Principal Time Scales Research Articles

Timescales of Magma Recharge and Reactivation of Large Silicic Systems from Ti Diffusion in Quartz

Timescales of magma chamber assembly and recharge are investigated here by applying 1D and 2D diffusion modeling techniques to high-resolution maps of titanium in quartz from a large-volume ignimbrite eruption in the Taupo Volcanic Zone, New Zealand. We compare quartz zonation patterns and associated diffusion timescales from the 340 kaWhakamaru super-eruption (magma volume 1000 km) with the Younger Toba Tuff super-eruption, 74 ka (2000 km), Sumatra, and the smaller volume 50 ka Earthquake Flat eruption (10 km), Okataina Caldera Complex, New Zealand. Two principal timescales are presented: that of chamber recharge and eruption triggering events, and that of magma generation (involving long-term assembly, stirring and reactivation). Synchrotron micro-X-ray fluorescence maps of core^rim quartz transects provide a high-resolution record of magma chamber conditions throughout quartz crystallization. Quartz crystals from the Whakamaru magma display complex zonation patterns indicating fluctuating pressure^temperature conditions throughout the crystallization history. Toba and Earthquake Flat, in contrast, display simple quartz-zoning patterns and record slightly longer periods of crystal residence in the chamber that fed the eruption. We apply Lattice Boltzmann 2D diffusion modeling to reconstruct the timescales of quartz crystal zonation, accounting for crystal boundary complexities. Quartz crystal orientation is also accounted for by using geometry constraints from the synchrotron data. Our calculations suggest that crystal-mush reactivation for the main Whakamaru magma reservoir occured over a period of the order of 10^10 years. Both the Earthquake Flat and Toba eruptions experienced a significant recharge event (causing a temperature and pressure change), which occurred within 100 years of eruption. In comparison, the complex Whakamaru quartz zoning patterns suggest that the magma body experienced numerous thermal and compositional fluctuations in the lead-up to eruption. The final magma recharge event, which most probably triggered the eruption, occurred within 10^60 years of the eruption. Even though the volume of these systems spans two orders of magnitude, there does not appear to be a relationship between magma volume and diffusion timescale, suggesting similar histories before eruption.

Efficient Singlet Fission Discovered in a Disordered Acene Film

Singlet exciton fission is a process that occurs in select organic semiconductors and entails the splitting of a singlet excited state into two lower triplet excitons located on adjacent chromophores. Research examining this phenomenon has recently seen a renaissance due to the potential to exploit singlet fission within the context of organic photovoltaics to prepare devices with the ability to circumvent the Shockley-Queisser limit. To date, high singlet fission yields have only been reported for crystalline or polycrystalline materials, suggesting that molecular disorder inhibits singlet fission. Here, we report the results of ultrafast transient absorption and time-resolved emission experiments performed on 5,12-diphenyl tetracene (DPT). Unlike tetracene, which tends to form polycrystalline films when vapor deposited, DPT's pendant phenyl groups frustrate crystal growth, yielding amorphous films. Despite the high level of disorder in these films, we find that DPT exhibits a surprisingly high singlet fission yield, with 1.22 triplets being created per excited singlet. This triplet production occurs over two principal time scales, with ~50% of the triplets appearing within 1 ps after photoexcitation followed by a slower phase of triplet growth over a few hundred picoseconds. To fit these kinetics, we have developed a model that assumes that due to molecular disorder, only a subset of DPT dimer pairs adopt configurations that promote fission. Singlet excitons directly excited at these sites can undergo fission rapidly, while singlet excitons created elsewhere in the film must diffuse to these sites to fission.

Identification of coherent structures of turbulence at the atmospheric surface layer

A parameter-free method based on orthonormal wavelet transforms is recommended for calculating the principal time scale of coherent structures in atmospheric boundary-layer measurements. First, the atmospheric turbulent signal is decomposed into the small scale vortex that has approximate isotropy and the large scale vortex with the digital filter. Then, the large scale vortex is used to detect coherent structures with this method. The principal time scale and profile of coherent structures for velocity components (u, v, w above rice fields are obtained. In order to testify the validity of this method, the correlation of coherent structures and non-coherent structures are also calculated.

Identification of the principal time scales in bubble column by wavelet analysis

Wavelet analysis of velocity–time data obtained from a bubble column using laser Doppler velocimeter (LDV) was carried out. The principal time scale/s, which contributes more to the coherent part of turbulence than the other time scales, was identified based on the analysis of scalewise wavelet coefficients and its variance. Three methods namely, derivative, global and local (Donoho's method) were applied and compared with each other. The results of the derivative method were validated by studying flatness factor, a quantitative measure of local intermittency in the wavelet coefficients at various scales. Further, a new methodology has been developed for the estimation of bubble chord-length distribution in the column using the information in the principal time scale.

An objective method for determining principal time scales of coherent eddy structures using orthonormal wavelets

A new, parameter-free method, based on orthonormal wavelet expansions is proposed for calculating the principal time scale of coherent structures in atmospheric surface layer measurements. These organized events play an important role in the exchange of heat, mass, and momentum between the land and the atmosphere. This global technique decomposes the energy contribution at each scale into organized and random eddy motion. The method is demonstrated on vertical wind velocity measurements above bare and vegetated surfaces. It is found to give nearly identical results to a local thresholding approach developed for signal de-noising that assigns the wavelet coefficients to organized and random motion. The effect of applying anti- and/or near-symmetrical wavelet basis functions is also investigated.

Choice of the best time scale for preventive maintenance in heterogeneous environments

A principal feature of the model considered in this paper is the presence of several time scales for lifetime measurements when similar objects operate in heterogeneous conditions. A typical example are lifetimes of an aircraft module which can be measured in the total time in air and in the number of flights. A family of lifetimes can be generated by considering a linear combination of the above two principal time scales. We consider a problem of finding an optimal maintenance period for an equipment operating during a single maintenance/replacement cycle, in heterogeneous environmental conditions. Our main concern is finding the time scale which provides the maximal value of the return (cost) functional. We consider two “principal” time scales (the operation time and the total number of shocks) and show numerically that the optimal linear combination of these two scales has also the minimal coefficient of variation (c.v.) of system lifetime. We develop some general theory to connect the optimality in terms of the return functional with the optimality in terms of c.v.

System state monitoring and lifetime scales—I

This paper is devoted to failure monitoring of critical systems. The monitoring is carried out by measuring a system's generalized age in a specially selected time-scale termed the best monitoring scale (BMS). The BMS is a linear combination of several observable ‘principal’ time-scales, like the operational time, the number of cycles, the calendar time. This time-scale has the property that the coefficient of variation of the lifetime in the time-scale is mininal. We discuss some theoretical aspects of finding the BMS and present a method for calculating it on the basis of failure data observed in two principal time-scales. The construction of BMS and its applications are illustrated using fatigue test data. We demonstrate the applications of the BMS to the nomination of system safe operational period and to the accelerated life testing. We describe the use of so-called damage counters (DCs) for system-state monitoring and explain that their efficiency depends on the properties of the time-scales created by the DCs.

Low-temperature vortex dynamics in a high-temperature superconductor.

Magnetic-field gradients in the mixed state of a type-II superconductor are studied using $^{205}\mathrm{Tl}$ nuclear magnetic resonance (NMR) on ${\mathrm{Tl}}_{2}$${\mathrm{Ba}}_{2}$${\mathrm{Ca}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{10+\mathrm{\ensuremath{\delta}}}$. An anomalous peak was observed in the temperature dependence of the transverse relaxation rate at T/${\mathit{T}}_{\mathit{c}}$\ensuremath{\approxeq}0.25. We attribute this behavior to magnetic-field flucutations from vortex dynamics. We interpret this behavior as a crossover of the principal time scale for vortex dynamics with that of the NMR experiment, approximately 100 \ensuremath{\mu}s. The temperature dependence of this time scale is discussed.

BEST TIME SCALE FOR AGE REPLACEMENT

The lifetime of a system is measured in two principal time scales, L and H. We consider a family of time scales of type Ta=(1−a) · L+a · H, for which the lifetime is T=(1−a) L+aH, a∈[0, 1], where L and H are the lifetimes in the principal time scales. The optimal time scale, by the definition, provides the minimal value of the coefficient of variation of system lifetime. We consider the age replacement model in time scale Ta and develop a nonparametric numerical procedure for finding the optimal weighting parameter a* that provides the smallest value of the corresponding cost function. This procedure is applied to fatigue test data, and it is demonstrated that the best time scale with respect to the age replacement cost function is very close to the optimal time scale. The same is true for a modified age replacement scheme in which the replacement age equals the p-quantile of system lifetime.

Wavelet Analysis of Coherent Structures at the Atmosphere-Forest Interface

Abstract Wavelet analysis was applied to turbulence data for temperature and vertical velocity within and above a deciduous forest. This method appears to provide an objective technique for examining thermal and flow fields associated with coherent structures occurring near the forest. The two-dimensional unfolding in time and scale by the wavelet transform illustrates discrete warm and cool centers associated with organized updrafts and downdrafts, which have similar patterns but different magnitudes at different heights. Wavelet variances computed for temperature and velocity at different heights appear to have local maximum values corresponding to certain time scales, which are self-consistent and useful for objective determination of the principal time scale of the structures. Within the canopy, the principal time scales of the structures determined by this technique are 56–60 s and 40–44 s for the temperature and vertical velocity fields, respectively. These time scales are close to those determined ...