Nonlinearities in shadowgraphy experiments on non-equilibrium fluctuations in polymer solutions.

Giant thermal and solutal non-equilibrium fluctuations are observed in shadowgraphy experiments on liquid mixtures subjected to a temperature gradient. For large temperature differences, both the temperature and the composition dependence of the relevant thermophysical parameters and the nonlinear terms in the diffusion equation need to be taken into account, leading to a nonlinear concentration profile. For temperature differences exceeding the inverse of the Soret coefficient, in our example approximately 10 K, the usual data evaluation yields increasingly wrong diffusion and Soret coefficients that are off by almost a factor of two for a temperature difference of 50 K. A local model that treats the measured shadowgraph signal as a superposition of the contributions from every layer of the sample is able to capture the essential trend and yields a good agreement with experimental data. The results are important for the application of shadowgraphy as a tool for the measurement of Soret and diffusion coefficients, where large temperature gradients promise a good signal-to-noise ratio.

Correlated and uncorrelated regions in heart-rate fluctuations during sleep.

Healthy sleep consists of several stages: deep sleep, light sleep, and rapid eye movement (REM) sleep. Here we show that these sleep stages can be characterized and distinguished by correlations of heart rates separated by n beats. Using the detrended fluctuation analysis (DFA) up to fourth order we find that long-range correlations reminiscent to the wake phase are present only in the REM phase. In the non-REM phases, the heart rates are uncorrelated above the typical breathing cycle time, pointing to a random regulation of the heartbeat during non-REM sleep.

Heart rate variability during sleep stages in normals and in patients with sleep apnea.

Heart rate and heart rate variability are under the control of the autonomous nervous system. It can be assumed that during sleep internal influences dominate the autonomous nervous system. During the different sleep stages heart rate regulation differs in normal subjects. Obstructive sleep apnea is a disorder which has its origin in sleep and has strong modulating effects on the autonomous nervous system with prominent heart rate variations in consequence. In order to separate the influences of sleep stages and sleep apnea on heart rate variability we applied detrended fluctuation analysis in 12 healthy subjects and 20 patients with sleep apnea. We could show that the differences between sleep stages observed in healthy subjects were still present in subjects with sleep apnea despite their cyclical variation in heart rate. We conclude, that detrended fluctuation analysis is able to separate the influences of sleep stages and sleep apnea on heart rate variability.