30 research outputs found

    MaxEnt power spectrum estimation using the Fourier transform for irregularly sampled data applied to a record of stellar luminosity

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    The principle of maximum entropy is applied to the spectral analysis of a data signal with general variance matrix and containing gaps in the record. The role of the entropic regularizer is to prevent one from overestimating structure in the spectrum when faced with imperfect data. Several arguments are presented suggesting that the arbitrary prefactor should not be introduced to the entropy term. The introduction of that factor is not required when a continuous Poisson distribution is used for the amplitude coefficients. We compare the formalism for when the variance of the data is known explicitly to that for when the variance is known only to lie in some finite range. The result of including the entropic measure factor is to suggest a spectrum consistent with the variance of the data which has less structure than that given by the forward transform. An application of the methodology to example data is demonstrated.Comment: 15 pages, 13 figures, 1 table, major revision, final version, Accepted for publication in Astrophysics & Space Scienc

    Sensitivity analysis for in-cylinder soot-particle size imaging with laser-induced incandescence

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    International audienceSoot particle sizes can be determined from time-resolved laser-induced incandescence (LII) in point measurements where full signal traces are detected. For instantaneous imaging, strategies are required that must cope with time-gated information and that rely on assumptions on the local boundary conditions. A model-based analysis is performed to identify the dependence of LII particle-size imaging on the assumed boundary conditions such as bath gas temperature, pressure, particle heat-up temperature, accommodation coefficients, and soot morphology. Various laser-fluence regimes and gas pressures are considered. For 60 bar, fluences that lead to particle heat-up temperatures of 3400– 3900 K provided the lowest sensitivity on particle-sizing. Effects of laser attenuation are evaluated. A combination of one detection gate starting at the signal peak and the other starting with 5 ns delay was found to provide the highest sensitivity at 60 bar. The optimum gate delays for different pressures are shown. The effects of timing jitter and poly-dispersity are investigated. Systematic errors in pyrometry imaging at 60 bar is evaluated

    Determination of small soot particles in the presence of large ones from time-resolved laser-induced incandescence

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    International audienceInformation about the polydispersity of soot can in principle be gained from time-resolved laser-induced incandescence (LII) using pre-assumed particle-size distributions. This paper introduces an alternative method, called two-exponential reverse fitting (TERF) that is based on combined mono-exponential fits to the LII signal decay at various delay times. The method approximates the particle-size distribution as a combination of one large and one small monodisperse equivalent mean particle size and does not require a distribution assumption. It also provides a ratio of the contribution of both size classes. The systematic error caused by describing LII signals by mono-exponential decays is calculated as less than 2% for LII signals simulated for monodisperse aggregated soot with heat-up temperatures for which evaporation is negligible. The effects of particle size, heat-up temperature, aggregate size, and pressure on this error are evaluated. The method is tested on simulated LII signals for lognormal and bimodal size distributions and applied to LII data acquired in a laminar non-premixed ethylene/air flame at various heights above burner. The results are compared to transmission electron microscopy (TEM) measurements of thermophoretically-sampled soot. The particle size of the large particle-size class evaluated with the method showed good consistency with TEM results, however the size of the small particle-size class and the relative contribution could not be compared due to missing information in the TEM results for small particles. These limitations of TEM measurements are discussed and the effect of the exposure time of the sampling grid is evaluated.

    Randomized Kaczmarz Converges Along Small Singular Vectors

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    Assessment of soot particle-size imaging with LII at Diesel engine conditions

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    International audienceTwo-time-step laser-induced incandescence (LII) imaging was performed in Diesel engine-relevant combustion to investigate its applicability for spatially-resolved measurements of soot primary particle sizes. The method is based on evaluating gated LII signals acquired with two cameras consecutively after the laser pulse and using LII modeling to deduce the particle size from the ratio of local signals. Based on a theoretical analysis, optimized detection times and durations were chosen to minimize measurement uncertainties. Experiments were conducted in a high-temperature high-pressure constant-volume pre-combustion vessel under the Engine Combustion Network's (ECN) "Spray A" conditions at 61–68 bar with additional parametric variations of injection pressure, gas temperature, and composition. The LII measurements were supported by pyrometric imaging measurements of particle heat-up temperatures. The results were compared to particle-size and size-dispersion measurements from transmission electron microscopy (TEM) of soot thermophoretically sampled at multiple axial distances from the injector. The discrepancies between the two measurement techniques are discussed to analyze uncertainties and related error sources of the two diagnostics. It is found that in such environment where particles are small and pressure is high, LII signal decay times are such that LII with standard nanosecond laser and detector equipment suffers from a strong bias towards large particles
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