Browsing by Subject "Approximation theory"
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Item Open Access Accurate method for obtaining band gaps in conducting polymers using a DFT/hybrid approach(American Chemical Society, 1998) Salzner, U.; Pickup, P. G.; Poirier, R. A.; Lagowski, J. B.DFT calculations on a series of oligomers have been used to estimate band gaps, ionization potentials, electron affinities, and bandwidths for polyacetylene, polythiophene, polypyrrole, polythiazole, and a thiophene - thiazole copolymer. Using a slightly modified hybrid functional, we obtain band gaps within 0.1 eV of experimental solid-state values Calculated bond lengths and bond angles for the central ring of sexithiophene differ by less than 0.026 Å and 0.7° from those of the sexithiopnene crystal structure. IPs and EAs are overestimated by up to 0.77 eV compared to experimental bulk values. Extrapolated bandwidths agree reasonably well with bandwidths from band structure calculations.Item Open Access Adaptive control design for nonlinear systems via successive approximations(ASME, 2017) Babaei, N.; Salamcı, M. U.; Karakurt, Ahmet HakanThe paper presents an approach to the Model Reference Adaptive Control (MRAC) design for nonlinear dynamical systems. A nonlinear reference system is considered such that its response is designed to be stable via Successive Approximation Approach (SAA). Having designed the stable reference model through the SAA, MRAC is then formulated for nonlinear plant dynamics with a new adaptation rule to guarantee the convergence of the nonlinear plant response to that of the response of the nonlinear reference model. The proposed design methodology is illustrated with examples for different case studies.Item Open Access Animation of deformable models(Pergamon Press, 1994) Güdükbay, Uğur; Özgüç, B.Although kinematic modelling methods are adequate for describing the shapes of static objects, they are insufficient when it comes to producing realistic animation. Physically based modelling remedies this problem by including forces, masses, strain energies and other physical quantities. The paper describes a system for the animation of deformable models. The system uses physically based modelling methods and approaches from elasticity theory for animating the models. Two different formulations, namely the primal formulation and the hybrid formulation, are implemented so that the user can select the one most suitable for an animation depending on the rigidity of the models. Collision of the models with impenetrable obstacles and constraining of the model points to fixed positions in space are implemented for use in the animations. © 1994.Item Open Access An approximate analytical method of analysis of a threshold maintenance policy for a multiphase multicomponent model(Springer, 2003) Anisimov, V. V.; Gürler, Ü.A multicomponent system is investigated that consists of n identical unreliable components whose nonfailure operating time consists of a number of sequential phases with exponential times. A maintenance policy is studied that proposes the instant replacement of all the components as soon as the number of components that are in some doubtful state (before a failure) amounts to a predefined threshold value. A cost function averaged over a large period is studied. For a fixed n, an analytical approach is considered. If n increases, a new approximate analytical approach is proposed, which is based on results of the type of the averaging principle for recurrent semi-Markovian processes. The conditions of existence and properties of the optimal strategy are studied. An example is considered and possibilities of generalizations are discussed.Item Open Access Approximations in compensator design: a duality(The Institution of Engineering and Technology (IET), 2002) Özgüler, A. B.; Gündeş, A. N.In classical controller design, poles fat to the left of dominant poles are sometimes ignored. Similarly, in some proportional-integral compensation techniques, the controller zero is placed close to the origin and design proceeds after cancelling this zero with a pole at the origin. A rigorous basis for these methods is provided, it being shown that there is a duality between the two.Item Open Access Automatic multimedia cross-modal correlation discovery(ACM, 2004-08) Pan, J.-Y.; Yang, H.-J.; Faloutsos, C.; Duygulu, PınarGiven an image (or video clip, or audio song), how do we automatically assign keywords to it? The general problem is to find correlations across the media in a collection of multimedia objects like video clips, with colors, and/or motion, and/or audio, and/or text scripts. We propose a novel, graph-based approach, "MMG", to discover such cross-modal correlations. Our "MMG" method requires no tuning, no clustering, no user-determined constants; it can be applied to any multi-media collection, as long as we have a similarity function for each medium; and it scales linearly with the database size. We report auto-captioning experiments on the "standard" Corel image database of 680 MB, where it outperforms domain specific, fine-tuned methods by up to 10 percentage points in captioning accuracy (50% relative improvement).Item Open Access Block SOR for Kronecker structured representations(Elsevier, 2004) Buchholz, P.; Dayar, TuğrulThe Kronecker structure of a hierarchical Markovian model (HMM) induces nested block partitionings in the transition matrix of its underlying Markov chain. This paper shows how sparse real Schur factors of certain diagonal blocks of a given partitioning induced by the Kronecker structure can be constructed from smaller component matrices and their real Schur factors. Furthermore, it shows how the column approximate minimum degree (COLAMD) ordering algorithm can be used to reduce fill-in of the remaining diagonal blocks that are sparse LU factorized. Combining these ideas, the paper proposes three-level block successive over-relaxation (BSOR) as a competitive steady state solver for HMMs. Finally, on a set of numerical experiments it demonstrates how these ideas reduce storage required by the factors of the diagonal blocks and improve solution time compared to an all LU factorization implementation of the BSOR solver. © 2004 Elsevier Inc. All rights reserved.Item Open Access Capacity bounds for an ultra-wideband channel model(IEEE, 2004-10) Arıkan, ErdalThere is an ongoing effort by the IEEE 802.15.3a subcommittee to reach a UWB personal area network standard. We estimate the achievable rates for such networks using a channel model specified by the same group. The analysis of this channel model is of interest in light of recent information-theoretic work on multipath fading channels which show that in order to take full advantage of such channels' capacity the transmitted signals have to be "peaky" in a certain sense. The immense bandwidth of the UWB channel also suggests at first that peaky signals should be used. However, unlike the many other wireless systems where the transmitter energy is limited, in the UWB channel only the power spectral density of the transmitted signal is constrained. As a result, the signal power can grow in proportion to the utilized bandwidth and peaky signals are not needed. © 2004 IEEE.Item Open Access Collective modes in a quasi-one-dimensional, two-component electron liquid(Pergamon Press, 1994) Tanatar, BilalUnder favorable conditions, a new collective mode besides the usual plasmons may exist in degenerate electron-hole liquids. We calculate the dispersion and damping of this new mode (called the acoustic plasmon mode) in a quasi-one-dimensional, two-component electron liquid. We carry out our calculations first within the random-phase approximation, then include the effects of local-field corrections using a Hubbard-like approximation. The latter decreases the acoustic plasmon dispersion. © 1994.Item Open Access Collective modes in flux line liquids(IOP, 2000) Tanatar, Bilal; Oral, A.We study the collective modes of flux line liquids such as occur in the type-II superconductors of recent interest composed of two-dimensional layered structures. Starting from the vortex-vortex interaction and employing the dielectric formalism within the random-phase approximation, we find propagating sound modes in the long-wavelength limit.Item Open Access Computation of holographic patterns between tilted planes(SPIE - International Society for Optical Engineering, 2006-05) Esmer, Gökhan Bora; Onural, LeventComputation of the diffraction pattern that gives the desired reconstruction of an object upon proper illumination is an important process in computer generated holography. A fast computational method, based on the plane wave decomposition of 3D field in free-space, is presented to find the desired diffraction pattern. The computational burden includes two FFT algorithms in addition to a shuffling of the frequency components that needs an interpolation in the frequency domain. The algorithm is based on the exact diffraction formulation; there is no need for Fresnel or Fraunhofer approximations. The developed model is utilized to calculate the scalar optical diffraction between tilted planes for monochromatic light. The performance of the presented algorithm is satisfactory for tilt angles up to 60°.Item Open Access Computationally efficient wavelet affine invariant functions for shape recognition(IEEE, 2004) Bala, E.; Çetin, A. EnisAn affine invariant function for object recognition is constructed from wavelet coefficients of the object boundary. In previous works, undecimated dyadic wavelet transform was used to construct affine invariant functions. In this paper, an algorithm based on decimated wavelet transform is developed to compute an affine invariant function. As a result computational complexity is reduced without decreasing recognition performance. Experimental results are presented. © 2004 IEEE.Item Open Access Confined optical phonon effects on the band gap renormalization in quantum wire structures(Elsevier Science, 1999) Bennett, C. R.; Güven, K.; Tanatar, BilalWe consider the different approximations for the bandgap renormalization (BGR) within the random phase approximation (RPA), the quasi-static limit and the plasmon-pole approximation, and compare with the full result. We then include bulk optical phonons and also the phonon confinement using the phonons from the dielectric continuum (DC) model. We show that the results are very similar except at low densities where the quasi-static results overestimate the renormalization.Item Open Access Correlation effects in a one-dimensional electron gas with short-range interaction(Pergamon Press, 1999) Demirel, E.; Tanatar, BilalWe study the correlation effects in a one-dimensional electron gas with repulsive delta-function interaction. The correlation effects are described by a local-field correction which takes into account the short-range correlations. We find that the ground state energy is in good agreement with the exact result up to intermediate coupling strengths, showing an improvement over the STLS approximation. The compressibility, the static structure factor and the pair-correlation function are also calculated within the present approximation.Item Open Access Cost-efficient approximation of linear systems with repeated and multi-channel filtering configurations(IEEE, 1998-05) Kutay, Mehmet Alper; Erden, M. F.; Özaktaş, Haldun M.; Arıkan, Orhan; Candan, Ç.; Güleryüz, Ö.It is possible to obtain either exact realizations or useful approximations of linear systems or matrix-vector products arising in many different applications, by synthesizing them in the form of repeated or multi-channel filtering operations in fractional Fourier domains, resulting in much more efficient implementations with acceptable decreases in accuracy. By varying the number and configuration of filter blocks, which may take the form of arbitrary flow graphs, it is possible to trade off between accuracy and efficiency in the desired manner. The proposed scheme constitutes a systematic way of exploiting the information inherent in the regularity or structure of a given linear system or matrix, even when that structure is not readily apparent.Item Open Access Coulomb drag effect in parallel cylindrical quantum wires(Pergamon Press, 1996) Tanatar, BilalWe study the Coulomb drag rate for electrons in two parallel quantum wires. The double-quantum wire structure is modeled for a GaAs material with cylindrical wires having infinite potential barriers. The momentum transfer rate between the wires (Coulomb drag effect) is calculated as a function of temperature for several wire separation distances. We employ the full wave vector and frequency dependent random-phase approximation (RPA) at finite temperature to describe the effective interwire Coulomb interaction. We find that the drag rate at high temperatures (i.e., T ≥ EF/2) is dominated by the collective modes (plasmons) of the system similar to the case in double-well structures. Including the local-field effects in an approximate way we estimate the importance of intrawire correlations to be significant. Copyright © 1996 Published by Elsevier Science Ltd.Item Open Access Coupled optical microcavities in one-dimensional photonic bandgap structures(Institute of Physics Publishing, 2001) Bayındır, Mehmet; Kural, C.; Özbay, EkmelWe present a detailed theoretical and experimental study of the evanescent coupled optical microcavity modes in one-dimensional photonic bandgap structures. The coupled-cavity samples are fabricated by depositing alternating hydrogenated amorphous silicon nitride and silicon oxide layers. Splitting of the eigenmodes and formation of a defect band due to interaction between the neighbouring localized cavity modes are experimentally observed. Corresponding field patterns and the transmission spectra are obtained by using transfer matrix method (TMM) simulations. A theoretical model based on the classical wave analogue of the tight-binding (TB) picture is developed and applied to these structures. Experimental results are in good agreement with the predictions of the TB approximation and the TMM simulations.Item Open Access Digital computation of the fractional Fourier transform(Institute of Electrical and Electronics Engineers, 1996-09) Özaktaş, Haldun M.; Arıkan, Orhan; Kutay, M. A.; Bozdağı, G.An algorithm for efficient and accurate computation of the fractional Fourier transform is given. For signals with time-bandwidth product N, the presented algorithm computes the fractional transform in O(NlogN) time. A definition for the discrete fractional Fourier transform that emerges from our analysis is also discussed.Item Open Access Dynamical screening effects in hot-electron scattering from electron-hole plasma and LO-phonon modes in quantum wires(Elsevier, 1996) Bennett, C. R.; Tanatar, Bilal; Constantinou, N. C.We present a fully dynamical and finite temperature study of the hot-electron momentum relaxation rate and the power loss in a coupled system of electron-hole plasma and bulk LO-phonons in a quantum wire structure. Interactions of the scattered electron with neutral plasma components and phonons are treated on an equal footing within the random-phase approximation. Coupled mode effects substantially change the transport properties of the system at low temperatures. Particularly, the "plasmon-like" and "LO-phonon-like" excitations yield comparable rates which, as a consequence of the singular nature of the ID density of states, can be large at the threshold. This is in contrast to room temperature results where only the LO-phonon mode contributes significantly to the rate. The density and temperature dependence of the power loss reveals that dynamical screening effects are important, and energy-momentum conservation cannot be satisfied above a certain density for a given initial energy.Item 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.