Multipole expansion of strongly focussed laser beams

Multipole expansion of an incident radiation field-that is, representation of the fields as sums of vector spherical wavefunctions-is essential for theoretical light scattering methods such as the T-matrix method and generalised Lorenz-Mie theory (GLMT). In general, it is theoretically straightforward to find a vector spherical wavefunction representation of an arbitrary radiation field. For example, a simple formula results in the useful case of an incident plane wave. Laser beams present some difficulties. These problems are not a result of any deficiency in the basic process of spherical wavefunction expansion, but are due to the fact that laser beams, in their standard representations, are not radiation fields, but only approximations of radiation fields. This results from the standard laser beam representations being solutions to the paraxial scalar wave equation. We present an efficient method for determining the multipole representation of an arbitrary focussed beam. (C) 2003 Elsevier Science Ltd. All rights reserved.

Quantum mechanics as an approximation to classical mechanics in Hilbert space

Classical mechanics is formulated in complex Hilbert space with the introduction of a commutative product of operators, an antisymmetric bracket and a quasidensity operator that is not positive definite. These are analogues of the star product, the Moyal bracket, and the Wigner function in the phase space formulation of quantum mechanics. Quantum mechanics is then viewed as a limiting form of classical mechanics, as Planck's constant approaches zero, rather than the other way around. The forms of semiquantum approximations to classical mechanics, analogous to semiclassical approximations to quantum mechanics, are indicated.

An investigation of localised soil heterogeneities on solute transport using a multisegment percolation system

A multisegment percolation system (MSPS) consisting of 25 individual collection wells was constructed to study the effects of localised soil heterogeneities on the transport of solutes in the vadose zone. In particular, this paper discusses the transport of water and nutrients (NO3-, Cl-, PO43-) through structurally stable, free-draining agricultural soil from Victoria, Australia. A solution of nutrients was irrigated onto the surface of a large undisturbed soil core over a 12-h period. This was followed by a continuous irrigation of distilled water at a fate which did not cause pending for a further 18 days. During this time, the volume of leachate and the concentration of nutrients in the leachate of each well were measured. Very significant variation in drainage patterns across a small spatial scale was observed. Leaching of nitrate-nitrogen and chloride from the core occurred two days after initial application. However, less than 1% of the total applied phosphate-phosphorus leached from the soil during the 18-day experiment, indicating strong adsorption. Our experiments indicate considerable heterogeneity in water flow patterns and solute leaching on a small spatial scale. These results have significant ramifications for modelling solute transport and predicting nutrient loadings on a larger scale.

Tidal fluctuations in a leaky confined aquifer: localised effects of an overlying phreatic aquifer

Damping of tidal head fluctuations in a leaky confined coastal aquifer is enhanced by leakage into an overlying phreatic aquifer. We show that the phreatic aquifer is, however, resistant to the leakage flow and in particular, a deep phreatic aquifer can reduce the leakage effects significantly. An analytical solution, based on a vertical flow model for the phreatic aquifer, is derived for quantifying the role of this upper free water body in tidal propagation in the lower semi-confined aquifer. (C) 2002 Elsevier Science B.V. All rights reserved.

Two-dimensional approximation for tidal dynamics in coastal aquifers: Capillarity correction

Most previous investigations on tide-induced watertable fluctuations in coastal aquifers have been based on one-dimensional models that describe the processes in the cross-shore direction alone, assuming negligible along-shore variability. A recent study proposed a two-dimensional approximation for tide-induced watertable fluctuations that took into account coastline variations. Here, we further develop this approximation in two ways, by extending the approximation to second order and by taking into account capillary effects. Our results demonstrate that both effects can markedly influence watertable fluctuations. In particular, with the first-order approximation, the local damping rate of the tidal signal could be subject to sizable errors.

Two-link approximation schemes for loss networks with linear structure and trunk reservation

Loss networks have long been used to model various types of telecommunication network, including circuit-switched networks. Such networks often use admission controls, such as trunk reservation, to optimize revenue or stabilize the behaviour of the network. Unfortunately, an exact analysis of such networks is not usually possible, and reduced-load approximations such as the Erlang Fixed Point (EFP) approximation have been widely used. The performance of these approximations is typically very good for networks without controls, under several regimes. There is evidence, however, that in networks with controls, these approximations will in general perform less well. We propose an extension to the EFP approximation that gives marked improvement for a simple ring-shaped network with trunk reservation. It is based on the idea of considering pairs of links together, thus making greater allowance for dependencies between neighbouring links than does the EFP approximation, which only considers links in isolation.

On the fast approximation of Green's functions in MPIE formulations for planar layered media

The numerical implementation of the complex image approach for the Green's function of a mixed-potential integralequation formulation is examined and is found to be limited to low values of k(0) rho (in this context k(0) rho = 2 pirho/ lambda(0), where rho is the distance between the source and the field points of the Green's function and lambda(0) is the free space wavelength). This is a clear limitation for problems of large dimension or high frequency where this limit is easily exceeded. This paper examines the various strategies and proposes a hybrid method whereby most of the above problems can be avoided. An efficient integral method that is valid for large k(0) rho is combined with the complex image method in order to take advantage of the relative merits of both schemes. It is found that a wide overlapping region exists between the two techniques allowing a very efficient and consistent approach for accurately calculating the Green's functions. In this paper, the method developed for the computation of the Green's function is used for planar structures containing both lossless and lossy media.

Micro-mechanical approximation to the stress field around an inclined fiber of FRCC

Matrix spalling or crushing is one of the important mechanisms of fiber-matrix interaction of fiber reinforced cementitious composites (FRCC). The fiber pullout mechanisms have been extensively studied for an aligned fiber but matrix failure is rarely investigated since it is thought not to be a major affect. However, for an inclined fiber, the matrix failure should not be neglected. Due to the complex process of matrix spalling, experimental investigation and analytical study of this mechanism are rarely found in literature. In this paper, it is assumed that the load transfer is concentrated within the short length of the inclined fiber from the exit point towards anchored end and follows the exponential law. The Mindlin formulation is employed to calculate the 3D stress field. The simulation gives much information about this field. The 3D approximation of the stress state around an inclined fiber helps to qualitatively understand the mechanism of matrix failure. Finally, a spalling criterion is proposed by which matrix spalling occurs only when the stress in a certain volume, rather than the stress at a small point, exceeds the material strength. This implies some local stress redistribution after first yield. The stress redistribution results in more energy input and higher load bearing capacity of the matrix. In accordance with this hypothesis, the evolution of matrix spalling is demonstrated. The accurate prediction of matrix spalling needs the careful determination of the parameters in this model. This is the work of further study. (C) 2002 Elsevier Science Ltd. All rights reserved.

Fast, scalable master equation solution algorithms. IV. Lanczos iteration with diffusion approximation preconditioned iterative inversion

In this paper we propose a second linearly scalable method for solving large master equations arising in the context of gas-phase reactive systems. The new method is based on the well-known shift-invert Lanczos iteration using the GMRES iteration preconditioned using the diffusion approximation to the master equation to provide the inverse of the master equation matrix. In this way we avoid the cubic scaling of traditional master equation solution methods while maintaining the speed of a partial spectral decomposition. The method is tested using a master equation modeling the formation of propargyl from the reaction of singlet methylene with acetylene, proceeding through long-lived isomerizing intermediates. (C) 2003 American Institute of Physics.

Fast, scalable master equation solution algorithms. III. Direct time propagation accelerated by a diffusion approximation preconditioned iterative solver

In this paper we propose a novel fast and linearly scalable method for solving master equations arising in the context of gas-phase reactive systems, based on an existent stiff ordinary differential equation integrator. The required solution of a linear system involving the Jacobian matrix is achieved using the GMRES iteration preconditioned using the diffusion approximation to the master equation. In this way we avoid the cubic scaling of traditional master equation solution methods and maintain the low temperature robustness of numerical integration. The method is tested using a master equation modelling the formation of propargyl from the reaction of singlet methylene with acetylene, proceeding through long lived isomerizing intermediates. (C) 2003 American Institute of Physics.

A reduced load approximation accounting for link interactions in a loss network

This paper is concerned with evaluating the performance of loss networks. Accurate determination of loss network performance can assist in the design and dimen- sioning of telecommunications networks. However, exact determination can be difficult and generally cannot be done in reasonable time. For these reasons there is much interest in developing fast and accurate approximations. We develop a reduced load approximation that improves on the famous Erlang fixed point approximation (EFPA) in a variety of circumstances. We illustrate our results with reference to a range of networks for which the EFPA may be expected to perform badly.

Identification of a Golgi-localised GRIP domain protein from Arabidopsis thaliana

A family of Golgi-localised molecules was recently described in animals and fungi possessing extensive coiled regions and a short (similar to40 residues) conserved C-terminal domain, called the GRIP domain, which is responsible for their location to this organelle. Using the model plant Arabidopsis thaliana, we identified a gene (AtGRIP) encoding a putative GRIP protein. We demonstrated that the C-terminal domain from AtGRIP functions as a Golgi-targeting sequence in plant cells. Localisation studies in living cells expressing the AtGRIP fused to a DsRed2 fluorescent probe, showed extensive co-location with the Golgi marker alpha-mannosidase I in transformed tobacco protoplasts. GRIP-like sequences were also found in genomic databases of rice, maize, wheat and alfalfa, suggesting that this domain may be a useful Golgi marker for immunolocalisation studies. Despite low sequence identity amongst GRIP domains, the plant GRIP sequence was able to target to the Golgi of mammalian cells. Taken together, these data indicate that GRIP domain proteins might be implicated in a targeting mechanism that is conserved amongst eukaryotes.

New approximation for free surface flow of groundwater: capillarity correction

An existing capillarity correction for free surface groundwater flow as modelled by the Boussinesq equation is re-investigated. Existing solutions, based on the shallow flow expansion, have considered only the zeroth-order approximation. Here, a second-order capillarity correction to tide-induced watertable fluctuations in a coastal aquifer adjacent to a sloping beach is derived. A new definition of the capillarity correction is proposed for small capillary fringes, and a simplified solution is derived. Comparisons of the two models show that the simplified model can be used in most cases. The significant effects of higher-order capillarity corrections on tidal fluctuations in a sloping beach are also demonstrated. (c) 2004 Elsevier Ltd. All rights reserved.