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Yayın Tulczyjew's triplet with an Ehresmann connection I: Trivialization and reduction(World Scientific, 2023-03-30) Esen, Oğul; Kudeyt, Mahmut; Sütlü, SerkanWe study the trivialization and the reduction of Tulczyjew's triplet, in the presence of a symmetry and an Ehresmann connection associated to it. We thus establish a geometric pathway for the Legendre transformations on singular dynamical systems.Yayın Numerical investigation of the effect of radial lip seal geometry on sealing performance(IOP Publishing Ltd, 2018) Tok, Görkem; Parlar, Zeynep; Temiz, VedatSealing elements are often needed in industry and especially in machine design. With the change and development of machine technology from day to day, sealing elements show continuous development and change in parallel with these developments. Many factors influence the performance of the sealing elements such as shaft surface roughness, radial force, lip geometry etc. In addition, the radial lip seals must have a certain pre-load and interference in order to provide a good sealing. This also affects the friction torque. Researchers are developing new seal designs to reduce friction losses in mechanical systems. In the presented study, the effect of the lip seal geometry on sealing performance will be examined numerically. The numerical model created for this purpose will be verified with experimental data firstly. In the numerical model, shaft and seal will be modeled as hyper-elastic in 2D and 3D. NBR (Nitrile Butadiene Rubber) as seal material will be analyzed for the rotating shaft state at constant speed by applying a uniform radial force.Yayın On complex solutions of the eikonal equation(IEEE, 2007) Hasanoğlu, ElmanIn this paper a new approach of complex rays in an inhomogeneous medium is presented. Complex rays are complex solutions of the eikonal equation, the main equation of the geometical optics. It is shown that solving the eikonal equation by using the characteristic method naturally leads to the pseudoriemann and Minkowski geometries. In framework of these geometries complex rays , like the real ones, can be drawn in real space and they may have caustics, and caustics also can be drawn in real space.Yayın An endoscopie imaging system based on a two-dimensional CMUT array: real-time imaging results(IEEE, 2005) Wygant, Ira O.; Zhuang, Xuefeng; Yeh, David T.; Vaithilingam, Srikant; Nikoozadeh, Amin; Oralkan, Ömer; Ergün, Arif Sanlı; Karaman, Mustafa; Khuri-Yakub, Butrus ThomasReal-time catheter-based ultrasound imaging tools are needed for diagnosis and image-guided procedures. The continued development of these tools is partially limited by the difficulty of fabricating two-dimensional array geometries of piezoelectric transducers. Using capacitive micromachined ultrasonic transducer (CMUT) technology, transducer arrays with widely varying geometries, high frequencies, and wide bandwidths can be fabricated. A volumetric ultrasound imaging system based on a two-dimensional, 16×l6-element, CMUT array is presented. Transducer arrays with operating frequencies ranging from 3 MHz to 7.5 MHz were fabricated for this system. The transducer array including DC bias pads measures 4 mm by 4.7 mm. The transducer elements are connected to flip-chip bond pads on the array back side with 400-?m long through-wafer interconnects. The array is flip-chip bonded to a custom-designed integrated circuit (IC) that comprises the front-end electronics. Integrating the front-end electronics with the transducer array reduces the effects of cable capacitance on the transducer's performance and provides a compact means of connecting to the transducer elements. The front-end IC provides a 27-V pulser and 10-MHz bandwidth amplifier for each element of the array. An FPGA-based data acquisition system is used for control and data acquisition. Output pressure of 230 kPa was measured for the integrated device. A receive sensitivity of 125 mV/kPa was measured at the output of the amplifier. Amplifier output noise at 5 Mhz is 112 nV/?Hz. Volumetric images of a wire phantom and vessel phantom are presented. Volumetric data for a wire phantom was acquired in real-time at 30 frames per second.Yayın Complex and real rays in three dimensional Minkowski space(IEEE, 2002) Hasanoğlu, ElmanA new approach to the theory of complex rays is proposed. It is shown that the Minkowski space is more appropriate for describing these rays than the usual, Euclidian spaces. Some illustrative examples are represented.Yayın On extensions, Lie-Poisson systems, and dissipation(Heldermann Verlag, 2022-07-06) Esen, Oğul; Özcan, Gökhan; Sütlü, SerkanLie-Poisson systems on the dual spaces of unified products are studied. Having been equipped with a twisted 2-cocycle term, the extending structure framework allows not only to study the dynamics on 2-cocycle extensions, but also to (de)couple mutually interacting Lie-Poisson systems. On the other hand, symmetric brackets; such as the double bracket, the Cartan-Killing bracket, the Casimir dissipation bracket, and the Hamilton dissipation bracket are worked out in detail. Accordingly, the collective motion of two mutually interacting irreversible dynamics, as well as the mutually interacting metriplectic flows, are obtained. The theoretical results are illustrated in three examples. As an infinite-dimensional physical model, decompositions of the BBGKY hierarchy are presented. As for the finite-dimensional examples, the coupling of two Heisenberg algebras, and the coupling of two copies of 3D dynamics are studied.Yayın Predictive vector quantization of 3-D polygonal mesh geometry by representation of vertices in local coordinate systems(IEEE, 2005) Bayazıt, Uluğ; Orcay, Özgür; Konur, Umut; Gürgen, Sadık FikretA large family of lossy 3-D mesh geometry compression schemes operate by predicting the position of each vertex from the coded neighboring vertices and encoding the prediction error vectors. In this work, we first employ entropy constrained extensions of the predictive vector quantization and asymptotically closed loop predictive vector quantization techniques that have been suggested in [3] for coding these prediction error vectors. Then we propose the representation of the prediction error vectors in a local coordinate system with an axis coinciding with the surface normal vector in order to cluster the prediction error vectors around a 2-D subspace. We adopt a least squares approach to estimate the surface normal vector from the non-coplanar, previously coded neighboring vertices. Our simulation results demonstrate that the prediction error vectors can be more efficiently vector quantized by representation in local coordinate systems than in global coordinate systems.Yayın Matched pair analysis of the Vlasov plasma(American Institute of Mathematical Sciences-AIMS, 2021-06) Esen, Oğul; Sütlü, SerkanWe present the Hamiltonian (Lie-Poisson) analysis of the Vlasov plasma, and the dynamics of its kinetic moments, from the matched pair decomposition point of view. We express these (Lie-Poisson) systems as couplings of mutually interacting (Lie-Poisson) subdynamics. The mutual interaction is beyond the well-known semi-direct product theory. Accordingly, as the geometric framework of the present discussion, we address the matched pair Lie-Poisson formulation allowing mutual interactions. Moreover, both for the kinetic moments and the Vlasov plasma cases, we observe that one of the constitutive subdynamics is the compressible isentropic fluid flow, and the other is the dynamics of the kinetic moments of order >= 2. In this regard, the algebraic/geometric (matched pair) decomposition that we offer, is in perfect harmony with the physical intuition. To complete the discussion, we present a momentum formulation of the Vlasov plasma, along with its matched pair decomposition.Yayın Semi-automatic adaptation of high-polygon wireframe face models through inverse perspective projection(Springer-Verlag, 2012) Benli, Kristin Surpuhi; Ağdoğan, Didem; Özgüz, Mete; Eskil, Mustafa TanerPrecise registration of a generic 3D face model with a subject's face is a critical stage for model based analysis of facial expressions. In this study we propose a semi-automatic model fitting algorithm to fit a high-polygon wireframe model to a single image of a face. We manually mark important landmark points both on the wireframe model and the face image. We carry out an initial alignment by translating and scaling the wireframe model. We then translate the landmark vertices in the 3D wireframe model so that they coincide with inverse perspective projections of image landmark points. The vertices that are not manually labeled as landmark are translated with a weighted sum of vectorial displacement of k neighboring landmark vertices, inversely weighted by their 3D distances to the vertex under consideration. Our experiments indicate that we can fit a high-polygon model to the subject's face with modest computational complexity.Yayın Transient multi-domain thermal modeling of interrupted cutting with coated tools(Springer Science and Business Media Deutschland GmbH, 2021-09) Karagüzel, UmutInterrupted cutting operations, such as milling, produce fluctuating tool temperatures which directly affect the process outputs. Thus, prediction of cutting tool temperatures enables process planning, selection of materials for tool substrate and coating layers, and tool geometric design for improved productivity in machining operations. Theoretical analysis of temperature is a cost effective way to predict the tool temperatures. Considering the industrial needs, a theoretical model should be fast, easy to implement, and reliable. To that end, a novel hybrid model, which assembles analytical and numerical methods, is proposed in this study. This novel transient thermal model simulates the interrupted cutting with coated cutting tools. The proposed model includes an analytical heat flux calculation at the tool-chip interface considering the sticking-sliding contact behavior. The determined heat flux is, then, used to perform a numerical solution of the transient heat conduction problem in the cutting tool geometry with temperature-dependent thermal properties. The developed model is validated with experimental results found in literature under different cutting conditions. The results show that the model can predict the maximum temperatures generated in a thermal cycle with an accuracy of 2–10%. Thus, the proposed model can be further used to determine the process parameters, properties of coating layers, and tool geometric design.
