Power-law persistence and trends in the atmosphere: a detailed study of long temperature records.

We use several variants of the detrended fluctuation analysis to study the appearance of long-term persistence in temperature records, obtained at 95 stations all over the globe. Our results basically confirm earlier studies. We find that the persistence, characterized by the correlation C(s) of temperature variations separated by s days, decays for large s as a power law, C(s) approximately s(-gamma). For continental stations, including stations along the coastlines, we find that gamma is always close to 0.7. For stations on islands, we find that gamma ranges between 0.3 and 0.7, with a maximum at gamma=0.4. This is consistent with earlier studies of the persistence in sea surface temperature records where gamma is close to 0.4. In all cases, the exponent gamma does not depend on the distance of the stations to the continental coastlines. By varying the degree of detrending in the fluctuation analysis we obtain also information about trends in the temperature records.

Structural properties of self-attracting walks.

Self-attracting walks (SATW) with attractive interaction u>0 display a swelling-collapse transition at a critical u(c) for dimensions d>or=2, analogous to the Theta transition of polymers. We are interested in the structure of the clusters generated by SATW below u(c) (swollen walk), above u(c) (collapsed walk), and at u(c), which can be characterized by the fractal dimensions of the clusters d(f) and their interface d(I). Using scaling arguments and Monte Carlo simulations, we find that for uu(c), the clusters are compact, i.e., d(f)=d and d(I)=d-1. At u(c), the SATW is in a new universality class. The clusters are compact in both d=2 and d=3, but their interface is fractal: d(I)=1.50+/-0.01 and 2.73+/-0.03 in d=2 and d=3, respectively. In d=1, where the walk is collapsed for all u and no swelling-collapse transition exists, we derive analytical expressions for the average number of visited sites and the mean time to visit S sites.

Multifractal behavior of linear polymers in disordered media.

The scaling behavior of linear polymers in disordered media modeled by self-avoiding random walks (SAWs) on the backbone of two- and three-dimensional percolation clusters at their critical concentrations p(c) is studied. All possible SAW configurations of N steps on a single backbone configuration are enumerated exactly. We find that the moments of order q of the total number of SAWs obtained by averaging over many backbone configurations display multifractal behavior; i.e., different moments are dominated by different subsets of the backbone. This leads to generalized coordination numbers mu(q) and enhancement exponents gamma(q), which depend on q. Our numerical results suggest that the relation mu(1)=p(c)mu between the first moment mu(1) and its regular lattice counterpart mu is valid.

Nanocrystalline versus microcrystalline Li(2)O:B(2)O3 composites: anomalous ionic conductivities and percolation theory

We study ionic transport in nano- and microcrystalline (1-x)Li(2)O:xB(2)O3 composites using standard impedance spectroscopy. In the nanocrystalline samples (average grain size of about 20 nm), the ionic conductivity sigma(dc) increases with increasing content x of B2O3 up to a maximum at x approximately 0.5. Above x approximately 0.92, sigma(dc) vanishes. By contrast, in the microcrystalline samples (grain size about 10 &mgr;m), sigma(dc) decreases monotonically with x and vanishes above x approximately 0. 55. We can explain this strikingly different behavior by a percolation model that assumes an enhanced conductivity at the interfaces between insulating and conducting phases in both materials and explicitly takes into account the different grain sizes.

Swelling-collapse transition of self-attracting walks

We study the structural properties of self-attracting walks in d dimensions using scaling arguments and Monte Carlo simulations. We find evidence of a transition analogous to the Theta transition of polymers. Above a critical attractive interaction u(c), the walk collapses and the exponents nu and k, characterizing the scaling with time t of the mean square end-to-end distance approximately t(2nu) and the average number of visited sites approximately t(k), are universal and given by nu=1/(d+1) and k=d/(d+1). Below u(c), the walk swells and the exponents are as with no interaction, i.e., nu=1/2 for all d, k=1/2 for d=1 and k=1 for d>/=2. At u(c), the exponents are found to be in a different universality class.

Influence of dipolar interaction on magnetic properties of ultrafine ferromagnetic particles

We use Monte Carlo simulations to study the influence of dipolar interaction and polydispersity on the magnetic properties of single-domain ultrafine ferromagnetic particles. From the zero field cooling (ZFC)/field cooling (FC) simulations we observe that the blocking temperature T(B) clearly increases with increasing strength of interaction, but it is almost not effected by a broadening of the distribution of particle sizes. While the dependence of the ZFC/FC curves on interaction and cooling rate are reminiscent of a spin glass transition at T(B), the relaxational behavior of the magnetic moments below T(B) is not in accordance with the picture of cooperative freezing.

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.

Optimal paths in disordered media: scaling of the crossover from self-similar to self-affine behavior.

We study optimal paths in disordered energy landscapes using energy distributions of the type P(log(10) E)=const that lead to the strong disorder limit. If we truncate the distribution, so that P(log(10) E)=const only for E(min) < or =E < or =E(max), and P(log(10) E)=0 otherwise, we obtain a crossover from self-similar (strong disorder) to self-affine (moderate disorder) behavior at a path length l(x). We find that l(x) proportional, variant[log(10)(E(max)/E(min))](kappa), where the exponent kappa has the value kappa=1.60 +/- 0.03 both in d=2 and d=3. We show how the crossover can be understood from the distribution of local energies on the optimal paths.

Sleep-wake differences in scaling behavior of the human heartbeat: analysis of terrestrial and long-term space flight data.

We compare scaling properties of the cardiac dynamics during sleep and wake periods for healthy individuals, cosmonauts during orbital flight, and subjects with severe heart disease. For all three groups, we find a greater degree of anticorrelation in the heartbeat fluctuations during sleep compared to wake periods. The sleep-wake difference in the scaling exponents for the three groups is comparable to the difference between healthy and diseased individuals. The observed scaling differences are not accounted for simply by different levels of activity, but appear related to intrinsic changes in the neuroautonomic control of the heartbeat.

Scaling in nature: from DNA through heartbeats to weather.

The purpose of this report is to describe some recent progress in applying scaling concepts to various systems in nature. We review several systems characterized by scaling laws such as DNA sequences, heartbeat rates and weather variations. We discuss the finding that the exponent alpha quantifying the scaling in DNA in smaller for coding than for noncoding sequences. We also discuss the application of fractal scaling analysis to the dynamics of heartbeat regulation, and report the recent finding that the scaling exponent alpha is smaller during sleep periods compared to wake periods. We also discuss the recent findings that suggest a universal scaling exponent characterizing the weather fluctuations.