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Publication Metadata only A LES/PDF simulator on block-structured meshes(Taylor & Francis Ltd, 2019) Pope, Stephen B.; N/A; Department of Mechanical Engineering; Türkeri, Hasret; Muradoğlu, Metin; PhD Student; Faculty Member; Department of Mechanical Engineering; Graduate School of Sciences and Engineering; College of Engineering; N/A; 46561A block-structured mesh large-eddy simulation (LES)/probability density function (PDF) simulator is developed within the OpenFOAM framework for computational modelling of complex turbulent reacting flows. The LES/PDF solver is a hybrid solution methodology consisting of (i) a finite-volume (FV) method for solving the filtered mass and momentum equations (LES solver), and (ii) a Lagrangian particle-based Monte Carlo algorithm (PDF solver) for solving the modelled transport equation of the filtered joint PDF of compositions. Both the LES and the PDF methods are developed and combined to form a hybrid LES/PDF simulator entirely within the OpenFOAM framework. The in situ adaptive tabulation method [S.B. Pope, Computationally efficient implementation of combustion chemistry using in situ adaptive tabulation, Combust. Theory Model. 1 (1997), pp. 41-63; L. Lu, S.R. Lantz, Z. Ren, and B.S. Pope, Computationally efficient implementation of combustion chemistry in parallel PDF calculations, J. Comput. Phys. 228 (2009), pp. 5490-5525] is incorporated into the new LES/PDF solver for efficient computations of combustion chemistry with detailed reaction kinetics. The method is designed to utilise a block-structured mesh and can readily be extended to unstructured grids. The three-stage velocity interpolation method of Zhang and Haworth [A general mass consistency algorithm for hybrid particle/finite-volume PDF methods, J. Comput. Phys. 194 (2004), pp. 156-193] is adapted to interpolate the LES velocity field onto particle locations accurately and to enforce the consistency between LES and PDF fields at the numerical solution level. The hybrid algorithm is fully parallelised using the conventional domain decomposition approach. A detailed examination of the effects of each stage and the overall performance of the velocity interpolation algorithm is performed. Accurate coupling of the LES and PDF solvers is demonstrated using the one-way coupling methodology. Then the fully two-way coupled LES/PDF solver is successfully applied to simulate the Sandia Flame-D, and a turbulent non-swirling premixed flame and a turbulent swirling stratified flame from the Cambridge turbulent stratified flame series [M.S. Sweeney, S. Hochgreb, M.J. Dunn, and R.S. Barlow, The structure of turbulent stratified and premixed methane/air flames I: Non-swirling flows, Combust. Flame 159 (2012), pp. 2896-2911; M.S. Sweeney, S. Hochgreb, M.J. Dunn, and R.S. Barlow, The structure of turbulent stratified and premixed methane/air flames II: Swirling flows, Combust. Flame 159 (2012), pp. 2912-2929]. It is found that the LES/PDF method is very robust and the results are in good agreement with the experimental data for both flames.Publication Metadata only A note on power bounded elements of von neumann algebras(Editura Acad Romane, 2014) Department of Mathematics; Ülger, Ali; Faculty Member; Department of Mathematics; College of Sciences; N/ALet A be a von Neumann algebra with predual A(*) and the unit element 1. An element a of A is said to be power bounded if sup(n >= 0) vertical bar vertical bar a(n)vertical bar vertical bar < infinity. In this note we show that, for any power bounded element a of A, theta = sigma(A, A(*)) - lim(n ->infinity)(1+a/2)(n) exists, theta is an idempotent and theta a = a theta = theta.Publication Metadata only A partial kite system of order n can be embedded in a kite system of order 8n+9(Charles Babbage Res Ctr, 2006) Lindner, Charles Curtis; Rodger, C.; Department of Mathematics; Küçükçifçi, Selda; Faculty Member; Department of Mathematics; College of Sciences; 105252In this paper, it is shown that a partial edge-disjoint decompostion of K-n into kites (that is, into copies of K-3 with a pendant edge attached) can be embedded in a complete edge-disjoint decompostion of K4t+9 into kites for all even t >= 2n. The proof requires first proving another interesting result, a generalization of an embeddding result on symmetric latin squares by L. D. Andersen, following a result by A. Cruse.Publication Metadata only A partial kite system of order n can be embedded in a kite system of order 8n+9(Charles Babbage Research Centre, 2006) Lindner, C.; Rodger, C.; Department of Mathematics; Küçükçifçi, Selda; Faculty Member; Department of Mathematics; College of Sciences; 105252In this paper, it is shown that a partial edge-disjoint decompostion of Kn into kites (that is, into copies of K3 with a pendant edge attached) can be embedded in a complete edge-disjoint decompostion of K4t+9 into kites for all even t ≥ 2n. The proof requires first proving another interesting result, a generalization of an embeddding result on symmetric latin squares by L. D. Andersen, following a result by A. Cruse.Publication Metadata only Adaptive stochastic search(Elsevier, 2019) Aguiar, Victor H.; Department of Economics; Kimya, Mert; Faculty Member; Department of Economics; College of Administrative Sciences and Economics; N/AWe characterize Simon's (1955) search and satisficing model with an adaptive threshold and random search (SM-AT). The decision maker (DM) consistent with the SM-AT is endowed with a utility function, a random search distribution, and a deterministic but menu-dependent threshold. On any given trial, the DM searches the menu and stops whenever she finds an item with a utility level that is above the threshold. This simple choice procedure accommodates the well-known compromise and attraction effects. The SM-AT is more general than the random utility model and allows for systematic departures from regularity. Its characterization lets us differentiate adaptive satisficing behavior from random preference maximization in a (limited) standard stochastic choice data set.Publication Open Access Application of stochastic flows to the sticky Brownian motion equation(Multidisciplinary Digital Publishing Institute (MDPI), 2017) Hajri, Hatem; Arnaudon, Marc; Department of Mathematics; Çağlar, Mine; Faculty Member; Department of Mathematics; College of Sciences; 105131We investigate the relationship between the levels of industry collaboration and entrepreneurial activities at universities and the employment choices of their science and engineering doctoral students. Using data from 176 U.S. universities over the period 1996-2005, we document that more interaction with industry at a university is typically associated with more of the university's doctoral students choosing industry employment. We also document a positive relationship between universities' licenses and startups and their graduates' post-doctoral study choices.Publication Metadata only Applications of bombieri-vinogradov type theorems to power-free integers(Ars Polona-Ruch, 2021) Department of Mathematics; Alkan, Emre; Faculty Member; Department of Mathematics; College of Sciences; 32803Studying a variant of a classical result of Walfisz on the number of representations of an integer as the sum of a prime number and a square-free integer with an extra additive constraint on the prime summand, we obtain an asymptotic formula for the number of representations of an integer N such that N - 1 is a prime number in the form p + N - p, where p is a prime number, N - p is square-free and p - 1 is cube-free. We improve the error term for the number of representations of an integer as the sum of a prime number and a k-free integer conditionally by assuming weaker forms of the Riemann hypothesis for Dirichlet L-functions. As a further application of our method, we find an asymptotic formula for the number of prime numbers p <= x such that p + 2y, 1 <= y <= 7, are all square-free. Our formula shows that a positive proportion of prime numbers leads to a longest possible progression of eight consecutive odd, square-free integers. A key ingredient in our approach is the Bombieri-Vinogradov theorem and its variant for sparse moduli due to Baier and Zhao which regulates the uniform distribution of prime numbers along certain short arithmetic progressions.Publication Metadata only Average r-rank artin conjecture(Polish Acad Sciences Inst Mathematics-IMPAN, 2016) Menici, Lorenzo; Department of Mathematics; Pehlivan, Cihan; Researcher; Department of Mathematics; College of Sciences; N/AN/APublication Metadata only Balanced and strongly balanced 4-kite designs(Utilitas Mathematica Publishing, 2013) Gionfriddo, Mario; Milazzo, Lorenzo; Department of Mathematics; Küçükçifçi, Selda; Faculty Member; Department of Mathematics; College of Sciences; 105252A G-design is called balanced if the degree of each vertex x is a constant. A G-design is called strongly balanced if for every i = 1, 2, ⋯, h, there exists a constant Ci such that dAi(x)= Ci for every vertex x, where AiS are the orbits of the automorphism group of G on its vertex-set and dAi(x) of a vertex is the number of blocks of containing x as an element of Ai. We say that a G-design is simply balanced if it is balanced, but not strongly balanced. In this paper we determine the spectrum of simply balanced and strongly balanced 4-kite designs.Publication Metadata only Blow-up of solutions of coupled parabolic systems and hyperbolic equations(Springer, 2022) Kalantarova, Jamila; Department of Mathematics; Kalantarov, Varga; Faculty Member; Department of Mathematics; College of Sciences; 117655The problem of the blow-up of solutions of coupled systems of nonlinear parabolic and hyperbolic equations of second order is studied. The concavity method and its modifications are used to find sufficient conditions for the blow-up of solutions for an arbitrary positive initial energy of the problem.