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 $F\in\mathbb{R}$ and the dimension $n\in\mathbb{N}$ as parameters and is $\mathbb{Z}_n$ equivariant. In this paper, we unravel its dynamics for $F<0$ 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 $F<0$ in specific dimensions $n$: In all even dimensions, the equilibrium $(F,\ldots,F)$ exhibits a supercritical pitchfork bifurcation. In dimensions $n=4k$, $k\in\mathbb{N}$, a second supercritical pitchfork bifurcation occurs simultaneously for both equilibria originating from the previous one. Furthermore, numerical observations reveal that in dimension $n=2^qp$, where $q\in\mathbb{N}\cup\{0\}$ and $p$ is odd, there is a finite cascade of exactly $q$ subsequent pitchfork bifurcations, whose bifurcation values are independent of $n$. 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