Collocation Methods for Weakly Singular Second-kind Volterra Integral Equations with Non-smooth Solution

Collocation type methods are studied for the numerical solutionof the weakly singular Volterra integral equation of the secondkind: where the solution (t) is assumedto have the form f(t) = x(t)+r^?(t), x and being sufficientlysmooth. The solution is approximated near zero by a linear combinationof powers of t?, and away from zero by the usual polynomialrepresentation. Convergence is proved and many numerical experimentsare carried out with examples from the literature. A comparisonis made with a method of Brunner & Norsett (1981), originallydeveloped for (1) with a smooth solution. Special attentionis paid to the numerical approximation of the so-called momentintegrals which emerge in the collocation scheme.     

Imaging and PDA analysis of a GDI spray in the near-nozzle region

This paper describes a combined LDA, PDA and imaging analysis of the pressure swirl spray in the near-nozzle region of a GDI injector. This innovative approach in the use of multiple, complementary diagnostics facilitates the interpretation of a complex spray flow field.The LDA and PDA data were ensemble-averaged into time bins to produce comprehensive time-history and spatial profiles of liquid velocity, droplet velocity and size and the sample number. They indicated times at which the spray exhibited seven different characteristics. These were identified as: (a) pre-swirl spray, (b) spray cone develops, (c) spray cone relaxes, (d) maximum velocity in spray cone, (e) fully developed steady state, (f) spray cone collapses and (g) the spray detaches from the nozzle. The most effective method to present the spatial and temporal development of the spray was to superimpose the velocity vector and drop size field plots onto the spray images.This article is part of the special issue 11^th International Symposium on Applications of Laser Techniques to Fluid Mechanics, Lisboa, Portugal, July 2002, January 2004, Vol. 36, Issue no. 1     

The degree of approximation of certain analytic continued fractions

Summary Continued fraction expansions of classes of holomorphic functions associate with each function its sequence of coefficients. If there is a probability measure on the sequence space one can investigate the almost everywhere convergence properties of the continued fraction. In this paper we compute the degree of approximation for the expansions of functions holomorphic and bounded in the disk and for the expansion of the PR functions used in network synthesis.This research was partially supported by National Science Foundation Grants GP-6852 and GP-6216.     

Rapid postcolumn methodology for determination of paralytic shellfish toxins in shellfish tissue

A rapid liquid chromatographic (LC) method with postcolumn oxidation and fluorescence detection (excitation 330 nm, emission 390 nm) for the determination of paralytic shellfish toxins (PSTs) in shellfish tissue has been developed. Extracts prepared for mouse bioassay (MBA) were treated with trichloroacetic acid to precipitate protein, centrifuged, and pH-adjusted for LC analysis. Saxitoxin (STX), neoSTX (NEO), decarbamoylSTX (dcSTX), and the gonyautoxins, GTX1, GTX2, GTX3, GTX4, GTX5, dcGTX2, and dcGTX3, were separated on a polar-linked alkyl reversed-phase column using a step gradient elution; the N-sulfocarbamoyl GTXs, C1, C2, C3, and C4, were determined on a C-8 reversed-phase column in the isocratic mode. Relative toxicities were used to determine STX-dihydrochloride salt (diHCl) equivalents (STXeq). Calibration graphs were linear for all toxins studied with STX showing a correlation coefficient of 0.999 and linearity between 0.18 and 5.9 ng STX-diHCI injected (equivalent to 3.9-128 microg STXeq/100 g in tissue). Detection limits for individual toxins ranged from 0.07 microg STXeq/100 g for C1 and C3 to 4.1 microg STXeq/100 g for GTX1. Spike recoveries ranged from 76 to 112% in mussel tissue. The relative standard deviation (RSD) of repeated injections of GTX and STX working standard solutions was < 4%. Uncertainty of measurement at a level of 195 microg STXeq/100 g was 9%, and within-laboratory reproducibility expressed as RSD was 4.6% using the same material. Repeatability of a 65 microg STXeq/100 g sample was 3.0% RSD. Seventy-three samples were analyzed by the new postcolumn method and both AOAC Official Methods for PST determination: the MBA (y = 1.22x + 13.99, r2 = 0.86) and the precolumn LC oxidation method of Lawrence (y = 2.06x + 12.21, r2 = 0.82).     

无机酸洗脱对胜利褐煤微晶结构及其自燃倾向性的影响

利用XRD、Raman、XPS和FT-IR表征技术,研究无机酸洗脱(HCl、H2SO4、HCl-HF)处理的胜利褐煤微晶结构的变化,采用自行设计的表面吸附仪-GC联用装置,对样品进行不同温度的低温脉冲氧化实验,考察了煤样在不同温度下氧吸附量的变化规律,通过低温脉冲氧吸附规律与TG/DTG和固定床燃烧实验关联,考察了煤样的自燃倾向。结果表明,无机酸洗脱对矿物质的脱除使得煤结构的有序度增加,石墨化程度提高,无机酸洗脱煤样与原煤相比吸氧量明显下降。随着吸附温度的升高,各煤样吸氧量明显增加,且随着脱除矿物质程度的增加,吸氧量呈减小的趋势,导致自燃倾向降低。     

Experimental Analysis of the Response of a Laser/Phase Doppler Anemometer System to a Partially Atomized Spray

This work describes a systematic approach adopted to establish Laser and Phase Doppler Anemometry, LDA/PDA, experimental techniques that would allow velocity and dropsize measurements to be made over wide velocity and size ranges with confidence in partially atomized sprays. The analysis considers the sprays generated by different gasoline direct injection (GDI) systems injecting into air under atmospheric conditions. The upper limit to the dropsize range in the fuel sprays was confirmed using (a) an Oxford Lasers' VisiSizer and (b) droplets of a known size produced by a mono‐dispersed droplet generator. GDI fuel sprays are highly transient, optically dense and provide a high degree of penetration and atomization. The measurement problem is therefore one of the detection of small, high speed droplets inside a dense cloud of surrounding droplets. Furthermore, under the transients found at the start and end of injection and during high fuel loads, fuel elements in the form of sheets, ligaments and filaments are also injected. These liquid fuel elements subsequently break‐up, downstream from the nozzle, to form droplets of a much larger size class but with a much lower number density [1]. The co‐existence of these liquid fuel elements and the widely different size classes in the spray are considered to pose a problem for dropsize measurements by the PDA technique. In particular: the wide dynamic range of light intensities scattered by the fuel elements and droplets; the trajectory of large drops through the edges of the PDA measurement volume with its Gaussian intensity distribution [2] and the high probability of non spherical droplets. The work concludes that the LDA/PDA measurement technique, as applied here, is robust. It can discriminate between partially and fully atomized sprays, has a high probability of accurately measuring dropsizes larger than the measurement volume and give a realistic indication of ‘sizes’ for non spherical droplets. However, specification of the PDA system parameters must be strictly compatible with the measurement task to yield unambiguous results.     

PIV analysis of in-cylinder flow structures over a range of realistic engine speeds

In-cylinder PIV measurements have been performed in a four-valve single cylinder optical gasoline direct injection engine, motored at speeds of 750, 2,000 and 3,500 rpm. Mean vector flow fields have been produced during the latter half of the intake stroke in the symmetry plane between the valve pairs. The flow fields show the development of the in-cylinder flow structures at 1.6, 2.4 and 3.2° crank angle steps for a time period of approximately 5 ms at each of the three engine speeds, respectively. Tumble ratios have been calculated for the available field of view showing a change in the flow structure between 2,000 and 3,500 rpm. This is believed to be caused by an increase in the flow of air traveling underneath the recirculation vortex at the higher engine speed. This translates the vortex position upwards and further to the right when compared to the lower engine speeds.