The response of a uniform horizontal temperature gradient to heating

The response of a uniform horizontal temperature gradient to prescribed fixed heating is calculated in the context of an extended version of surface quasigeostrophic dynamics. It is found that for zero mean surface flow and weak cross-gradient structure the prescribed heating induces a mean temperature anomaly proportional to the spatial Hilbert transform of the heating. The interior potential vorticity generated by the heating enhances this surface response. The time-varying part is independent of the heating and satisfies the usual linearized surface quasigeostrophic dynamics. It is shown that the surface temperature tendency is a spatial Hilbert transform of the temperature anomaly itself. It then follows that the temperature anomaly is periodically modulated with a frequency proportional to the vertical wind shear. A strong local bound on wave energy is also found. Reanalysis diagnostics are presented that indicate consistency with key findings from this theory.

Unimodality of wave amplitude in the northern Hemisphere

A novel statistic for local wave amplitude of the 500-hPa geopotential height field is introduced. The statistic uses a Hilbert transform to define a longitudinal wave envelope and dynamical latitude weighting to define the latitudes of interest. Here it is used to detect the existence, or otherwise, of multimodality in its distribution function. The empirical distribution function for the 1960-2000 period is close to a Weibull distribution with shape parameters between 2 and 3. There is substantial interdecadal variability but no apparent local multimodality or bimodality. The zonally averaged wave amplitude, akin to the more usual wave amplitude index, is close to being normally distributed. This is consistent with the central limit theorem, which applies to the construction of the wave amplitude index. For the period 1960-70 it is found that there is apparent bimodality in this index. However, the different amplitudes are realized at different longitudes, so there is no bimodality at any single longitude. As a corollary, it is found that many commonly used statistics to detect multimodality in atmospheric fields potentially satisfy the assumptions underlying the central limit theorem and therefore can only show approximately normal distributions. The author concludes that these techniques may therefore be suboptimal to detect any multimodality.

The application of the Hilbert spectrum to the analysis of electromyographic signals

This paper investigates the application of the Hilbert spectrum (HS), which is a recent tool for the analysis of nonlinear and nonstationary time-series, to the study of electromyographic (EMG) signals. The HS allows for the visualization of the energy of signals through a joint time-frequency representation. In this work we illustrate the use of the HS in two distinct applications. The first is for feature extraction from EMG signals. Our results showed that the instantaneous mean frequency (IMNF) estimated from the HS is a relevant feature to clinical practice. We found that the median of the IMNF reduces when the force level of the muscle contraction increases. In the second application we investigated the use of the HS for detection of motor unit action potentials (MUAPs). The detection of MUAPs is a basic step in EMG decomposition tools, which provide relevant information about the neuromuscular system through the morphology and firing time of MUAPs. We compared, visually, how MUAP activity is perceived on the HS with visualizations provided by some traditional (e.g. scalogram, spectrogram, Wigner-Ville) time-frequency distributions. Furthermore, an alternative visualization to the HS, for detection of MUAPs, is proposed and compared to a similar approach based on the continuous wavelet transform (CWT). Our results showed that both the proposed technique and the CWT allowed for a clear visualization of MUAP activity on the time-frequency distributions, whereas results obtained with the HS were the most difficult to interpret as they were extremely affected by spurious energy activity. (c) 2008 Elsevier Inc. All rights reserved.

Dunford-Pettis properties, Hilbert spaces and projective tensor products

We study complete continuity properties of operators onto ℓ2 and prove several results in the Dunford–Pettis theory of JB∗-triples and their projective tensor products, culminating in characterisations of the alternative Dunford–Pettis property for where E and F are JB∗-triples.

Spatial covariation of Azotobacter abundance and soil properties: A case study using the wavelet transform

The soil microflora is very heterogeneous in its spatial distribution. The origins of this heterogeneity and its significance for soil function are not well understood. A problem for understanding spatial variation better is the assumption of statistical stationarity that is made in most of the statistical methods used to assess it. These assumptions are made explicit in geostatistical methods that have been increasingly used by soil biologists in recent years. Geostatistical methods are powerful, particularly for local prediction, but they require the assumption that the variability of a property of interest is spatially uniform, which is not always plausible given what is known about the complexity of the soil microflora and the soil environment. We have used the wavelet transform, a relatively new innovation in mathematical analysis, to investigate the spatial variation of abundance of Azotobacter in the soil of a typical agricultural landscape. The wavelet transform entails no assumptions of stationarity and is well suited to the analysis of variables that show intermittent or transient features at different spatial scales. In this study, we computed cross-variograms of Azotobacter abundance with the pH, water content and loss on ignition of the soil. These revealed scale-dependent covariation in all cases. The wavelet transform also showed that the correlation of Azotobacter abundance with all three soil properties depended on spatial scale, the correlation generally increased with spatial scale and was only significantly different from zero at some scales. However, the wavelet analysis also allowed us to show how the correlation changed across the landscape. For example, at one scale Azotobacter abundance was strongly correlated with pH in part of the transect, and not with soil water content, but this was reversed elsewhere on the transect. The results show how scale-dependent variation of potentially limiting environmental factors can induce a complex spatial pattern of abundance in a soil organism. The geostatistical methods that we used here make assumptions that are not consistent with the spatial changes in the covariation of these properties that our wavelet analysis has shown. This suggests that the wavelet transform is a powerful tool for future investigation of the spatial structure and function of soil biota. (c) 2006 Elsevier Ltd. All rights reserved.

Assessment of the consistency of near-infrared water vapor line intensities using high-spectral-resolution ground-based Fourier transform measurements of solar radiation

Calculations of the absorption of solar radiation by atmospheric gases, and water vapor in particular, are dependent on the quality of databases of spectral line parameters. There has been increasing scrutiny of databases such as HITRAN in recent years, but this has mostly been performed on a band-by-band basis. We report nine high-spectral-resolution (0.03 cm(-1)) measurements of the solar radiation reaching the surface in southern England over the wave number range 2000 to 12,500 cm(-1) (0.8 to 5 mm) that allow a unique assessment of the consistency of the spectral line databases over this entire spectral region. The data are assessed in terms of the modeled water vapor column that is required to bring calculations and observations into agreement; for an entirely consistent database, this water vapor column should be constant with frequency. For the HITRAN01 database, the spread in water vapor column is about 11%, with distinct shifts between different spectral regions. The HITRAN04 database is in significantly better agreement (about 5% spread) in the completely updated 3000 to 8000 cm(-1) spectral region, but inconsistencies between individual spectral regions remain: for example, in the 8000 to 9500 cm(-1) spectral region, the results indicate an 18% (+/- 1%) underestimate in line intensities with respect to the 3000 to 8000 cm(-1) region. These measurements also indicate the impact of isotopic fractionation of water vapor in the 2500 to 2900 cm(-1) range, where HDO lines dominate over the lines of the most abundant isotope of H2O.

Fourier transform infrared spectra of H2CS and D2CS

Infrared spectra of thoformaldehyde, H2CS and D2CS, were observed in the gas phase at a resolution of better than 0.1 cm−1 from 4000 to 400 cm−1 using a Nicolet FTIR system. Vibrational band origins and rotational constants were determined for ν2, ν3, ν4, and ν6 of H2CS and for ν1, ν2, ν3, ν4, and ν6 of D2CS. The ν3, ν4, and ν6 bands of H2CS were analyzed as a set of three Coriolis interacting bands, and three Coriolis constants were determined; similarly the ν4 and ν6 bands of D2CS were analyzed as a pair of interacting bands and one Coriolis constant was determined. A general harmonic force field was determined, without constraints, to fit the vibrational wavenumbers, Coriolis constants, and centrifugal distortion constants. A zero-point (rz) structure was determined from the ground-state rotational constants, and the equilibrium (re) bond lengths were estimated.

The Klein-Gordon equation on the half line: a Riemann-Hilbert approach

We solve an initial-boundary problem for the Klein-Gordon equation on the half line using the Riemann-Hilbert approach to solving linear boundary value problems advocated by Fokas. The approach we present can be also used to solve more complicated boundary value problems for this equation, such as problems posed on time-dependent domains. Furthermore, it can be extended to treat integrable nonlinearisations of the Klein-Gordon equation. In this respect, we briefly discuss how our results could motivate a novel treatment of the sine-Gordon equation.

Spectral analysis of the elliptic sine-Gordon equation in the quarter plane

We study the elliptic sine-Gordon equation in the quarter plane using a spectral transform approach. We determine the Riemann-Hilbert problem associated with well-posed boundary value problems in this domain and use it to derive a formal representation of the solution. Our analysis is based on a generalization of the usual inverse scattering transform recently introduced by Fokas for studying linear elliptic problems.

Remote gas detection and quantitative analysis from infrared emission spectra obtained by Fourier transform infrared spectroscopy

Techniques for obtaining quantitative values of the temperatures and concentrations of remote hot gaseous effluents from their measured passive emission spectra have been examined in laboratory experiments. The high sensitivity of the spectrometer in the vicinity of the 2397 cm-1 band head region of CO2 has allowed the gas temperature to be calculated from the relative intensity of the observed rotational lines. The spatial distribution of the CO2 in a methane flame has been reconstructed tomographically using a matrix inversion technique. The spectrometer has been calibrated against a black body source at different temperatures and a self absorption correction has been applied to the data avoiding the need to measure the transmission directly. Reconstruction artifacts have been reduced by applying a smoothing routine to the inversion matrix.