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Publication Open Access 2D hybrid meshes for direct simulation Monte Carlo solvers(Institute of Physics (IOP) Publishing, 2013) Şengil, Nevsan; Department of Mathematics; Şengil, Uluç; Master Student; Department of Mathematics; College of SciencesThe efficiency of the direct simulation Monte Carlo (DSMC) method decreases considerably if gas is not rarefied. In order to extend the application range of the DSMC method towards non-rarefied gas regimes, the computational efficiency of the DSMC method should be increased further. One of the most time consuming parts of the DSMC method is to determine which DSMC molecules are in close proximity. If this information is calculated quickly, the efficiency of the DSMC method will be increased. Although some meshless methods are proposed, mostly structured or non-structured meshes are used to obtain this information. The simplest DSMC solvers are limited with the structured meshes. In these types of solvers, molecule indexing according to the positions can be handled very fast using simple arithmetic operations. But structured meshes are geometry dependent. Complicated geometries require the use of unstructured meshes. In this case, DSMC molecules are traced cell-by-cell. Different cell-by-cell tracing techniques exist. But, these techniques require complicated trigonometric operations or search algorithms. Both techniques are computationally expensive. In this study, a hybrid mesh structure is proposed. Hybrid meshes are both less dependent on the geometry like unstructured meshes and computationally efficient like structured meshes.Publication Open Access A class of Banach algebras whose duals have the Schur property(TÜBİTAK, 1999) Mustafayev, H.; Department of Mathematics; Ülger, Ali; Faculty Member; Department of Mathematics; College of SciencesCall a commutative Banach algebra A a γ-algebra if it contains a bounded group Λ such that aco(Λ) contains a multiple of the unit ball of A. In this paper, first by exhibiting several concrete examples, we show that the class of γ-algebras is quite rich. Then, for a γ-algebra A, we prove that A* has the Schur property iff the Gelfand spectrum Σ of A is scattered iff A* = ap(A) iff A* = Span(Σ).Publication Open Access A comparison of game-theoretic models for parallel trade(World Scientific Publishing, 2018) Gnecco, Giorgio; Pammolli, Fabio; Department of Economics; Alpanda, Berna Tuncay; Faculty Member; Department of Economics; College of Administrative Sciences and EconomicsWithin the EU Single Market for medicines, differences in drug prices, regulations, and transaction costs may create, under suitable conditions, arbitrage opportunities well before patent expiration, giving an incentive to the occurrence of parallel trade. When this is permitted, parallel traders may obtain a profit from buying drugs in a country where prices are lower, then re-selling them in a country where prices are higher. This phenomenon may came inefficiencies from a global welfare perspective, and reduce the manufacturers' incentive to invest in Research and Development (R & D). Given this framework, in this paper, we investigate the efficiency (expressed in terms of the price of anarchy) of the subgame-perfect Nash equilibria associated with five dynamic noncooperative game-theoretic models for the parallel trade of pharmaceuticals. We also compare such models with regard to the manufacturer's incentive to invest in R & D. More specifically, first we find in closed form the optimal value of the global welfare of two countries, which is obtained by solving a suitable quadratic optimization problem modeling the decision-making process of a global planner. Then, we use such a result. to evaluate and compare the prices of anarchy of five games modeling the interaction between a manufacturer in the first country and a potential parallel trader in the second country. The first three games refer, respectively, to the cases of no parallel trade threat, parallel trade threat, and parallel trade occurrence at equilibrium. Then, we investigate two modifications of the third game, in which its transfer payment from the potential parallel trader to the manufacturer is, respectively, removed/determined by Nash bargaining. For completeness, we also consider a decision-theoretic model of no parallel trade threat. For what concerns the incentive for the manufacturer to invest in R & D, the results of our numerical comparison show that the decision-theoretic model of no parallel trade threat is always the one with the highest incentive, whereas the two game-theoretic models of parallel trade threat/occurrence that do not include the transfer payment provide typically the lowest incentives. Moreover, the latter two models have the highest prices of anarchy (i.e., their equilibria have the lowest efficiencies). From a policy-making perspective, improvements are obtained if suitable countermeasures are taken to help the manufacturer recover from the costs of R & D, such as the inclusion of a transfer payment in the model.Publication Open Access A note on weakly compact homomorphisms between uniform algebras(Polish Academy of Sciences, 1997) Department of Mathematics; Ülger, Ali; Faculty Member; Department of Mathematics; College of SciencesPublication Open Access A polynomial embedding of pair of partial orthogonal latin squares(Elsevier, 2014) Donovan, Diane M.; Department of Mathematics; Yazıcı, Emine Şule; Faculty Member; Department of Mathematics; College of Sciences; 27432We show that a pair of orthogonal partial Latin squares of order n can be embedded in a pair of orthogonal Latin squares of order at most 16n(4) and all orders greater than or equal to 48n(4). This paper provides the first direct polynomial order embedding construction for pairs of orthogonal partial Latin squares.Publication Open Access A review on computational modeling tools for MOF-based mixed matrix membranes(Multidisciplinary Digital Publishing Institute (MDPI), 2019) Department of Chemical and Biological Engineering; Keskin, Seda; Faculty Member; Department of Chemical and Biological Engineering; College of Engineering; 40548Computational modeling of membrane materials is a rapidly growing field to investigate the properties of membrane materials beyond the limits of experimental techniques and to complement the experimental membrane studies by providing insights at the atomic-level. In this study, we first reviewed the fundamental approaches employed to describe the gas permeability/selectivity trade-off of polymer membranes and then addressed the great promise of mixed matrix membranes (MMMs) to overcome this trade-off. We then reviewed the current approaches for predicting the gas permeation through MMMs and specifically focused on MMMs composed of metal organic frameworks (MOFs). Computational tools such as atomically-detailed molecular simulations that can predict the gas separation performances of MOF-based MMMs prior to experimental investigation have been reviewed and the new computational methods that can provide information about the compatibility between the MOF and the polymer of the MMM have been discussed. We finally addressed the opportunities and challenges of using computational studies to analyze the barriers that must be overcome to advance the application of MOF-based membranes.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 Open Access A stochastic representation for mean curvature type geometric flows(Institute of Mathematical Statistics (IMS), 2003) Touzi, N.; Department of Mathematics; Soner, Halil Mete; Faculty Member; Department of Mathematics; College of Administrative Sciences and EconomicsA smooth solution {Gamma(t)}(tis an element of[0,T]) subset of R-d of a parabolic geometric flow is characterized as the reachability set of a stochastic target problem. In this control problem the controller tries to steer the state process into a given deterministic set T with probability one. The reachability set, V(t), for the target problem is the set of all initial data x from which the state process X-X(v)(t) is an element of T for some control process v. This representation is proved by studying the squared distance function to Gamma(t). For the codimension k mean curvature flow, the state process is dX(t) = root2P dW(t), where W(t) is a d-dimensional Brownian motion, and the control P is any projection matrix onto a (d - k)-dimensional plane. Smooth solutions of the inverse mean curvature flow and a discussion of non smooth solutions are also given.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 Open Access An uncountable ergodic Roth theorem and applications(American Institute of Mathematical Sciences, 2022) Schmid, Polona durcik; Greenfeld, Rachel; Iseli, Annina; Jamneshan; Madrid, Jose; Department of Mathematics; Jamneshan, Asgar; Faculty Member; Department of Mathematics; College of Sciences; 332404We establish an uncountable amenable ergodic Roth theorem, in which the acting group is not assumed to be countable and the space need not be separable. This generalizes a previous result of Bergelson, McCutcheon and Zhang, and complements a result of Zorin-Kranich. We establish the following two additional results: First, a combinatorial application about triangular patterns in certain subsets of the Cartesian square of arbitrary amenable groups, extending a result of Bergelson, McCutcheon and Zhang for countable amenable groups. Second, a new uniformity aspect in the double recurrence theorem for Gamma-systems for uniformly amenable groups Gamma. As a special case, we obtain this uniformity over all Z-systems, and our result seems to be novel already in this case. Our uncountable Roth theorem is crucial in the proof of both of these results.