219 resultados para Mathematical English
Resumo:
The purpose of this study was to mathematically characterize the effects of defined experimental parameters (probe speed and the ratio of the probe diameter to the diameter of sample container) on the textural/mechanical properties of model gel systems. In addition, this study examined the applicability of dimensional analysis for the rheological interpretation of textural data in terms of shear stress and rate of shear. Aqueous gels (pH 7) were prepared containing 15% w/w poly(methylvinylether-co-maleic anhydride) and poly(vinylpyrrolidone) (PVP) (0, 3, 6, or 9% w/w). Texture profile analysis (TPA) was performed using a Stable Micro Systems texture analyzer (model TA-XT 2; Surrey, UK) in which an analytical probe was twice compressed into each formulation to a defined depth (15 mm) and at defined rates (1, 3, 5, 8, and 10 mm s-1), allowing a delay period (15 s) between the end of the first and beginning of the second compressions. Flow rheograms were performed using a Carri-Med CSL2-100 rheometer (TA Instruments, Surrey, UK) with parallel plate geometry under controlled shearing stresses at 20.0°?±?0.1°C. All formulations exhibited pseudoplastic flow with no thixotropy. Increasing concentrations of PVP significantly increased formulation hardness, compressibility, adhesiveness, and consistency. Increased hardness, compressibility, and consistency were ascribed to enhanced polymeric entanglements, thereby increasing the resistance to deformation. Increasing probe speed increased formulation hardness in a linear manner, because of the effects of probe speed on probe displacement and surface area. The relationship between formulation hardness and probe displacement was linear and was dependent on probe speed. Furthermore, the proportionality constant (gel strength) increased as a function of PVP concentration. The relationship between formulation hardness and diameter ratio was biphasic and was statistically defined by two linear relationships relating to diameter ratios from 0 to 0.4 and from 0.4 to 0.563. The dramatically increased hardness, associated with diameter ratios in excess of 0.4, was accredited to boundary effects, that is, the effect of the container wall on product flow. Using dimensional analysis, the hardness and probe displacement in TPA were mathematically transformed into corresponding rheological parameters, namely shearing stress and rate of shear, thereby allowing the application of the power law (??=?k?n) to textural data. Importantly, the consistencies (k) of the formulations, calculated using transformed textural data, were statistically similar to those obtained using flow rheometry. In conclusion, this study has, firstly, characterized the relationships between textural data and two key instrumental parameters in TPA and, secondly, described a method by which rheological information may be derived using this technique. This will enable a greater application of TPA for the rheological characterization of pharmaceutical gels and, in addition, will enable efficient interpretation of textural data under different experimental parameters.
Resumo:
Phylogeography has provided a new approach to the analysis of the postglacial history of a wide range of taxa but, to date, little is known about the effect of glacial periods on the marine biota of Europe. We have utilized a combination of nuclear, plastid and mitochondrial genetic markers to study the biogeographic history of the red seaweed Palmaria palmata in the North Atlantic. Analysis of the nuclear rDNA operon (ITS1-5.8S-ITS2), the plastid 16S-trnI-trnA-23S-5S, rbcL-rbcS and rpl12-rps31-rpl9 regions and the mitochondrial cox2–3 spacer has revealed the existence of a previously unidentified marine refugium in the English Channel, along with possible secondary refugia off the southwest coast of Ireland and in northeast North America and/or Iceland. Coalescent and mismatch analyses date the expansion of European populations from approximately 128 000 bp and suggest a continued period of exponential growth since then. Consequently, we postulate that the penultimate (Saale) glacial maximum was the main event in shaping the biogeographic history of European P. palmata populations which persisted throughout the last (Weichselian) glacial maximum (c. 20 000 bp) in the Hurd Deep, an enigmatic trench in the English Channel.