7 resultados para Geometry of numbers
em Greenwich Academic Literature Archive - UK
Resumo:
Rhodanines (2-thio-4-oxothiazolidines) are synthetic small molecular weight organic molecules with diverse applications in biochemistry, medicinal chemistry, photochemistry, coordination chemistry and industry. The X-ray crystal structure determination of two rhodanine derivatives, namely (I), 3-aminorhodanine [3-amino-2-thio-4-oxothiazolidine], C3H4N2OS2, and (II) 3-methylrhodanine [3-methyl-2-thio-4-oxothiazolidine], C4H5NOS2, have been conducted at 100 K. I crystallizes in the monoclinic space group P2(1)/n with unit cell parameters a = 9.662(2), b = 9.234(2), c = 13.384(2) angstrom, beta = 105.425(3)degrees, V = 1151.1(3) angstrom(3), Z = 8 (2 independent molecules per asymmetric unit), density (calculated) = 1.710 mg/m(3), absorption coefficient = 0.815 mm(-1). II crystallizes in the orthorhombic space group Iba2 with unit cell a = 20.117(4), b = 23.449(5), c = 7.852(2) angstrom, V = 3703.9(12) angstrom(3), Z = 24 (three independent molecules per asymmetric unit), density (calculated) = 1.584 mg/m(3), absorption coefficient 0.755 mm(-1). For I in the final refinement cycle the data/restraints/parameter ratios were 2639/0/161, goodness-of-fit on F-2 = 0.934, final R indices [I > 2sigma(I)] were R1 = 0.0299, wR2 = 0.0545 and R indices (all data) R1 = 0.0399, wR2 = 0.0568. The largest difference peak and hole were 0.402 and -0.259 e angstrom(-3). For II in the final refinement cycle the data/restraints/parameter ratios were 3372/1/221, goodness-of-fit on F(2) = 0.950, final R indices [I > 2sigma(I)] were R1 = 0.0407, wR2 = 0.1048 and R indices (all data) R1 = 0.0450, wR2 = 0.1088. The absolute structure parameter = 0.19(9) and largest difference peak and hole 0.934 and -0.301 e angstrom(-3). Details of the geometry of the five molecules (two for I and three for II) and the crystal structures are fully discussed. Corresponding features of the molecular geometry are highly consistent and firmly establish the geometry of the rhodanine
Resumo:
We consider the problem of finding the heat distribution and the shape of the liquid fraction during laser welding of a thick steel plate using the finite volume CFD package PHYSICA. Since the shape of the keyhole is not known in advance, the following two-step approach to handling this problem has been employed. In the first stage, we determine the geometry of the keyhole for the steady-state case and form an appropriate mesh that includes both the workpiece and the keyhole. In the second stage, we impose the boundary conditions by assigning temperature to the walls of the keyhole and find the heat distribution and the shape of the liquid fraction for a given welding speed and material properties. We construct a fairly accurate approximation of the keyhole as a sequence of include sliced cones. A formula for finding the initial radius of the keyhole is derived by determining the radius of the vaporisation isotherm for the line heat source. We report on the results of a series of computational experiments for various heat input values and welding velocities.
Resumo:
Purpose: To develop an improved mathematical model for the prediction of dose accuracy of Dosators - based upon the geometry of the machine in conjunction with measured flow properties of the powder. Methods: A mathematical model has been created, based on a analytical method of differential slices - incorporating measured flow properties. The key flow properties of interest in this investigation were: flow function, effective angle of wall friction, wall adhesion, bulk density, stress ratio K and permeability. To simulate the real process and (very importantly) validate the model, a Dosator test-rig has been used to measure the forces acting on the Dosator during the filling stage, the force required to eject the dose and the dose weight. Results: Preliminary results were obtained from the Dosator test-rig. Figure 1 [Omitted] shows the dose weight for different depths to the bottom of the powder bed at the end of the stroke and different levels of pre-compaction of the powder bed. A strong influence over dose weight arising from the proximity between the Dosator and the bottom of the powder bed at the end of the stroke and the conditions of the powder bed has been established. Conclusions: The model will provide a useful tool to predict dosing accuracy and, thus, optimise the future design of Dosator based equipment technology – based on measured bulk properties of the powder to be handled. Another important factor (with a significant influence) on Dosator processes, is the condition of the powder bed and the clearance between the Dosator and the bottom of the powder bed.
Resumo:
Purpose – The purpose of this paper is to develop a quality control tool based on rheological test methods for solder paste and flux media. Design/methodology/approach – The rheological characterisation of solder pastes and flux media was carried out through the creep-recovery, thixotropy and viscosity test methods. A rheometer with a parallel plate measuring geometry of 40mm diameter and a gap height of 1mm was used to characterise the paste and associated flux media. Findings – The results from the study showed that the creep-recovery test can be used to study the deformation and recovery of the pastes, which can be used to understand the slump behaviour in solder pastes. In addition, the results from the thixotropic and viscosity test were unsuccessful in determining the differences in the rheological flow behaviour in the solder pastes and the flux medium samples. Research limitations/implications – More extensive rheological and printing testing is needed in order to correlate the findings from this study with the printing performance of the pastes. Practical implications – The rheological test method presented in the paper will provide important information for research and development, quality control and production staff to facilitate the manufacture of solder pastes and flux media. Originality/value – The paper explains how the rheological test can be used as a quality control tool to identify the suitability of a developmental solder paste and flux media used for the printing process.
Resumo:
This paper describes recent developments made to the stress analysis module within FLOTHERM, extending its capability to handle viscoplastic behavior. It also presents the validation of this approach and results obtained for an SMT resistor as an illustrative example. Lifetime predictions are made using the creep strain energy based models of Darveaux. Comment is made about the applicability of the damage model to the geometry of the joint under study.
Resumo:
A design methodology based on numerical modelling, integrated with optimisation techniques and statistical methods, to aid the process control of micro and nano-electronics based manufacturing processes is presented in this paper. The design methodology is demonstrated for a micro-machining process called Focused Ion Beam (FIB). This process has been modelled to help understand how a pre-defined geometry of micro- and nano- structures can be achieved using this technology. The process performance is characterised on the basis of developed Reduced Order Models (ROM) and are generated using results from a mathematical model of the Focused Ion Beam and Design of Experiment (DoE) methods. Two ion beam sources, Argon and Gallium ions, have been used to compare and quantify the process variable uncertainties that can be observed during the milling process. The evaluations of the process performance takes into account the uncertainties and variations of the process variables and are used to identify their impact on the reliability and quality of the fabricated structure. An optimisation based design task is to identify the optimal process conditions, by varying the process variables, so that certain quality objectives and requirements are achieved and imposed constraints are satisfied. The software tools used and developed to demonstrate the design methodology are also presented.
Resumo:
The numeracy skill of student is a continued concern with numeracy highlighted as a key skill in Foundation degrees and other vocational courses such as nursing (DfES 1999, NMC 2007). Numeracy is seen as a requirement to being able to undertake work based skills that require the use of numbers and calculations. However numeracy skills developed in the classroom does not necessarily prepare students for work-based calculations and similarly nor does poor numeracy skills necessarily mean that students cannot perform complex mathematical calculations in their work place. This paper will explore the role of context, the difference between formal and work based mathematics and questions the continued focus on numeracy skills, using examples from my own research with nurses.