On the existence of solutions to boundary value problems on time scales

This work formulates existence theorems for solutions to two-point boundary value problems on time scales. The methods used include maximum principles, a priori bounds and topological degree theory.

Rainfall variability at decadal and longer time scales: signal or noise?

Rainfall variability occurs over a wide range of temporal scales. Knowledge and understanding of such variability can lead to improved risk management practices in agricultural and other industries. Analyses of temporal patterns in 100 yr of observed monthly global sea surface temperature and sea level pressure data show that the single most important cause of explainable, terrestrial rainfall variability resides within the El Nino-Southern Oscillation (ENSO) frequency domain (2.5-8.0 yr), followed by a slightly weaker but highly significant decadal signal (9-13 yr), with some evidence of lesser but significant rainfall variability at interclecadal time scales (15-18 yr). Most of the rainfall variability significantly linked to frequencies tower than ENSO occurs in the Australasian region, with smaller effects in North and South America, central and southern Africa, and western Europe. While low-frequency (LF) signals at a decadal frequency are dominant, the variability evident was ENSO-like in all the frequency domains considered. The extent to which such LF variability is (i) predictable and (ii) either part of the overall ENSO variability or caused by independent processes remains an as yet unanswered question. Further progress can only be made through mechanistic studies using a variety of models.

Complex temporal patterns in molecular dynamics:a direct measure of the phase-space exploration by the trajectory at macroscopic time scales

Computer simulated trajectories of bulk water molecules form complex spatiotemporal structures at the picosecond time scale. This intrinsic complexity, which underlies the formation of molecular structures at longer time scales, has been quantified using a measure of statistical complexity. The method estimates the information contained in the molecular trajectory by detecting and quantifying temporal patterns present in the simulated data (velocity time series). Two types of temporal patterns are found. The first, defined by the short-time correlations corresponding to the velocity autocorrelation decay times (â‰0.1â€ps), remains asymptotically stable for time intervals longer than several tens of nanoseconds. The second is caused by previously unknown longer-time correlations (found at longer than the nanoseconds time scales) leading to a value of statistical complexity that slowly increases with time. A direct measure based on the notion of statistical complexity that describes how the trajectory explores the phase space and independent from the particular molecular signal used as the observed time series is introduced. © 2008 The American Physical Society.

Fractional and time-scales differential equations

Resumo indisponível.

Turbulent Time and Length Scale Measurements in High-Velocity Open Channel Flows

In high-velocity open channel flows, the measurements of air-water flow properties are complicated by the strong interactions between the flow turbulence and the entrained air. In the present study, an advanced signal processing of traditional single- and dual-tip conductivity probe signals is developed to provide further details on the air-water turbulent level, time and length scales. The technique is applied to turbulent open channel flows on a stepped chute conducted in a large-size facility with flow Reynolds numbers ranging from 3.8 E+5 to 7.1 E+5. The air water flow properties presented some basic characteristics that were qualitatively and quantitatively similar to previous skimming flow studies. Some self-similar relationships were observed systematically at both macroscopic and microscopic levels. These included the distributions of void fraction, bubble count rate, interfacial velocity and turbulence level at a macroscopic scale, and the auto- and cross-correlation functions at the microscopic level. New correlation analyses yielded a characterisation of the large eddies advecting the bubbles. Basic results included the integral turbulent length and time scales. The turbulent length scales characterised some measure of the size of large vortical structures advecting air bubbles in the skimming flows, and the data were closely related to the characteristic air-water depth Y90. In the spray region, present results highlighted the existence of an upper spray region for C > 0.95 to 0.97 in which the distributions of droplet chord sizes and integral advection scales presented some marked differences with the rest of the flow.

Chemical labelling of oyster shells used for time-calibrated high-resolution Mg/Ca ratios: A tool for estimation of past seasonal temperature variations

The geochemical compositions of biogenic carbonates are increasingly used for palaeoenvironmental reconstructions. The skeletal delta O-18 temperature relationship is dependent on water salinity, so many recent studies have focused on the Mg/Ca and Sr/Ca ratios because those ratios in water do not change significantly on short time scales. Thus, those elemental ratios are considered to be good palaeotemperature proxies in many biominerals, although their use remains ambiguous in bivalve shells. Here, we present the high-resolution Mg/Ca ratios of two modern species of juvenile and adult oyster shells, Crassostrea gigas and Ostrea edulis. These specimens were grown in controlled conditions for over one year in two different locations. In situ monthly Mn-marking of the shells has been used for day calibration. The daily Mg/Ca.ratios in the shell have been measured with an electron microprobe. The high frequency Mg/Ca variation of all specimens displays good synchronism with lunar cycles, suggesting that tides strongly influence the incorporation of Mg/Ca into the shells. Highly significant correlation coefficients (0.70<R<0.83, p<0.0001) between the Mg/Ca ratios and the seawater temperature are obtained only for juvenile C. gigas samples, while metabolic control of Mg/Ca incorporation and lower shell growth rates preclude the use of the Mg/Ca ratio in adult shells as a palaeothermometer. Data from three juvenile C. gigas shells from the two study sites are selected to establish a relationship: T = 3.77Mg/Ca + 1.88, where T is in degrees C and Mg/Ca in mmol/mol. (c) 2012 Elsevier B.V. All rights reserved.

Time-scale and other invariants of integrative mechanical behavior in living cells.

In dealing with systems as complex as the cytoskeleton, we need organizing principles or, short of that, an empirical framework into which these systems fit. We report here unexpected invariants of cytoskeletal behavior that comprise such an empirical framework. We measured elastic and frictional moduli of a variety of cell types over a wide range of time scales and using a variety of biological interventions. In all instances elastic stresses dominated at frequencies below 300 Hz, increased only weakly with frequency, and followed a power law; no characteristic time scale was evident. Frictional stresses paralleled the elastic behavior at frequencies below 10 Hz but approached a Newtonian viscous behavior at higher frequencies. Surprisingly, all data could be collapsed onto master curves, the existence of which implies that elastic and frictional stresses share a common underlying mechanism. Taken together, these findings define an unanticipated integrative framework for studying protein interactions within the complex microenvironment of the cell body, and appear to set limits on what can be predicted about integrated mechanical behavior of the matrix based solely on cytoskeletal constituents considered in isolation. Moreover, these observations are consistent with the hypothesis that the cytoskeleton of the living cell behaves as a soft glassy material, wherein cytoskeletal proteins modulate cell mechanical properties mainly by changing an effective temperature of the cytoskeletal matrix. If so, then the effective temperature becomes an easily quantified determinant of the ability of the cytoskeleton to deform, flow, and reorganize.

Synchronization reveals topological scales in complex networks

We study the relationship between topological scales and dynamic time scales in complex networks. The analysis is based on the full dynamics towards synchronization of a system of coupled oscillators. In the synchronization process, modular structures corresponding to well-defined communities of nodes emerge in different time scales, ordered in a hierarchical way. The analysis also provides a useful connection between synchronization dynamics, complex networks topology, and spectral graph analysis.

Reconstruction of gusty wind speed time series from autonomous data logger records

The collection of wind speed time series by means of digital data loggers occurs in many domains, including civil engineering, environmental sciences and wind turbine technology. Since averaging intervals are often significantly larger than typical system time scales, the information lost has to be recovered in order to reconstruct the true dynamics of the system. In the present work we present a simple algorithm capable of generating a real-time wind speed time series from data logger records containing the average, maximum, and minimum values of the wind speed in a fixed interval, as well as the standard deviation. The signal is generated from a generalized random Fourier series. The spectrum can be matched to any desired theoretical or measured frequency distribution. Extreme values are specified through a postprocessing step based on the concept of constrained simulation. Applications of the algorithm to 10-min wind speed records logged at a test site at 60 m height above the ground show that the recorded 10-min values can be reproduced by the simulated time series to a high degree of accuracy.

Stabilizing Nonstationary Electrochemical Time Series

Electrochemical systems are ideal working-horses for studying oscillatory dynamics. Experimentally obtained time series, however, are usually associated with a spontaneous drift in some uncontrollable parameter that triggers transitions among different oscillatory patterns, despite the fact that all controllable parameters are kept constant. Herein we present an empirical method to stabilize experimental potential time series. The method consists of applying a negative galvanodynamic sweep to compensate the spontaneous drift and was tested for the oscillatory electro-oxidation of methanol on platinum. For a wide range of applied currents, the base system presents spontaneous transitions from quasi-harmonic to mixed mode oscillations. Temporal patterns were stabilized by galvanodynamic sweeps at different rates. The procedure resulted in a considerable increase in the number of oscillatory cycles from 5 to 20 times, depending on the specific temporal pattern. The spontaneous drift has been associated with uncompensated oscillations, in which the coverage of some adsorbed species are not reestablished after one cycle; i.e., there is a net accumulation and/or depletion of adsorbed species during oscillations. We interpreted the rate of the galvanodynamic sweep in terms of the time scales of the poisoning processes that underlies the uncompensated oscillations and thus the spontaneous slow drift.

Coordinate and time-dependent diffusion dynamics in protein folding

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

THREE TIME SCALE SINGULAR PERTURBATION PROBLEMS AND NONSMOOTH DYNAMICAL SYSTEMS

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A study of the errors of the averaged models in the restricted three-body problem in a short time scale

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Relating network rigidity, time scale hierarchies, and expression noise in gene networks

Fluctuation-dissipation theorems can be used to predict characteristics of noise from characteristics of the macroscopic response of a system. In the case of gene networks, feedback control determines the "network rigidity," defined as resistance to slow external changes. We propose an effective Fokker-Planck equation that relates gene expression noise to topology and to time scales of the gene network. We distinguish between two situations referred to as normal and inverted time hierarchies. The noise can be buffered by network feedback in the first situation, whereas it can be topology independent in the latter.