Analog to Digital Conversion in Physical Measurements

There exist measuring devices where an analog input is converted into a digital output. Such converters can have a nonlinear internal dynamics. We show how measurements with such converting devices can be understood using concepts from symbolic dynamics. Our approach is based on a nonlinear one-to-one mapping between the analog input and the digital output of the device. We analyze the Bernoulli shift and the tent map which are realized in specific analog/digital converters. Furthermore, we discuss the sources of errors that are inevitable in physical realizations of such systems and suggest methods for error reduction.Comment: 9 pages in LATEX, 4 figures in ps.; submitted to 'Chaos, Solitons & Fractals

Plankton blooms in vortices: The role of biological and hydrodynamic time scales

We study the interplay of hydrodynamic mesoscale structures and the growth of plankton in the wake of an island, and its interaction with a coastal upwelling. Our focus is on a mechanism for the emergence of localized plankton blooms in vortices. Using a coupled system of a kinematic flow mimicking the mesoscale structures behind the island and a simple three component model for the marine ecosystem, we show that the long residence times of nutrients and plankton in the vicinity of the island and the confinement of plankton within vortices are key factors for the appearance of localized plankton bloomsComment: 29 pages, 9 figure

Biological activity in the wake of an island close to a coastal upwelling

Hydrodynamic forcing plays an important role in shaping the dynamics of marine organisms, in particular of plankton. In this work we study the planktonic biological activity in the wake of an island which is close to an upwelling region. Our research is based on numerical analysis of a kinematic flow mimicking the hydrodynamics in the wake, coupled to a three-component plankton model. Depending on model parameters different phenomena are described: a) The lack of transport of nutrients and plankton across the wake, so that the influence of upwelling on primary production on the other side of the wake is blocked. b) For sufficiently high vorticity, the role of the wake in facilitating this transport and leading to an enhancement of primary production. Finally c) we show that under certain conditions the interplay between wake structures and biological growth leads to plankton blooms inside mesoscale hydrodynamic vortices that act as incubators of primary production.Comment: 42 pages, 9 figure

Multistability and nonsmooth bifurcations in the quasiperiodically forced circle map

It is well-known that the dynamics of the Arnold circle map is phase-locked in regions of the parameter space called Arnold tongues. If the map is invertible, the only possible dynamics is either quasiperiodic motion, or phase-locked behavior with a unique attracting periodic orbit. Under the influence of quasiperiodic forcing the dynamics of the map changes dramatically. Inside the Arnold tongues open regions of multistability exist, and the parameter dependency of the dynamics becomes rather complex. This paper discusses the bifurcation structure inside the Arnold tongue with zero rotation number and includes a study of nonsmooth bifurcations that happen for large nonlinearity in the region with strange nonchaotic attractors.Comment: 25 pages, 22 colored figures in reduced quality, submitted to Int. J. of Bifurcation and Chaos, a supplementary website (http://www.mpipks-dresden.mpg.de/eprint/jwiersig/0004003/) is provide

Rate-induced tipping in ecosystems and climate: the role of unstable states, basin boundaries and transient dynamics

The climate system as well as ecosystems might undergo relatively sudden qualitative changes in the dynamics when environmental parameters or external forcings vary due to anthropogenic influences. The study of these qualitative changes, called tipping phenomena, requires the development of new methodological approaches that allow phenomena observed in nature to be modeled, analyzed and predicted, especially concerning the climate crisis and its consequences. Here we briefly review the mechanisms of classical tipping phenomena and investigate rate-dependent tipping phenomena which occur in non-autonomous systems characterized by multiple timescales in more detail. We focus on the mechanism of rate-induced tipping caused by basin boundary crossings. We unravel the mechanism of this transition and analyze, in particular, the role of such basin boundary crossings in non-autonomous systems when a parameter drift induces a saddle-node bifurcation in which new attractors and saddle points emerge, including their basins of attraction. Furthermore, we study the detectability of those bifurcations by monitoring single trajectories in state space and find that depending on the rate of environmental parameter drift, such saddle-node bifurcations might be masked or hidden, and they can only be detected if a critical rate of environmental drift is crossed. This analysis reveals that unstable states of saddle type are the organizing centers of the global dynamics in non-autonomous multistable systems and as such need much more attention in future studies.</p

Statistical measures of distribution patterns of silicon and calcium in marine sedimentary layers

International audienceWe analyze electron microscope X-ray spectroscopy data of recent supratidal marine sediments. Statistical measures are used to characterize the distribution of silicon and calcium in different layers of the sediments. We also use cluster analysis and symbolic dynamics to filter measurement noise and to classify different density regions. This allows to calculate characteristic patch sizes which reflect the sizes of individual clastic grains and the corresponding pore sizes. Silicon indicates the independent processes in the sedimentation history of certain grains. Calcium is capable to monitor intrinsic early diagenetic processes of biogeochemical calcium mineralization of primary organic matter as documented in more organized distributions with higher clustering

Numerical simulations of aggregate breakup in bounded and unbounded turbulent flows

Breakup of small aggregates in fully developed turbulence is studied by means of direct numerical simulations in a series of typical bounded and unbounded flow configurations, such as a turbulent channel flow, a developing boundary layer and homogeneous isotropic turbulence. The simplest criterion for breakup is adopted, whereas aggregate breakup occurs when the local hydrodynamic stress $\sigma\sim \varepsilon^{1/2}$, with $\varepsilon$ being the energy dissipation at the position of the aggregate, overcomes a given threshold $\sigma_\mathrm{cr}$, which is characteristic for a given type of aggregates. Results show that the breakup rate decreases with increasing threshold. For small thresholds, it develops a universal scaling among the different flows. For high thresholds, the breakup rates show strong differences between the different flow configurations, highlighting the importance of non-universal mean-flow properties. To further assess the effects of flow inhomogeneity and turbulent fluctuations, theresults are compared with those obtained in a smooth stochastic flow. Furthermore, we discuss the limitations and applicability of a set of independent proxies.Comment: 15 pages, 12 figures, Refinded discussion in Section 2.1, results unchange

Fractal Spectrum of a Quasi_periodically Driven Spin System

We numerically perform a spectral analysis of a quasi-periodically driven spin 1/2 system, the spectrum of which is Singular Continuous. We compute fractal dimensions of spectral measures and discuss their connections with the time behaviour of various dynamical quantities, such as the moments of the distribution of the wave packet. Our data suggest a close similarity between the information dimension of the spectrum and the exponent ruling the algebraic growth of the 'entropic width' of wavepackets.Comment: 17 pages, RevTex, 5 figs. available on request from [email protected]