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The range of validity of the Rayleigh-Debye-Gans approximation for the optical cross sections of fractal aggregates (RDG-FA) that are formed by uniform small particles was evaluated in comparison with the integral equation formulation for scattering (IEFS), which accounts for the effects of multiple scattering and self-interaction. Numerical simulations were performed to create aggregates that exhibit mass fractallike characteristics with a wide range of particle and aggregate sizes and morphologies, including [x.sub.p] = 0.01-1.0, [absolute value of m - 1] = 0.1-2.0, N = 16-256, and [D.sub.f] = 1.0-3.0. The percent differences between both scattering theories were presented as error contour charts in the [absolute value of m - 1][x.sub.p] domains for various size aggregates, emphasizing fractal properties representative of diffusion-limited cluster-cluster aggregation. These charts conveniently identified the regions in which the differences were less than 10%, between 10% and 30%, and more than 30% for easy to use general guidelines for suitability of the RDG-FA theory in any scattering applications of interest, such as laser-based particulate diagnostics. Various types of aggregate geometry ranging from straight chains ([D.sub.f] [approximately equal to] 1.0) to compact clusters ([D.sub.f] [approximately equal to] 3.0) were also considered for generalization of the findings. For the present computational conditions, the RDG-FA theory yielded accurate predictions to within 10% for [absolute value of m - 1] to approximately 1 or more as long as the primary particles in aggregates were within the Rayleigh scattering limit ([x.sub.p] [less than or equal to] 0.3). Additionally, the effect of fractal dimension on the performance of the RDG-FA was generally found to be insignificant. The results suggested that the RDG-FA theory is a reasonable approximation for optics of a wide range of fractal aggregates, considerably extending its domain of applicability. Key words: Rayleigh-Debye-Gans, optical cross sections, fractal aggregates, laser diagnostics.

The approximate Rayleigh-Debye-Gans (RDG)/fractal-aggregate (FA) theory for the optical properties of soot aggregates is evaluated by using the models developed on the basis of the ICP algorithm. The evaluation emphasizes Guinier regime of the RDG-FA theory. The evaluation reveals that the RDG-FA theory is consistent with the numerical uncertainties model. The scattering properties and refractive indices of the soot are accurately provided by the RDG-FA theory.

Abstract: NO x emission standards are becoming stringiest over the world especially for heavy-duty vehicles. To comply with current and future regulations some vehicle manufacturers are adopting exhaust aftertreatment systems known as Selective Catalytic Reduction (SCR). The catalysts are based on Vanadium (Va) and the reductant agent based on ammonia. However, Va is listed on the California Proposition 65 List as potentially causing cancer and alternatives are being studied. This paper presents a model based on neural networks that integrated with a road vehicle simulator allows to estimate NO x emission factors for different powertrain configurations, along different driving conditions, and covering commercial, zeolite and mordenite alternatives as the base monolith for SCR. The research included the experimental study of copper based and iron based zeolites (ZSM5 and Cuban natural mordenite). The response of NO x conversion efficiency was monitored in a laboratory for varying space velocity, oxygen, sulfur, water, NO x and SO2 emulating the conditions of a Diesel engine exhaust along a trip. The experimental data was used for training neural networks and obtaining a mathematical correlation between the outputs and inputs of the SCR system. The developed correlation was integrated with ADVISOR road vehicle simulator to obtain NO x emission factors and to test each SCR system installed on light-duty and heavy-duty vehicles for standardized driving cycles and real measured driving cycles. Despite having lower NO x conversion efficiencies than the CATCO in the ETC/ESC and NEDC cycles, FeZSM5 maintain the Euro regulation level. Therefore FeZSM5 can be a possible candidate as far as pollutants regulation is considered. [Copyright &y& Elsevier]