Power laws and scaling of rain events and dry spells in the Catalonia region

We analyze the statistics of rain-event sizes, rain-event durations, and dry-spell durations in a network of 20 rain gauges scattered in an area situated close to the NW Mediterranean coast. Power-law distributions emerge clearly for the dryspell durations, with an exponent around 1.50 ± 0.05, although for event sizes and durations the power-law ranges are rather limited, in some cases. Deviations from power-law behavior are attributed to finite-size effects. A scaling analysis helps to elucidate the situation, providing support for the existence of scale invariance in these distributions. It is remarkable that rain data of not very high resolution yield findings in agreement with self-organized critical phenomena.

A note on the dual scaling of dominance data and its relationship to correspondence analysis

Dual scaling of a subjects-by-objects table of dominance data (preferences,paired comparisons and successive categories data) has been contrasted with correspondence analysis, as if the two techniques were somehow different. In this note we show that dual scaling of dominance data is equivalent to the correspondence analysis of a table which is doubled with respect to subjects. We also show that the results of both methods can be recovered from a principal components analysis of the undoubled dominance table which is centred with respect to subject means.

Dynamical scaling of imbibition in columnar geometries

compatible with the usual nonlocal model governed by surface tension that results from a macroscopic description. To explore this discrepancy, we exhaustively analyze numerical integrations of a phase-field model with dichotomic columnar disorder. We find that two distinct behaviors are possible depending on the capillary contrast between the two values of disorder. In a high-contrast case, where interface evolution is mainly dominated by the disorder, an inherent anomalous scaling is always observed. Moreover, in agreement with experimental work, the interface motion has to be described through a local model. On the other hand, in a lower-contrast case, the interface is dominated by interfacial tension and can be well modeled by a nonlocal model. We have studied both spontaneous and forced-flow imbibition situations, giving a complete set of scaling exponents in each case, as well as a comparison to the experimental results.

Magnetic field scaling of relaxation curves in small particle systems

We study the effects of the magnetic field on the relaxation of the magnetization of smallmonodomain noninteracting particles with random orientations and distribution of anisotropyconstants. Starting from a master equation, we build up an expression for the time dependence of themagnetization which takes into account thermal activation only over barriers separating energyminima, which, in our model, can be computed exactly from analytical expressions. Numericalcalculations of the relaxation curves for different distribution widths, and under different magneticfields H and temperatures T, have been performed. We show how a T ln(t/t0) scaling of the curves,at different T and for a given H, can be carried out after proper normalization of the data to theequilibrium magnetization. The resulting master curves are shown to be closely related to what wecall effective energy barrier distributions, which, in our model, can be computed exactly fromanalytical expressions. The concept of effective distribution serves us as a basis for finding a scalingvariable to scale relaxation curves at different H and a given T, thus showing that the fielddependence of energy barriers can be also extracted from relaxation measurements.

Statistical tests for scaling in the inter-event times of earthquakes in California

We explore in depth the validity of a recently proposed scaling law for earthquake inter-event time distributions in the case of the Southern California, using the waveform cross-correlation catalog of Shearer et al. Two statistical tests are used: on the one hand, the standard two-sample Kolmogorov-Smirnov test is in agreement with the scaling of the distributions. On the other hand, the one-sample Kolmogorov-Smirnov statistic complemented with Monte Carlo simulation of the inter-event times, as done by Clauset et al., supports the validity of the gamma distribution as a simple model of the scaling function appearing on the scaling law, for rescaled inter-event times above 0.01, except for the largest data set (magnitude greater than 2). A discussion of these results is provided.

A system to reduce the effect of CCDs saturation

Colour image segmentation based on the hue component presents some problems due to the physical process of image formation. One of that problems is colour clipping, which appear when at least one of the sensor components is saturated. We have designed a system, that works for a trained set of colours, to recover the chromatic information of those pixels on which colour has been clipped. The chromatic correction method is based on the fact that hue and saturation are invariant to the uniform scaling of the three RGB components. The proposed method has been validated by means of a specific colour image processing board that has allowed its execution in real time. We show experimental results of the application of our method

The contributions of rare objects in correspondence analysis

Correspondence analysis, when used to visualize relationships in a table of counts(for example, abundance data in ecology), has been frequently criticized as being too sensitiveto objects (for example, species) that occur with very low frequency or in very few samples. Inthis statistical report we show that this criticism is generally unfounded. We demonstrate this inseveral data sets by calculating the actual contributions of rare objects to the results ofcorrespondence analysis and canonical correspondence analysis, both to the determination ofthe principal axes and to the chi-square distance. It is a fact that rare objects are oftenpositioned as outliers in correspondence analysis maps, which gives the impression that theyare highly influential, but their low weight offsets their distant positions and reduces their effecton the results. An alternative scaling of the correspondence analysis solution, the contributionbiplot, is proposed as a way of mapping the results in order to avoid the problem of outlying andlow contributing rare objects.

Weighted metric multidimensional scaling

This paper establishes a general framework for metric scaling of any distance measure between individuals based on a rectangular individuals-by-variables data matrix. The method allows visualization of both individuals and variables as well as preserving all the good properties of principal axis methods such as principal components and correspondence analysis, based on the singular-value decomposition, including the decomposition of variance into components along principal axes which provide the numerical diagnostics known as contributions. The idea is inspired from the chi-square distance in correspondence analysis which weights each coordinate by an amount calculated from the margins of the data table. In weighted metric multidimensional scaling (WMDS) we allow these weights to be unknown parameters which are estimated from the data to maximize the fit to the original distances. Once this extra weight-estimation step is accomplished, the procedure follows the classical path in decomposing a matrix and displaying its rows and columns in biplots.

Influence of disorder strength on phase-field models of interfacial growth

We study the influence of disorder strength on the interface roughening process in a phase-field model with locally conserved dynamics. We consider two cases where the mobility coefficient multiplying the locally conserved current is either constant throughout the system (the two-sided model) or becomes zero in the phase into which the interface advances (one-sided model). In the limit of weak disorder, both models are completely equivalent and can reproduce the physical process of a fluid diffusively invading a porous media, where super-rough scaling of the interface fluctuations occurs. On the other hand, increasing disorder causes the scaling properties to change to intrinsic anomalous scaling. In the limit of strong disorder this behavior prevails for the one-sided model, whereas for the two-sided case, nucleation of domains in front of the invading front are observed.

Design and construction of precision heat fluxmeters

The possibility of local elastic instabilities is considered in a first¿order structural phase transition, typically a thermoelastic martensitic transformation, with associated interfacial and volumic strain energy. They appear, for instance, as the result of shape change accommodation by simultaneous growth of different crystallographic variants. The treatment is phenomenological and deals with growth in both thermoelastic equilibrium and in nonequilibrium conditions produced by the elastic instability. Scaling of the transformed fraction curves against temperature is predicted only in the case of purely thermoelastic growth. The role of the transformation latent heat on the relaxation kinetics is also considered, and it is shown that it tends to increase the characteristic relaxation times as adiabatic conditions are approached, by keeping the system closer to a constant temperature. The analysis also reveals that the energy dissipated in the relaxation process has a double origin: release of elastic energy Wi and entropy production Si. The latter is shown to depend on both temperature rate and thermal conduction in the system.

From caging to rouse dynamics in polymer melts with intramolecular barriers: a critical test of the mode coupling theory

By means of computer simulations and solution of the equations of the mode coupling theory (MCT),we investigate the role of the intramolecular barriers on several dynamic aspects of nonentangled polymers. The investigated dynamic range extends from the caging regime characteristic of glass-formers to the relaxation of the chain Rouse modes. We review our recent work on this question,provide new results, and critically discuss the limitations of the theory. Solutions of the MCT for the structural relaxation reproduce qualitative trends of simulations for weak and moderate barriers. However, a progressive discrepancy is revealed as the limit of stiff chains is approached. This dis-agreement does not seem related with dynamic heterogeneities, which indeed are not enhanced by increasing barrier strength. It is not connected either with the breakdown of the convolution approximation for three-point static correlations, which retains its validity for stiff chains. These findings suggest the need of an improvement of the MCT equations for polymer melts. Concerning the relaxation of the chain degrees of freedom, MCT provides a microscopic basis for time scales from chain reorientation down to the caging regime. It rationalizes, from first principles, the observed deviations from the Rouse model on increasing the barrier strength. These include anomalous scaling of relaxation times, long-time plateaux, and nonmonotonous wavelength dependence of the mode correlators.