Fluctuation analysis of the time dynamics of laser distance data measured in the medieval Jeroným Mine (Czech Republic)

Fractal tools are used to investigate the hourly time fluctuations of the ceiling height of a chamber located in the medieval Jeroným Mine, which is one of the Cultural National Heritage sites of the Czech Republic. The data were measured from 2008 to 2010 by a laser distance meter (Leica DISTO^TMA4). The scaling behavior is revealed by means of different statistics: the power spectrum method, the detrended fluctuation analysis, the Higuchi analysis and the mean distance spanned within time L. The values of the scaling exponents estimated by means of these methods indicate that the temporal fluctuations of the ceiling height are not typical of a purely random stochastic process (i.e. white noise), but evidence the presence of long-range correlations. Furthermore, it is found that these correlations are linear.     

Violin frequency response - bridge mobility and bridge feet distance

Good violins have a broad hill in the 2-3 kHz range of their frequency response. This hill has previously been attributed to the first in-plane resonance of the violin bridge. Experiments prove, however, that the hill is the result of two forces acting in opposite directions at the bridge feet. The experiments reported here show that the hill can be “tuned” by altering the distance between the bridge feet. It can be tuned both in terms of frequency and level but the properties of the violin cannot be neglected.     

Perceptual thresholds for detecting modifications applied to the acoustical properties of a violin

This study is the first step in the psychoacoustic exploration of perceptual differences between the sounds of different violins. A method was used which enabled the same performance to be replayed on different "virtual violins," so that the relationships between acoustical characteristics of violins and perceived qualities could be explored. Recordings of real performances were made using a bridge-mounted force transducer, giving an accurate representation of the signal from the violin string. These were then played through filters corresponding to the admittance curves of different violins. Initially, limits of listener performance in detecting changes in acoustical characteristics were characterized. These consisted of shifts in frequency or increases in amplitude of single modes or frequency bands that have been proposed previously to be significant in the perception of violin sound quality. Thresholds were significantly lower for musically trained than for nontrained subjects but were not significantly affected by the violin used as a baseline. Thresholds for the musicians typically ranged from 3 to 6 dB for amplitude changes and 1.5%-20% for frequency changes. Interpretation of the results using excitation patterns showed that thresholds for the best subjects were quite well predicted by a multichannel model based on optimal processing.     

Scaling characteristics of ocean wave height time series

Fluctuations in the significant wave height can be quantified by using scaling statistics. In this paper, the scaling properties of the significant wave height were explored by using a large data set of hourly series from 25 monitoring stations located off the west coast of the US. Detrended fluctuation analysis (DFA) was used to investigate the scaling properties of the series. DFA is a robust technique that can be used to detect long-range correlations in nonstationary time series. The significant wave height data was analyzed by using scales from hourly to monthly. It was found that a common scaling behavior can be observed for all stations. A breakpoint in the scaling region around 4-5 days was apparent. Spectral analysis confirms this result. This breakpoint divided the scaling region into two distinct parts. The first part was for finer scales (up to 4 days) which exhibited Brown noise characteristics, while the second one showed 1/f noise behavior at coarser scales (5 days to 1 month). The first order and the second order DFA (DFA1 and DFA2) were used to check the effect of seasonality. It was found that there were no differences between DFA1 and DFA2 results, indicating that there is no effect of trends in the wave height time series. The resulting scaling coefficients range from 0.696 to 0.890 indicating that the wave height exhibits long-term persistence. There were no coherent spatial variations in the scaling coefficients.     

The violin bridge as filter

The violin bridge filter role was investigated using modal and acoustic measurements on 12 quality-rated violins combined with systematic bridge rocking frequency f(rock) and wing mass decrements deltam on four bridges for two other violins. No isolated bridge resonances were observed; bridge motions were complex (including a "squat" mode near 0.8 kHz) except for low frequency rigid body pivot motions, all more or less resembling rocking motion at higher frequencies. A conspicuous broad peak near 2.3 kHz in bridge driving point mobility (labeled BH) was seen for good and bad violins. Similar structure was seen in averaged bridge, bridge feet, corpus mobilities and averaged radiativity. No correlation between violin quality and BH driving point, averaged corpus mobility magnitude, or radiativity was found. Increasing averaged-over-f(rock) deltam(g) from 0 to 0.12 generally increased radiativity across the spectrum. Decreasing averaged-over-deltam f(rock) from 3.6 to 2.6 kHz produced consistent decreases in radiativity between 3 and 4.2 kHz, but only few-percent decreases in BH frequency. The lowest f(rock) values were accompanied by significantly reduced radiation from the Helmholtz A0 mode near 280 Hz; this, combined with reduced high frequency output, created overall radiativity profiles quite similar to "bad" violins among the quality-rated violins.     

Long-range correlations in two-dimensional spatio-temporal seismic fluctuations

We analysed the scaling behaviour of the two-dimensional (2-D) sequence (Δs, Δt) of the 1981–1998 southern California seismicity, where Δs is the distance between two consecutive earthquakes (jump) and Δt is their interevent interval. The 2-D seismic spatio-temporal fluctuations were investigated by means of the detrended fluctuation analysis (DFA), well-known methodology used to detect scaling behaviour in observational time series possibly affected by nonstationarities. The estimated scaling exponents α_DFA, larger than 0.5, indicate the presence of persistent long-range correlations in the 2-D sequence analysed. The variation of the scaling exponent with the increase of threshold magnitude shows a two-fold behaviour: in the range between 1.5 (the completeness magnitude of the catalog) and 3.0, the scaling exponent is quite constant and denoting a flicker-noise dynamics; while for magnitudes larger than 3.0 it decreases with the increase of magnitude, indicating a tendency toward a 2-D space–time Poissonian process for large events.     

Modelling fluctuations of financial time series: from cascade process to stochastic volatility model

In this paper, we provide a simple, “generic” interpretation of multifractal scaling laws and multiplicative cascade process paradigms in terms of volatility correlations. We show that in this context 1/f power spectra, as recently observed in reference [23], naturally emerge. We then propose a simple solvable “stochastic volatility” model for return fluctuations. This model is able to reproduce most of recent empirical findings concerning financial time series: no correlation between price variations, long-range volatility correlations and multifractal statistics. Moreover, its extension to a multivariate context, in order to model portfolio behavior, is very natural. Comparisons to real data and other models proposed elsewhere are provided. Received 22 May 2000     

Hydrodynamic interactions in self similar structures, such as polymers

We study the hydrodynamic properties of polymers and more generally self-similar structures using a new recursion model. The hydrodynamic interaction between monomers is modeled by the standard Green's function of Stokes flow in which an ultrametric distance is substituted for the usual Euclidean distance. This leads to a model where the long-range hydrodynamic interactions and the long-range correlations of the polymer conformation can both be accounted for and yet allow for analytical solutions. We explore the asymptotic as well as the finite size corrections to the scaling behavior with this model. In order to compare the results of the present scheme with more conventional techniques a generalized version of the existing mean field results by Kirkwood and Riseman for the hydrodynamic drag is introduced. Received 26 August 1998 and Received in final form 7 December 1998     

Thermodynamics and dynamics of systems with long-range interactions

We review simple aspects of the thermodynamic and dynamical properties of systems with long-range pairwise interactions (LRI), which decay as 1/r^d+σ at large distances r in d dimensions. Two broad classes of such systems are discussed. (i) Systems with a slow decay of the interactions, termed “strong” LRI, where the energy is super-extensive. These systems are characterized by unusual properties such as inequivalence of ensembles, negative specific heat, slow decay of correlations, anomalous diffusion and ergodicity breaking. (ii) Systems with faster decay of the interaction potential, where the energy is additive, thus resulting in less dramatic effects. These interactions affect the thermodynamic behavior of systems near phase transitions, where long-range correlations are naturally present. Long-range correlations are often present in systems driven out of equilibrium when the dynamics involves conserved quantities. Steady state properties of driven systems with local dynamics are considered within the framework outlined above.     

Asymmetric multifractal scaling behavior in the Chinese stock market: Based on asymmetric MF-DFA

We utilized asymmetric multifractal detrended fluctuation analysis in this study to examine the asymmetric multifractal scaling behavior of Chinese stock markets with uptrends or downtrends. Results show that the multifractality degree of Chinese stock markets with uptrends is stronger than that of Chinese stock markets with downtrends. Correlation asymmetries are more evident in large fluctuations than in small fluctuations. By discussing the source of asymmetric multifractality, we find that multifractality is related to long-range correlations when the market is going up, whereas it is related to fat-tailed distribution when the market is going down. The main source of asymmetric scaling behavior in the Shanghai stock market are long-range correlations, whereas that in the Shenzhen stock market is fat-tailed distribution. An analysis of the time-varying feature of scaling asymmetries shows that the evolution trends of these scaling asymmetries are similar in the two Chinese stock markets. Major financial and economical events may enhance scaling asymmetries.     

Multifractal properties of the Indian financial market

We investigate the multifractal properties of the logarithmic returns of the Indian financial indices (BSE & NSE) by applying the multifractal detrended fluctuation analysis. The results are compared with that of the US S&P 500 index. Numerically we find that qth-order generalized Hurst exponents h(q) and τ(q) change with the moments q. The nonlinear dependence of these scaling exponents and the singularity spectrum f(α) show that the returns possess multifractality. By comparing the MF-DFA results of the original series to those for the shuffled series, we find that the multifractality is due to the contributions of long-range correlations as well as the broad probability density function. The financial markets studied here are compared with the Binomial Multifractal Model (BMFM) and have a smaller multifractal strength than the BMFM.     

Detecting long-range correlations in fire sequences with Detrended fluctuation analysis

The spatial-temporal power-law distributions are found in many natural systems, which have self-similarity and fractal behavior. By analyzing the time series of such systems, we could expect to explore and understand the underlying mechanisms. In this paper, the Detrended fluctuation analysis (DFA) is used to analyze the long-range correlations of forest and urban fires in Japan and China. It is found that the interevent time series of both forest and urban fires have the persistent long-range power-law correlations, and they all have two scaling exponents, α₁ and α₂, which are both bigger than 0.5 and smaller than 1.0, despite the different regions and countries. For forest fires, 0.61<α₁<0.73,0.87<α₂<0.98 and for urban fires, 0.52<α₁<0.61,0.59<α₂<0.88. The result suggests that fires have self-similarity characteristics. The occurrence of forest fires may have connection with the weather fluctuations, which have significant effects on the ignition and have the similar temporal correlations. It is shown that the interval sequences of urban fires closely resemble that of white noise in small timescale, and the correlations are weaker than that of forest fires. Human behavior and human density may affect the long-range correlation in some way. This seems to be helpful to understand the complexity of fire system in temporal aspect.     

Long-range anticorrelations and non-Gaussian behavior of the heartbeat

We find that the successive increments in the cardiac beat-to-beat intervals of healthy subjects display scale-invariant, long-range anticorrelations (up to 10(4) heart beats). Furthermore, we find that the histogram for the heartbeat intervals increments is well described by a Lévy stable distribution. For a group of subjects with severe heart disease, we find that the distribution is unchanged, but the long-range correlations vanish. Therefore, the different scaling behavior in health and disease must relate to the underlying dynamics of the heartbeat.     

Non-uniform scaling behavior in ultra-low-frequency (ULF) earthquake-related geomagnetic signals

Investigating highly non-stationary time series, which typically exhibit long-range correlations, is a classic problem in physics. Here, we analyze the scaling properties of the dynamics of ultra-low-frequency (ULF) geomagnetic data (in the frequency range between 1 mHz and 10 Hz) observed at Izu Peninsula in Japan. On the basis of the detrended fluctuation analysis (DFA), deviations from uniform power-law scaling were quantified. Our findings point out to a significant non-uniform scaling behavior in ULF geomagnetic data in relationship with the occurrence of intense seismic clusters.     

Detrended fluctuation analysis of heart intrabeat dynamics

We investigate scaling properties of electrocardiogram (ECG) recordings of healthy subjects and heart failure patients based on detrended fluctuation analysis (DFA). While the vast majority of scaling analysis has focused on the characterization of the long-range correlations of interbeat (i.e., beat-to-beat) dynamics, in this work we consider instead the characterization of intrabeat dynamics. That is, here we use DFA to study correlations for time scales smaller than one heart beat period (about 0.75 s). Our results show that intrabeat dynamics of healthy subject are less correlated than for heart failure dynamics. As in the case of interbeat dynamics, the DFA scaling exponents can be used to discriminate healthy and pathological data. It is shown that 0.5 h recordings suffices to characterize the ECG correlation properties.     

Scale-Free Static and Dynamical Correlations in Melts of Monodisperse and Flory-Distributed Homopolymers

It has been assumed until very recently that all long-range correlations are screened in three-dimensional melts of linear homopolymers on distances beyond the correlation length ?? characterizing the decay of the density fluctuations. Summarizing simulation results obtained by means of a variant of the bond-fluctuation model with finite monomer excluded volume interactions and topology violating local and global Monte Carlo moves, we show that due to an interplay of the chain connectivity and the incompressibility constraint, both static and dynamical correlations arise on distances r???. These correlations are scale-free and, surprisingly, do not depend explicitly on the compressibility of the solution. Both monodisperse and (essentially) Flory-distributed equilibrium polymers are considered.     

Transition on the relationship between fractal dimension and Hurst exponent in the long-range connective sandpile models

The relationships between the Hurst exponent H and the power-law scaling exponent B in a new modification of sandpile models, i.e. the long-range connective sandpile (LRCS) models, exhibit a strong dependence upon the system size L. As L decreases, the LRCS model can demonstrate a transition from the negative to positive correlations between H- and B-values. While the negative and null correlations are associated with the fractional Gaussian noise and generalized Cauchy processes, respectively, the regime with the positive correlation between the Hurst and power-law scaling exponents may suggest an unknown, interesting class of the stochastic processes.     

Nodal line optimization and its application to violin top plate design

In the literature, most problems of structural vibration have been formulated to adjust a specific natural frequency: for example, to maximize the first natural frequency. In musical instruments like a violin; however, mode shapes are equally important because they are related to sound quality in the way that natural frequencies are related to the octave. The shapes of nodal lines, which represent the natural mode shapes, are generally known to have a unique feature for good violins. Among the few studies on mode shape optimization, one typical study addresses the optimization of nodal point location for reducing vibration in a one-dimensional beam structure. However, nodal line optimization, which is required in violin plate design, has not yet been considered. In this paper, the central idea of controlling the shape of the nodal lines is proposed and then applied to violin top plate design. Finite element model for a violin top plate was constructed using shell elements. Then, optimization was performed to minimize the square sum of the displacement of selected nodes located along the target nodal lines by varying the thicknesses of the top plate. We conducted nodal line optimization for the second and the fifth modes together at the same time, and the results showed that the nodal lines obtained match well with the target nodal lines. The information on plate thickness distribution from nodal line optimization would be valuable for tailored trimming of a violin top plate for the given performances.