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Objective: Several different measures of heart rate variability, and particularly of respiratory sinus arrhythmia, are widely used in research and clinical applications. For many purposes it is important to know which features of heart rate variability are directly related to respiration and which are caused by other aspects of cardiac dynamics. Approach: Inspired by ideas from the theory of coupled oscillators, we use simultaneous measurements of respiratory and cardiac activity to perform a nonlinear disentanglement of the heart rate variability into the respiratory-related component and the rest. Main results: The theoretical consideration is illustrated by the analysis of 25 data sets from healthy subjects. In all cases we show how the disentanglement is manifested in the different measures of heart rate variability. Significance: The suggested technique can be exploited as a universal preprocessing tool, both for the analysis of respiratory influence on the heart rate and in cases when effects of other factors on the heart rate variability are in focus.
Unipolar, axisymmetric sunspots are figuratively called “theoretician's sunspots” because their simplicity supposedly makes them more suitable for theoretical descriptions or numerical models. On November 18, 2013, a very large specimen (active region NOAA 11899) crossed the central meridian of the sun. The moat flow associated with this very large spot is quantitatively compared to that of a medium and a small sunspot to determine the extent of the moat flow in different environments. We employ continuum images and magnetograms of the Helioseismic and Magnetic Imager (HMI) as well as extreme ultraviolet (EUV) images at λ160 nm of the Atmospheric Imaging Assembly (AIA), both on board the Solar Dynamics Observatory (SDO), to measure horizontal proper motions with Local Correlation Tracking (LCT) and flux transport velocities with the Differential Affine Velocity Estimator (DAVE). We compute time-averaged flow maps (±6 hr around meridian passage) and radial averages of photometric, magnetic, and flow properties. Flow fields of a small- and a medium-sized axisymmetric sunspot provide the context for interpreting the results. All sunspots show outward moat flow and the advection of moving magnetic features (MMFs). However, the extent of the moat flow varies from spot to spot, and a correlation of flow properties with size is tenuous, if at all present. The moat flow is asymmetric and predominantly in the east–west direction, whereby deviations are related to the tilt angle of the sunspot group as well as to the topology and activity level of the trailing plage.
The occurrence of earthquakes is characterized by a high degree of spatiotemporal complexity. Although numerous patterns, e.g. fore- and aftershock sequences, are well-known, the underlying mechanisms are not observable and thus not understood. Because the recurrence times of large earthquakes are usually decades or centuries, the number of such events in corresponding data sets is too small to draw conclusions with reasonable statistical significance. Therefore, the present study combines both, numerical modeling and analysis of real data in order to unveil the relationships between physical mechanisms and observational quantities. The key hypothesis is the validity of the so-called "critical point concept" for earthquakes, which assumes large earthquakes to occur as phase transitions in a spatially extended many-particle system, similar to percolation models. New concepts are developed to detect critical states in simulated and in natural data sets. The results indicate that important features of seismicity like the frequency-size distribution and the temporal clustering of earthquakes depend on frictional and structural fault parameters. In particular, the degree of quenched spatial disorder (the "roughness") of a fault zone determines whether large earthquakes occur quasiperiodically or more clustered. This illustrates the power of numerical models in order to identify regions in parameter space, which are relevant for natural seismicity. The critical point concept is verified for both, synthetic and natural seismicity, in terms of a critical state which precedes a large earthquake: a gradual roughening of the (unobservable) stress field leads to a scale-free (observable) frequency-size distribution. Furthermore, the growth of the spatial correlation length and the acceleration of the seismic energy release prior to large events is found. The predictive power of these precursors is, however, limited. Instead of forecasting time, location, and magnitude of individual events, a contribution to a broad multiparameter approach is encouraging.