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

A Dirac-type Characterization of k-chordal Graphs

Characterization of k-chordal graphs based on the existence of a "simplicial path" was shown in [Chv{\'a}tal et al. Note: Dirac-type characterizations of graphs without long chordless cycles. Discrete Mathematics, 256, 445-448, 2002]. We give a characterization of k-chordal graphs which is a generalization of the known characterization of chordal graphs due to [G. A. Dirac. On rigid circuit graphs. Abh. Math. Sem. Univ. Hamburg, 25, 71-76, 1961] that use notions of a "simplicial vertex" and a "simplicial ordering".Comment: 3 page

LP approaches to improved approximation for clique transversal in perfect graphs

Given an undirected simple graph G, a subset T of vertices is an r-clique transversal if it has at least one vertex from every r-clique in G. I.e. T is an r-clique transversal if G-S is K r -free. r-clique transversals generalize vertex covers as a vertex cover is a set of vertices whose deletion results in a graph that is K 2-free. Perfect graphs are a well-studied class of graphs on which a minimum vertex cover can be obtained in polynomial time. However, the problem of finding a minimum r-clique transversal is NP-hard even for r=3. As any induced odd length cycle in a perfect graph is a triangle, a triangle-free perfect graph is bipartite. I.e. in perfect graphs, a 3-clique transversal is an odd cycle transversal. In this work, we describe an(r+1/2) -approximation algorithm for r-clique transversal on weighted perfect graphs improving on the straightforward r-approximation algorithm. We then show that 3-Clique Transversal is APX-hard on perfect graphs and it is NP-hard to approximate it within any constant factor better than 4/3 assuming the unique games conjecture. We also show intractability results in the parameterized complexity framework. © 2014 Springer-Verlag Berlin Heidelberg.SCOPUS: cp.kSCOPUS: cp.kinfo:eu-repo/semantics/publishe

Approximability of Clique Transversal in Perfect Graphs

Given an undirected simple graph G, a set of vertices is an r-clique transversal if it has at least one vertex from every r-clique. Such sets generalize vertex covers as a vertex cover is a 2-clique transversal. Perfect graphs are a well-studied class of graphs on which a minimum weight vertex cover can be obtained in polynomial time. Further, an r-clique transversal in a perfect graph is also a set of vertices whose deletion results in an (r- 1) -colorable graph. In this work, we study the problem of finding a minimum weight r-clique transversal in a perfect graph. This problem is known to be NP-hard for r≥ 3 and admits a straightforward r-approximation algorithm. We describe two different r+12-approximation algorithms for the problem. Both the algorithms are based on (different) linear programming relaxations. The first algorithm employs the primal–dual method while the second uses rounding based on a threshold value. We also show that the problem is APX-hard and describe hardness results in the context of parameterized algorithms and kernelization.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Oxidation kinetics of methyl crotonate : A comprehensive modeling and experimental study

The current study explores the combustion behavior of methyl crotonate (CH3CH=CHC(=O)OCH3), which is a short ester representative of large unsaturated methyl esters. Starting with a detailed kinetic model for methyl butanoate (CH3CH2CH2C(=O)OCH3) oxidation, revisions are introduced to the C0-C4 chemistry based on the recent Aramco mechanism 3.0. The resulting mechanism is combined with a short model for methyl crotonate, derived from a suitable reference mechanism. Several new classes of reactions are included and the rate constants of the existing reactions are revised based on various theoretical studies and analogies to reactions of similar species. Furthermore, the low-temperature chemistry of methyl crotonate has been implemented in the current study to extend the validity of the mechanism to lower temperatures. The resulting methyl crotonate combustion mechanism has been comprehensively validated using various experiments in the literature. In addition, experiments are performed using a heat flux burner at atmospheric conditions to measure the laminar burning velocities of methyl crotonate at different unburnt mixture temperatures (318, 338, and 358 K). The mechanism is found to reproduce the experimental data for high-temperature combustion of methyl crotonate satisfactorily. The mechanism is also found to predict the low-temperature ignition delays accurately. Sensitivity and path flux analysis are performed to delineate the importance of the different reaction classes in methyl crotonate chemistry. The current study presents a comprehensive mechanism for methyl crotonate combustion, along with a new set of experimental results complementing the existing experimental database in the literature