Wavelets and the generalization of the variogram

The experimental variogram computed in the usual way by the method of moments and the Haar wavelet transform are similar in that they filter data and yield informative summaries that may be interpreted. The variogram filters out constant values; wavelets can filter variation at several spatial scales and thereby provide a richer repertoire for analysis and demand no assumptions other than that of finite variance. This paper compares the two functions, identifying that part of the Haar wavelet transform that gives it its advantages. It goes on to show that the generalized variogram of order k=1, 2, and 3 filters linear, quadratic, and cubic polynomials from the data, respectively, which correspond with more complex wavelets in Daubechies's family. The additional filter coefficients of the latter can reveal features of the data that are not evident in its usual form. Three examples in which data recorded at regular intervals on transects are analyzed illustrate the extended form of the variogram. The apparent periodicity of gilgais in Australia seems to be accentuated as filter coefficients are added, but otherwise the analysis provides no new insight. Analysis of hyerpsectral data with a strong linear trend showed that the wavelet-based variograms filtered it out. Adding filter coefficients in the analysis of the topsoil across the Jurassic scarplands of England changed the upper bound of the variogram; it then resembled the within-class variogram computed by the method of moments. To elucidate these results, we simulated several series of data to represent a random process with values fluctuating about a mean, data with long-range linear trend, data with local trend, and data with stepped transitions. The results suggest that the wavelet variogram can filter out the effects of long-range trend, but not local trend, and of transitions from one class to another, as across boundaries.

Pb-210-Ra-226 and Ra-228-Th-232 systematics in young arc lavas: implications for magma degassing and ascent rates

New data show that island arc rocks have (Pb-210/Ra-226)(o) ratios which range from as low as 0.24 up to 2.88. In contrast, (Ra-22S/Th-232) appears always within error of I suggesting that the large Ra-226-excesses observed in arc rocks were generated more than 30 years ago. This places a maximum estimate on melt ascent velocities of around 4000 m/year and provides further confidence that the Ra-226 excesses reflect deep (source) processes rather than shallow level alteration or seawater contamination. Conversely, partial melting must have occurred more than 30 years prior to eruption. The Pb-210 deficits are most readily explained by protracted magma degassing. Using published numerical models, the data suggest that degassing occurred continuously for periods up to several decades just prior to eruption but no link with eruption periodicity was found. Longer periods are required if degassing is discontinuous, less than 100% efficient or if magma is recharged or stored after degassing. The long durations suggest much of this degassing occurs at depth with implications for the formation of hydrothermal and copper-porphyry systems. A suite of lavas erupted in 1985-1986 from Sangeang Api volcano in the Sunda arc are characterised by deficits of Pb-210 relative to Ra-226 from which 6-8 years of continuous Rn-222 degassing would be inferred from recent numerical models. These data also form a linear (Pb-210)/Pb-(Ra-226)/Pb array which might be interpreted as a 71-year isochron. However, the array passes through the origin suggesting displacement downwards from the equiline in response to degassing and so the slope of the array is inferred not to have any age significance. Simple modelling shows that the range of (Ra-226)/Pb ratios requires thousands of years to develop consistent with differentiation occurring in response to cooling at the base of the crust. Thus, degassing post-dated, and was not responsible for magma differentiation. The formation, migration and extraction of gas bubbles must be extremely efficient in mafic magma whereas the higher viscosity of more siliceous magmas retards the process and can lead to Pb-210 excesses. A possible negative correlation between (Pb-210/Ra-226)(o) and SO2 emission rate requires further testing but may have implications for future eruptions. (C) 2004 Elsevier B.V. All rights reserved.

Representing El Niño in coupled ocean–atmosphere GCMs: the dominant role of the atmospheric component

A systematic modular approach to investigate the respective roles of the ocean and atmosphere in setting El Niño characteristics in coupled general circulation models is presented. Several state-of-the-art coupled models sharing either the same atmosphere or the same ocean are compared. Major results include 1) the dominant role of the atmosphere model in setting El Niño characteristics (periodicity and base amplitude) and errors (regularity) and 2) the considerable improvement of simulated El Niño power spectra—toward lower frequency—when the atmosphere resolution is significantly increased. Likely reasons for such behavior are briefly discussed. It is argued that this new modular strategy represents a generic approach to identifying the source of both coupled mechanisms and model error and will provide a methodology for guiding model improvement.

Time series analysis of lava flux

We have applied time series analytical techniques to the flux of lava from an extrusive eruption. Tilt data acting as a proxy for flux are used in a case study of the May–August 1997 period of the eruption at Soufrière Hills Volcano, Montserrat. We justify the use of such a proxy by simple calibratory arguments. Three techniques of time series analysis are employed: spectral, spectrogram and wavelet methods. In addition to the well-known ~9-hour periodicity shown by these data, a previously unknown periodic flux variability is revealed by the wavelet analysis as a 3-day cycle of frequency modulation during June–July 1997, though the physical mechanism responsible is not clear. Such time series analysis has potential for other lava flux proxies at other types of volcanoes.

Aperiodicity, structure, and dynamics in Ni(CN)(2)

By combining the results of both x-ray diffraction and neutron total-scattering experiments, we show that Ni(CN)(2) exhibits long-range structural order only in two dimensions, with no true periodicity perpendicular to its gridlike layers. Reverse Monte Carlo analysis gives an experimental distinction between M-C and M-N bond lengths in a homometallic cyanide framework and identifies the vibrational modes responsible for anomalous positive and negative thermal expansion in the title compound.

Melt structure and its transformation by sequential crystallization of the two blocks within poly(L-lactide)-block-poly(epsilon-caprolactone) double crystalline diblock copolymers

Sequential crystallization of poly(L-lactide) (PLLA) followed by poly(epsilon-caprolactone) (PCL) in double crystalline PLLA-b-PCL diblock copolymers is studied by differential scanning calorimetry (DSC), polarized optical microscopy (POM), wide-angle X-ray scattering (WAXS) and small-angle X-ray scattering (SAXS). Three samples with different compositions are studied. The sample with the shortest PLLA block (32 wt.-% PLLA) crystallizes from a homogeneous melt, the other two (with 44 and 60% PLLA) from microphase separated structures. The microphase structure of the melt is changed as PLLA crystallizes at 122 degrees C (a temperature at which the PCL block is molten) forming spherulites regardless of composition, even with 32% PLLA. SAXS indicates that a lamellar structure with a different periodicity than that obtained in the melt forms (for melt segregated samples). Where PCL is the majority block, PCL crystallization at 42 degrees C following PLLA crystallization leads to rearrangement of the lamellar structure, as observed by SAXS, possibly due to local melting at the interphases between domains. POM results showed that PCL crystallizes within previously formed PLLA spherulites. WAXS data indicate that the PLLA unit cell is modified by crystallization of PCL, at least for the two majority PCL samples. The PCL minority sample did not crystallize at 42 degrees C (well below the PCL homopolymer crystallization temperature), pointing to the influence of pre-crystallization of PLLA on PCL crystallization, although it did crystallize at lower temperature. Crystallization kinetics were examined by DSC and WAXS, with good agreement in general. The crystallization rate of PLLA decreased with increase in PCL content in the copolymers. The crystallization rate of PCL decreased with increasing PLLA content. The Avrami exponents were in general depressed for both components in the block copolymers compared to the parent homopolymers. Polarized optical micrographs during isothermal crystalli zation of (a) homo-PLLA, (b) homo-PCL, (c) and (d) block copolymer after 30 min at 122 degrees C and after 15 min at 42 degrees C.

Phase mixing and phase separation accompanying the catalytic oxidation of CO on Ir{100}

The co-adsorption of CO and O on the unreconstructed (1 x 1) phase of Ir {100} was examined by low energy electron diffraction (LEED) and temperature programmed desorption (TPD). When CO is adsorbed at 188 K onto the Ir{100} surface precovered with 0.5 ML O, a mixed c(4 x 2)-(2O + CO) overlayer is formed. All CO is oxidised upon heating and desorbs as CO2 in three distinct stages at 230 K, 330 K and 430 K in a 2:1:2 ratio. The excess oxygen left on the surface after all CO has reacted forms an overlayer with a LEED pattern with p(2 x 10) periodicity. This overlayer consists of stripes with a local p(2 x 1)-O arrangement of oxygen atoms separated by stripes of uncovered It. When CO is adsorbed at 300 K onto the surface precovered with 0.5 ML O an apparent (2 x 2) LEED pattern is observed. LEED IV analysis reveals that this pattern is a superposition of diffraction patterns from islands of c(2 x 2)-CO and p(2 x 1)-O structures on the surface. Heating this co-adsorbed overlayer leads to the desorption of CO, in two stages at 330 K and 430 K; the excess CO (0.1 ML) desorbs at 590 K. LEED IV structural analysis of the mixed c(4 x 2) O and CO overlayer shows that both the CO molecules and the O atoms occupy bridge sites. The O atoms show significant lateral displacements of 0.14 angstrom away from the CO molecules; the C-O bond is slightly expanded with respect to the gas phase (1.19 angstrom); the modifications of the Ir substrate with respect to the bulk-terminated surface are very small. (c) 2006 Elsevier B.V. All rights reserved.

Thermo-responsive poly(methyl methacrylate)-block-poly(N-isopropylacrylamide) block copolymers synthesized by RAFT polymerization: micellization and gelation

RAFT polymerization was used to prepare PMMA-b-PNIPAM copolymers. Two different chain transfer agents, tBDB and MCPDB, were used to mediate the sequential polymerizations. Micellar solutions and gels were prepared from the resulting copolymers in aqueous solution. When heated above T-c of PNIPAM (about 31 degrees C), DLS revealed that PNIPAM coronas collapsed, resulting in aggregation of the original micelles. The micellar gels underwent syneresis above T-c as water was expelled from the ordered gel structure, the lattice periodicity of which was determined by SANS. A large decrease in lattice spacing was observed above T-c. The gel became more viscoelastic at high temperature, as revealed by shear rheometry which showed a large increase in G".

Phase separated structures in tethered dPS–PMMA copolymer films revealed using X-ray scattering with a novel contrast enhancement agent

Tethered deuterated polystyrene-block-polymethyl methacrylate films have been examined by X-ray scattering both in their native state and following treatment with ruthenium tetroxide. The use of the stain, while increasing the thickness of the films, does not significantly alter the lateral structure or periodicity of the films and provides contrast between the two blocks. Both the periodicity of the films and the structure normal to the surface have been identified following staining. Experiments were also performed on films treated by a solvent exchange process, and the effects of staining on these films are discussed.

Modulating self-assembly of a nanotape-forming peptide amphiphile with an oppositely charged surfactant

A peptide amphiphile (PA) C16-KTTKS, containing a pentapeptide headgroup based on a sequence from procollagen I attached to a hexadecyl lipid chain, self-assembles into extended nanotapes in aqueous solution. The tapes are based on bilayer structures, with a 5.2 nm spacing. Here, we investigate the effect of addition of the oppositely charged anionic surfactant sodium dodecyl sulfate (SDS) via AFM, electron microscopic methods, small-angle X-ray scattering and X-ray diffraction among other methods. We show that addition of SDS leads to a transition from tapes to fibrils, via intermediate states that include twisted ribbons. Addition of SDS is also shown to enhance the development of remarkable lateral ‘‘stripes’’ on the nanostructures, which have a 4 nm periodicity. This is ascribed to counterion condensation. The transition in the nanostructure leads to changes in macroscopic properties, in particular a transition from sol to gel is noted on increasing SDS (with a further reentrant transition to sol on further increase of SDS concentration). Formation of a gel may be useful in applications of this PA in skincare applications and we show that this can be controlled via development of a network of fine stranded fibrils.

Correlation between Fourier series expansion and Hückel orbital theory

The Fourier series can be used to describe periodic phenomena such as the one-dimensional crystal wave function. By the trigonometric treatements in Hückel theory it is shown that Hückel theory is a special case of Fourier series theory. Thus, the conjugated π system is in fact a periodic system. Therefore, it can be explained why such a simple theorem as Hückel theory can be so powerful in organic chemistry. Although it only considers the immediate neighboring interactions, it implicitly takes account of the periodicity in the complete picture where all the interactions are considered. Furthermore, the success of the trigonometric methods in Hückel theory is not accidental, as it based on the fact that Hückel theory is a specific example of the more general method of Fourier series expansion. It is also important for education purposes to expand a specific approach such as Hückel theory into a more general method such as Fourier series expansion.

A 27 day persistence model of near-Earth solar wind conditions: a long lead-time forecast and a benchmark for dynamical models

Geomagnetic activity has long been known to exhibit approximately 27 day periodicity, resulting from solar wind structures repeating each solar rotation. Thus a very simple near-Earth solar wind forecast is 27 day persistence, wherein the near-Earth solar wind conditions today are assumed to be identical to those 27 days previously. Effective use of such a persistence model as a forecast tool, however, requires the performance and uncertainty to be fully characterized. The first half of this study determines which solar wind parameters can be reliably forecast by persistence and how the forecast skill varies with the solar cycle. The second half of the study shows how persistence can provide a useful benchmark for more sophisticated forecast schemes, namely physics-based numerical models. Point-by-point assessment methods, such as correlation and mean-square error, find persistence skill comparable to numerical models during solar minimum, despite the 27 day lead time of persistence forecasts, versus 2–5 days for numerical schemes. At solar maximum, however, the dynamic nature of the corona means 27 day persistence is no longer a good approximation and skill scores suggest persistence is out-performed by numerical models for almost all solar wind parameters. But point-by-point assessment techniques are not always a reliable indicator of usefulness as a forecast tool. An event-based assessment method, which focusses key solar wind structures, finds persistence to be the most valuable forecast throughout the solar cycle. This reiterates the fact that the means of assessing the “best” forecast model must be specifically tailored to its intended use.

Scanning tunneling microscopy and molecular dynamics study of the Li2TiO3(001) surface

We have investigated the (001) surface structure of lithium titanate (Li2TiO3) using auger electron spectroscopy (AES), low-energy electron diffraction (LEED), and scanning tunneling microscopy (STM). Li2TiO3 is a potential fusion reactor blanket material. After annealing at 1200 K, LEED demonstrated that the Li2TiO3(001) surface was well ordered and not reconstructed. STM imaging showed that terraces are separated in height by about 0.3 nm suggesting a single termination layer. Moreover, hexagonal patterns with a periodicity of ∼0.4 nm are observed. On the basis of molecular dynamics (MD) simulations, these are interpreted as a dynamic arrangement of Li atoms.

On the environmental valuation of catastrophe: revisiting mining disasters in the United Kingdom, 1851-1962

In the context of environmental valuation of natural disasters, an important component of the evaluation procedure lies in determining the periodicity of events. This paper explores alternative methodologies for determining such periodicity, illustrating the advantages and the disadvantages of the separate methods and their comparative predictions. The procedures employ Bayesian inference and explore recent advances in computational aspects of mixtures methodology. The procedures are applied to the classic data set of Maguire et al (Biometrika, 1952) which was subsequently updated by Jarrett (Biometrika, 1979) and which comprise the seminal investigations examining the periodicity of mining disasters within the United Kingdom, 1851-1962.

Solar cycle evolution of dipolar and pseudostreamer belts and their relation to the slow solar wind

Dipolar streamers are coronal structures formed by open solar flux converging from coronal holes of opposite polarity. Thus the dipolar streamer belt traces the coronal foot print of the heliospheric current sheet (HCS), and it is strongly associated with the origin of slow solar wind. Pseudostreamers, on the other hand, separate converging regions of open solar flux from coronal holes of the same polarity and do not contain current sheets. They have recently received a great deal of interest as a possible additional source of slow solar wind. Here we add to that growing body of work by using the potential-field source-surface model to determine the occurrence and location of dipolar and pseudostreamers over the last three solar cycles. In addition to providing new information about pseudostreamer morphology, the results help explain why the observations taken during the first Ulysses perihelion pass in 1995 showed noncoincidence between dipolar streamer belt and the locus of slowest flow. We find that Carrington rotation averages of the heliographic latitudes of dipolar and pseudostreamer belts are systematically shifted away from the equator, alternately in opposite directions, with a weak solar cycle periodicity, thus keeping slow wind from the web of combined streamer belts approximately symmetric about the equator. The largest separation of dipolar and pseudostreamer belts occurred close to the Ulysses pass, allowing a unique opportunity to see that slow wind from pseudostreamer belts north of the southward-displaced dipolar belt was responsible for the noncoincident pattern.