On the convergence of the no response test

The no response test is a new scheme in inverse problems for partial differential equations which was recently proposed in [D. R. Luke and R. Potthast, SIAM J. Appl. Math., 63 (2003), pp. 1292–1312] in the framework of inverse acoustic scattering problems. The main idea of the scheme is to construct special probing waves which are small on some test domain. Then the response for these waves is constructed. If the response is small, the unknown object is assumed to be a subset of the test domain. The response is constructed from one, several, or many particular solutions of the problem under consideration. In this paper, we investigate the convergence of the no response test for the reconstruction information about inclusions D from the Cauchy values of solutions to the Helmholtz equation on an outer surface $\partial\Omega$ with $\overline{D} \subset \Omega$. We show that the one‐wave no response test provides a criterion to test the analytic extensibility of a field. In particular, we investigate the construction of approximations for the set of singular points $N(u)$ of the total fields u from one given pair of Cauchy data. Thus, the no response test solves a particular version of the classical Cauchy problem. Also, if an infinite number of fields is given, we prove that a multifield version of the no response test reconstructs the unknown inclusion D. This is the first convergence analysis which could be achieved for the no response test.

Conducting nanofibres produced by electrospinning

Electrospun fibres based on polypyrrole have been prepared. The incorporation of preformed polypyrrole into fibres electrospun from a carrier polymer can only be achieved when materials are prepared with particulates smaller than the cross-section of the fibre; even so there are some problems, with the substantial loss of material from the electrode tip. As an alternative approach, soluble polypyrroles can be prepared but these are not of sufficient viscosity to prepare electrospun fibres, once again a carrier polymer must be employed. More effective loadings are gained by the process of coating the outer surface of a pre-spun fibre; in this way electrospun fibres coated with polypyrrole can be prepared. This approach has been adapted to produce silver coated polymer fibres by the use of copolymers of styrene and 3-vinyl benzaldehyde.

A calibrated, non-invasive method for measuring the internal interface height field at high resolution in the rotating, two-layer annulus

We describe a remote sensing method for measuring the internal interface height field in a rotating, two-layer annulus laboratory experiment. The method is non-invasive, avoiding the possibility of an interaction between the flow and the measurement device. The height fields retrieved are accurate and highly resolved in both space and time. The technique is based on a flow visualization method developed by previous workers, and relies upon the optical rotation properties of the working liquids. The previous methods returned only qualitative interface maps, however. In the present study, a technique is developed for deriving quantitative maps by calibrating height against the colour fields registered by a camera which views the flow from above. We use a layer-wise torque balance analysis to determine the equilibrium interface height field analytically, in order to derive the calibration curves. With the current system, viewing an annulus of outer radius 125 mm and depth 250 mm from a distance of 2 m, the inferred height fields have horizontal, vertical and temporal resolutions of up to 0.2 mm, 1 mm and 0.04 s, respectively.

Decomposition in soil and chemical characteristics of pollen

The input to soils made by pollen and its subsequent mineralization has rarely been investigated from a soil microbiological point of view even though the small but significant quantities of C and N in pollen may make an important contribution to nutrient cycling. The relative resistance to decomposition of pollen exines (outer layers) has led to much of the focus of pollen in soil being on its preservation for archaeological and palaeo-ecological purposes. We have examined aspects of the chemical composition and decomposition of pollen from birch (Betula alba) and maize (Zea mays) in soil. The relatively large N contents, small C-to-N ratios and large water-soluble contents of pollen from both species indicated that they would be readily mineralized in soil. When added to soil and incubated at 16 degrees C an amount of C equivalent to 22-26% of the added pollen C was lost as CO2 within 22 days, with the Z. mays pollen decomposing faster. For B. alba pollen, the water-soluble fraction decomposed faster than the whole pollen and the insoluble fraction decomposed more slowly over 22 days. By contrast, there were no significant differences in the decomposition rates of the different fractions from Z. mays pollen. Solid-state C-13 nuclear magnetic resonance (NMR) revealed no gross chemical differences between the pollen of these two species, with strong resonances in the alkyl- and methyl-C region (0-45 p.p.m.) indicative of aliphatic compounds, the O-alkyl-C (60-90 p.p.m.) and the acetal- and ketal-C region (90-110 p.p.m.) indicative of polysaccharides, and the carbonyl-C region indicative of peptides and carboxylic acids. In addition, both pollens gave a small but distinct resonance at 55 p.p.m. attributed to N-alkyl-C. The resonances attributed to polysaccharides were lost completely or substantially reduced after decomposition.

Characterization of mineral surfaces using FIB and TEM: a case study of naturally weathered alkali feldspars

Using a focused ion beam (FIB) instrument, electron-transparent samples (termed foils) have been cut from the naturally weathered surfaces of perthitic alkali feldspars recovered from soils overlying the Shap granite, northwest England. Characterization of these foils by transmission electron microscopy (TEM) has enabled determination of the crystallinity and chemical composition of near-surface regions of the feldspar and an assessment of the influence of intragranular microtextures on the microtopography of grain surfaces and development of etch pits. Damage accompanying implantation of the 30 kV Ga+ ions used for imaging and deposition of protective platinum prior to ion milling creates amorphous layers beneath outer grain surfaces, but can be overcome by coating grains with > 85 nm of gold before FIB work. The sidewalls of the foil and feldspar surrounding original voids are also partially amorphized during later stages of ion milling. No evidence was found for the presence of amorphous or crystalline weathering products or amorphous "leached layers" immediately beneath outer grain surfaces. The absence of a leached layer indicates that chemical weathering of feldspar in the Shap soils is stoichiometric, or if non-stoichiometric, either the layer is too thin to resolve by the TEM techniques used (i.e., <=similar to 2.5 nm) or an insufficient proportion of ions have been leached from near-surface regions so that feldspar crystallinity is maintained. No evidence was found for any difference in the mechanisms of weathering where a microbial filament rests on the feldspar surface. Sub-micrometer-sized steps on the grain surface have formed where subgrains and exsolution lamellae have influenced the propagation of fractures during physical weathering, whereas finer scale corrugations form due to compositional or strain-related differences in dissolution rates of albite platelets and enclosing tweed orthoclase. With progressive weathering, etch pits that initiated at the grain surface extend into grain interiors as etch tubes by exploiting preexisting networks of nanopores that formed during the igneous history of the grain. The combination of FIB and TEM techniques is an especially powerful way of exploring mechanisms of weathering within the "internal zone" beneath outer grain surfaces, but results must be interpreted with caution owing to the ease with which artifacts can be created by the high-energy ion and electron beams used in the preparation and characterization of the foils.

The Soil: Nature, Sustainable Use, Management, and Protection - An Overview

Soil forms the outer skin of the earth's land surface. Often less than a metre in depth, it is essential to sustain natural terrestrial ecosystems and human life. Soils result from the interactions over time between climate, parent material, topography, vegetation, and biota. They vary from place to place. Mineral soils are composed of mineral matter, organic matter, and gas- or liquid-filled pores in varying proportions. Soils perform a wide range of functions and provide many ecosystem or environmental services; with the climate problem, the soil is increasingly being recognised as a potential sink for carbon from the atmosphere. In part because of humankind's (over)use of soils and in part because of natural and human-induced environmental change, there is a widespread decline in soil quality and an increasing number of threats to soil, which jeopardise both the soil's natural functions and its use by humans. As a limited resource, soils must be used sustainably. Soil protection strategies have been indirectly embodied in a number of United Nations conventions, and there are now national and supranational developments towards specific regulations and legislation to protect soils and their functions.

Seascapes and landscapes in Orkney and northern Scotland

Much of what has been written and researched about the chambered cairns of Orkney and northern mainland Scotland has concentrated on constructing complex monument typologies. This paper investigates the monuments' locations with specific reference to the sea, especially their visibility. Indeed, in relation to location and visibility, it is the outer form of the monuments that makes the greatest perceptual impact. A complex typology of monument forms is abandoned in favour of two basic and distinct types: round and elongated cairns. The cairns in both areas are sited in similar topographical locations. In Orkney many were located to be visible from the sea, in mainland northern Scotland they were sited to be visible from the likely areas of settlement.

Adsorption of water vapor by bare soil in an olive grove in southern Spain

Data for water vapor adsorption and evaporation are presented for a bare soil (sandy loam, clay content 15%) in a southern Spanish olive grove. Water losses and gains were measured using eight high-precision minilysimeters, placed around an olive tree, which had been irrigated until the soil reached field capacity (similar to 0.22 m(3) m(-3)). They were subsequently left to dry for 10 days. A pair of lysimeters was situated at each of the main points of the compass (N, E, S, W), at a distance of 1 m (the inner set of lysimeters; ILS) and 2 m (the outer set of lysimeters; OLS), respectively, from the tree trunk. Distinct periods of moisture loss (evaporation) and moisture gain (vapor adsorption) could be distinguished for each day. Vapor adsorption often started just after noon and generally lasted until the (early) evening. Values of up to 0.7 mm of adsorbed water per day were measured. Adsorption was generally largest for the OLS (up to 100% more on a daily basis), and increased during the dry down. This was mainly the result of lower OLS surface soil moisture contents (period-average absolute difference similar to 0.005 m(3) m(-3)), as illustrated using various analyses employing a set of micrometeorological equations describing the exchange of water vapor between bare soil and the atmosphere. These analyses also showed that the amount of water vapor adsorbed by soils is very sensitive to changes in atmospheric forcing and surface variables. The use of empirical equations to estimate vapor adsorption is therefore not recommended.

Decomposition in soil and chemical characteristics of pollen

The input to soils made by pollen and its subsequent mineralization has rarely been investigated from a soil microbiological point of view even though the small but significant quantities of C and N in pollen may make an important contribution to nutrient cycling. The relative resistance to decomposition of pollen exines (outer layers) has led to much of the focus of pollen in soil being on its preservation for archaeological and palaeo-ecological purposes. We have examined aspects of the chemical composition and decomposition of pollen from birch (Betula alba) and maize (Zea mays) in soil. The relatively large N contents, small C-to-N ratios and large water-soluble contents of pollen from both species indicated that they would be readily mineralized in soil. When added to soil and incubated at 16 degrees C an amount of C equivalent to 22-26% of the added pollen C was lost as CO2 within 22 days, with the Z. mays pollen decomposing faster. For B. alba pollen, the water-soluble fraction decomposed faster than the whole pollen and the insoluble fraction decomposed more slowly over 22 days. By contrast, there were no significant differences in the decomposition rates of the different fractions from Z. mays pollen. Solid-state C-13 nuclear magnetic resonance (NMR) revealed no gross chemical differences between the pollen of these two species, with strong resonances in the alkyl- and methyl-C region (0-45 p.p.m.) indicative of aliphatic compounds, the O-alkyl-C (60-90 p.p.m.) and the acetal- and ketal-C region (90-110 p.p.m.) indicative of polysaccharides, and the carbonyl-C region indicative of peptides and carboxylic acids. In addition, both pollens gave a small but distinct resonance at 55 p.p.m. attributed to N-alkyl-C. The resonances attributed to polysaccharides were lost completely or substantially reduced after decomposition.

Orographic Enhancement of Precipitation inside Hurricane Dean

On 17 August 2007, the center of Hurricane Dean passed within 92 km of the mountainous island of Dominica in the West Indies. Despite its distance from the island and its category 1–2 state, Dean brought significant total precipitation exceeding 500 mm and caused numerous landslides. Four rain gauges, a Moderate Resolution Imaging Spectroradiometer (MODIS) image, and 5-min radar scans from Guadeloupe and Martinique are used to determine the storm’s structure and the mountains’ effect on precipitation. The encounter is best described in three phases: (i) an east-northeast dry flow with three isolated drifting cells; (ii) a brief passage of the narrow outer rainband; and (iii) an extended period with south-southeast airflow in a nearly stationary spiral rainband. In this final phase, from 1100 to 2400 UTC, heavy rainfall from the stationary rainband was doubled by orographic enhancement. This enhancement pushed the sloping soils past the landslide threshold. The enhancement was caused by a modified seeder–feeder accretion mechanism that created a “dipole” pattern of precipitation, including a dry zone over the ocean in the lee. In contrast to normal trade-wind conditions, no terrain triggering of convection was identified in the hurricane environment.

The unsteady flow of a weakly compressible fluid in a thin porous layer. I: Two-dimensional theory

We consider the problem of determining the pressure and velocity fields for a weakly compressible fluid flowing in a two-dimensional reservoir in an inhomogeneous, anisotropic porous medium, with vertical side walls and variable upper and lower boundaries, in the presence of vertical wells injecting or extracting fluid. Numerical solution of this problem may be expensive, particularly in the case that the depth scale of the layer h is small compared to the horizontal length scale l. This is a situation which occurs frequently in the application to oil reservoir recovery. Under the assumption that epsilon=h/l<<1, we show that the pressure field varies only in the horizontal direction away from the wells (the outer region). We construct two-term asymptotic expansions in epsilon in both the inner (near the wells) and outer regions and use the asymptotic matching principle to derive analytical expressions for all significant process quantities. This approach, via the method of matched asymptotic expansions, takes advantage of the small aspect ratio of the reservoir, epsilon, at precisely the stage where full numerical computations become stiff, and also reveals the detailed structure of the dynamics of the flow, both in the neighborhood of wells and away from wells.

The variation of solar wind correlation lengths over three solar cycles

We present the results of a study of solar wind velocity and magnetic field correlation lengths over the last 35 years. The correlation length of the magnetic field magnitude λ | B| increases on average by a factor of two at solar maxima compared to solar minima. The correlation lengths of the components of the magnetic field λ_{B_{XYZ}} and of the velocity λ_{V_{YZ}} do not show this change and have similar values, indicating a continual turbulent correlation length of around 1.4×106 km. We conclude that a linear relation between λ | B|, VB 2, and Kp suggests that the former is related to the total magnetic energy in the solar wind and an estimate of the average size of geoeffective structures, which is, in turn, proportional to VB 2. By looking at the distribution of daily correlation lengths we show that the solar minimum values of λ | B| correspond to the turbulent outer scale. A tail of larger λ | B| values is present at solar maximum causing the increase in mean value.

On the evolution of the solar wind between 1 and 5 AU at the time of the Cassini Jupiter flyby: Multispacecraft observations of interplanetary coronal mass ejections including the formation of a merged interaction region

The Cassini flyby of Jupiter occurred at a time near solar maximum. Consequently, the pre-Jupiter data set reveals clear and numerous transient perturbations to the Parker Spiral solar wind structure. Limited plasma data are available at Cassini for this period due to pointing restrictions imposed on the instrument. This renders the identification of the nature of such structures ambiguous, as determinations based on the magnetic field data alone are unreliable. However, a fortuitous alignment of the planets during this encounter allowed us to trace these structures back to those observed previously by the Wind spacecraft near the Earth. Of the phenomena that we are satisfactorily able to trace back to their manifestation at 1 AU, two are identified as being due to interplanetary coronal mass ejections. One event at Cassini is shown to be a merged interaction region, which is formed from the compression of a magnetic cloud by two anomalously fast solar wind streams. The flux-rope structure associated with this magnetic cloud is not as apparent at Cassini and has most likely been compressed and deformed. Confirmation of the validity of the ballistic projections used here is provided by results obtained from a one-dimensional magnetohydrodynamic projection of solar wind parameters measured upstream near the Earth. It is found that when the Earth and Cassini are within a few tens of degrees in heliospheric longitude, the results of this one-dimensional model predict the actual conditions measured at 5 AU to an impressive degree. Finally, the validity of the use of such one-dimensional projections in obtaining quasi-solar wind parameters at the outer planets is discussed.