Moonlets wandering on a leash-ring

Since the Voyager flybys, embedded moonlets have been proposed to explain some of the surprising structures observed in Saturn's narrow F ring. Experiments conducted with the Cassini spacecraft support this suggestion. Images of the F ring show bright compact spots, and seven occultations of stars by the F ring, monitored by ultraviolet and infrared experiments, revealed nine events of high optical depth. These results point to a large number of such objects, but it is not clear whether they are solid moonlets or rather loose particle aggregates. Subsequent images suggested an irregular motion of these objects so that a determination of their orbits consistent with the F ring failed. Some of these features seem to cross the whole ring. Here we show that these observations are explained by chaos in the F ring driven mainly by the 'shepherd' moons Prometheus and Pandora. It is characterized by a rather short Lyapunov time of about a few hundred orbital periods. Despite this chaotic diffusion, more than 93 per cent of the F-ring bodies remain confined within the F ring because of the shepherding, but also because of a weak radial mobility contrasted by an effective longitudinal diffusion. This chaotic stirring of all bodies involved prevents the formation of 'propellers' typical of moonlets, but their frequent ring crossings explain the multiple radial 'streaks' seen in the F ring. The related 'thermal' motion causes more frequent collisions between all bodies which steadily replenish F-ring dust and allow for ongoing fragmentation and re-accretion processes (ring recycling).

Uniform estimates of attracting sets of extended Lurie systems using LMIs

This research presents a systematic procedure to obtain estimates, via extended Lyapunov functions, of attracting sets of a class of nonlinear systems, as well as an estimate of their stability regions. The considered class of nonlinear systems, called in this note the extended Lurie system, consists of nonlinear systems like those of the Lurie problem where one of the nonlinear functions can violate the sector conditions of the Lurie problem around the origin. In case of nonautonomous systems the concept of absolute stability is extended and uniform estimates of the attracting set are obtained. Two classical nonlinear systems, the forced duffing equation and the Van der Pol system, are analyzed with the proposed procedure.

On a control of a non-ideal mono-rail system with periodics coefficients

In this work, the problem in the loads transport (in platforms or suspended by cables) it is considered. The system in subject is composed for mono-rail system and was modeled through the system: inverted pendulum, car and motor and the movement equations were obtained through the Lagrange equations. In the model, was considered the interaction among of the motor and system dynamics for several potencies motor, that is, the case studied is denominated a non-ideal periodic problem. The non-ideal periodic problem dynamics was analyzed, qualitatively, through the comparison of the stability diagrams, numerically obtained, for several motor torque constants. Furthermore, one was made it analyzes quantitative of the problem through the analysis of the Floquet multipliers. Finally, the non-ideal problem was controlled. The method that was used for analysis and control of non-ideal periodic systems is based on the Chebyshev polynomial expansion, in the Picard iterative method and in the Lyapunov-Floquet transformation (L-F trans formation). This method was presented recently in [3-9].

Structural evolution of aerogels prepared from TEOS sono-hydrolysis upon heat treatment up to 1100 degrees C

The structural evolution of aerogels prepared from TEOS sono-hydrolysis was studied as a function of the temperature of heat treatment up to 1100 degreesC by means of small angle X-ray scattering (SAXS) and density measurements. The mass fractal structure of the original wet sonogel (with scattering exponent alpha similar to 2.2) apparently transforms to a surface fractal structure in a length scale lesser than similar to1.5 nm, upon the process resulting in aerogel. Such a structural transformation is interpreted by the formation of new particles with characteristic dimension of similar to1.5 nm, with rough boundaries or electronic density fluctuations (or ultra-micropores) in their interior. The structural arrangement of these particles seem to preserve part of mass fractal characteristics of the original wet sonogel, now in a length scale greater than similar to1.5 nm. The electronic density heterogeneities in the particles start to be eliminated at around 800 degreesC and, at 900 degreesC, the particles become perfectly homogeneous, so the structure can be described as a porous structure with a porosity of similar to68% with similar to9.0 nm mean size pores and similar to4.3 nm mean size solid particles. Above 900 degreesC, a vigorous viscous flux sintering process sets in, eliminating most of the porosity and increasing rapidly the bulk density in an aerogel-glass transformation. (C) 2003 Elsevier B.V. All rights reserved.

Thermally stimulated depolarizations: Disclosing an approximate universality

This paper presents an approximate universality displayed by thermally stimulated depolarization currents ruled by stretched exponential relaxations when properly re-scaled. A visually perfect universality occurs especially when the energy and the heating rate are varied. It becomes somewhat poorer when the frequency factor or the stretched exponent changes. Empirical relations between the half widths and other pertinent parameters are given.

FRACTAL CHARACTERISTICS OF THE HORIZONTAL MOVEMENT OF WATER IN SOILS

Observed deviations from traditional concepts of soil-water movement are considered in terms of fractals. A connection is made between this movement and a Brownian motion, a random and self-affine type of fractal, to account for the soil-water diffusivity function having auxiliary time dependence for unsaturated soils. The position of a given water content is directly proportional to t(n), where t is time, and exponent n for distinctly unsaturated soil is less than the traditional 0.50. As water saturation is approached, n approaches 0.50. Macroscopic fractional Brownian motion is associated with n < 0.50, but shifts to regular Brownian motion for n = 0.50.

Electrical transport properties of doped poly (p-phenylene)

An experimental study of the temperature dependent dc electrical conductivity of doped poly (p-phenylene) in the range of 50-300 K has been presented. The results have been analyzed in the framework of some hopping models. We have observed that hopping models are not consistent with the temperature dependence of the conductivity data over the entire temperature range of measurement. We find that the logarithmic conductivity is proportional to T-beta, wherethe exponent beta is independent of temperature. It is shown that the most probable transport process in this material for the entire range of temperature is due to multiphonon-assisted hopping of the charge carriers that interact weakly with phonons. The parameters obtained from the fits of the experimental data to this model appear reasonable.

Fluctuating dimension in a discrete model for quantum gravity based on the spectral principle

The spectral principle of Connes and Chamseddine is used as a starting point to define a discrete model for Euclidean quantum gravity. Instead of summing over ordinary geometries, we consider the sum over generalized geometries where topology, metric, and dimension can fluctuate. The model describes the geometry of spaces with a countable number n of points, and is related to the Gaussian unitary ensemble of Hermitian matrices. We show that this simple model has two phases. The expectation value , the average number of points in the Universe, is finite in one phase and diverges in the other. We compute the critical point as well as the critical exponent of . Moreover, the space-time dimension delta is a dynamical observable in our model, and plays the role of an order parameter. The computation of is discussed and an upper bound is found, < 2.

On non-linear dynamics and a periodic control design applied to the potential of membrane action

The Fitzhugh-Nagumo (fn) mathematical model characterizes the action potential of the membrane. The dynamics of the Fitzhugh-Nagumo model have been extensively studied both with a view to their biological implications and as a test bed for numerical methods, which can be applied to more complex models. This paper deals with the dynamics in the (FH) model. Here, the dynamics are analyzed, qualitatively, through the stability diagrams to the action potential of the membrane. Furthermore, we also analyze quantitatively the problem through the evaluation of Floquet multipliers. Finally, the nonlinear periodic problem is controlled, based on the Chebyshev polynomial expansion, the Picard iterative method and on Lyapunov-Floquet transformation (L-F transformation).

A SAXS study of kinetics of aggregation of TEOS-derived sonogels at different temperatures

The kinetics of aggregation of tetraethoxysilane (TEOS)-derived silica sols, produced by acid-catalyzed and ultrasound-stimulated hydrolysis, were studied by 'in situ' measurements of small-angle X-ray scattering (SAXS) at the temperatures 40 degreesC, 60 degreesC and 70 degreesC. The results were analyzed in terms of the evolution with time (t) of the SAXS intensity probing the mass fractal characteristics of the system, the average radius of gyration (Rc,) of the clusters and the number of primary particles per cluster. The aggregation process yields mass fractal structures which exhibit a scattering exponent (alpha) practically equal to 2, in the probed length scale range (5.3 nm < 1/q < 0.22 nm), beneath and even far beyond the gel point. This suggests that a is a direct measure of the real mass fractal dimension (D) of the structure. The precursor sol (pH = 2) exhibits I nm mean sized clusters with mass fractal dimension D similar to 1.9. Increasing the pH to 4.5, the cluster mean size and the number of primary particles per cluster increase but the system keeps a more opened structure (D similar to 1.4). In the first aggregation stages, D increases up to similar to2 by incorporating primary particles to the clusters without changing their mean size. From this stage, the aggregation progresses following a thermally activated scaling law well described by R-G similar tot(1/D) in all cases. This is indicative of a diffusion-controlled cluster-cluster aggregation process. The activation energy of the process was found to be 91.7 kJ/mol. (C) 2001 Elsevier B.V. B.V. All rights reserved.

Multifractal characterization of saprolite particle-size distributions after topsoil removal

Multifractal analysis is now increasingly used to characterize soil properties as it may provide more information than a single fractal model. During the building of a large reservoir on the Parana River (Brazil), a highly weathered soil profile was excavated to a depth between 5 and 8 m. Excavation resulted in an abandoned area with saprolite materials and, in this area, an experimental field was established to assess the effectiveness of different soil rehabilitation treatments. The experimental design consisted of randomized blocks. The aim of this work was to characterize particle-size distributions of the saprolite material and use the information obtained to assess between-block variability. Particle-size distributions of the experimental plots were characterized by multifractal techniques. Ninety-six soil samples were analyzed routinely for particle-size distribution by laser diffractometry in a range of scales, varying from 0.390 to 2000 mu m. Six different textural classes (USDA) were identified with a clay content ranging from 16.9% to 58.4%. Multifractal models described reasonably well the scaling properties of particle-size distributions of the saprolite material. This material exhibits a high entropy dimension, D-1. Parameters derived from the left side (q > 0) of the f(alpha) spectra, D-1, the correlation dimension (D-2) and the range (alpha(0)-alpha(q+)), as well as the total width of the spectra (alpha(max) - alpha(min)) all showed dependence on the clay content. Sand, silt and clay contents were significantly different among treatments as a consequence of soil intrinsic variability. The D, and the Holder exponent of order zero, alpha(0), were not significantly different between treatments; in contrast, D-2 and several fractal attributes describing the width of the f(alpha) spectra were significantly different between treatments. The only parameter showing significant differences between sampling depths was (alpha(0) - alpha(q+)). Scale independent fractal attributes may be useful for characterizing intrinsic particle-size distribution variability. (c) 2006 Elsevier B.V. All rights reserved.

Small-angle X-ray scattering study of the smart thermo-optical behavior of zirconyl aqueous colloids

The smart thermo-optical systems studied here are based on the unusual thermoreversible sol-gel transition of zirconyl chloride aqueous solution modified by sulfuric acid in the molar ratio Zr/SO4:3/1. The transparency to the visible light changes during heating due to light scattering. This feature is related to the aggregates growth that occurs during gelation. These reversible changes can be controlled by the amount of chloride ions in solution. The thermoreversible sol-gel transition temperature increases from 323 to 343 K by decreasing the molar ratio Cl/Zr from 7.0 to 1.3. In this work the effect of the concentration of chloride ions on the structural characteristics of the system has been analyzed by in situ SAXS measurements during the sol-gel transition carried out at 323 and 333 K. The experimental SAXS curves of sols exhibit three regions at small, medium and high scattering vectors characteristics of Guinier, fractal and Porod regimes, respectively. The radius of primary particles, obtained from the crossover between the fractal and Porod regimes, remains almost invariable with the chloride concentration, and the value (4 Angstrom) is consistent with the size of the molecular precursor. During the sol-gel transition the aggregates grow with a fractal structure and the fractal dimensionality decreases from 2.4 to 1.8. This last value is characteristic of a cluster-cluster aggregation controlled by a diffusion process. Furthermore, the time exponent of aggregate growth presents values of 0.33 and 1, typical of diffusional and hydrodynamic motions. A crossover between these two regimes is observed.

Psychophysical power functions for apparent area in perceptive, memory, and inference conditions for observers of different age groups

The purpose of this research was to verify the effect of age on the exponent of the power function in Perceptive, Memory, and Inference experimental conditions. In the Memory condition the intervals of 2 min., 8, 24, and 48 hr. and 1 wk. were used between acquisition of information and remembering. For each experimental condition the ages of observers ranged between 17 and 35 years (Group I), 40-55 years (Group II), and 60-77 years (Group III), and education ranged from high school to graduate school. The observers estimated the areas of the Brazilian states using the psychophysical method of magnitude estimation. No significant differences were obtained for Groups I, II, and III for each experimental condition, except in the Memory Condition with the 24-hr. interval. Analysis for experimental conditions and ages showed a significant difference between the Perceptive Condition and each of the others, but no difference between the Inference and Memory Conditions. These results indicated that in the remembering processes there is no loss of information as a function of age. From the small variability in the power function exponents for the three ages, we may assume that age could be related to amount of education of the observers, which suggests study is important.

Electrical relaxation in proton conductor composites based on (NH4)H2PO4/TiO2

We report on electrical relaxation measurements of (1-x)NH4H2PO4-xTiO(2) (x = 0.1) composites by admittance spectroscopy, in the 40-Hz-5-MHz frequency range and at temperatures between 303 and 563 K. Simultaneous thermal and electrical measurements on the composites identify a stable crystalline phase between 373 and 463 K. The real part of the conductivity, sigma', shows a power-law frequency dependence below 523 K, which is well described by Jonscher's expression sigma' = sigma(0)(1 + (omega/omega(p))(n)), where sigma(0) is the dc conductivity, omega(p)/2 pi = f(p) is a characteristic relaxation frequency, and n is a fractional exponent between 0 and 1. Both sigma(0) and f(p) are thermally activated with nearly the same activation energy in the II region, indicating that the dispersive conductivity originates from the migration of protons. However, activation energies decrease from 0.55 to 0.35 eV and n increases toward 1.0, as the concentration of TiO2 nanoparticles increases, thus, enhancing cooperative correlation among moving ions. The highest dc conductivity is obtained for the composite x = 0.05 concentration, with values above room temperature about three orders of magnitude higher than that of crystalline NH4H2PO4 (ADP), reaching values on the order of 0.1 (Omega cm)(-1) above 543 K.

Widespread Amazon forest tree mortality from a single cross-basin squall line event

Climate change is expected to increase the intensity of extreme precipitation events in Amazonia that in turn might produce more forest blowdowns associated with convective storms. Yet quantitative tree mortality associated with convective storms has never been reported across Amazonia, representing an important additional source of carbon to the atmosphere. Here we demonstrate that a single squall line (aligned cluster of convective storm cells) propagating across Amazonia in January, 2005, caused widespread forest tree mortality and may have contributed to the elevated mortality observed that year. Forest plot data demonstrated that the same year represented the second highest mortality rate over a 15-year annual monitoring interval. Over the Manaus region, disturbed forest patches generated by the squall followed a power-law distribution (scaling exponent alpha = 1.48) and produced a mortality of 0.3-0.5 million trees, equivalent to 30% of the observed annual deforestation reported in 2005 over the same area. Basin-wide, potential tree mortality from this one event was estimated at 542 +/- 121 million trees, equivalent to 23% of the mean annual biomass accumulation estimated for these forests. Our results highlight the vulnerability of Amazon trees to wind-driven mortality associated with convective storms. Storm intensity is expected to increase with a warming climate, which would result in additional tree mortality and carbon release to the atmosphere, with the potential to further warm the climate system. Citation: Negron-Juarez, R. I., J. Q. Chambers, G. Guimaraes, H. Zeng, C. F. M. Raupp, D. M. Marra, G. H. P. M. Ribeiro, S. S. Saatchi, B. W. Nelson, and N. Higuchi (2010), Widespread Amazon forest tree mortality from a single cross-basin squall line event, Geophys. Res. Lett., 37, L16701, doi:10.1029/2010GL043733.