a b s t r a c tA multi-scale methodology for the radiative transfer analysis of heterogeneous media composed of morphologically-complex components on two distinct scales is presented. The methodology incorporates the exact morphology at the various scales and utilizes volume-averaging approaches with the corresponding effective properties to couple the scales. At the continuum level, the volume-averaged coupled radiative transfer equations are solved utilizing ( i ) effective radiative transport properties obtained by direct Monte Carlo simulations at the pore level, and ( ii ) averaged bulk material properties obtained at particle level by Lorenz-Mie theory or discrete dipole approximation calculations. This model is applied to a soot-contaminated snow layer, and is experimentally validated with reflectance measurements of such layers. A quantitative and decoupled understanding of the morphological effect on the radiative transport is achieved, and a significant influence of the dual-scale morphology on the macroscopic optical behavior is observed. Our results show that with a small amount of soot particles, of the order of 1ppb in volume fraction, the reduction in reflectance of a snow layer with large ice grains can reach up to 77% (at a wavelength of 0.3 μm). Soot impurities modeled as compact agglomerates yield 2-3% lower reduction of the reflectance in a thick show layer compared to snow with soot impurities modeled as chain-like agglomerates. Soot impurities modeled as equivalent spherical particles underestimate the reflectance reduction by 2-8%. This study implies that the morphology of the heterogeneities in a media significantly affects the macroscopic optical behavior and, specifically for the soot-contaminated snow, indicates the non-negligible role of soot on the absorption behavior of snow layers. It can be equally used in technical applications for the assessment and optimization of optical performance in multi-scale media.
In the analysis of next‐generation sequencing technology, massive discrete data are generated from short read counts with varying biological coverage. Conducting conditional hypothesis testing such as Fisher's Exact Test at every genomic region of interest thus leads to a heterogeneous multiple discrete testing problem. However, most existing multiple testing procedures for controlling the false discovery rate (FDR) assume that test statistics are continuous and become conservative for discrete tests. To overcome the conservativeness, in this article, we propose a novel multiple testing procedure for better FDR control on heterogeneous discrete tests. Our procedure makes decisions based on the marginal critical function (MCF) of randomized tests, which enables achieving a powerful and non‐randomized multiple testing procedure. We provide upper bounds of the positive FDR (pFDR) and the positive false non‐discovery rate (pFNR) corresponding to our procedure. We also prove that the set of detections made by our method contains every detection made by a naive application of the widely‐used q‐value method. We further demonstrate the improvement of our method over other existing multiple testing procedures by simulations and a real example of differentially methylated region (DMR) detection using whole‐genome bisulfite sequencing (WGBS) data.
Solar thermochemical redox cycles provide a sustainable pathway for solar fuel processing. If done in porous (ceria) structures, they can profit from faster reaction rates owned to the enhanced heat and mass transport characteristics. However, the exact porous structure and operating conditions significantly affect the performance. We present a transient volume-averaged fixed-bed model of a thermochemical redox reactor utilizing macroporous ceria. We studied the porosity-dependent (ε=0.4-0.9) and operating condition-dependent (solar concentration ratio, ratio of oxygen partial pressure to total pressure, gas flow rate) performance of the fixed-bed ceria redox cycle. Structures with large porosity (ε=0.9) showed better performance than low-porosity structures, owning to the enhanced heat absorption and resulting higher temperatures. We show that the cycle duration requires optimization according to the porosity of the structure. Two hours of operation for a structure with ε=0.75 resulted in the largest hydrogen production (115.78) if the single cycle duration was 240 s (i.e. 30 cycles in 2 hours), while nearly five times less was produced for a 15 times longer single cycle duration (i.e. 2 cycles in 2 hours). We subsequently introduced porous structures with different types of non-uniform porosity distributions. For an average porosity of ε=0.75, the most favorable non-uniform porosity media exhibited higher porosity at the boundaries and a denser core. The fuel production of the best non-uniform porous structure was six times larger compared to a uniform porous structure. Adjusting on top of this the cycling conditions, a 14.6 times production gain was achieved. This work suggests that under non-isothermal operation condition for macroporous ceria redox fixed-bed cycling, non-uniform porous structure with higher porosity boundaries and a dense core benefit fuel production and porosity-dependent cycle duration modulation can be used to increase performance.
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