Macroscopic effects of the spectral structure in turbulent flows

Two aspects of turbulent flows have been the subject of extensive, split research efforts: macroscopic properties, such as the frictional drag experienced by a flow past a wall, and the turbulent spectrum. The turbulent spectrum may be said to represent the fabric of a turbulent state; in practice it is a power law of exponent \alpha (the "spectral exponent") that gives the revolving velocity of a turbulent fluctuation (or "eddy") of size s as a function of s. The link, if any, between macroscopic properties and the turbulent spectrum remains missing. Might it be found by contrasting the frictional drag in flows with differing types of spectra? Here we perform unprecedented measurements of the frictional drag in soap-film flows, where the spectral exponent \alpha = 3 and compare the results with the frictional drag in pipe flows, where the spectral exponent \alpha = 5/3. For moderate values of the Reynolds number Re (a measure of the strength of the turbulence), we find that in soap-film flows the frictional drag scales as Re^{-1/2}, whereas in pipe flows the frictional drag scales as Re^{-1/4} . Each of these scalings may be predicted from the attendant value of \alpha by using a new theory, in which the frictional drag is explicitly linked to the turbulent spectrum. Our work indicates that in turbulence, as in continuous phase transitions, macroscopic properties are governed by the spectral structure of the fluctuations.Comment: 6 pages, 3 figure

Dealing with missing standard deviation and mean values in meta-analysis of continuous outcomes: a systematic review

Background: Rigorous, informative meta-analyses rely on availability of appropriate summary statistics or individual participant data. For continuous outcomes, especially those with naturally skewed distributions, summary information on the mean or variability often goes unreported. While full reporting of original trial data is the ideal, we sought to identify methods for handling unreported mean or variability summary statistics in meta-analysis. Methods: We undertook two systematic literature reviews to identify methodological approaches used to deal with missing mean or variability summary statistics. Five electronic databases were searched, in addition to the Cochrane Colloquium abstract books and the Cochrane Statistics Methods Group mailing list archive. We also conducted cited reference searching and emailed topic experts to identify recent methodological developments. Details recorded included the description of the method, the information required to implement the method, any underlying assumptions and whether the method could be readily applied in standard statistical software. We provided a summary description of the methods identified, illustrating selected methods in example meta-analysis scenarios. Results: For missing standard deviations (SDs), following screening of 503 articles, fifteen methods were identified in addition to those reported in a previous review. These included Bayesian hierarchical modelling at the meta-analysis level; summary statistic level imputation based on observed SD values from other trials in the meta-analysis; a practical approximation based on the range; and algebraic estimation of the SD based on other summary statistics. Following screening of 1124 articles for methods estimating the mean, one approximate Bayesian computation approach and three papers based on alternative summary statistics were identified. Illustrative meta-analyses showed that when replacing a missing SD the approximation using the range minimised loss of precision and generally performed better than omitting trials. When estimating missing means, a formula using the median, lower quartile and upper quartile performed best in preserving the precision of the meta-analysis findings, although in some scenarios, omitting trials gave superior results. Conclusions: Methods based on summary statistics (minimum, maximum, lower quartile, upper quartile, median) reported in the literature facilitate more comprehensive inclusion of randomised controlled trials with missing mean or variability summary statistics within meta-analyses

Assessing architectural evolution: A case study

This is the post-print version of the Article. The official published can be accessed from the link below - Copyright @ 2011 SpringerThis paper proposes to use a historical perspective on generic laws, principles, and guidelines, like Lehman’s software evolution laws and Martin’s design principles, in order to achieve a multi-faceted process and structural assessment of a system’s architectural evolution. We present a simple structural model with associated historical metrics and visualizations that could form part of an architect’s dashboard. We perform such an assessment for the Eclipse SDK, as a case study of a large, complex, and long-lived system for which sustained effective architectural evolution is paramount. The twofold aim of checking generic principles on a well-know system is, on the one hand, to see whether there are certain lessons that could be learned for best practice of architectural evolution, and on the other hand to get more insights about the applicability of such principles. We find that while the Eclipse SDK does follow several of the laws and principles, there are some deviations, and we discuss areas of architectural improvement and limitations of the assessment approach

Fracture-fill calcite as a record of microbial methanogenesis and fluid migration: a case study from the Devonian Antrim Shale, Michigan Basin

The Devonian Antrim Shale is an organic-rich, naturally fractured black shale in the Michigan Basin that serves as both a source and reservoir for natural gas. A well-developed network of major, through-going vertical fractures controls reservoir-scale permeability in the Antrim Shale. Many fractures are open, but some are partially sealed by calcite cements that retain isotopic evidence of widespread microbial methanogenesis. Fracture filling calcite displays an unusually broad spectrum of δ 13 C values (+34 to −41‰ PDB), suggesting that both aerobic and anaerobic bacterial processes were active in the reservoir. Calcites with high δ 13 C values (>+15‰) record cementation of fractures from dissolved inorganic carbon (DIC) generated during bacterial methanogenesis. Calcites with low δ 13 C values (<−32‰) are solely associated with outcrop samples and record methane oxidation during cement precipitation. Fracture-fill calcite with δ 13 C values between −10 and −30‰ can be attributed to variable organic matter oxidation pathways, methane oxidation, and carbonate rock buffering. Identification of 13 C-rich calcite provides unambiguous evidence of biogenic methane generation and may be used to identify gas deposits in other sedimentary basins. It is likely that repeated glacial advances and retreats exposed the Antrim Shale at the basin margin, enhanced meteoric recharge into the shallow part of the fractured reservoir, and initiated multiple episodes of bacterial methanogenesis and methanotrophic activity that were recorded in fracture-fill cements. The δ 18 O values in both formation waters and calcite cements increase with depth in the basin (−12 to −4‰ SMOW, and +21 to +27‰ PDB, respectively). Most fracture-fill cements from outcrop samples have δ 13 C values between −41 and −15‰ PDB. In contrast, most cement in cores have δ 13 C values between +15 and +34‰ PDB. Radiocarbon and 230 Th dating of fracture-fill calcite indicates that the calcite formed between 33 and 390 ka, well within the Pleistocene Epoch.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/75720/1/j.1468-8123.2002.00036.x.pd

Membranes by the Numbers

Many of the most important processes in cells take place on and across membranes. With the rise of an impressive array of powerful quantitative methods for characterizing these membranes, it is an opportune time to reflect on the structure and function of membranes from the point of view of biological numeracy. To that end, in this article, I review the quantitative parameters that characterize the mechanical, electrical and transport properties of membranes and carry out a number of corresponding order of magnitude estimates that help us understand the values of those parameters.Comment: 27 pages, 12 figure