TY - JOUR A1 - Cser, Adrienn A1 - Donner, Reik Volker A1 - Schwarz, Udo A1 - Otto, Andreas H. A1 - Geiger, M. A1 - Feudel, Ulrike T1 - Towards a better understanding of laser beam melt ablation using methods of statistical analysis N2 - Laser beam melt ablation, as a contact free machining process, offers several advantages compared to conventional processing mechanisms. Although the idea behind it is rather simple, the process has a major limitation: with increasing ablation rate surface quality of the workpiece processed declines rapidly. The structures observed show a clear dependence of the line energy. In dependence of this parameter several regimes of the process have been separated. These are clearly distinguishable as well in the surfaces obtained as in the signals gained by the measurement of the process emissions which is the observed quantity chosen. Y1 - 2002 SN - 88-87030-44-8 ER - TY - JOUR A1 - Cser, Adrienn A1 - Donner, Reik Volker A1 - Schwarz, Udo A1 - Feudel, Ulrike A1 - Otto, Andreas H. T1 - Statistical parameters of a control strategy of laser beam melt ablation N2 - Laser beam melt ablation - a contact-free machining process - offers several advantages compared to conventional processing mechanisms: there exists no tool wear and even extremely hard or brittle materials can be processed. During ablation the workpiece is molten by a CO2-laser beam, this melt is then driven out by the impulse of a process gas. The idea behind laser ablation is rather simple, but it has a major limitation in practical applications: with increasing ablation rates surface quality of the workpiece processed declines rapidly. At high ablation rates, depending on the process parameters different periodic-like structures can be observed on the ablated surface. These structures show a dependence on the line energy, which has been identified as a fundamental control parameter. In dependence on this parameter several regimes with different behaviours of the process have been separated. These regimes are distinguishable as well in the surfaces obtained as in the signals gained by the measurement of the process emissions. Further aim is to identify the different modes of the system and reach a deeper understanding of the dynamics of the molten material in order to understand the formation of these surface structures. With this it should be possible to influence the system in the direction of avoiding structure formation even at high ablation rates. Relying on the results on-line monitoring and control of the process should be studied. Y1 - 2001 UR - http://www.agnld.uni-potsdam.de/~shw/Paper/2001-EIS.ps ER - TY - JOUR A1 - Krämer, Hauke Kai A1 - Donner, Reik Volker A1 - Heitzig, Jobst A1 - Marwan, Norbert T1 - Recurrence threshold selection for obtaining robust recurrence characteristics in different embedding dimensions JF - Chaos : an interdisciplinary journal of nonlinear science N2 - The appropriate selection of recurrence thresholds is a key problem in applications of recurrence quantification analysis and related methods across disciplines. Here, we discuss the distribution of pairwise distances between state vectors in the studied system’s state space reconstructed by means of time-delay embedding as the key characteristic that should guide the corresponding choice for obtaining an adequate resolution of a recurrence plot. Specifically, we present an empirical description of the distance distribution, focusing on characteristic changes of its shape with increasing embedding dimension. Our results suggest that selecting the recurrence threshold according to a fixed percentile of this distribution reduces the dependence of recurrence characteristics on the embedding dimension in comparison with other commonly used threshold selection methods. Numerical investigations on some paradigmatic model systems with time-dependent parameters support these empirical findings. Recurrence plots (RPs) provide an intuitive tool for visualizing the (potentially multi-dimensional) trajectory of a dynamical system in state space. In case only univariate observations of the system’s overall state are available, time-delay embedding has become a standard procedure for qualitatively reconstructing the dynamics in state space. The selection of a threshold distance 𝜀 , which distinguishes close from distant pairs of (reconstructed) state vectors, is known to have a substantial impact on the recurrence plot and its quantitative characteristics, but its corresponding interplay with the embedding dimension has not yet been explicitly addressed. Here, we point out that the results of recurrence quantification analysis (RQA) and related methods are qualitatively robust under changes of the (sufficiently high) embedding dimension only if the full distribution of pairwise distances between state vectors is considered for selecting 𝜀, which is achieved by consideration of a fixed recurrence rate. Y1 - 2018 U6 - https://doi.org/10.1063/1.5024914 SN - 1054-1500 SN - 1089-7682 VL - 28 IS - 8 PB - American Institute of Physics CY - Melville ER - TY - JOUR A1 - Donges, Jonathan Friedemann A1 - Donner, Reik Volker A1 - Trauth, Martin H. A1 - Marwan, Norbert A1 - Schellnhuber, Hans Joachim A1 - Kurths, Jürgen T1 - Nonlinear detection of paleoclimate-variability transitions possibly related to human evolution JF - Proceedings of the National Academy of Sciences of the United States of America N2 - Potential paleoclimatic driving mechanisms acting on human evolution present an open problem of cross-disciplinary scientific interest. The analysis of paleoclimate archives encoding the environmental variability in East Africa during the past 5 Ma has triggered an ongoing debate about possible candidate processes and evolutionary mechanisms. In this work, we apply a nonlinear statistical technique, recurrence network analysis, to three distinct marine records of terrigenous dust flux. Our method enables us to identify three epochs with transitions between qualitatively different types of environmental variability in North and East Africa during the (i) Middle Pliocene (3.35-3.15 Ma B. P.), (ii) Early Pleistocene (2.25-1.6 Ma B. P.), and (iii) Middle Pleistocene (1.1-0.7 Ma B. P.). A deeper examination of these transition periods reveals potential climatic drivers, including (i) large-scale changes in ocean currents due to a spatial shift of the Indonesian throughflow in combination with an intensification of Northern Hemisphere glaciation, (ii) a global reorganization of the atmospheric Walker circulation induced in the tropical Pacific and Indian Ocean, and (iii) shifts in the dominating temporal variability pattern of glacial activity during the Middle Pleistocene, respectively. A reexamination of the available fossil record demonstrates statistically significant coincidences between the detected transition periods and major steps in hominin evolution. This result suggests that the observed shifts between more regular and more erratic environmental variability may have acted as a trigger for rapid change in the development of humankind in Africa. KW - African climate KW - Plio-Pleistocene KW - climate-driven evolution KW - dynamical transitions KW - nonlinear time series analysis Y1 - 2011 U6 - https://doi.org/10.1073/pnas.1117052108 SN - 0027-8424 VL - 108 IS - 51 SP - 20422 EP - 20427 PB - National Acad. of Sciences CY - Washington ER - TY - JOUR A1 - Siegmund, Jonatan F. A1 - Sanders, Tanja G. M. A1 - Heinrich, Ingo A1 - van der Maaten, Ernst A1 - Simard, Sonia A1 - Helle, Gerhard A1 - Donner, Reik Volker T1 - Meteorological Drivers of Extremes in Daily Stem Radius Variations of Beech, Oak, and Pine in Northeastern Germany: An Event Coincidence Analysis JF - Frontiers in plant science N2 - Observed recent and expected future increases in frequency and intensity of climatic extremes in central Europe may pose critical challenges for domestic tree species. Continuous dendrometer recordings provide a valuable source of information on tree stem radius variations, offering the possibility to study a tree's response to environmental influences at a high temporal resolution. In this study, we analyze stem radius variations (SRV) of three domestic tree species (beech, oak, and pine) from 2012 to 2014. We use the novel statistical approach of event coincidence analysis (ECA) to investigate the simultaneous occurrence of extreme daily weather conditions and extreme SRVs, where extremes are defined with respect to the common values at a given phase of the annual growth period. Besides defining extreme events based on individual meteorological variables, we additionally introduce conditional and joint ECA as new multivariate extensions of the original methodology and apply them for testing 105 different combinations of variables regarding their impact on SRV extremes. Our results reveal a strong susceptibility of all three species to the extremes of several meteorological variables. Yet, the inter-species differences regarding their response to the meteorological extremes are comparatively low. The obtained results provide a thorough extension of previous correlation-based studies by emphasizing on the timings of climatic extremes only. We suggest that the employed methodological approach should be further promoted in forest research regarding the investigation of tree responses to changing environmental conditions. KW - dendrometer measurements KW - event coincidence analysis KW - climate extremes KW - growth response Y1 - 2016 U6 - https://doi.org/10.3389/fpls.2016.00733 SN - 1664-462X VL - 7 SP - 4701 EP - 4712 PB - Frontiers Research Foundation CY - Lausanne ER - TY - JOUR A1 - Donner, Reik Volker A1 - Seehafer, Norbert A1 - Sanjuan, Miguel Angel Fernandez A1 - Feudel, Fred T1 - Low-dimensional dynamo modelling and symmetry-breaking bifurcations JF - Physica. D, Nonlinear phenomena N2 - Motivated by the successful Karlsruhe dynamo experiment, a relatively low-dimensional dynamo model is proposed. It is based on a strong truncation of the magnetohydrodynamic (MHD) equations with an external forcing of the Roberts type and the requirement that the model system satisfies the symmetries of the full MHD system, so that the first symmetry-breaking bifurcations can be captured. The backbone of the Roberts dynamo is formed by the Roberts flow, a helical mean magnetic field and another part of the magnetic field coupled to these two by triadic mode interactions. A minimum truncation model (MTM) containing only these energetically dominating primary mode triads is fully equivalent to the widely used first-order smoothing approximation. However, it is shown that this approach works only in the limit of small wave numbers of the excited magnetic field or small magnetic Reynolds numbers ($Rm ll 1$). To obtain dynamo action under more general conditions, secondary mode Y1 - 2006 UR - http://www.sciencedirect.com/science/journal/01672789 U6 - https://doi.org/10.1016/j.physd.2006.08.022 SN - 0167-2789 VL - 223 IS - 2 SP - 151 EP - 162 PB - Elsevier CY - Amsterdam ER - TY - JOUR A1 - Bube, Kevin A1 - Neto, Camilo Rodrigues A1 - Donner, Reik Volker A1 - Schwarz, Udo A1 - Feudel, Ulrike T1 - Linear and nonlinear characterization of surfaces from a laser beam melt ablation process N2 - We apply linear and nonlinear methods to study the properties of surfaces generated by a laser beam melt ablation process. As a result we present a characterization and ordering of the surfaces depending on the adjusted process parameters. Our findings give some insight into the performance of two widely applied multifractal analysis methods-the detrended fluctuation analysis and the wavelet transform modulus maxima method-on short real world data Y1 - 2006 UR - http://iopscience.iop.org/0022-3727/ U6 - https://doi.org/10.1088/0022-3727/39/7/011 SN - 0022-3727 ER - TY - JOUR A1 - Baumbach, Lukas A1 - Siegmund, Jonatan F. A1 - Mittermeier, Magdalena A1 - Donner, Reik Volker T1 - Impacts of temperature extremes on European vegetation during the growing season JF - Biogeosciences N2 - Temperature is a key factor controlling plant growth and vitality in the temperate climates of the mid-latitudes like in vast parts of the European continent. Beyond the effect of average conditions, the timings and magnitudes of temperature extremes play a particularly crucial role, which needs to be better understood in the context of projected future rises in the frequency and/or intensity of such events. In this work, we employ event coincidence analysis (ECA) to quantify the likelihood of simultaneous occurrences of extremes in daytime land surface temperature anomalies (LSTAD) and the normalized difference vegetation index (NDVI). We perform this analysis for entire Europe based upon remote sensing data, differentiating between three periods corresponding to different stages of plant development during the growing season. In addition, we analyze the typical elevation and land cover type of the regions showing significantly large event coincidences rates to identify the most severely affected vegetation types. Our results reveal distinct spatio-temporal impact patterns in terms of extraordinarily large co-occurrence rates between several combinations of temperature and NDVI extremes. Croplands are among the most frequently affected land cover types, while elevation is found to have only a minor effect on the spatial distribution of corresponding extreme weather impacts. These findings provide important insights into the vulnerability of European terrestrial ecosystems to extreme temperature events and demonstrate how event-based statistics like ECA can provide a valuable perspective on environmental nexuses. Y1 - 2017 U6 - https://doi.org/10.5194/bg-14-4891-2017 SN - 1726-4170 SN - 1726-4189 VL - 14 SP - 4891 EP - 4903 PB - Copernicus CY - Göttingen ER - TY - JOUR A1 - Siegmund, Jonatan F. A1 - Wiedermann, Marc A1 - Donges, Jonathan Friedemann A1 - Donner, Reik Volker T1 - Impact of temperature and precipitation extremes on the flowering dates of four German wildlife shrub species JF - Biogeosciences N2 - Ongoing climate change is known to cause an increase in the frequency and amplitude of local temperature and precipitation extremes in many regions of the Earth. While gradual changes in the climatological conditions have already been shown to strongly influence plant flowering dates, the question arises if and how extremes specifically impact the timing of this important phenological phase. Studying this question calls for the application of statistical methods that are tailored to the specific properties of event time series. Here, we employ event coincidence analysis, a novel statistical tool that allows assessing whether or not two types of events exhibit similar sequences of occurrences in order to systematically quantify simultaneities between meteorological extremes and the timing of the flowering of four shrub species across Germany. Our study confirms previous findings of experimental studies by highlighting the impact of early spring temperatures on the flowering of the investigated plants. However, previous studies solely based on correlation analysis do not allow deriving explicit estimates of the strength of such interdependencies without further assumptions, a gap that is closed by our analysis. In addition to direct impacts of extremely warm and cold spring temperatures, our analysis reveals statistically significant indications of an influence of temperature extremes in the autumn preceding the flowering. Y1 - 2016 U6 - https://doi.org/10.5194/bg-13-5541-2016 SN - 1726-4170 SN - 1726-4189 VL - 13 SP - 5541 EP - 5555 PB - Copernicus CY - Göttingen ER - TY - JOUR A1 - Donges, Jonathan Friedemann A1 - Donner, Reik Volker A1 - Rehfeld, Kira A1 - Marwan, Norbert A1 - Trauth, Martin H. A1 - Kurths, Jürgen T1 - Identification of dynamical transitions in marine palaeoclimate records by recurrence network analysis JF - Nonlinear processes in geophysics N2 - The analysis of palaeoclimate time series is usually affected by severe methodological problems, resulting primarily from non-equidistant sampling and uncertain age models. As an alternative to existing methods of time series analysis, in this paper we argue that the statistical properties of recurrence networks - a recently developed approach - are promising candidates for characterising the system's nonlinear dynamics and quantifying structural changes in its reconstructed phase space as time evolves. In a first order approximation, the results of recurrence network analysis are invariant to changes in the age model and are not directly affected by non-equidistant sampling of the data. Specifically, we investigate the behaviour of recurrence network measures for both paradigmatic model systems with non-stationary parameters and four marine records of long-term palaeoclimate variations. We show that the obtained results are qualitatively robust under changes of the relevant parameters of our method, including detrending, size of the running window used for analysis, and embedding delay. We demonstrate that recurrence network analysis is able to detect relevant regime shifts in synthetic data as well as in problematic geoscientific time series. This suggests its application as a general exploratory tool of time series analysis complementing existing methods. Y1 - 2011 U6 - https://doi.org/10.5194/npg-18-545-2011 SN - 1023-5809 VL - 18 IS - 5 SP - 545 EP - 562 PB - Copernicus CY - Göttingen ER -