205 research outputs found
Pseudo resonance induced quasi-periodic behavior in stochastic threshold dynamics
Here we present a simple stochastic threshold model consisting of a
deterministic slowly decaying term and a fast stochastic noise term. The
process shows a pseudo-resonance, in the sense that for small and large
intensities of the noise the signal is irregular and the distribution of
threshold crossings is broad, while for a tuned intermediate value of noise
intensity the signal becomes quasi-periodic and the distribution of threshold
crossings is narrow. The mechanism captured by the model might be relevant for
explaining apparent quasi-periodicity of observed climatic variations where no
internal or external periodicities can be identified.Comment: 8 pages, 4 figures, to appear in Stochastics and Dynamic
Warning of a forthcoming collapse of the Atlantic meridional overturning circulation
Tipping to an undesired state in the climate when a control parameter slowly
approaches a critical value is a growing concern with increasing greenhouse gas
concentrations. Predictions rely on detecting early warning signals (EWSs) in
observations of the system. The primary EWSs are increase in variance, (loss of
resilience), and increased autocorrelation (critical slow down). These measures
are statistical in nature, which implies that the reliability and statistical
significance of the detection depends on the sample size in observations and
the magnitude of the change away from the base value prior to the approach to
the tipping point. Thus, the possibility of providing useful early warning
depends on the relative magnitude of several interdependent time scales in the
system. These are (a) the time before the critical value is reached, (b) the
(inverse) rate of approach to the tipping point, (c) the size of the time
window required to detect a significant change in the EWS and finally, (d) the
escape time for noise-induced transition (prior to the tipping). Conditions for
early warning of tipping of the Atlantic meridional overturning circulation
(AMOC) are marginally fulfilled for the existing past 150 years of proxy
observations where indicators of tipping have recently been reported. Here we
provide statistical significance and data driven estimators for the time of
tipping. We estimate a collapse of the AMOC to occur around the year 2057 under
the assumption of a "business as usual" scenario of future emissions.Comment: 18 pages, 7 figure
Healthy food is nutritious, but organic food is healthy because it is pure: The negotiation of healthy food choices by Danish consumers of organic food.
There is increasing demand for organic food products throughout the Western world. Health concerns have frequently been found to be the main motivation of consumers purchasing organic products, but the literature on consumer preferences and behavior is less clear about what âhealthâ means to consumers of these products, and because of this it remains unclear what exactly drives consumers to choose organic products. This article investigates health from the perspective of consumers, and analyzes negotiations of, and justifications behind, their consumption preferences. The analysis is based on a focus group study conducted in Denmark in 2016. Three different understandings of health can be found when consumers explain their preferences for organic products: Health as purity; Health as pleasure, and a Holistic perspective on health. The first two are familiar from the literature on food. The third, which reflects principles behind organic agriculture, is less documented in the context of consumption. Health as purity was the dominant understanding of health used by the participants when explaining why they purchased organic food products. When participants discussed healthy eating in general, detached from a specific context, most employed a purely nutritional perspective as a definitive argument in supporting claims about healthy eating. The paperâs findings have implications for future research on organic consumption. They also have practical implications for organic food producers and manufacturers
The middle Pleistocene transition as a generic bifurcation on a slow manifold
The final publication is available at Springer via http://dx.doi.org/10.1007/s00382-015-2501-9The Quaternary period has been characterised by a cyclical series of glaciations, which are attributed to the change in the insolation (incoming solar radiation) from changes in the Earthâs orbit around the Sun. The spectral power in the climate record is very different from that of the orbital forcing: prior to 1000 kyr before present most of the spectral power is in the 41 kyr band while since then the power has been in the 100 kyr band. The change defines the middle Pleistocene transition (MPT). The MPT does not indicate any noticeable difference in the orbital forcing. The climate response to the insolation is thus far from linear, and appears to be structurally different before and after the MPT. This paper presents a low order conceptual model for the oscillatory dynamics of the ice sheets in terms of a relaxation oscillator with multiple levels subject to the Milankovitch forcing. The model exhibits smooth transitions between three different climate states; an interglacial (i), a mild glacial (g) and a deep glacial (G) as proposed by Paillard (Nature 391:378â381, 1998). The model suggests a dynamical explanation in terms of the structure of a slow manifold for the observed allowed and âforbiddenâ transitions between the three climate states. With the model, the pacing of the climate oscillations by the astronomical forcing is through the mechanism of phase-resetting of relaxation oscillations in which the internal phase of the oscillation is affected by the forcing. In spite of its simplicity as a forced ODE, the model is able to reproduce not only general features but also many of the details of oscillations observed in the climate record. A particular novelty is that it includes a slow drift in the form of the slow manifold that reproduces the observed dynamical change at the MPT. We explain this change in terms of a transcritical bifurcation in the fast dynamics on varying the slow variable; this bifurcation can induce a sudden change in periodicity and amplitude of the cycle and we suggest that this is associated with a branch of âcanard oscillationsâ that appear for a small range of parameters. The model is remarkably robust at simulating the climate record before, during and after the MPT. Even though the conceptual model does not point to specific mechanisms, the physical implication is that the major reorganisation of the climate response to the orbital forcing does not necessarily imply that there was a big change in the environmental conditions
A climatic thermostat making Earth habitable
The mean surface temperature on Earth and other planets with atmospheres is
determined by the radiative balance between the non-reflected incoming solar
radiation and the outgoing long-wave black-body radiation from the atmosphere.
The surface temperature is higher than the black-body temperature due to the
greenhouse warming. Balancing the ice-albedo cooling and the greenhouse warming
gives rise to two stable climate states. A cold climate state with a
completelyice-covered planet, called Snowball Earth, and a warm state similar
to our present climate where greenhouse warming prevents the total glacition.
The warm state has dominated Earth in most of its geological history despite a
30 % fainter young Sun. The warming could have been controlled by a greenhouse
thermostat operating by temperature control of the weathering process depleting
the atmosphere from . This temperature control has permitted life to
evolve as early as the end of the heavy bombartment 4 billion years ago.Comment: 4 figures, Proceedings, NORDITA conf. Astrobiology 200
The recurrence time of Dansgaard-Oeschger events and limits on the possible periodic component
By comparing the high-resolution isotopic records from the GRIP and NGRIP
icecores, we approximately separate the climate signal from local noise to
obtain an objective criterion for defining Dansgaard-Oeschger events. Our
analysis identifies several additional short lasting events, increasing the
total number of DO events to 27 in the period 12-90 kyr BP. The quasi-regular
occurrence of the DO events could indicate a stochastic or coherent resonance
mechanism governing their origin. From the distribution of waiting times we
obtain a statistical upper bound on the strength of a possible periodic
forcing. This finding indicates that the climate shifts are purely noise driven
with no underlying periodicity.Comment: 9 figure
Refined central limit theorem and infinite density tail of the Lorentz gas from Levy walk
We consider point particle that collides with a periodic array of hard-core
elastic scatterers where the length of the free flights is unbounded (the
infinite-horizon Lorentz gas, LG). The Bleher central limit theorem (CLT)
states that the distribution of the particle displacement divided by
is Gaussian in the limit of infinite time . However it was
stressed recently that the slow convergence makes this result unobservable.
Using a L\'{e}vy walk model (LW) of the LG, it was proposed that the use of a
rescaled Lambert function instead of provides a fast
convergent, observable CLT, which was confirmed by the LG simulations. We
demonstrate here that this result can simplified to a mixed CLT where the
scaling factor combines normal and anomalous diffusions. For narrow infinite
corridors the particle for long time obeys the usual normal diffusion, which
explains the previous numerical observations. In the opposite limit of small
scatterers the Bleher CLT gives a good guiding. In the intermediate cases the
mixed CLT applies. The Gaussian peak determines moments of order smaller than
two. In contrast, the CLT gives only half the coordinate dispersion. The
missing half of the dispersion and also moments of order higher than two are
described by the distribution's tail (the infinite density) which we derive
here. The tail is supported along the infinite corridors and formed by
anomalously long flights whose duration is comparable with the whole time of
observation. The moments' calculation from the tail is confirmed by direct
calculation of the fourth moment from the statistics of the backward recurrence
time defined as time that elapsed since the last collision. This completes the
solution of the LW model allowing full comparison with the LG
Bifurcation of critical sets and relaxation oscillations in singular fast-slow systems
Fast-slow dynamical systems have subsystems that evolve on vastly different
timescales, and bifurcations in such systems can arise due to changes in any or
all subsystems. We classify bifurcations of the critical set (the equilibria of
the fast subsystem) and associated fast dynamics, parametrized by the slow
variables. Using a distinguished parameter approach we are able to classify
bifurcations for one fast and one slow variable. Some of these bifurcations are
associated with the critical set losing manifold structure. We also conjecture
a list of generic bifurcations of the critical set for one fast and two slow
variables. We further consider how the bifurcations of the critical set can be
associated with generic bifurcations of attracting relaxation oscillations
under an appropriate singular notion of equivalence.Comment: 60 pages, 18 Figure
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