Complementarity in classical dynamical systems

The concept of complementarity, originally defined for non-commuting observables of quantum systems with states of non-vanishing dispersion, is extended to classical dynamical systems with a partitioned phase space. Interpreting partitions in terms of ensembles of epistemic states (symbols) with corresponding classical observables, it is shown that such observables are complementary to each other with respect to particular partitions unless those partitions are generating. This explains why symbolic descriptions based on an \emph{ad hoc} partition of an underlying phase space description should generally be expected to be incompatible. Related approaches with different background and different objectives are discussed.Comment: 18 pages, no figure

Recurrence quantification and recurrence network analysis of global photosynthetic activity

In this chapter, the potential of Recurrence Analysis (RA) for applications in the biogeosciences is demonstrated.We investigate the fraction of absorbed photosynthetically active radiation (FAPAR), an index based on multispectral reflectance properties of land surfaces which relates to the carbon uptake by plants. FAPAR is available with global coverage from satellites. We combine observations from two sensors, SeaWifs on board SeaStar and MERIS on board Envisat, to produce time series with 10 days resolution for a period of 14 years (1998–2011) at a spatial resolution of 0:5ı latitude 0:5ı longitude. After careful quality checking and gap-filling, more than 30,000 individual time series are obtained covering all terrestrial ecosystems and climates apart from Antarctica and major deserts. To characterize the different dynamical behaviour as a function of spatial location, we employ Recurrence Quantification Analysis (RQA) and Recurrence Network Analysis (RNA). They deliver detailed information on the nonlinear dynamics in phase space through embedding. RQA and network measures are calculated for individual time series using identical recurrence parameters, and results are visualized on world maps. Taken together, the recurrence analysis leads to a partitioning of the terrestrial biosphere into regions with distinct dynamical patterns of photosynthetic activity

Radio Pulsars

Almost 50 years after radio pulsars were discovered in 1967, our understanding of these objects remains incomplete. On the one hand, within a few years it became clear that neutron star rotation gives rise to the extremely stable sequence of radio pulses, that the kinetic energy of rotation provides the reservoir of energy, and that electromagnetic fields are the braking mechanism. On the other hand, no consensus regarding the mechanism of coherent radio emission or the conversion of electromagnetic energy to particle energy yet exists. In this review, we report on three aspects of pulsar structure that have seen recent progress: the self-consistent theory of the magnetosphere of an oblique magnetic rotator; the location, geometry, and optics of radio emission; and evolution of the angle between spin and magnetic axes. These allow us to take the next step in understanding the physical nature of the pulsar activity.Comment: Invited review for Space Science Review