139 research outputs found
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
, with being the energy dissipation
at the position of the aggregate, overcomes a given threshold
, 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]
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