A survey of partial differential equations in geometric design

Computer-aided geometric design is an area where the improvement of surface generation techniques is an everlasting demand, since faster and more accurate geometric models are required. Traditional methods for generating surfaces were initially mainly based upon interpolation algorithms. Recently, partial differential equations (PDE) were introduced as a valuable tool for geometric modelling, since they offer a number of features from which these areas can benefit. This work summarizes the uses given to PDE surfaces as a surface generation technique together with some other applications to computer graphics.     

Spatial Distributions of Legacy Contaminants in Sediments of Lakes Huron and Superior

The sediments of Lake Superior, Lake Huron, and Georgian Bay were sampled in 2001 and 2002 in order to evaluate the extent of surficial sediment contamination of polychlorinated biphenyls (PCBs), organochlorine pesticides (OCs), polycyclic aromatic hydrocarbons (PAHs), and metals. Sediment concentrations of PCBs, OCs, PAHs, and mercury were generally low and up to 2 orders of magnitude less than in Lakes Erie and Ontario. In contrast, concentrations of metals such as arsenic, copper, and nickel were comparable to those in Lakes Erie and Ontario. These elevated Lakes Superior and Huron metal concentrations were attributed to naturally occurring metals within the bedrock, soil, and sediment of the study region. Concentrations of all contaminants were typically below the Canadian Sediment Quality Probable Effect Level (PEL) guidelines. With regard to spatial patterns, most contaminants were focused primarily in the depositional basins and atmospheric deposition was likely the major source of these chemicals to the lakes. The major exception was for metals (not including mercury) whose patterns were also influenced by natural sources as well as extensive mining activity. A comparison between surficial sediment contamination of samples collected as part of this survey and those collected in the late 1960s/early 1970s using similar methods showed that concentrations of DDT, PCB, lead, and mercury were generally similar between these two time periods. These results are not consistent with production and usage patterns that have declined substantially in the past 3 decades. We hypothesize that the lack of temporal trends is an artifact due to slow sediment accumulation rates as well as differences in analytical protocols between the two time periods.     

Kinematic instabilities in two-layer eccentric annular flows,part 1: Newtonian fluids

Primary-cementing displacement flows occur in long narrow eccentric annuli during the construction of oil and gas wells. A common problem is that the displacing fluid fingers up the upper wide side of the annulus, leaving behind a “mud channel” of displaced fluid on the lower narrow side of the annulus. Tehrani et al. report that the interface between displacing fluid and mud channel can in certain circumstances become unstable, and a similar phenomenon has been observed in our ongoing experiments. Here an explanation for these instabilities is provided via analysis of the stability of two-layer eccentric annular Hele-Shaw flows, using a transient version of the usual Hele-Shaw approach, in which fluid acceleration terms are retained. Two Newtonian fluids are considered, as a simplification of the general case in which the fluids are shear-thinning yield-stress fluids. It is shown that negative azimuthal buoyancy gradients are in general stabilizing in inclined wells, but that buoyancy may also have a destabilizing effect via axial buoyancy forces that influence the base-flow interfacial velocity. In a variety of special cases where buoyancy is not dominant, it is found that instability is suppressed by a positive product of interfacial velocity difference and reduced Reynolds-number difference between fluids. Even a small positive azimuthal buoyancy gradient, (heavy fluid over light fluid), can be stabilized in this way. Eccentricity of the annulus seems to amplify the effect of buoyancy on stability or instability, e.g. stably stratified fluid layers become more stable as the eccentricity is increased.     

Pressed booster compositions prepared by coating RDX using polymer dispersions

Abstract

The viability of preparing booster compositions from RDX and commercially available aqueous polyurethane, acrylic and ethylene-vinyl acetate dispersions has been assessed. These dispersions were coagulated in hot aqueous slurries of RDX by electrolyte addition and the use of thermal coagulation aids. When polymer coating of the RDX crystals occurred the precipitated polymer particles were deposited across the surfaces of the crystals. These coatings were often porous; however when softer polymers were used, coalescence occurred and more uniform coatings were obtained. Compositions containing these softer polymers were less sensitive to initiation by shock and impact. The flow properties of these compositions were usually improved by applying an additional coating of zinc stearate. The impact sensitiveness, shock sensitivity and cookoff behaviour of a number of candidate booster compositions have been assessed and suitable compositions have been identified.     

Selective oxidation of styrenes under oxygen catalyzed by cobalt chloride

The cobalt(II) chloride-catalyzed oxidative cleavage of -methylstyrene with oxygen in t-BuOH gives acetophenone and formaldehyde in good yield. The competing reactions between C=C cleavage and formation of polymeric products are strongly affected by the solvent, cobalt catalyst and concentration used, as well as the reaction temperature. A free radical mechanism involving a cyclic peroxide intermediate is proposed to give the cleavage products. Oxidation of various alkenes using CoCl₂/t-BuOH/O₂ system shows that only activated styrenes can be oxidized effectively. The reactivity of various styrenes and their selectivity towards giving cleavage products or polymers are strongly influenced by the electronic and steric properties of the substrate.     

A comparison of the electro-osmotic properties of charged polymer membranes and those predicted from binary electrolyte solution models Part I. Univalent forms of sulphonate membranes and chloride electrolyte models

By changing from the usual solvent-fixed frame of reference for flows to one based upon a fixed anion, electro-osmotic transference numbers are defined for any electrolyte, for which transport numbers are known. For sulphonate membranes, chloride electrolyte analogues were chosen. Agreement between observed transference numbers and those of the model electrolytes are shown to be excellent for both polystyrene based and perfluoro-sulphonic acid membranes.From irreversible thermodynamics it is shown that the transference number for any membrane will have a maximum value equal to the molar ratio of water to fixed charge in the membrane and independent of ionic form. The observed value is in addition, proportional to the fraction of the total water friction, which is due to water interaction with counterion. It is the latter which is estimated successfully from model electrolytes. The ionic forms used were Li⁺, Na⁺, K⁺, Rb⁺, Cs⁺ and H⁺ at 25°C in membranes in which electrolyte exclusion was almost complete.     

The Instabilisation of Dye-Fibre Bonds by Peroxide Treatments

The results are presented of an investigation into the instability induced in dye-fibre bonds by peroxide treatments. The nature of the reactions involved are discussed.     

Property-composition relationships for diesel and kerosene fuels

A range of 18 diesel fuels and 21 kerosene fuels from mainly Australian petroleum and synthetic fuel sources, including coal, shale and peat, was investigated. Compositional details were defined as the weight per cent abundances of n-alkanes, branched plus cyclic saturates, single-ring aromatics, doublering aromatics and polynuclear aromatics, using both h.p.l.c. and ¹³C n.m.r. techniques. Relationships between fuel composition and a range of fuel properties were sought. Simple linear relationships between property values and compositional data were used. Explicit correlative expressions were derived using multiple linear regression analysis, with the coefficient of multiple determination, R², indicating the quality of the fit between observed and calculated property values. In most cases good correlations were achieved. For diesels the properties investigated, with R² values in parentheses, were: inverse specific gravity (0.99); ¹³C n.m.r. aromaticity (0.99); ¹H n.m.r. aromaticity (0.88); cetane index (0.97); aniline point (0.96); diesel index (0.98); and FIA-measured aromatics content (0.77). For kerosenes the properties, with R² values in parentheses, were: ¹³C n.m.r. aromaticity (0.98); ¹H n.m.r. aromaticity (0.97); smoke point (0.88); and FIA-measured aromatics content (0.94). The results are shown to be of value in assessing the potential and limitations of hydrotreating as a process for upgrading synfuels.