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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 Metadata only 3D shape correspondence by isometry-driven greedy optimization(IEEE Computer Soc, 2010) N/A; Department of Computer Engineering; Sahillioğlu, Yusuf; Yemez, Yücel; PhD Student; Faculty Member; Department of Computer Engineering; Graduate School of Sciences and Engineering; College of Engineering; 215195; 107907We present an automatic method that establishes 3D correspondence between isometric shapes. Our goal is to find an optimal correspondence between two given (nearly) isometric shapes, that minimizes the amount of deviation from isometry. We cast the problem as a complete surface correspondence problem. Our method first divides the given shapes to be matched into surface patches of equal area and then seeks for a mapping between the patch centers which we refer to as base vertices. Hence the correspondence is established in a fast and robust manner at a relatively coarse level as imposed by the patch radius. We optimize the isometry cost in two steps. in the first step, the base vertices are transformed into spectral domain based on geodesic affinity, where the isometry errors are minimized in polynomial time by complete bipartite graph matching. the resulting correspondence serves as a good initialization for the second step of optimization in which we explicitly minimize the isometry cost via an iterative greedy algorithm in the original 3D Euclidean space. We demonstrate the performance of our method on various isometric (or nearly isometric) pairs of shapes for some of which the ground-truth correspondence is available.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 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 An analytical model based on G/M/1 with self-similar input to provide end-to-end QoS in 3G networks(Association for Computing Machinery (ACM), 2006) Iftikhar, M.; Landfeldt, B.; Department of Mathematics; Çağlar, Mine; Faculty Member; Department of Mathematics; College of Sciences; 105131The dramatic increase in demand for wireless Internet access has lead to the introduction of new wireless architectures and systems including 3G, Wi-Fi and WiMAX. 3G systems such as UMTS and CDMA2000 are leaning towards an all-IP architecture for transporting IP multimedia services, mainly due to its scalability and promising capability of inter-working heterogeneous wireless access networks. During the last ten years, substantial work has been done to understand the nature of wired IP traffic and it has been proven that IP traffic exhibits self-similar properties and burstiness over a large range of time scales. Recently, because of the large deployment of new wireless architectures, researchers have focused their attention towards understanding the nature of traffic carried by different wireless architecture and early studies have shown that wireless data traffic also exhibits strong long-range dependency. Thus, the classical tele-traffic theory based on a simple Markovian process cannot be used to evaluate the performance of wireless networks. Unfortunately, the area of understanding and modeling of different kinds of wireless traffic is still immature which constitutes a problem since it is crucial to guarantee tight bound QoS parameters to heterogeneous end users of the mobile Internet. In this paper, we make several contributions to the accurate modeling of wireless IP traffic by presenting a novel analytical model that takes into account four different classes of self-similar traffic. The model consists of four queues and is based on a G/M/1 queueing system. We analyze it on the basis of priority with no preemption and find exact packet delays. To date, no closed form expressions have been presented for G/M/1 with priority.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.