Rayleigh scattering by hexagonal ice crystals and the interpretation of dual-polarisation radar measurements

Dual-polarisation radar measurements provide valuable information about the shapes and orientations of atmospheric ice particles. For quantitative interpretation of these data in the Rayleigh regime, common practice is to approximate the true ice crystal shape with that of a spheroid. Calculations using the discrete dipole approximation for a wide range of crystal aspect ratios demonstrate that approximating hexagonal plates as spheroids leads to significant errors in the predicted differential reflectivity, by as much as 1.5 dB. An empirical modification of the shape factors in Gans's spheroid theory was made using the numerical data. The resulting simple expressions, like Gans's theory, can be applied to crystals in any desired orientation, illuminated by an arbitrarily polarised wave, but are much more accurate for hexagonal particles. Calculations of the scattering from more complex branched and dendritic crystals indicate that these may be accurately modelled using the new expression, but with a reduced permittivity dependent on the volume of ice relative to an enclosing hexagonal prism.

Infrared intensities of furan, pyrrole and thiophene: beyond the double harmonic approximation

Infrared intensities of the fundamental, overtone and combination transitions in furan, pyrrole and thiophene have been calculated using the variational normal coordinate code MULTIMODE. We use pure vibrational wavefunctions, and quartic force fields and cubic dipole moment vector surfaces, generated by density functional theory. The results are compared graphically with second-order perturbation calculations and with relative intensities from experiment for furan and pyrrole.

A relative path attenuation approximation algorithm for DVB-T systems

In the United Kingdom and in fact throughout Europe, the chosen standard for digital terrestrial television is the European Telecommunications Standards Institute (ETSI) ETN 300 744 also known as Digital Video Broadcasting - Terrestrial (DVB-T). The modulation method under this standard was chosen to be Orthogonal Frequency Division Multiplex (0FD4 because of the apparent inherent capability for withstanding the effects of multipath. Within the DVB-T standard, the addition of pilot tones was included that can be used for many applications such as channel impulse response estimation or local oscillator phase and frequency offset estimation. This paper demonstrates a technique for an estimation of the relative path attenuation of a single multipath signal that can be used as a simple firmware update for a commercial set-top box. This technique can be used to help eliminate the effects of multipath(1).

The price of risk in construction projects: contingency approximation model (CAM)

Little attention has been focussed on a precise definition and evaluation mechanism for project management risk specifically related to contractors. When bidding, contractors traditionally price risks using unsystematic approaches. The high business failure rate our industry records may indicate that the current unsystematic mechanisms contractors use for building up contingencies may be inadequate. The reluctance of some contractors to include a price for risk in their tenders when bidding for work competitively may also not be a useful approach. Here, instead, we first define the meaning of contractor contingency, and then we develop a facile quantitative technique that contractors can use to estimate a price for project risk. This model will help contractors analyse their exposure to project risks; and help them express the risk in monetary terms for management action. When bidding for work, they can decide how to allocate contingencies strategically in a way that balances risk and reward.

Sparse kernel density estimation technique based on zero-norm constraint

A sparse kernel density estimator is derived based on the zero-norm constraint, in which the zero-norm of the kernel weights is incorporated to enhance model sparsity. The classical Parzen window estimate is adopted as the desired response for density estimation, and an approximate function of the zero-norm is used for achieving mathemtical tractability and algorithmic efficiency. Under the mild condition of the positive definite design matrix, the kernel weights of the proposed density estimator based on the zero-norm approximation can be obtained using the multiplicative nonnegative quadratic programming algorithm. Using the -optimality based selection algorithm as the preprocessing to select a small significant subset design matrix, the proposed zero-norm based approach offers an effective means for constructing very sparse kernel density estimates with excellent generalisation performance.

Sparse polynomial approximation in positive order Sobolev spaces with bounded mixed derivatives and applications to elliptic problems with random loading

In the present paper we study the approximation of functions with bounded mixed derivatives by sparse tensor product polynomials in positive order tensor product Sobolev spaces. We introduce a new sparse polynomial approximation operator which exhibits optimal convergence properties in L2 and tensorized View the MathML source simultaneously on a standard k-dimensional cube. In the special case k=2 the suggested approximation operator is also optimal in L2 and tensorized H1 (without essential boundary conditions). This allows to construct an optimal sparse p-version FEM with sparse piecewise continuous polynomial splines, reducing the number of unknowns from O(p2), needed for the full tensor product computation, to View the MathML source, required for the suggested sparse technique, preserving the same optimal convergence rate in terms of p. We apply this result to an elliptic differential equation and an elliptic integral equation with random loading and compute the covariances of the solutions with View the MathML source unknowns. Several numerical examples support the theoretical estimates.

Effect of mycorrhizae and pH change at the root-soil interface on phosphorus uptake by Sorghum using a rhizocylinder technique

Sorghum (Sorghum bicolor) was grown for 40 days in. rhizocylinder (a growth container which permitted access to rh zosphere and nonrhizosphere soil), in two soils of low P status. Soils were fertilized with different rates of ammonium and nitrate and supplemented with 40 mg phosphorus (P) kg(-1) and inoculated with either Glomus mosseae (Nicol. and Gerd.) or nonmycorrhizal root inoculum.. N-serve (2 mg kg(-1)) was added to prevent nitrification. At harvest, soil from around the roots was collected at distances of 0-5, 5-10, and 10-20 mm from the root core which was 35 mm diameter. Sorghum plants, with and without mycorrhiza, grew larger with NH4+ than with NO3- application. After measuring soil pH, 4 3 suspensions of the same sample were titrated against 0.01 M HCl or 0.01 M NaOH until soil pH reached the nonplanted pH level. The acid or base requirement for each sample was calculated as mmol H+ or OFF kg(-1) soil. The magnitude of liberated acid or base depended on the form and rate of nitrogen and soil type. When the plant root was either uninfected or infected with mycorrhiza., soil pH changes extended up to 5 mm from the root core surface. In both soils, ammonium as an N source resulted in lower soil pH than nitrate. Mycorrhizal (VAM) inoculation did not enhance this difference. In mycorrhizal inoculated soil, P depletion extended tip to 20 mm from the root surface. In non-VAM inoculated soil P depletion extended up to 10 mm from the root surface and remained unchanged at greater distances. In the mycorrhizal inoculated soils, the contribution of the 0-5 mm soil zone to P uptake was greater than the core soil, which reflects the hyphal contribution to P supply. Nitrogen (N) applications that caused acidification increased P uptake because of increased demand; there is no direct evidence that the increased uptake was due to acidity increasing the solubility of P although this may have been a minor effect.

The use of FT-IR as a screening technique for organic residue analysis of archaeological samples

A range of archaeological samples have been examined using FT-IR spectroscopy. These include suspected coprolite samples from the Neolithic site of Catalhoyuk in Turkey, pottery samples from the Roman site of Silchester, UK and the Bronze Age site of Gatas, Spain and unidentified black residues on pottery sherds from the Roman sites of Springhead and Cambourne, UK. For coprolite samples the aim of FT-IR analysis is identification. Identification of coprolites in the field is based on their distinct orange colour; however, such visual identifications can often be misleading due to their similarity with deposits such as ochre and clay. For pottery the aim is to screen those samples that might contain high levels of organic residues which would be suitable for GC-MS analysis. The experiments have shown coprolites to have distinctive spectra, containing strong peaks from calcite, phosphate and quartz; the presence of phosphorus may be confirmed by SEM-EDX analysis. Pottery containing organic residues of plant and animal origin has also been shown to generally display strong phosphate peaks. FT-IR has distinguished between organic resin and non-organic compositions for the black residues, with differences also being seen between organic samples that have the same physical appearance. Further analysis by CC-MS has confirmed the identification of the coprolites through the presence of coprostanol and bile acids, and shows that the majority of organic pottery residues are either fatty acids or mono- or di-acylglycerols from foodstuffs, or triterpenoid resin compounds exposed to high temperatures. One suspected resin sample was shown to contain no organic residues. and it is seen that resin samples with similar physical appearances have different chemical compositions. FT-IR is proposed as a quick and cheap method of screening archaeological samples before subjecting them to the more expensive and time-consuming method of GC-MS. This will eliminate inorganic samples such as clays and ochre from CC-MS analysis, and will screen those samples which are most likely to have a high concentration of preserved organic residues. (C) 2008 Elsevier B.V. All rights reserved.

Finite element approximation of a sixth order nonlinear degenerate parabolic equation

We consider a finite element approximation of the sixth order nonlinear degenerate parabolic equation ut = ?.( b(u)? 2u), where generically b(u) := |u|? for any given ? ? (0,?). In addition to showing well-posedness of our approximation, we prove convergence in space dimensions d ? 3. Furthermore an iterative scheme for solving the resulting nonlinear discrete system is analysed. Finally some numerical experiments in one and two space dimensions are presented.

Two Independent Triggers for the Indian Ocean Dipole/Zonal Mode in a Coupled GCM

The question of whether and how tropical Indian Ocean dipole or zonal mode (IOZM) interannual variability is independent of El Nino-Southern Oscillation (ENSO) variability in the Pacific is addressed in a comparison of twin 200-yr runs of a coupled climate model. The first is a reference simulation, and the second has ENSO-scale variability suppressed with a constraint on the tropical Pacific wind stress. The IOZM can exist in the model without ENSO, and the composite evolution of the main anomalies in the Indian Ocean in the two simulations is virtually identical. Its growth depends on a positive feedback between anomalous equatorial easterly winds, upwelling equatorial and coastal Kelvin waves reducing the thermocline depth and sea surface temperature off the coast of Sumatra, and the atmospheric dynamical response to the subsequently reduced convection. Two IOZM triggers in the boreal spring are found. The first is an anomalous Hadley circulation over the eastern tropical Indian Ocean and Maritime Continent, with an early northward penetration of the Southern Hemisphere southeasterly trades. This situation grows out of cooler sea surface temperatures in the southeastern tropical Indian Ocean left behind by a reinforcement of the late austral summer winds. The second trigger is a consequence of a zonal shift in the center of convection associated with a developing El Nino, a Walker cell anomaly. The first trigger is the only one present in the constrained simulation and is similar to the evolution of anomalies in 1994, when the IOZM occurred in the absence of a Pacific El Nino state. The presence of these two triggers-the first independent of ENSO and the second phase locking the IOZM to El Nino-allows an understanding of both the existence of IOZM events when Pacific conditions are neutral and the significant correlation between the IOZM and El Nino.

The omega equation and potential vorticity

Two fundamental perspectives on the dynamics of midlatitude weather systems are provided by potential vorticity (PV) and the omega equation. The aim of this paper is to investigate the link between the two perspectives, which has so far received very little attention in the meteorological literature. It also aims to give a quantitative basis for discussion of quasi-geostrophic vertical motion in terms of components associated with system movement, maintaining a constant thermal structure, and with the development of that structure. The former links with the isentropic relative-flow analysis technique. Viewed in a moving frame of reference, the measured development of a system depends on the velocity of that frame of reference. The requirement that the development should be a minimum provides a quantitative method for determining the optimum system velocity. The component of vertical velocity associated with development is shown to satisfy an omega equation with forcing determined from the relative advection of interior PV and boundary temperature. The analysis carries through in the presence of diabatic heating provided the omega equation forcing is based on the interior PV and boundary thermal tendencies, including the heating effect. The analysis is shown to be possible also at the level of the semi-geostrophic approximation. The analysis technique is applied to a number of idealized problems that can be considered to be building blocks for midlatitude synoptic-scale dynamics. They focus on the influences of interior PV, boundary temperature, an interior boundary, baroclinic instability associated with two boundaries, and also diabatic heating. In each case, insights yielded by the new perspective are sought into the dynamical behaviour, especially that related to vertical motion. Copyright © 2003 Royal Meteorological Society