Browsing by Subject "Mathematical analysis"

Now showing 1 - 20 of 24

Open Access
Algebraic reconstraction for 3D magnetic resonance-electrical impedance tomography (MREIT) using one component of magnetic flux density
(Institute of Physics and Engineering in Medicine, 2004) Ider, Y. Z.; Onart, S.
Magnetic resonance-electrical impedance tomography (MREIT) algorithms fall into two categories: those utilizing internal current density and those utilizing only one component of measured magnetic flux density. The latter group of algorithms have the advantage that the object does not have to be rotated in the magnetic resonance imaging (MRI) system. A new algorithm which uses only one component of measured magnetic flux density is developed. In this method, the imaging problem is formulated as the solution of a non-linear matrix equation which is solved iteratively to reconstruct resistivity. Numerical simulations are performed to test the algorithm both for noise-free and noisy cases. The uniqueness of the solution is monitored by looking at the singular value behavior of the matrix and it is shown that at least two current injection profiles are necessary. The method is also modified to handle region-of-interest reconstructions. In particular it is shown that, if the image of a certain xy-slice is sought for, then it suffices to measure the z-component of magnetic flux density up to a distance above and below that slice. The method is robust and has good convergence behavior for the simulation phantoms used.
Open Access
Analysis of blood cell production under growth factors switching
(Elsevier B.V., 2017) Djema, W.; Özbay, Hitay; Bonnet, C.; Fridman, E.; Mazenc, F.; Clairambault, J.
Hematopoiesis is a highly complicated biological phenomenon. Improving its mathematical modeling and analysis are essential steps towards consolidating the common knowledge about mechanisms behind blood cells production. On the other hand, trying to deepen the mathematical modeling of this process has a cost and may be highly demanding in terms of mathematical analysis. In this paper, we propose to describe hematopoiesis under growth factor-dependent parameters as a switching system. Thus, we consider that different biological functions involved in hematopoiesis, including aging velocities, are controlled through multiple growth factors. Then we attempt a new approach in the framework of time-delay switching systems, in order to interpret the behavior of the system around its possible positive steady states. We start here with the study of a specific case in which switching is assumed to result from drug infusions. In a broader context, we expect that interpreting cell dynamics using switching systems leads to a good compromise between complexity of realistic models and their mathematical analysis. © 2017
Open Access
Analytical regularization based analysis of a spherical reflector symmetrically illuminated by an acoustic beam
(IEEE, 2000) Vinogradov, S. S.; Vinogradova, E. D.; Nosich, A. I.; Altintaş, A.
A mathematically accurate and numerically efficient method of analysis of a spherical reflector, fed by a scalar beam produced by a complex source- point feed, is presented. Two cases, soft and hard reflector surface, are considered. In each case the solution of the full-wave integral equation is reduced to dual series equations and then further to a regularized infinite- matrix equation. The latter procedure is based on the analytical inversion of the static part of the problem. Sample numerical results for 50-λ reflectors demonstrate features that escape a high-frequency asymptotic analysis. (C) 2000 Acoustical Society of America.
Open Access
Atomic scale study of superlow friction between hydrogenated diamond surfaces
(American Physical Society, 2004) Dag, S.; Çıracı, Salim
Strong attractive interaction between two clean diamond (001) slabs turns repulsive upon the hydrogenation of surfaces. This repulsive interaction serves as if a boundary lubricant and prevents the sliding surfaces from being closer to each other even under high normal forces. As a result, calculated lateral force variation generated during sliding has small magnitude under high constant loading forces. Superlow friction observed earlier between diamondlike carbon-coated surfaces can be understood by the steady repulsive interaction between sliding surfaces, as well as strong and stiff carbon-carbon and carbon-hydrogen bonds which do not favor energy dissipation. In ambient conditions, the steady repulsive interaction is, however, destroyed by oxygen atoms which chemically modify those stiff surface bonds.
Open Access
Dynamic correlation effects on the plasmon dispersion in a two-dimensional electron gas
(The American Physical Society, 2003) Yurtsever, A.; Moldoveanu, V.; Tanatar, Bilal
The charge-density oscillations (plasmons) of a low-density two-dimensional uniform electron gas are studied within the framework of finite temperature and frequency dependent (dynamic) version of Singwi, Tosi, Land, and Sjölander theory and compared with the recent experimental results. The use of the Hartree-Fock approximation for the static structure factor leads to a finite temperature dynamical counterpart of the static Hubbard approximation. We observe important differences between dynamic and static local-field factors as well as between the corresponding plasmon dispersion laws. Our calculated plasmon energies that include dynamic correlations are in very-good agreement with the recent experimental results.
Open Access
Electron momentum and energy relaxation rates in GaN and AlN in the high-field transport regime
(The American Physical Society, 2003) Bulutay, C.; Ridley, B. K.; Zakhleniuk, N. A.
Momentum and energy relaxation characteristics of electrons in the conduction band of GaN and AlN are investigated using two different theoretical approaches corresponding to two high electric-field regimes, one up to 1-2 MV/ cm values for incoherent dynamics, and the other at even higher fields for coherent dynamics where semiballistic and ballistic processes become important. For the former, ensemble Monte Carlo technique is utilized to evaluate these rates as a function of electron energy up to an electric-field value of 1 MV/cm (2 MV/cm) for GaN (AlN). Momentum and energy relaxation rates within this incoherent transport regime in the presence of all standard scattering mechanisms are computed as well as the average drift velocity as a function of the applied field. Major scattering mechanisms are identified as polar optical phonon (POP) scattering and the optical deformation potential (ODP) scattering. Roughly, up to fields where the steady-state electron velocity attains its peak value, the POP mechanism dominates, whereas at higher fields ODP mechanism takes over. Next, aiming to characterize coherent dynamics, the total out-scattering rate from a quantum state (chosen along a high-symmetry direction) due to these two scattering mechanisms are then computed using a first-principles full-band approach. In the case of POP scattering, momentum relaxation rate differs from the total out-scattering rate from that state; close to the conduction-band minimum, momentum relaxation rate is significantly lower than the scattering rate because of forward-scattering character of the intravalley POP emission., However, close to the zone boundary the difference between these two rates diminishes due to isotropic nature of intervalley scatterings. Finally, a simple estimate for the velocity-field behavior in the coherent transport regime is attempted, displaying a negative differential mobility due to the negative band effective mass along the electric-field direction.
Open Access
Enhancing higher harmonics of a tapping cantilever by excitation at a submultiple of its resonance frequency
(American Physical Society, 2005-03) Balantekin, M.; Atalar, Abdullah
In a tapping-mode atomic force microscope, the frequency spectrum of the oscillating cantilever contains higher harmonics at integer multiples of the excitation frequency. When the cantilever oscillates at its fundamental resonance frequency w 1, the high Q-factor damps the amplitudes of the higher harmonics to negligible levels, unless the higher flexural eigenmodes are coincident with those harmonics. One can enhance the nth harmonic by the Q factor when the cantilever is excited at a submultiple of its resonance frequency (w 1/n). Hence, the magnitude of the nth harmonic can be measured easily and it can be utilized to examine the material properties. We show theoretically that the amplitude of enhanced higher harmonic increases monotonically for a range of sample stiffness, if the interaction is dominated by elastic force.
Open Access
Graphene field effect devices operating in differential circuit configuration
(Elsevier, 2015) Nyffeler, C.; Hanay, M. S.; Sacchetto, D.; Leblebici, Y.
We study the concept of a basic building block for circuits using differential signaling and being based on graphene field effect devices. We fabricated a number of top-gated graphene FETs using commercially available graphene and employing electron beam lithography along with other semiconductor manufacturing processes. These devices were then systematically measured in an automated setup and their DC characteristics analyzed in terms of a simple but effective analytical model. This model together with the collected data allowed us to proceed further with both mathematical analysis of circuit characteristics as well as numerical simulation in a dedicated circuit analysis software.
Open Access
How angel know-how shapes ownership sharing in stage-based contracts
(Sage Publications, 2019) Erzurumlu, S. S.; Joglekar, N.; Le´vesque, M.; Tanrısever, Fehmi
We draw upon stewardship theory to formally derive bounds on the investment amount in a business prospect, and to characterize ownership sharing when investors offer two-stage financing along with know-how to increase the prospect’s valuation. In the early-development stage, we show that the direct effect of investor know-how increases the entrepreneur’s share while the indirect effect from that know-how due to its interaction with the investment size, decreases it. In the subsequent growth stage, the direct effect decreases the entrepreneur’s share while the indirect effect increases it. These tradeoffs offer theoretical and practical implications for writing investment contracts involving investor know-how.
Open Access
Identification of relative protein bands in polyacrylamide gel electrophoresis (PAGE) using a multi-resolution snake algorithm
(Informa Healthcare, 1999-06) Gürcan, M. N.; Koyutürk, M.; Yildiz, H. S.; Çetin-Atalay R.; Çetin, A. Enis
In polyacrylamide gel electrophoresis (PAGE) image analysis, it is important to determine the percentage of the protein of interest of a protein mixture. This study presents reliable computer software to determine this percentage. The region of interest containing the protein band is detected using the snake algorithm. The iterative snake algorithm is implemented in a multi-resolutional framework. The snake is initialized on a low-resolution image. Then, the final position of the snake at the low resolution is used as the initial position in the higher-resolution image. Finally, the area of the protein is estimated as the area enclosed by the final position of the snake.
Open Access
Josephson effect in superconductive SNS heterostructures with barriers
(The American Physical Society, 2003) Cakir, O.; Kulik, I. O.
The dc Josephson effect in a planar superconductor-normal-metal-superconductor (SNS) junction is studied in the existence of a δ barrier in the normal region. The Green function of the structure is obtained by solving the Gorkov equations for the structure and then the current is calculated from the Green functions. The effect of the strength and position of the barrier is investigated. The current shows a weak dependence on the position of the barrier and it is seen to be maximum when the barrier is at the middle of the normal region. Also it is found that the current shows a stronger dependence on the strength of the barrier at low temperatures. A comparative discussion of three possible types of Josephson junctions, the SIS, SCS, and SNS contacts, is presented.
Open Access
Kanser tanısı için kolon bezlerinin matematiksel analizi
(IEEE, 2009-04) Çığır, Celal; Sökmensüer, C.; Gündüz-Demir, Çiğdem
Neoplastic diseases including cancer cause organizational changes in tissues. Histopathological examination, which is routinely used for the diagnosis and grading of these diseases, relies on pathologists to identify such tissue changes under a microscope. However, as this examination mainly relies on the visual interpretation of pathologists, it may lead to a considerable amount of subjectivity. To reduce the subjectivity level, it is proposed to use computational methods that provide objective measures. These methods quantify the tissue changes associated with disease by defining features on tissue images. In this paper, colon glands are mathematically analyzed making use of different feature extraction approaches. In this analysis, morphological, intensity-based, and textural features are investigated and glands are classified using these features. Working on the images of 108 colon tissues of 36 patients, our experiments demonstrate that this classification leads to promising results for differentiating normal glands from the cancerous ones. ©2009 IEEE.
Open Access
Observer-based control of a class of chaotic systems
(Elsevier, 2001) Solak, E.; Morgül, O.; Ersoy, U.
We consider the control of a class of chaotic systems, which covers the forced chaotic oscillators. We focus on two control problems. The first one is to change the dynamics of the system to a new one which exhibits a desired behavior, and the second one is the tracking problem, i.e., to force the solutions of the chaotic system to track a given trajectory. To solve these problems we use observers which could be used to estimate the unknown states of the system to be controlled. We apply the proposed method to the control of Duffing equation and the Van der Pol oscillator and present some simulation results. © 2001 Elsevier Science B.V.
Open Access
On the stabilization of periodic orbits for discrete time chaotic systems
(Elsevier, 2005-02) Morgül, Ö.
In this Letter we consider the stabilization problem of unstable periodic orbits of discrete time chaotic systems. We propose a novel and simple periodic delayed feedback law and present some stability results. These results show that all hyperbolic periodic orbits as well as some non-hyperbolic periodic orbits can be stabilized with the proposed method. The stability proofs also give the possible feedback gains which achieve stabilization. We will also present some simulation results.
Open Access
Persistent currents in helical structures
(American Physical Society, 2004) Iskin, M.; Kulik, I. O.
The recent discovery of mesoscopic electronic structures, in particular the carbon nanotubes, made necessary an investigation of what effect a helical symmetry of the conductor (metal or semiconductor) may have on the persistent current oscillations, We investigate persistent currents in helical structures which are nondecaying in time, not requiring a voltage bias, dissipationless stationary flow of electrons in a normal-metallic or semiconducting cylinder or circular wire of mesoscopic dimension. In the presence of magnetic flux along the toroidal structure, helical symmetry couples circular and longitudinal currents to each other. Our calculations suggest that circular persistent currents in these structures have two components with periods Φ0 and Φ0/s (s is an integer specific to any geometry). However, resultant circular persistent current oscillations have Φ0 period.
Open Access
Point normal metal-superconductor (NS) contact in nonballistic regime
(World Scientific Publishing, 2003) Askerzade, İ. N.; Kulik, Igor Orestovich
We analyze the point NS contact conductivity taking into account the depression of superconductivity at high-injection current density and Andreev reflection at the adaptive NS boundary. The dependence of the excess current on the voltage, as well as conductivity of contact at arbitrary voltage is obtained.
Open Access
Power dissipation analysis in tapping-mode atomic force microscopy
(American Physical Society, 2003) Balantekin, M.; Atalar, Abdullah
In a tapping-mode atomic force microscope, a power is dissipated in the sample during the imaging process. While the vibrating tip taps on the sample surface, some part of its energy is coupled to the sample. Too much dissipated power may mean the damage of the sample or the tip. The amount of power dissipation is related to the mechanical properties of a sample such as viscosity and elasticity. In this paper, we first formulate the steady-state tip-sample interaction force by a simple analytical expression, and then we derive the expressions for average and maximum power dissipated in the sample by means of sample parameters. Furthermore, for a given sample elastic properties we can determine approximately the sample damping constant by measuring the average power dissipation. Simulation results are in close agreement with our analytical approach.
Open Access
Quantum effects of thermal conductance through atomic chains
(2001) Ozpineci, A.; Çıracı, Salim
We present a formalism for an atomic scale study of phononic heat transfer. The expression of thermal energy current can be cast in the Landauer form and incorporates the transmission coefficient explicitly. Calculation of the thermal conductance of a monoatomic chain of N atoms between two reservoirs shows interesting quantum features. The conductance density appears as Lorentzian type resonances at the eigenfrequencies of the chain. At low-temperature limit the discrete vibrational frequency spectrum of a "soft" chain may reflect on the thermal conductance by giving rise to a sudden increase. At room temperature, the conductance through a "stiff" chain may oscillate with the number of chain atoms. The obtained quantum features are compared with similar effects found in the quantized electrical conductance.
Open Access
Radiochemical study of Co2+ sorption on chlorite and kaolinite
(Akademiai Kiado Rt., 1999) Shahwan, T.; Erten, H. N.
In this work, the sorption behavior of Co(II) ions on natural chlorite and kaolinite as a function of time, concentration and temperature was studied. 60Co radiotracer method and the batch technique were used. The kinetic results indicated that about one day of contact time was enough to achieve equilibrium. The sorption process was described by Freundlich type isotherms. Sorption of Co(II) ions on both clays was found to be endothermic with ΔH(o) (kJ/mol) and ΔS(o) (kJ/mol·K) being 33 and 0.14 for kaolinite and 17 and 0.102 for chlorite, respectively. The magnitudes of the corresponding ΔG(o) values suggest that sorption occur mainly via an ion exchange mechanism on both clays.
Open Access
Resonant harmonic response in tapping-mode atomic force microscopy
(American Physical Society, 2004) Sahin, O.; Quate, C. F.; Solgaard, O.; Atalar, Abdullah
Higher harmonics in tapping-mode atomic force microscopy offers the potential for imaging and sensing material properties at the nanoscale. The signal level at a given harmonic of the fundamental mode can be enhanced if the cantilever is designed in such a way that the frequency of one of the higher harmonics of the fundamental mode (designated as the resonant harmonic) matches the resonant frequency of a higher-order flexural mode. Here we present an analytical approach that relates the amplitude and phase of the cantilever vibration at the frequency of the resonant harmonic to the elastic modulus of the sample. The resonant harmonic response is optimized for different samples with a proper design of the cantilever. It is found that resonant harmonics are sensitive to the stiffness of the material under investigation.