1,501 research outputs found
The landscape of nonlinear structural dynamics: an introduction.
Nonlinear behaviour is ever-present in vibrations and other dynamical motions of engineering structures. Manifestations of nonlinearity include amplitude-dependent natural frequencies, buzz, squeak and rattle, self-excited oscillation and non-repeatability. This article primarily serves as an extended introduction to a theme issue in which such nonlinear phenomena are highlighted through diverse case studies. More ambitiously though, there is another goal. Both the engineering context and the mathematical techniques that can be used to identify, analyse, control or exploit these phenomena in practice are placed in the context of a mind-map, which has been created through expert elicitation. This map, which is available in software through the electronic supplementary material, attempts to provide a practitioner's guide to what hitherto might seem like a vast and complex research landscape.This project has arisen from a collaboration between the five UK universities and eight industrial collaborators on the EPSRC ‘Engineering Nonlinearity’ Programme Grant (EPSRC grant no. EP/K003836/1). T.B. is funded by an RAEng/EPSRC Research Fellowship.This is the final version of the article. It was first available from Royal Society Publishing via http://dx.doi.org/10.1098/rsta.2014.040
How can a glacial inception be predicted?
The Early Anthropogenic Hypothesis considers that greenhouse gas
concentrations should have declined during the Holocene in absence of humankind
activity, leading to glacial inception around the present. It partly relies on
the fact that present levels of northern summer incoming solar radiation are
close to those that, in the past, preceded a glacial inception phenomenon,
associated to declines in greenhouse gas concentrations. However, experiments
with various numerical models of glacial cycles show that next glacial
inception may still be delayed by several ten thousands of years, even with the
assumption of greenhouse gas concentration declines during the Holocene.
Furthermore, as we show here, conceptual models designed to capture the gross
dynamics of the climate system as a whole suggest also that small disturbances
may sometimes cause substantial delays in glacial events, causing a fair level
of unpredictability on ice age dynamics. This suggests the need of a validated
mathematical description of the climate system dynamics that allows us to
quantify uncertainties on predictions. Here, it is proposed to organise our
knowledge about the physics and dynamics of glacial cycles through a Bayesian
inference network. Constraints on the physics and dynamics of climate can be
encapsulated into a stochastic dynamical system. These constraints include, in
particular, estimates of the sensitivity of the components of climate to
external forcings, inferred from plans of experiments with large simulators of
the atmosphere, oceans and ice sheets. On the other hand, palaeoclimate
observations are accounted for through a process of parameter calibration. We
discuss promises and challenges raised by this programme.Comment: Contribution to the special issue of 'The Holocene' on the Early
Anthropogenic Hypotheses. W.R. Ruddiman, M. Crucifix, F. Oldfiel
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Weather, climate and the nature of predictability
The prediction and simulation of future weather and climate is a key ingredient in good weather risk management. This chapter briefly reviews the nature and underlying sources of predictability on timescales from hours-ahead to centuries-ahead. The traditional distinction between ‘weather’ and ‘climate’ predictions is described, and the role of recent scientific developments in driving a convergence of these two classic problems is highlighted. The chapter concludes by outlining and comparing the two main strategies used for creating weather and climate predictions, and discussing the challenges of using predictions in quantitative applications
Generalised Quasilinear Approximation of the Interaction of Convection and Mean Flows in a Thermal Annulus
In this paper, we examine the interaction of convection, rotation and mean flows in a thermal annulus. In this system, mean flows are driven by correlations induced by rotation leading to non-trivial Reynolds stresses. The mean flows act back on the convective turbulence acting as a barrier to transport. For this system, we demonstrate that the generalized quasilinear approximation (Marston et al. 2016 Phys. Rev. Lett.116, 214501. (doi:10.1103/PhysRevLett.116.214501)) may provide a much better approximation to the complicated full nonlinear dynamics than the widely used quasilinear approximation. This result will enable the construction of more accurate statistical theories for the description of geophysical and astrophysical flows
Symbolic Toolkit for Chaos Explorations
New computational technique based on the symbolic description utilizing
kneading invariants is used for explorations of parametric chaos in a two
exemplary systems with the Lorenz attractor: a normal model from mathematics,
and a laser model from nonlinear optics. The technique allows for uncovering
the stunning complexity and universality of the patterns discovered in the
bi-parametric scans of the given models and detects their organizing centers --
codimension-two T-points and separating saddles.Comment: International Conference on Theory and Application in Nonlinear
Dynamics (ICAND 2012
Lagrangian Reachabililty
We introduce LRT, a new Lagrangian-based ReachTube computation algorithm that
conservatively approximates the set of reachable states of a nonlinear
dynamical system. LRT makes use of the Cauchy-Green stretching factor (SF),
which is derived from an over-approximation of the gradient of the solution
flows. The SF measures the discrepancy between two states propagated by the
system solution from two initial states lying in a well-defined region, thereby
allowing LRT to compute a reachtube with a ball-overestimate in a metric where
the computed enclosure is as tight as possible. To evaluate its performance, we
implemented a prototype of LRT in C++/Matlab, and ran it on a set of
well-established benchmarks. Our results show that LRT compares very favorably
with respect to the CAPD and Flow* tools.Comment: Accepted to CAV 201
DADA: data assimilation for the detection and attribution of weather and climate-related events
A new nudging method for data assimilation, delay‐coordinate nudging, is presented. Delay‐coordinate nudging makes explicit use of present and past observations in the formulation of the forcing driving the model evolution at each time step. Numerical experiments with a low‐order chaotic system show that the new method systematically outperforms standard nudging in different model and observational scenarios, also when using an unoptimized formulation of the delay‐nudging coefficients. A connection between the optimal delay and the dominant Lyapunov exponent of the dynamics is found based on heuristic arguments and is confirmed by the numerical results, providing a guideline for the practical implementation of the algorithm. Delay‐coordinate nudging preserves the easiness of implementation, the intuitive functioning and the reduced computational cost of the standard nudging, making it a potential alternative especially in the field of seasonal‐to‐decadal predictions with large Earth system models that limit the use of more sophisticated data assimilation procedures
Physics-Informed Echo State Networks for Chaotic Systems Forecasting
We propose a physics-informed Echo State Network (ESN) to predict the
evolution of chaotic systems. Compared to conventional ESNs, the
physics-informed ESNs are trained to solve supervised learning tasks while
ensuring that their predictions do not violate physical laws. This is achieved
by introducing an additional loss function during the training of the ESNs,
which penalizes non-physical predictions without the need of any additional
training data. This approach is demonstrated on a chaotic Lorenz system, where
the physics-informed ESNs improve the predictability horizon by about two
Lyapunov times as compared to conventional ESNs. The proposed framework shows
the potential of using machine learning combined with prior physical knowledge
to improve the time-accurate prediction of chaotic dynamical systems.Comment: 7 pages, 3 figure
Physics-Informed Echo State Networks for Chaotic Systems Forecasting
We propose a physics-informed Echo State Network (ESN)
to predict the evolution of chaotic systems. Compared to conventional
ESNs, the physics-informed ESNs are trained to solve supervised learning
tasks while ensuring that their predictions do not violate physical laws.
This is achieved by introducing an additional loss function during the
training of the ESNs, which penalizes non-physical predictions without
the need of any additional training data. This approach is demonstrated
on a chaotic Lorenz system, where the physics-informed ESNs improve
the predictability horizon by about two Lyapunov times as compared to
conventional ESNs. The proposed framework shows the potential of using
machine learning combined with prior physical knowledge to improve the
time-accurate prediction of chaotic dynamical systems
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