Sources and mixing state of size-resolved elemental carbon particles in a European megacity: Paris

An Aerosol Time-Of-Flight Mass Spectrometer (ATOFMS) was deployed to investigate the size-resolved chemical composition of single particles at an urban background site in Paris, France, as part of the MEGAPOLI winter campaign in January/February 2010. ATOFMS particle counts were scaled to match coincident Twin Differential Mobility Particle Sizer (TDMPS) data in order to generate hourly size-resolved mass concentrations for the single particle classes observed. The total scaled ATOFMS particle mass concentration in the size range 150–1067 nm was found to agree very well with the sum of concurrent High-Resolution Time-of-Flight Aerosol Mass Spectrometer (HR-ToF-AMS) and Multi-Angle Absorption Photometer (MAAP) mass concentration measurements of organic carbon (OC), inorganic ions and black carbon (BC) (R2 = 0.91). Clustering analysis of the ATOFMS single particle mass spectra allowed the separation of elemental carbon (EC) particles into four classes: (i) EC attributed to biomass burning (ECbiomass), (ii) EC attributed to traffic (ECtraffic), (iii) EC internally mixed with OC and ammonium sulfate (ECOCSOx), and (iv) EC internally mixed with OC and ammonium nitrate (ECOCNOx). Average hourly mass concentrations for EC-containing particles detected by the ATOFMS were found to agree reasonably well with semi-continuous quantitative thermal/optical EC and optical BC measurements (r2 = 0.61 and 0.65–0.68 respectively, n = 552). The EC particle mass assigned to fossil fuel and biomass burning sources also agreed reasonably well with BC mass fractions assigned to the same sources using seven-wavelength aethalometer data (r2 = 0.60 and 0.48, respectively, n = 568). Agreement between the ATOFMS and other instrumentation improved noticeably when a period influenced by significantly aged, internally mixed EC particles was removed from the intercomparison. 88% and 12% of EC particle mass was apportioned to fossil fuel and biomass burning respectively using the ATOFMS data compared with 85% and 15% respectively for BC estimated from the aethalometer model. On average, the mass size distribution for EC particles is bimodal; the smaller mode is attributed to locally emitted, mostly externally mixed EC particles, while the larger mode is dominated by aged, internally mixed ECOCNOx particles associated with continental transport events. Periods of continental influence were identified using the Lagrangian Particle Dispersion Model (LPDM) "FLEXPART". A consistent minimum between the two EC mass size modes was observed at approximately 400 nm for the measurement period. EC particles below this size are attributed to local emissions using chemical mixing state information and contribute 79% of the scaled ATOFMS EC particle mass, while particles above this size are attributed to continental transport events and contribute 21% of the EC particle mass. These results clearly demonstrate the potential benefit of monitoring size-resolved mass concentrations for the separation of local and continental EC emissions. Knowledge of the relative input of these emissions is essential for assessing the effectiveness of local abatement strategies.

Aerosol properties associated with air masses arriving into the North East Atlantic during the 2008 Mace Head EUCAARI intensive observing period: an overview

As part of the EUCAARI Intensive Observing Period, a 4-week campaign to measure aerosol physical, chemical and optical properties, atmospheric structure, and cloud microphysics was conducted from mid-May to mid-June, 2008 at the Mace Head Atmospheric Research Station, located at the interface of Western Europe and the N. E. Atlantic and centered on the west Irish coastline. During the campaign, continental air masses comprising both young and aged continental plumes were encountered, along with polar, Arctic and tropical air masses. Polluted-continental aerosol concentrations were of the order of 3000 cm(-3), while background marine air aerosol concentrations were between 400-600 cm(-3). The highest marine air concentrations occurred in polar air masses in which a 15 nm nucleation mode, with concentration of 1100 cm(-3), was observed and attributed to open ocean particle formation. Continental air submicron chemical composition (excluding refractory sea salt) was dominated by organic matter, closely followed by sulphate mass. Although the concentrations and size distribution spectral shape were almost identical for the young and aged continental cases, hygroscopic growth factors (GF) and cloud condensation nuclei (CCN) to total condensation nuclei (CN) concentration ratios were significantly less in the younger pollution plume, indicating a more oxidized organic component to the aged continental plume. The difference in chemical composition and hygroscopic growth factor appear to result in a 40-50% impact on aerosol scattering coefficients and Aerosol Optical Depth, despite almost identical aerosol microphysical properties in both cases, with the higher values been recorded for the more aged case. For the CCN/CN ratio, the highest ratios were seen in the more age plume. In marine air, sulphate mass dominated the sub-micron component, followed by water soluble organic carbon, which, in turn, was dominated by methanesulphonic acid (MSA). Sulphate concentrations were highest in marine tropical air - even higher than in continental air. MSA was present at twice the concentrations of previously-reported concentrations at the same location and the same season. Both continental and marine air exhibited aerosol GFs significantly less than ammonium sulphate aerosol pointing to a significant organic contribution to all air mass aerosol properties.

Uniformly convergent finite element and finite difference methods for singularly perturbed ordinary differential equations

This thesis is concerned with uniformly convergent finite element and finite difference methods for numerically solving singularly perturbed two-point boundary value problems. We examine the following four problems: (i) high order problem of reaction-diffusion type; (ii) high order problem of convection-diffusion type; (iii) second order interior turning point problem; (iv) semilinear reaction-diffusion problem. Firstly, we consider high order problems of reaction-diffusion type and convection-diffusion type. Under suitable hypotheses, the coercivity of the associated bilinear forms is proved and representation results for the solutions of such problems are given. It is shown that, on an equidistant mesh, polynomial schemes cannot achieve a high order of convergence which is uniform in the perturbation parameter. Piecewise polynomial Galerkin finite element methods are then constructed on a Shishkin mesh. High order convergence results, which are uniform in the perturbation parameter, are obtained in various norms. Secondly, we investigate linear second order problems with interior turning points. Piecewise linear Galerkin finite element methods are generated on various piecewise equidistant meshes designed for such problems. These methods are shown to be convergent, uniformly in the singular perturbation parameter, in a weighted energy norm and the usual L2 norm. Finally, we deal with a semilinear reaction-diffusion problem. Asymptotic properties of solutions to this problem are discussed and analysed. Two simple finite difference schemes on Shishkin meshes are applied to the problem. They are proved to be uniformly convergent of second order and fourth order respectively. Existence and uniqueness of a solution to both schemes are investigated. Numerical results for the above methods are presented.

Uniformly convergent finite element methods for singularly perturbed parabolic partial differential equations

This thesis is concerned with uniformly convergent finite element methods for numerically solving singularly perturbed parabolic partial differential equations in one space variable. First, we use Petrov-Galerkin finite element methods to generate three schemes for such problems, each of these schemes uses exponentially fitted elements in space. Two of them are lumped and the other is non-lumped. On meshes which are either arbitrary or slightly restricted, we derive global energy norm and L2 norm error bounds, uniformly in the diffusion parameter. Under some reasonable global assumptions together with realistic local assumptions on the solution and its derivatives, we prove that these exponentially fitted schemes are locally uniformly convergent, with order one, in a discrete L∞norm both outside and inside the boundary layer. We next analyse a streamline diffusion scheme on a Shishkin mesh for a model singularly perturbed parabolic partial differential equation. The method with piecewise linear space-time elements is shown, under reasonable assumptions on the solution, to be convergent, independently of the diffusion parameter, with a pointwise accuracy of almost order 5/4 outside layers and almost order 3/4 inside the boundary layer. Numerical results for the above schemes are presented. Finally, we examine a cell vertex finite volume method which is applied to a model time-dependent convection-diffusion problem. Local errors away from all layers are obtained in the l2 seminorm by using techniques from finite element analysis.

Variations in total and differential milk somatic cell counts and plasmin levels and their role in proteolysis and quality of milk and cheese

Increased plasmin and plasminogen levels and elevated somatic cell counts (SCC) and polymorphonuclear leucocyte levels (PMN) were evident in late lactation milk. Compositional changes in these milks were associated with increased SCC. The quality of late lactation milks was related to nutritional status of herds, with milks from herds on a high plane of nutrition having composition and clotting properties similar to, or superior to, early-mid lactation milks. Nutritionally-deficient cows had elevated numbers of polymorphonuclear leucocytes (PMNs) in their milk, elevated plasmin levels and increased overall proteolytic activity. The dominant effect of plasmin on proteolysis in milks of low SCC was established. When present in elevated numbers, somatic cells and PMNs in particular had a more significant influence on the proteolysis of both raw and pasteurised milks than plasmin. PMN protease action on the caseins showed proteolysis products of two specific enzymes, cathepsin B and elastase, which were also shown in high SCC milk. Crude extracts of somatic cells had a high specificity on αs1-casein. Cheeses made from late lactation milks had increased breakdown of αs1-casein, suggestive of the action of somatic cell proteinases, which may be linked to textural defects in cheese. Late lactation cheeses also showed decreased production of small peptides and amino acids, the reason for which is unknown. Plasmin, which is elevated in activity in late lactation milk, accelerated the ripening of Gouda-type cheese, but was not associated with defects of texture or flavour. The retention of somatic cell enzymes in cheese curd was confirmed, and a potential role in production of bitter peptides identified. Cheeses made from milks containing high levels of PMNs had accelerated αs1-casein breakdown relative to cheeses made from low PMN milk of the same total SCC, consistent with the demonstrated action of PMN proteinases. The two types of cheese were determined significantly different by blind triangle testing.

Differential and numerical models of hysteretic systems with stochastic and deterministic inputs

Many deterministic models with hysteresis have been developed in the areas of economics, finance, terrestrial hydrology and biology. These models lack any stochastic element which can often have a strong effect in these areas. In this work stochastically driven closed loop systems with hysteresis type memory are studied. This type of system is presented as a possible stochastic counterpart to deterministic models in the areas of economics, finance, terrestrial hydrology and biology. Some price dynamics models are presented as a motivation for the development of this type of model. Numerical schemes for solving this class of stochastic differential equation are developed in order to examine the prototype models presented. As a means of further testing the developed numerical schemes, numerical examination is made of the behaviour near equilibrium of coupled ordinary differential equations where the time derivative of the Preisach operator is included in one of the equations. A model of two phenotype bacteria is also presented. This model is examined to explore memory effects and related hysteresis effects in the area of biology. The memory effects found in this model are similar to that found in the non-ideal relay. This non-ideal relay type behaviour is used to model a colony of bacteria with multiple switching thresholds. This model contains a Preisach type memory with a variable Preisach weight function. Shown numerically for this multi-threshold model is a pattern formation for the distribution of the phenotypes among the available thresholds.

Dilute nitride semiconductors : band structure, scattering and high field transport

The substitution of a small fraction x of nitrogen atoms, for the group V elements in conventional III-V semiconductors such as GaAs and GaSb strongly perturbs the conduction band of the host semiconductor. In this thesis we investigate the effects of nitrogen states on the band dispersion, carrier scattering and mobility of dilute nitride alloys. In the supercell model we solve the single particle Hamiltonian for a very large supercell containing randomly placed nitrogen. This model predicts a gap in the density of states of GaNxAs1−x, where this gap is filled in the Green’s function model. Therefore we develop a self-consistent Green’s function (SCGF) approach, which provides excellent agreement with supercell calculations and reveals a gap in the DOS, in contrast with the results of previous non-self-consistent Green’s function calculations. However, including the distribution of N states destroys this gap, as seen in experiment. We then examine the high field transport of carriers by solving the steadystate Boltzmann transport equation and find that it is necessary to include the full distribution of N levels in order to account for the small, low-field mobility and the absence of a negative differential velocity regime observed experimentally with increasing x. Overall the results account well for a wide range of experimental data. We also investigate the band structure, scattering and mobility of carriers by finding the poles of the SCGF, which gives lower carrier mobility for GaNxAs1−x, compared to those already calculated, in better agreement with experiments. The calculated optical absorption spectra for InyGa1−yNxAs1−x and GaNxSb1−x using the SCGF agree well with the experimental data, confirming the validity of this approach to study the band structure of these materials.