Nonlinear softening as a predictive precursor to climate tipping

Approaching a dangerous bifurcation, from which a dynamical system such as the Earth's climate will jump (tip) to a different state, the current stable state lies within a shrinking basin of attraction. Persistence of the state becomes increasingly precarious in the presence of noisy disturbances. We consider an underlying potential, as defined theoretically for a saddle-node fold and (via averaging) for a Hopf bifurcation. Close to a stable state, this potential has a parabolic form; but approaching a jump it becomes increasingly dominated by softening nonlinearities. If we have already detected a decrease in the linear decay rate, nonlinear information allows us to estimate the propensity for early tipping due to noise. We argue that one needs to extract information about the nonlinear features (a "softening") of the underlying potential from the time series to judge the probability and timing of tipping. This analysis is the logical next step if one has detected a decrease of the linear decay rate. If there is no discernable trend in the linear analysis, nonlinear softening is even more important in showing the proximity to tipping. After extensive normal form calibration studies, we check two geological time series from paleo-climate tipping events for softening of the underlying well. For the ending of the last ice age, where we find no convincing linear precursor, we identify a statistically significant nonlinear softening towards increasing temperature. The analysis has thus successfully detected a warning of the imminent tipping event.Comment: 22 pages, 11 figures, changed title back, corrected smaller mistakes, updated reference

Partial Regularity of solutions to the Four-dimensional Navier-Stokes equations at the first blow-up time

The solutions of incompressible Navier-Stokes equations in four spatial dimensions are considered. We prove that the two-dimensional Hausdorff measure of the set of singular points at the first blow-up time is equal to zero.Comment: 19 pages, a comment regarding five or higher dimensional case is added in Remark 1.3. accepted by Comm. Math. Phy

A Bioassay To Investigate Movement of Wood Preservatives From Poles Into Soil A Research Note

A promising method was found for investigating migration of preservative from preservative-treated poles into surrounding soil. The presence and relative amounts of preservative are indicated by suppression of decay (weight loss) in birch coffee-stirring sticks buried at various distances from the pole

Biaxial Testing of Elastomers: Experimental Setup, Measurement and Experimental Optimisation of Specimen’s Shape

The present article deals with the setup and the control of a biaxial tension test device for characterising the material properties of elastomers. After a short introduction into the experimental setup a brief explanation of the benefits of a biaxial tension test is given. Furthermore the analysis of this test will be discussed. Therefore, the used optical field measurement by digital image correlation for analysing the strains is shortly introduced to the reader. Additionally, the basic concepts of the calculation of an inverse boundary problem for identifying the material’s parameters are imposed. However the main focus is laid on the experimental optimisation of the specimen’s geometry, whereupon a nearly hyperelastic, incompressible silicone is used to get the experimental results. The resulting geometry will be specially fitted to the requirements of elastomers. The tested geometries and the evaluation of the experiments will be explained as well as the resulting quality factor for the suitability of a specimen’s shape. After all, a short validation of the foregoing considerations will be presented

Implementation of the strongly pronounced non-linear viscoelasticity of an incompressible filled rubber

Filled rubber materials regularly show a pronounced non-linear viscoelasticity with very long relaxation times. In this contribution, a phenomenological description for an incompressible carbon black-filled EPDM (ethylene propylene diene monomer) is given, which also shows the abovementioned characteristic behaviour. In order to represent the non-linear viscoelastic material, the relaxation times of the model are chosen not as constant material parameters but as process-dependent functions. This contribution presents two different realisations of the model’s implementation. At first, this work provides an implementation of the material model, which is able to describe complex geometries and loading conditions. In this realisation, the three-dimensional model is implemented in the open source finite element library deal.II for finite deformations. Hence, real applications can be represented. In an alternative numerical solution, the model is reduced to the single case of uniaxial tension. The model is simplified to scalar equations, which are quite easy to handle for the implementation. This procedure provides a more simple identification process, but it presents the roblem that the model character is extremely restricted for the individual case of uniaxial tension. For the numerical realisation, at first, special attention has to be turned on the determination of the inelastic part of the kinematics. A detailed evaluation of the necessary evolution equations is provided in this contribution. Finally, he results of the different implementations are compared with respect to different loading conditions, like relaxation tests or cyclic loading

Independent analysis of the orbits of Pioneer 10 and 11

Independently developed orbit determination software is used to analyze the orbits of Pioneer 10 and 11 using Doppler data. The analysis takes into account the gravitational fields of the Sun and planets using the latest JPL ephemerides, accurate station locations, signal propagation delays (e.g., the Shapiro delay, atmospheric effects), the spacecrafts' spin, and maneuvers. New to this analysis is the ability to utilize telemetry data for spin, maneuvers, and other on-board systematic effects. Using data that was analyzed in prior JPL studies, the anomalous acceleration of the two spacecraft is confirmed. We are also able to put limits on any secondary acceleration (i.e., jerk) terms. The tools that were developed will be used in the upcoming analysis of recently recovered Pioneer 10 and 11 Doppler data files.Comment: 22 pages, 5 figures; accepted for publication in IJMP

Climate bifurcation during the last deglaciation?

There were two abrupt warming events during the last deglaciation, at the start of the Bølling-Allerød and at the end of the Younger Dryas, but their underlying dynamics are unclear. Some abrupt climate changes may involve gradual forcing past a bifurcation point, in which a prevailing climate state loses its stability and the climate tips into an alternative state, providing an early warning signal in the form of slowing responses to perturbations, which may be accompanied by increasing variability. Alternatively, short-term stochastic variability in the climate system can trigger abrupt climate changes, without early warning. Previous work has found signals consistent with slowing down during the last deglaciation as a whole, and during the Younger Dryas, but with conflicting results in the run-up to the Bølling-Allerød. Based on this, we hypothesise that a bifurcation point was approached at the end of the Younger Dryas, in which the cold climate state, with weak Atlantic overturning circulation, lost its stability, and the climate tipped irreversibly into a warm interglacial state. To test the bifurcation hypothesis, we analysed two different climate proxies in three Greenland ice cores, from the Last Glacial Maximum to the end of the Younger Dryas. Prior to the Bølling warming, there was a robust increase in climate variability but no consistent slowing down signal, suggesting this abrupt change was probably triggered by a stochastic fluctuation. The transition to the warm Bølling-Allerød state was accompanied by a slowing down in climate dynamics and an increase in climate variability. We suggest that the Bølling warming excited an internal mode of variability in Atlantic meridional overturning circulation strength, causing multi-centennial climate fluctuations. However, the return to the Younger Dryas cold state increased climate stability. We find no consistent evidence for slowing down during the Younger Dryas, or in a longer spliced record of the cold climate state before and after the Bølling-Allerød. Therefore, the end of the Younger Dryas may also have been triggered by a stochastic perturbation

Large-scale literature mining to assess the relation between anti-cancer drugs and cancer types

Background:There is a huge body of scientific literature describing the relation between tumor types and anti-cancer drugs. The vast amount of scientific literature makes it impossible for researchers and physicians to extract all relevant information manually.Methods:In order to cope with the large amount of literature we applied an automated text mining approach to assess the relations between 30 most frequent cancer types and 270 anti-cancer drugs. We applied two different approaches, a classical text mining based on named entity recognition and an AI-based approach employing word embeddings. The consistency of literature mining results was validated with 3 independent methods: first, using data from FDA approvals, second, using experimentally measured IC-50 cell line data and third, using clinical patient survival data.Results:We demonstrated that the automated text mining was able to successfully assess the relation between cancer types and anti-cancer drugs. All validation methods showed a good correspondence between the results from literature mining and independent confirmatory approaches. The relation between most frequent cancer types and drugs employed for their treatment were visualized in a large heatmap. All results are accessible in an interactive web-based knowledge base using the following link: https://knowledgebase.microdiscovery.de/heatmap.Conclusions:Our approach is able to assess the relations between compounds and cancer types in an automated manner. Both, cancer types and compounds could be grouped into different clusters. Researchers can use the inter-active knowledge base to inspect the presented results and follow their own research questions, for example the identification of novel indication areas for known drugs