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Publication Open Access A statistical subgrid scale model for large eddy simulations(American Institute of Physics (AIP) Publishing, 2013) Kara, Rukiye; Department of Mathematics; Çağlar, Mine; Faculty Member; Department of Mathematics; College of Sciences; 105131Çinlar velocity is a promising subgrid velocity model for large eddy simulation. The energy spectrum plays a central role for modeling the subgrid stress term in filtered Navier-Stokes equations. Considering a truncated Gamma distribution for radius of eddies, the subgrid scale energy spectrum has been computed analytically. In this study, we develop a new subgrid stress model for representing the small scale effects in LES by defining the parameters of the energy spectrum.
Publication Metadata only A support function based algorithm for optimization with eigenvalue constraints(Siam Publications, 2017) N/A; Department of Mathematics; Mengi, Emre; Faculty Member; Department of Mathematics; College of Sciences; 113760Optimization of convex functions subject to eigenvalue constraints is intriguing because of peculiar analytical properties of eigenvalue functions and is of practical interest because of a wide range of applications in fields such as structural design and control theory. Here we focus on the optimization of a linear objective subject to a constraint on the smallest eigenvalue of an analytic and Hermitian matrix-valued function. We propose a numerical approach based on quadratic support functions that overestimate the smallest eigenvalue function globally. the quadratic support functions are derived by employing variational properties of the smallest eigenvalue function over a set of Hermitian matrices. We establish the local convergence of the algorithm under mild assumptions and deduce a precise rate of convergence result by viewing the algorithm as a fixed point iteration. the convergence analysis reveals that the algorithm is immune to the nonsmooth nature of the smallest eigenvalue. We illustrate the practical applicability of the algorithm on the pseudospectral functions.Publication Open Access Adiabatic approximation, semiclassical scattering, and unidirectional invisibility(Institute of Physics (IOP) Publishing, 2014) Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231The transfer matrix of a possibly complex and energy-dependent scattering potential can be identified with the S-matrix of a two-level time-dependent non-Hermitian Hamiltonian H(tau). We show that the application of the adiabatic approximation to H(tau) corresponds to the semiclassical description of the original scattering problem. In particular, the geometric part of the phase of the evolving eigenvectors of H(tau) gives the pre-exponential factor of the WKB wave functions. We use these observations to give an explicit semiclassical expression for the transfer matrix. This allows for a detailed study of the semiclassical unidirectional reflectionlessness and invisibility. We examine concrete realizations of the latter in the realm of optics.Publication Metadata only Alternative polynomial and holomorphic Dunford-Pettis properties(Scientific and Technical research Council of Turkey - TUBITAK/Türkiye Bilimsel ve Teknik Araştırma Kurumu, 1999) Department of Mathematics; Freedman, Walden; Faculty Member; Department of Mathematics; College of Sciences; N/AAlternatives to the Polynomial Dunford-Pettis property and the Holomorphic Dunford-Pettis property, called the PDP1 and HDP1 properties, respectively, are introduced. These are shown to be equivalent to the DP1 property, an alternative Dunford-Pettis property previously introduced by the author, thus mirroring the equivalence of the three original properties. © TÜBİTAK.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 Open Access Area minimizing surfaces in mean convex 3-manifolds(De Gruyter, 2015) Bourni, Theodora; Department of Mathematics; Coşkunüzer, Barış; Faculty Member; Department of Mathematics; College of SciencesIn this paper, we give several results on area minimizing surfaces in strictly mean convex 3-manifolds. First, we study the genus of absolutely area minimizing surfaces in a compact, orientable, strictly mean convex 3-manifold M bounded by a simple closed curve in partial derivative M. Our main result is that for any g >= 0, the space of simple closed curves in partial derivative M where all the absolutely area minimizing surfaces they bound in M has genus >= g is open and dense in the space A of nullhomologous simple closed curves in partial derivative M. For showing this we prove a bridge principle for absolutely area minimizing surfaces. Moreover, we show that for any g >= 0, there exists a curve gamma(g) in A such that the minimum genus of the absolutely area minimizing surfaces gamma(g) bounds is exactly g. As an application of these results, we further prove that the simple closed curves in partial derivative M bounding more than one minimal surface in M is an open and dense subset of A. We also show that there are disjoint simple closed curves in partial derivative M bounding minimal surfaces in M which are not disjoint. This allows us to answer a question of Meeks, by showing that for any strictly mean convex 3-manifold M, there exists a simple closed curve Gamma in partial derivative M which bounds a stable minimal surface which is not embedded. We also gave some applications of these results to the simple closed curves in R-3.Publication Open Access Asymptotic H-Plateau problem in H-3(Mathematical Sciences Publishers (MSP), 2016) Department of Mathematics; Coşkunüzer, Barış; Faculty Member; Department of Mathematics; College of SciencesWe show that for any Jordan curve Gamma in S-infinity(2) (H-3) with at least one smooth point, there exists an embedded H-plane P-H in H-3 with partial derivative P-infinity(H) = Gamma for any H is an element of [0, 1).Publication Open Access Biembeddings of cycle systems using integer Heffter arrays(Wiley, 2020) Cavenagh, Nicholas J.; Donovan, Diane M.; Department of Mathematics; Yazıcı, Emine Şule; Faculty Member; Department of Mathematics; College of Sciences; 27432In this paper, we use constructions of Heffter arrays to verify the existence of face 2-colorable embeddings of cycle decompositions of the complete graph. Specifically, forn degrees 1(mod 4)andk degrees 3(mod4),n >> k > 7and whenn degrees 0(mod 3)thenk degrees 7(mod 12), there exist face 2-colorable embeddings of the complete graphK2nk+1onto an orientable surface where each face is a cycle of a fixed lengthk. In these embeddings the vertices ofK2nk+1will be labeled with the elements ofZ2nk+1in such a way that the group,(Z2nk+1,+)acts sharply transitively on the vertices of the embedding. This result is achieved by verifying the existence of nonequivalent Heffter arrays,H(n;k), which satisfy the conditions: (1) for each row and each column the sequential partial sums determined by the natural ordering must be distinct modulo2nk+1; (2) the composition of the natural orderings of the rows and columns is equivalent to a single cycle permutation on the entries in the array. The existence of Heffter arraysH(n;k)that satisfy condition (1) was established earlier in Burrage et al. and in this current paper, we vary this construction and show, fork > 11, that there are at least(n-2)[((k-11)/4)!/e]2such nonequivalentH(n;k)that satisfy both conditions (1) and (2).Publication Metadata only Big Heegner point Kolyvagin system for a family of modular forms(Springer International Publishing Ag, 2014) Department of Mathematics; Büyükboduk, Kazım; Faculty Member; Department of Mathematics; College of Sciences; N/AThe principal goal of this paper is to develop Kolyvagin's descent to apply with the big Heegner point Euler system constructed by Howard for the big Galois representation attached to a Hida family of elliptic modular forms. In order to achieve this, we interpolate and control the Tamagawa factors attached to each member of the family at bad primes, which should be of independent interest. Using this, we then work out the Kolyvagin descent on the big Heegner point Euler system so as to obtain a big Kolyvagin system that interpolates the collection of Kolyvagin systems obtained by Fouquet for each member of the family individually. This construction has standard applications to Iwasawa theory, which we record at the end.Publication Open Access Bilevel programming for generating discrete representations in multiobjective optimization(Springer, 2018) Kirlik, Gökhan; Department of Business Administration; Sayın, Serpil; Faculty Member; Department of Business Administration; College of Administrative Sciences and Economics; 6755The solution to a multiobjective optimization problem consists of the nondominated set that portrays all relevant trade-off information. The ultimate goal is to identify a Decision Maker's most preferred solution without generating the entire set of nondominated solutions. We propose a bilevel programming formulation that can be used to this end. The bilevel program is capable of delivering an efficient solution that maps into a given set, provided that one exits. If the Decision Maker's preferences are known a priori, they can be used to specify the given set. Alternatively, we propose a method to obtain a representation of the nondominated set when the Decision Maker's preferences are not available. This requires a thorough search of the outcome space. The search can be facilitated by a partitioning scheme similar to the ones used in global optimization. Since the bilevel programming formulation either finds a nondominated solution in a given partition element or determines that there is none, a representation with a specified coverage error level can be found in a finite number of iterations. While building a discrete representation, the algorithm also generates an approximation of the nondominated set within the specified error factor. We illustrate the algorithm on the multiobjective linear programming problem.