Browsing by Subject "Geometry"

Now showing 1 - 20 of 46

Open Access
Accurate simulation of reflector antennas by the complex source-dual series approach
(Institute of Electrical and Electronics Engineers, 1995-08) Oğuzer, T.; Altıntaş, A.; Nosich, A. I.
The radiation from circular cylindrical reflector antennas is treated in an accurate manner for both polarizations. The problem is first formulated in terms of the dual series equations and then is regularized by the Riemann-Hilbert problem technique. The resulting matrix equation is solved numeridy with a guaranteed accuracy, and remarkably Little CPU time is needed. The feed directivity is included in the analysis by the complex source point method. Various characteristic patterns are obtained for the front and offset-fed reflector antenna geometries with this analysis, and some comparisons are made with the high frequency techniques. The directivity and radiated power properties are also studied.
Open Access
Active pixel merging on hypercube multicomputers
(Springer, Berlin, Heidelberg, 1996) Kurç, Tahsin M.; Aykanat, Cevdet; Özgüç, Bülent
This paper presents algorithms developed for pixel merging phase of object-space parallel polygon rendering on hypercube-connected multicomputers. These algorithms reduce volume of communication in pixel merging phase by only exchanging local foremost pixels. In order to avoid message fragmentation, local foremost pixels should be stored in consecutive memory locations. An algorithm, called modified seanline z-buffer, is proposed to store local foremost pixels efficiently. This algorithm also avoids the initialization of scanline z-buffer for each scanline on the screen. Good processor utilization is achieved by subdividing the image-space among the processors in pixel merging phase. Efficient algorithms for load balancing in the pixel merging phase are also proposed and presented. Experimental results obtained on a 16-processor Intel's iPSC/2 hypercube multicomputer are presented. © Springer-Verlag Berlin Heidelberg 1996.
Open Access
“Books i used as a child were mathematically incorrect”: reasons to use children’s shape-related books as a resource to improve mathematical knowledge for teaching
(Modestum Publishing Ltd., 2021-04-05) Alexander, Anita N.; Nurnberger-Haag, Julie; Singh, Rashmi; Wernet, Jamie L. W.
Some goals of mathematics teacher education include ensuring that pre-service teachers (PSTs) have strong content knowledge, the skill to anticipate and interpret student thinking, the ability to plan how to respond, and the ability to critically select resources for instruction. These goals are especially challenging for the topic of geometric shapes. Thus, we share an instructional activity that focuses PSTs’ attention on an inaccurate resource of geometric information, children’s books, to accomplish these goals in mathematics content as well as methods courses. Analyses of surveys and content assessments conducted to assess efficacy of the Shape Book Critique Activity were interpreted with the Mathematical Knowledge for Teaching (MKT) framework. Based on the findings we suggest that this short 40-minute activity is a promising way to promote PSTs’ growth in three aspects of MKT for geometric shapes.
Open Access
Circular-planned diagrid systems and an interrelated technique using planar elements
(Birkhaeuser Science, 2018) Kinayoğlu, Gökhan; Şenyapılı, Burcu
This paper presents the development of circular-planned diagrid systems in architecture and varying approaches in patents in relation to these developments, together with a technique introduced for producing diagrid implementations using planar elements. A circular plan creates a curved surface at its periphery that leads to the diagrid system on a curved surface, resulting in unique geometric configurations. Patents based on these geometric configurations and their details, registered between 1896 and 2016, are documented. A technique is devised by the authors as a reinterpretation of the diagrid system via planar components with its own parameters and principles. This technique may be utilized by design offices or by the students of architecture for prototyping or modelling a circular-planned diagrid structure in a precise, fast and economical manner by means of conventional CNC manufacturing techniques.
Open Access
Closed-form Green's functions for general sources and stratified media
(Institute of Electrical and Electronics Engineers, 1995-07) Dural, G.; Aksun, M. I.
The closed-form Green's functions of the vector and scalar potentials in the spatial domain are presented for the sources of horizontal electric, magnetic, and vertical electric, magnetic dipoles embedded in general, multilayer, planar media. First, the spectral domain Green's functions in an arbitrary layer are derived analytically from the Green's functions in the source layer by using a recursive algorithm. Then, the spatial domain Green's functions are obtained by adding the contributions of the direct terms, surface waves, and complex images approximated by the Generalized Pencil of Functions Method (GPOF). In the derivations, the main emphasis is to put these closed-form representations in a suitable form for the solution of the mixed potential integral equation (MPIE) by the method of moments in a general three-dimensional geometry. The contributions of this paper are: 1) providing the complete set of closed-form Green's functions in spectral and spatial domains for general stratified media; 2) using the GPOF method, which is more robust and less noise sensitive, in the derivation of the closed-form spatial domain Green's functions; and 3) casting the closed-form Green's functions in a form to provide efficient applications of the method of moments.
Open Access
Combined-field solution of composite geometries involving open and closed conducting surfaces
(IEEE, 2005-04) Ergül, Özgür; Gürel, Levent
Combined-field integral equation (CFIE) is modified and generalized to formulate the electromagnetic problems of composite geometries involving both open and closed conducting surfaces. These problems are customarily formulated with the electric-field integral equation (EFIE) due to the presence of the open surfaces. With the new definition and application of the CFIE, iterative solutions of these problems are now achieved with significantly improved efficiency compared to the EFIE solution, without sacrificing the accuracy. © 2005 ACES.
Open Access
Comparative evaluation of absorbing boundary conditions using Green's functions for layered media
(Institute of Electrical and Electronics Engineers, 1996-02) Aksun, M. İrşadi; Dural, G.
Absorbing boundary conditions are comparatively studied using the Green's functions of the vector and scalar potentials for multilayer geometries and general sources. Since the absorbing boundaries are introduced as additional layers with predefined reflection coefficients into the calculation of the Green's functions, this approach provides an absolute measure of the effectiveness of different absorbing boundaries. The Green's functions are calculated using different reflection coefficients corresponding to different absorbing boundaries and compared to those obtained with no absorbing boundary. It is observed that the perfectly matched layer (PML) is by far the best among the other absorbing boundary conditions whose reflection coefficients are available.
Open Access
Comparative study of acceleration techniques for integrals and series in electromagnetic problems
(IEEE, 1995-06) Kinayman, Noyan; Aksun, M. I.
Most of the electromagnetic problems can be reduced down to either integrating oscillatory integrals or summing up complex series. However, limits of the integrals and the series usually extend to infinity. In addition, they may be slowly convergent. Therefore, numerically efficient techniques for evaluating the integrals or for calculating the sum of infinite series have to be used to make the numerical solution feasible and attractive. In the literature, there are a wide range of applications of such methods to various EM problems. In this paper, our main aim is to critically examine the popular series transformation (acceleration) methods which are used in electromagnetic problems and compare them by numerical examples.
Open Access
Design and determination of stator geometry for axial flux permanent magnet free rod rotor synchronous motor
(2011) Kalender O.; Ege, Y.; Nazlibilek, S.
During designing a new axial flux permanent magnet free rod rotor synchronous motor, it is important to know before hand in which phase the largest angular velocity can occur, what is the ways to reduce the power consumption, how to achieve to increase or decrease the rotation speed by changing the core geometry. Therefore, presenting these preliminary information that are necessary for the design of a free rod rotor synchronous motor to the researchers is the aim of this work. In this respect, this study presents the design and geometrical dimensions of the stator for a new synchronous motor which is an axial flux permanent magnet free rod machine with three, four, five and six phases. This type of motors are an innovative approach especially for the applications used in industrial stirrers. Each type of stator is designed such that it has an appropriate number of phases. The rotating magnetic field over the stator is established by a PIC based microcontroller feeding the interface circuit to the stator wounds. The maximum angular speeds of bar magnet rotors with four different lengths and masses are calculated theoretically and determined experimentally. In addition, the effects of the distance between the rotor and stator, the angular speed of the rotor within the limits of the operation, and the volume of the liquid to be stirred to the power applied are investigated. Furthermore, the effects of the lengths and angular speeds of the bar magnet rotors to the distance between the rotor and stator are determined. In the light of the information obtained and taking into account the power used, the most appropriate parameters and variables such as the stator geometry changing with the phase used, the length of rotor, the distance between the rotor and stator and the angular speeds of rotor are determined. © 2011 Elsevier Ltd. All rights reserved.
Open Access
Effect of cross-sectional geometry on the RPA plasmons of quantum wires
(Pergamon Press, 1994) Bennett, C. R.; Tanatar, Bilal; Constantinou, N. C.; Babiker, M.
The effect of cross-sectional geometry on both the intrasubband plasmon and intersubband plasmon of a quantum wire is investigated within a two-subband RPA scheme. Exact analytical electronic wavefunctions for circular, elliptical and rectangular wires are employed within the infinite barrier approximation. It is found that for fixed cross-sectional area and linear electron concentration, the intrasubband plasmon energy is only marginally dependent on the wire geometry whereas the intersubband plasmon energy may change considerably due to its dependence on the electronic subband energy difference. © 1994.
Open Access
Efficient use of closed-form Green's functions for three-dimensional problems involving multilayered media
(IEEE, 1994-06) Aksun, M. Irsadi; Mittra, R.
With the use of casting the spatial domain Green's functions into closed forms approach, it was demonstrated that the computational efficiency of the method of moments (MoM) for the solution of the mixed potential integral equations can be improved significantly for planar microstrip geometries. However, this approach is not effective in the improvement in the computational efficiency achieved for three-dimensional geometries in planar layered media. In this paper, discussed are the difficulties involved in using the spatial domain, closed-form Green's functions in the Method of Moments formulation for three-dimensional geometries and proposed a technique to improve the computational efficiency of the MoM.
Open Access
European collaboration in conformal antenna research
(IEEE, 2007-09) Sipus, Z.; Persson P.; Lanne, M.; Heckler, M.; Maci, S.; Campos, J. L. M.; Knott, P.; Ertürk, Vakur; Vandenbosch, G.
The work carried out within Work Package 2.4-3 of the EU network "Antenna Centre of Excellence" (ACE) is presented in this paper. This work package is concerned with structuring research on conformal antennas. In more details, the work is focused on the problems associated with full benchmarking of conformal antennas, on development of hybrid programs for analyzing different classes of conformal antennas, and on investigation of properties of algorithms for optimizing beam synthesis and beam-steering for conformal arrays.
Open Access
Evolution of the Hofstadter butterfly in a tunable optical lattice
(American Physical Society, 2015) Yllmaz, F.; Ünal, F. N.; Oktel, M. O.
Recent advances in realizing artificial gauge fields on optical lattices promise experimental detection of topologically nontrivial energy spectra. Self-similar fractal energy structures generally known as Hofstadter butterflies depend sensitively on the geometry of the underlying lattice, as well as the applied magnetic field. The recent demonstration of an adjustable lattice geometry [L. Tarruell, D. Greif, T. Uehlinger, G. Jotzu, and T. Esslinger, Nature (London) 483, 302 (2012)NATUAS0028-083610.1038/nature10871] presents a unique opportunity to study this dependence. In this paper, we calculate the Hofstadter butterflies that can be obtained in such an adjustable lattice and find three qualitatively different regimes. We show that the existence of Dirac points at zero magnetic field does not imply the topological equivalence of spectra at finite field. As the real-space structure evolves from the checkerboard lattice to the honeycomb lattice, two square-lattice Hofstadter butterflies merge to form a honeycomb lattice butterfly. This merging is topologically nontrivial, as it is accomplished by sequential closings of gaps. Ensuing Chern number transfer between the bands can be probed with the adjustable lattice experiments. We also calculate the Chern numbers of the gaps for qualitatively different spectra and discuss the evolution of topological properties with underlying lattice geometry.
Open Access
Examining the annealing schedules for RNA design algorithm
(IEEE, 2016-07) Erhan, H. E.; Sav, Sinem; Kalashnikov, S.; Tsang, H. H.
RNA structures are important for many biological processes in the cell. One important function of RNA are as catalytic elements. Ribozymes are RNA sequences that fold to form active structures that catalyze important chemical reactions. The folded structure for these RNA are very important; only specific conformations maintain these active structures, so it is very important for RNA to fold in a specific way. The RNA design problem describes the prediction of an RNA sequence that will fold into a given RNA structure. Solving this problem allows researchers to design RNA; they can decide on what folded secondary structure is required to accomplish a task, and the algorithm will give them a primary sequence to assemble. However, there are far too many possible primary sequence combinations to test sequentially to see if they would fold into the structure. Therefore we must employ heuristics algorithms to attempt to solve this problem. This paper introduces SIMARD, an evolutionary algorithm that uses an optimization technique called simulated annealing to solve the RNA design problem. We analyzes three different cooling schedules for the annealing process: 1) An adaptive cooling schedule, 2) a geometric cooling schedule, and 3) a geometric cooling schedule with warm up. Our results show that an adaptive annealing schedule may not be more effective at minimizing the Hamming distance between the target structure and our folded sequence's structure when compared with geometric schedules. The results also show that warming up in a geometric cooling schedule may be useful for optimizing SIMARD. © 2016 IEEE.
Open Access
Extraction of target features using infrared intensity signals
(IEEE, 2005-09) Aytaç, Tayfun; Barshan, Billur
We propose the use of angular intensity signals obtained with low-cost infrared (IR) sensors and present an algorithm to simultaneously extract the geometry and surface properties of commonly encountered features or targets in indoor environments. The method is verified experimentally with planes, 90° corners, and 90° edges covered with aluminum, white cloth, and Styrofoam packaging material. An average correct classification rate of 80% of both geometry and surface over all target types is achieved and targets are localized within absolute range and azimuth errors of 1.5 cm and 1.1°, respectively. Taken separately, the geometry and surface type of targets can be correctly classified with rates of 99% and 81%, respectively, which shows that the geometrical properties of the targets are more distinctive than their surface properties, and surface determination is the limiting factor. The method demonstrated shows that simple IR sensors, when coupled with appropriate signal processing, can be used to extract substantially more information than such devices are commonly employed for.
Open Access
Finite element modeling of micro-particle separation using ultrasonic standing waves
(ASME, 2014) Büyükkoçak, S.; Çetin, Barbaros; Özer, M. B.
Acoustophoresis which means separation of particles and cells using acoustic waves is becoming an intensive research subject. The method is based on inducing an ultrasonic compression standing wave inside a microchannel. A finite element approach is used to model the acoustic and electro-mechanical behavior of the piezoelectric material, the micro-channel geometry as well as the fluid inside the channel. The choices of silicon and PDMS materials are investigated as the chip materials for the resonator. A separation channel geometry which is commonly used in the literature is implemented in this study and the fluid flow inside the microchannel geometry is simulated using computational fluid dynamics. The acoustic field inside the fluid channel is also be simulated using the finite element method. For the separation process to be successful micro-particles of different diameter groups should end up in different channels of the micro-separator. In order to simulate real life scenarios, each particle size group have a size distribution within themselves. For realistic simulation results the particles will be released into the micro separator from a different starting locations (starting location distribution). The results of this Monte-Carlo based finite element simulation approach will be compared with the reported experimental results.
Open Access
Fitting matrix geometric distributions by model reduction
(Taylor and Francis Inc., 2015) Akar, N.
A novel algorithmic method is proposed to fit matrix geometric distributions of desired order to empirical data or arbitrary discrete distributions. The proposed method effectively combines two existing approaches from two different disciplines: well-established model reduction methods used in system theory and moment matching methods of applied probability that employ second-order discrete phase-type distributions. The proposed approach is validated with exhaustive numerical examples including well-known statistical data. Copyright
Open Access
Fresnel lamb wave and V-groove lenses with tunable mode selectivity
(IEEE, 1995) Yaralıoğlu, Göksen Göksenin; Atalar, Abdullah; Köymen, Hayrettin
The Lamb wave and V-groove lenses are distinguished by their high surface wave excitation efficiencies. However, due to the fixed incidence angle, a particular lens can only be used for materials having surface wave velocities within a limited range. Hence, it is desirable to have lenses with adjustable incidence angle. Conventional spherical lenses implemented in Fresnel planar lens form have been demonstrated earlier. In this work, Lamb wave and V-groove lenses constructed as Fresnel lenses are presented. We also discuss the feasibility of Fresnel lenses with air as the coupling medium. It is shown that it is possible to build air coupled Fresnel lenses with a reasonable conversion efficiency into subsurface waves.
Open Access
Gate bias characterization of CNT-TFT DNA sensors
(IEEE, 2009-12) Aktaş, Özgür; Töral, Taylan
This paper follows the approach in the works of Gui et al. (2007), that use the change in the current of carbon nanotube thin film transistors (CNT-TFT) with DNA attachment and DNA hybridization. The authors have studied the response of CNT-TFTs to DNA binding and hybridization. It was demonstrated for the first time that an increase in sensitivity is observed around the threshold voltage when sweeping the gate bias from negative to positive values. The results presented in this work suggest an improved approach to measuring the response of CNT-TFTs to DNA hybridization.
Open Access
The geometry of sheaves on sites
(2021-01) Parsizadeh, Pejman
In this work, we study doing geometry on sheaves on sites. Categories of our sites consist of objects that are building blocks for a given geometry. Generalized spaces then will be sheaves on these sort of sites. Next we introduce the notion of varieties, and show the relationship between certain class of varieties known as diﬀeologies with the category of smooth manifolds. Along the way, the notion of schemes will be generalized as a variety on symmetric monoidal categories. And we show how a diﬀerential geometric construction on a site can be translated to a construction on generalized spaces.