An accurate, fast, mathematically robust, universal, non-iterative algorithm for computing multi-component diffusion velocities

Using accurate multi-component diffusion treatment in numerical combustion studies remains formidable due to the computational cost associated with solving for diffusion velocities. To obtain the diffusion velocities, for low density gases, one needs to solve the Stefan-Maxwell equations along with the zero diffusion flux criteria, which scales as $\mathcal{O}(N^3)$, when solved exactly. In this article, we propose an accurate, fast, direct and robust algorithm to compute multi-component diffusion velocities. To our knowledge, this is the first provably accurate algorithm (the solution can be obtained up to an arbitrary degree of precision) scaling at a computational complexity of $\mathcal{O}(N)$ in finite precision. The key idea involves leveraging the fact that the matrix of the reciprocal of the binary diffusivities, $V$, is low rank, with its rank being independent of the number of species involved. The low rank representation of matrix $V$ is computed in a fast manner at a computational complexity of $\mathcal{O}(N)$ and the Sherman-Morrison-Woodbury formula is used to solve for the diffusion velocities at a computational complexity of $\mathcal{O}(N)$. Rigorous proofs and numerical benchmarks illustrate the low rank property of the matrix $V$ and scaling of the algorithm.Comment: 16 pages, 7 figures, 1 table, 1 algorith

Towards bacterial valorization of low molecular weight lignin

Lignin is one of the major constituents in lignocellulosic biomass and is the mostabundant source of renewable aromatics on terrestrial ecosystems. The workcarried out in this thesis concerns bacterial conversion of low molecular weightlignin. This thesis is divided into three major sections, with an initial emphasison screening and characterization of selected bacterial species on lignin modelcompounds, followed by testing their performance on treated lignin substrates,and finally progressing towards strain improvement via metabolic engineering. During screening for bacteria using samples from natural and man-madeenvironments, Pseudomonas species were found dominant. Some of theseisolates, and the well-known aromatic degrader – Pseudomonas putida KT2440– were cultivated on lignin model compounds. P. putida and Pseudomonas sp.isolate 9.1 attained specific growth rates of about 0.21-0.27 h-1 and 0.12-0.30 h-1 respectively, on several compounds from the coniferyl, p-coumaryl and benzoyl branches of the funnelling pathways. Meanwhile, a contaminant was found growing on syringate plates, and was later identified to be a bacterium belonging to the Microbacterium genus. This Gram-positive bacterium, named RG1, was able to consume syringate and syringaldehyde besides other aromatic compounds from the coniferyl and p-coumaryl branches. Due to its interesting abilities to assimilate syringyl compounds, the genome of this strain was sequenced to identify genes involved in a putative syringyl pathway.To assess the performance of selected bacteria on lignin substrates, cultivationswere performed using alkaline- and oxidatively-treated Kraft lignin. P. putida and P. fluorescens consumed 4-HBA, vanillin, and vanillate in the complex ligninmixture that likely contained various toxic products. In addition, Rhodococcusopacus and Sphingobium sp. SYK-6 assimilated guaiacol and acetovanillonerespectively, from the lignin mixture. Interestingly, P. fluorescens was able tobreak down the higher molecular weight lignin and produce several smallermolecules.P. putida was selected as a host organism for genetic engineering aimed atexpanding the range of substrates utilized. Heterologous expression of thecytochrome P450 and oxidoreductase genes from R. rhodochrous enabled P.putida to assimilate guaiacol – one of the major depolymerization products fromsoftwood lignin – as the sole carbon source. Furthermore, the identification anddeletion of an aldehyde reductase in a P. putida strain that converts ferulate tovanillin, increased the yield of vanillin by eliminating the formation of vanillylalcohol as by-product

Kernel Analog Forecasting: Multiscale Test Problems

Data-driven prediction is becoming increasingly widespread as the volume of data available grows and as algorithmic development matches this growth. The nature of the predictions made, and the manner in which they should be interpreted, depends crucially on the extent to which the variables chosen for prediction are Markovian, or approximately Markovian. Multiscale systems provide a framework in which this issue can be analyzed. In this work kernel analog forecasting methods are studied from the perspective of data generated by multiscale dynamical systems. The problems chosen exhibit a variety of different Markovian closures, using both averaging and homogenization; furthermore, settings where scale-separation is not present and the predicted variables are non-Markovian, are also considered. The studies provide guidance for the interpretation of data-driven prediction methods when used in practice.Comment: 30 pages, 14 figures; clarified several ambiguous parts, added references, and a comparison with Lorenz' original method (Sec. 4.5

Balancing Justice Needs and Private Property in Constitutional Takings Provisions: A Comparative Assessment of India, Australia, and the United States

This Article explores the relationship between justice needs and private property in the constitutional takings provisions of the Indian, Australian, and American constitutions. Building upon established scholarship, it develops a theoretical framework within which to consider the way in which a state balances the requirement to provide minimal levels of justice for its citizens through the re-distribution of goods and resources with the need to protect the private property of individuals. We summarize this framework in what we refer to as the “Justice Needs-Protection of Private Property Continuum.” Using the framework developed, the Article provides an outline of the takings provisions found in the Indian, Australian, and American constitutions. Part I examines Article 300A of the Constitution of India, which contains the scope of the power of compulsory acquisition exercised by the Indian state. Part II assesses Section 51(xxxi) of the Australian Constitution which, unlike its American and Indian counterparts, operates as both a grant of power to the federal government, as well as a limitation imposed upon that power, which may, it seems, operate so as to provide some minimal protection for individual private property interests. Part III considers the Takings Clause of the Fifth Amendment to the United States Constitution which, as interpreted by the Supreme Court, provides perhaps the most robust means among the three jurisdictions considered for protecting the individual private property interests as against state takings. The Conclusion offers comparative reflections on the nature of the takings provision found in each jurisdiction.Krithika Ashok, Paul T. Babie, & John V. Ort