A pilot study to assess soil spectroscopic methods for mapping key topsoil properties in the Blackwater sub-catchments (Wensum DTC)

This report describes findings from sampling and analyses of soils across the Blackwater drain catchments, part of the Wensum demonstration test catchment (DTC) project funded by Defra. Recent studies have shown how spectroscopic techniques can be used to estimate soil properties and airborne spectroscopy could be an effective means to aid continuous mapping of soil properties across the landscape. Before an airborne survey is undertaken it is important to assess whether the relationships between infra red (IR) spectra and soil properties are sufficiently strong for the cost of the airborne survey to be justified. A secondary objective was to determine the concentrations of soil organic carbon (SOC) in soils across the cultivated parts of the catchment to determine whether there is any evidence that low SOC concentrations might indicate that the topsoil may exhibit poor structural stability contributing to enhanced sediment in stream and drainage channels

A bifurcated circular waveguide problem

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in IMA Journal of Applied Mathematics following peer review. The definitive publisher-authenticated version A D Rawlins. A bifurcated circular waveguide problem. J.I.M.A. 54 (1995) 59-81. Oxford University press is available online at: http://imamat.oxfordjournals.org/cgi/reprint/54/1/59.pdfA rigorous and exact solution is obtained for the problem of the radiation of sound from a semi-infinite rigid duct inserted axially into a larger acoustically lined tube of infinite length. The solution to this problem is obtained by the Wiener-Hopf technique. The transmission and reflection coefficients, when the fundamental mode propagates in the semi-infinite tube, are obtained. The present results could be of use for exhaust design, and as a possible instrument for impedance measurement

A note on Wiener-Hopf matrix factorisation

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Quarterly Journal of Mechanics and Applied Mathematics following peer review. The definitive publisher-authenticated version Rawlins, A D (1985). A note on Wiener-Hopf matrix factorisation. Quarterly Journal of Mechanics and Applied Mathematics. 38 (3) 433-437 is available online at: http://qjmam.oxfordjournals.org/cgi/reprint/38/3/433.pdfIn this paper the most general class of 2 x 2 matrices is determined which permit a Wiener-Hopf factorization by the procedure of Rawlins and Williams (1). According to this procedure, the factorization problem is reduced to a matrix Hilbert problem on a half-line, where the matrix involved in the Hilbert problem is required to have zero diagonal elements

In bloom

Much of the phosphorus which ends up in stream sediment, either through soil erosion or via field drains, is transported attached to particles. The quantity and chemical form of phosphorus in the stream sediment largely controls its concentration in stream water. The phosphorus in the sediments is associated with particular components such as organic matter, iron-bearing minerals and clay minerals

The optimum orientation of an absorbing barrier

In the following work, we solve the problem of the best orientation of a rigid noise barrier, which has one face lined with absorbent material, between a noise source and a receiver point in the shadow region of the barrier. By the ‘best orientation’, we mean that positioning of the barrier which yields the least noise level at the receiving point for a given barrier and source position

Approximate boundary conditions for diffraction by thin transmissive media

The object of this note is to describe a method that can be used to obtain useful boundary conditions to model various situations that arise in diffraction theory. In particular when wanting to apply the Wiener-Hopf technique to diffraction problems that involve thin transmissive media. Transmissive here means that the thin layer medium suffers a change in the physical quantities of density, acoustic velocity, and wave number from the surrounding medium. The present approach can be used to obtain approximate boundary conditions for other physical applications where thin strata of transmissive material arise

On the roots of a Bessel function equation (problem)

For the abstract of this paper, please see the PDF file

A Green's function for diffraction by a rational wedge

In this paper we derive an expression for the point source Green's function for the reduced wave equation, valid in an angular sector whose angle is equal to a rational multiple of 77. This Green's function can be used to find new expressions for the field produced by the diffraction of a spherical wave by a wedge whose angle can be expressed as a rational multiple of n. The expressions obtained will be in the form of source terms and real integrals representing the diffracted field. The general result obtained is used to derive a new representation for the solution of the problem of diffraction by a mixed hard-soft half plane

A note on point source diffraction by a wedge

The object of this paper is to give new expressions for the wave field produced when a time harmonic point source is diffracted by a wedge with Dirichlet or Neumann boundary conditions on its faces. The representation of the total field is expressed in terms of quadratures of elementary functions, rather than Bessel functions, which is usual in the literature. An analogous expression is given for the three-dimensional free-space Green's function