interpreted in light of the symmetries
of the model.Comment: 31 pages, 9 figures and 3 table
Gas Hydrate Analysis and Modelling of Monoethylene Glycol Regeneration and the Impact of Additives
Monoethylene glycol (MEG) is injected to inhibit gas hydrate formation. In this study, significant experimental and computational effort has been applied to investigate MEG degradation, the regeneration and reclamation process during water breakthrough, and to produce empirical models. Hydrate phase equilibria of numerous corrosion inhibitors, oxygen scavengers, amines and scale inhibitors were produced suggesting an inhibitory effect on gas hydrates predominantly. Furthermore, the impact of methyldiethanolamine (MDEA) was modelled empirically and thermodynamically
A Review of VLBI Instrumentation
The history of VLBI is summarized with emphasis on the technical aspects. A
summary of VLBI systems which are in use is given, and an outlook to the future
of VLBI instrumentation.Comment: 8 pages. No figures. Proceedings of the 7th European VLBI Network
Symposium held in Toledo, Spain on October 12-15, 2004. Editors: R.
Bachiller, F. Colomer, J.-F. Desmurs, P. de Vicente (Observatorio Astronomico
Nacional), p. 237-244. Needs evn2004.cl
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