Fourier spectral methods for fractional-in-space reaction-diffusion equations

Fractional differential equations are becoming increasingly used as a powerful modelling approach for understanding the many aspects of nonlocality and spatial heterogeneity. However, the numerical approximation of these models is demanding and imposes a number of computational constraints. In this paper, we introduce Fourier spectral methods as an attractive and easy-to-code alternative for the integration of fractional-in-space reaction-diffusion equations described by the fractional Laplacian in bounded rectangular domains ofRn. The main advantages of the proposed schemes is that they yield a fully diagonal representation of the fractional operator, with increased accuracy and efficiency when compared to low-order counterparts, and a completely straightforward extension to two and three spatial dimensions. Our approach is illustrated by solving several problems of practical interest, including the fractional Allen–Cahn, FitzHugh–Nagumo and Gray–Scott models, together with an analysis of the properties of these systems in terms of the fractional power of the underlying Laplacian operator.

Development of multi-rotor localised surveillance using multi-spectral sensors for plant biosecurity

This report describes a proof of concept for multi-rotor localised surveillance using a multi-spectral sensor for plant biosecurity applications. A literature review was conducted on previous applications using airborne multispectral imaging for plant biosecurity purposes. A ready built platform was purchased and modified in order to fit and provide suitable clearance for a Tetracam Mini-MCA multispectral camera. The appropriate risk management documents were developed allowing the platform and the multi-spectral camera to be tested extensively. However, due to technical difficulties with the platform the Mini- MCA was not mounted to the platform. Once a suitable platform is developed, future extensions can be conducted into the suitability of the Mini-MCA for airborne surveillance of Australian crops.

Constrained Linear Spectral Unmixing Technique for Regional Land Cover Mapping Using MODIS Data

Over the last few decades, there has been a significant land cover (LC) change across the globe due to the increasing demand of the burgeoning population and urban sprawl. In order to take account of the change, there is a need for accurate and up-to-date LC maps. Mapping and monitoring of LC in India is being carried out at national level using multi-temporal IRS AWiFS data. Multispectral data such as IKONOS, Landsat-TM/ETM+, IRS-ICID LISS-III/IV, AWiFS and SPOT-5, etc. have adequate spatial resolution (similar to 1m to 56m) for LC mapping to generate 1:50,000 maps. However, for developing countries and those with large geographical extent, seasonal LC mapping is prohibitive with data from commercial sensors of limited spatial coverage. Superspectral data from the MODIS sensor are freely available, have better temporal (8 day composites) and spectral information. MODIS pixels typically contain a mixture of various LC types (due to coarse spatial resolution of 250, 500 and 1000 in), especially in more fragmented landscapes. In this context, linear spectral unmixing would be useful for mapping patchy land covers, such as those that characterise much of the Indian subcontinent. This work evaluates the existing unmixing technique for LC mapping using MODIS data, using end-members that are extracted through Pixel Purity Index (PPI), Scatter plot and N-dimensional visualisation. The abundance maps were generated for agriculture, built up, forest, plantations, waste land/others and water bodies. The assessment of the results using ground truth and a LISS-III classified map shows 86% overall accuracy, suggesting the potential for broad-scale applicability of the technique with superspectral data for natural resource planning and inventory applications. Index Terms-Remote sensing, digital

Sidewall inclined slot in a rectangular waveguide: Theory and experiment

A novel analysis to compute the admittance characteristics of the slots cut in the narrow wall of a rectangular waveguide, which includes the corner diffraction effects and the finite waveguide wall thickness, is presented. A coupled magnetic field integral equation is formulated at the slot aperture which is solved by the Galerkin approach of the method of moments using entire domain sinusoidal basis functions. The externally scattered fields are computed using the finite difference method (FDM) coupled with the measured equation of invariance (MEI). The guide wall thickness forms a closed cavity and the fields inside it are evaluated using the standard FDM. The fields scattered inside the waveguide are formulated in the spectral domain for faster convergence compared to the traditional spatial domain expansions. The computed results have been compared with the experimental results and also with the measured data published in previous literature. Good agreement between the theoretical and experimental results is obtained to demonstrate the validity of the present analysis.

1H and 13C NMR spectra of some unsymmetric N,N-dipyridyl ureas: spectral assignments and molecular conformation

Abstract: The H-1 NMR spectra of N-(2-pyridyl), N'-(3-pyridyl)ureas and N-(2-pyridyl), N'-(4-pyridyl)ureas in CDCl3 and (CD3)(2)CO have been assigned with the aid of COSY and NOE experiments and chemical shift and coupling constant correlations, The C-13 NMR spectra in CDCl3 were analysed utilizing the HETCOR and proton coupled spectra, The H-1 NMR spectra, NOE effects and MINDO/3 calculations have been utilized to show that the molecular conformation of these compounds has the 2-pyridyl ring coplanar with the urea plane with the N-H group hydrogen bonded to the nitrogen of the 2-pyridyl group on the other urea nitrogen while the 3/4-pyridyl group rotates rapidly about the N-C-3/N-C-4 bond.

Gaussian Schell-model beams and general shape invariance

We present two six-parameter families of anisotropic Gaussian Schell-model beams that propagate in a shape-invariant manner, with the intensity distribution continuously twisting about the beam axis. The two families differ in the sense or helicity of this beam twist. The propagation characteristics of these shape-invariant beams are studied, and the restrictions on the beam parameters that arise from the optical uncertainty principle are brought out. Shape invariance is traced to a fundamental dynamical symmetry that underlies these beams. This symmetry is the product of spatial rotation and fractional Fourier transformation.

Spectral and thermal sensing for nitrogen and water status in rainfed and irrigated wheat environments

Variable-rate technologies and site-specific crop nutrient management require real-time spatial information about the potential for response to in-season crop management interventions. Thermal and spectral properties of canopies can provide relevant information for non-destructive measurement of crop water and nitrogen stresses. In previous studies, foliage temperature was successfully estimated from canopy-scale (mixed foliage and soil) temperatures and the multispectral Canopy Chlorophyll Content Index (CCCI) was effective in measuring canopy-scale N status in rainfed wheat (Triticum aestivum L.) systems in Horsham, Victoria, Australia. In the present study, results showed that under irrigated wheat systems in Maricopa, Arizona, USA, the theoretical derivation of foliage temperature unmixing produced relationships similar to those in Horsham. Derivation of the CCCI led to an r2 relationship with chlorophyll a of 0.53 after Zadoks stage 43. This was later than the relationship (r2 = 0.68) developed for Horsham after Zadoks stage 33 but early enough to be used for potential mid-season N fertilizer recommendations. Additionally, ground-based hyperspectral data estimated plant N (g kg)1) in Horsham with an r2 = 0.86 but was confounded by water supply and N interactions. By combining canopy thermal and spectral properties, varying water and N status can potentially be identified eventually permitting targeted N applications to those parts of a field where N can be used most efficiently by the crop.

A Spectral Iteration Technique For The Analysis Of Yagi-Uda Arrays

The paper present a spectral iteration technique for the analysis of linear arrays of unequally spaced dipoles of unequal lengths. As an example, the Yagi-Uda array is considered for illustration. Analysis is carried out in both the spatial as well as the spectral domains, the two being linked by the Fourier transform. The fast Fourier transform algorithm is employed to obtain an iterative solution to the electric field integral equation and the need for matrix inversion is circumvented. This technique also provides a convenient means for testing the satisfaction of the boundary conditions on the array elements. Numerical comparison of the input impedance and radiation pattern have been made with results deduced elsewhere by other methods. The computational efficency of this technique has been found to be significant for large arrays.

Spectral Sensing for Cognitive Radio: Estimation of Adaptive Frequency Hopping Signal

The issue of dynamic spectrum scene analysis in any cognitive radio network becomes extremely complex when low probability of intercept, spread spectrum systems are present in environment. The detection and estimation become more complex if frequency hopping spread spectrum is adaptive in nature. In this paper, we propose two phase approach for detection and estimation of frequency hoping signals. Polyphase filter bank has been proposed as the architecture of choice for detection phase to efficiently detect the presence of frequency hopping signal. Based on the modeling of frequency hopping signal it can be shown that parametric methods of line spectral analysis are well suited for estimation of frequency hopping signals if the issues of order estimation and time localization are resolved. An algorithm using line spectra parameter estimation and wavelet based transient detection has been proposed which resolves above issues in computationally efficient manner suitable for implementation in cognitive radio. The simulations show promising results proving that adaptive frequency hopping signals can be detected and demodulated in a non cooperative context, even at a very low signal to noise ratio in real time.

Detection of nitrogen deficiency in wheat from spectral reflectance indices and basic crop eco-physiological concepts

We tested the capacity of several published multispectral indices to estimate the nitrogen nutrition of wheat canopies grown under different levels of water supply and plant density and derived a simple canopy reflectance index that is greatly independent of those factors. Planar domain geometry was used to account for mixed signals from the canopy and soil when the ground cover was low. A nitrogen stress index was developed, which adjusts shoot %N for plant biomass and area, thereby accounting for environmental conditions that affect growth, such as crop water status. The canopy chlorophyll content index (CCCi) and the modified spectral ratio planar index (mSRPi) could explain 68 and 69% of the observed variability in the nitrogen nutrition of the crop as early as Zadoks 33, irrespective of water status or ground cover. The CCCi was derived from the combination of 3 wavebands 670, 720 and 790 nm, and the mSRPi from 445, 705 and 750 nm, together with broader bands in the NIR and RED. The potential for their spatial application over large fields/paddocks is discussed.

The Connor-Davidson Resilience Scale (CD-RISC): Dimensionality and age-related measurement invariance with Australian cricketers

Objective This study explored the dimensionality and measurement invariance of the 25-item Connor-Davidson Resilience Scale (CD-RISC; Connor & Davidson, 2003) across samples of adult (n = 321; aged 20–36) and adolescent (n = 199; aged 12–18) Australian cricketers. Design Cross-sectional, self-report survey Methods An online, multi-section questionnaire. Results Confirmatory factor and item level analyses supported the psychometric superiority of a revised 10-item, unidimensional model of resilience over the original 25-item, five-factor measurement model. Positive and moderate correlations with hardiness as well as negative and moderate correlations with burnout components were evidenced thereby providing support for the convergent validity of the unidimensional model. Measurement invariance analyses of the unidimensional model across the two age-group samples supported configural (i.e., same factor structure across groups), metric (i.e., same pattern of factor loadings across the groups), and partial scalar invariance (i.e., mostly the same intercepts across the groups). Conclusion Evidence for a psychometrically sound measure of resilient qualities of the individual provides an important foundation upon which researchers can identify the antecedents to and outcomes of resilience in sport contexts.

Estimation of peak ground acceleration and spectral acceleration for South India with local site effects: probabilistic approach

In this work an attempt has been made to evaluate the seismic hazard of South India (8.0 degrees N-20 degrees N; 72 degrees E-88 degrees E) based on the probabilistic seismic hazard analysis (PSHA). The earthquake data obtained from different sources were declustered to remove the dependent events. A total of 598 earthquakes of moment magnitude 4 and above were obtained from the study area after declustering, and were considered for further hazard analysis. The seismotectonic map of the study area was prepared by considering the faults, lineaments and the shear zones in the study area which are associated with earthquakes of magnitude 4 and above. For assessing theseismic hazard, the study area was divided into small grids of size 0.1 degrees x0.1 degrees, and the hazard parameters were calculated at the centre of each of these grid cells by considering all the seismic sources with in a radius of 300 km. Rock level peak horizontal acceleration (PHA) and spectral acceleration (SA) values at 1 corresponding to 10% and 2% probability of exceedance in 50 years have been calculated for all the grid points. The contour maps showing the spatial variation of these values are presented here. Uniform hazard response spectrum (UHRS) at rock level for 5% damping and 10% and 2% probability of exceedance in 50 years were also developed for all the grid points. The peak ground acceleration (PGA) at surface level was calculated for the entire South India for four different site classes. These values can be used to find the PGA values at any site in South India based on site class at that location. Thus, this method can be viewed as a simplified method to evaluate the PGA values at any site in the study area.

Conformation of some N,N'-arylalkyl thioureas by 1H-NMR and infrared spectral analysis

Several N,N-²-arylalkyl thioureas were examined with 1H-NMR and i.r. spectra in order to study the conformation of the -NHCSNH- group. The influence of temperature and substituents on the chemical shift of the N---H protons has been investigated. Formation of a strong intramolecular hydrogen bond stabilizes the trans-cis conformation for most systems, while for the others the prevalence of different rotational isomers can be postulated. The influence of the steric effect on hydrogen bonding and molecular conformation is discussed.

Measuring and predicting canopy nitrogen nutrition in wheat using a spectral index—The canopy chlorophyll content index (CCCI).

Varying the spatial distribution of applied nitrogen (N) fertilizer to match demand in crops has been shown to increase profits in Australia. Better matching the timing of N inputs to plant requirements has been shown to improve nitrogen use efficiency and crop yields and could reduce nitrous oxide emissions from broad acre grains. Farmers in the wheat production area of south eastern Australia are increasingly splitting N application with the second timing applied at stem elongation (Zadoks 30). Spectral indices have shown the ability to detect crop canopy N status but a robust method using a consistent calibration that functions across seasons has been lacking. One spectral index, the canopy chlorophyll content index (CCCI) designed to detect canopy N using three wavebands along the "red edge" of the spectrum was combined with the canopy nitrogen index (CNI), which was developed to normalize for crop biomass and correct for the N dilution effect of crop canopies. The CCCI-CNI index approach was applied to a 3-year study to develop a single calibration derived from a wheat crop sown in research plots near Horsham, Victoria, Australia. The index was able to predict canopy N (g m-2) from Zadoks 14-37 with an r2 of 0.97 and RMSE of 0.65 g N m-2 when dry weight biomass by area was also considered. We suggest that measures of N estimated from remote methods use N per unit area as the metric and that reference directly to canopy %N is not an appropriate method for estimating plant concentration without first accounting for the N dilution effect. This approach provides a link to crop development rather than creating a purely numerical relationship. The sole biophysical input, biomass, is challenging to quantify robustly via spectral methods. Combining remote sensing with crop modelling could provide a robust method for estimating biomass and therefore a method to estimate canopy N remotely. Future research will explore this and the use of active and passive sensor technologies for use in precision farming for targeted N management.