Researcher:
Atay, Fatihcan

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Faculty Member

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Fatihcan

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Atay

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Atay, Fatihcan

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1996 - 19997

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Researcher Of Publications: search.filters.isAuthorOfPublication.aa5c6231-73a5-41ab-8e5e-393e421fddd3

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Now showing 1 - 7 of 7
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    Phase-space reconstruction in Hamiltonian systems through multiple time series
    (Elsevier Science Bv, 1997) Department of Chemistry; Department of Chemistry; Atay, Fatihcan; Yurtsever, İsmail Ersin; Faculty Member; Faculty Member; College of Sciences; 253074
    A method which combines the various time series originating from a single source in order to reconstruct the phase-space dynamics is applied to a chaotic Hamiltonian system. It is shown that for a large energy range the variation of the maximum Lyapunov exponents can be reproduced more accurately than the results obtained from a single time series, for both clean and noisy signals. Especially in cases where the maximum exponent is close to zero, using multiple series can give better results, providing a more reliable way of detecting chaos.
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    Quantitative study of laser beam propagation in a thermally loaded absorber
    (Optical Society of America, 1997) Department of Physics; Department of Mathematics; Department of Mathematics; Department of Physics; Department of Mathematics; Sennaroğlu, Alphan; Aşkar, Attila; Atay, Fatihcan; Faculty Member; Faculty Member; Faculty Member; College of Sciences; College of Sciences; College of Sciences; 23851; 178822; 253074
    The effect of thermal loading on the propagation of Gaussian laser beams in a solid-state absorber is modeled by a novel quantitative scheme. The zeroth-order Gaussian beam solution of the wave equation in a homogeneous, cylindrically symmetric absorbing medium is used as the source term in the heat equation to calculate the temperature field. Modifications in the beam parameters caused by the temperature dependence of the absorption coefficient and the index of refraction are then calculated as first-order corrections. The formulation identifies a dimensionless parameter that controls the strength of thermal effects. Numerical results that show the dependence of crystal transmission and the spatial beam spot-size variation on incident pump power are presented. In particular, the power transmission of the crystal is found to decrease with increasing incident power, and power-dependent thermal lensing is observed. The asymptotic behavior of the solutions yields explicit formulas for the focal length of the thermal lens and the power transmission of the crystal. These explicit formulas should prove useful as a rule of thumb for experimentalists.
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    Laser beam propagation in a thermally loaded absorber
    (Optica Publishing Group, 1996) Department of Physics; Department of Mathematics; Department of Mathematics; Department of Physics; Department of Mathematics; Sennaroğlu, Alphan; Aşkar, Attila; Atay, Fatihcan; Faculty Member; Faculty Member; Faculty Member; College of Sciences; College of Sciences; College of Sciences; 23851; 178822; 253074
    Beam propagation in a thermally loaded absorber is analyzed by a novel method. The formulation identifies a dimensionless parameter controlling the strength of thermal effects.
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    Modeling reflex asymmetries with implicit delay differential equations
    (Elsevier, 1998) Mallet-Paret, J; Department of Mathematics; Department of Mathematics; Atay, Fatihcan; Faculty Member; College of Sciences; 253074
    Neuromuscular reflexes with time-delayed negative feedback, such as the pupil light reflex, have different rates depending on the direction of movement. This asymmetry is modeled by an implicit first-order delay differential equation in which the value of the rate constant depends on the direction of movement. Stability analyses are presented for the cases when the rate is: (1) an increasing and (2) a decreasing function of the direction of movement. It is shown that the stability of equilibria in these dynamical systems depends on whether the rate constant is a decreasing or increasing function. In particular, when the asymmetry has the shape of an increasing step function, it is possible to have stability which is independent of the value of the time delay or the steepness (i.e., gain) of the negative feedback. (C) 1998 Society for Mathematical Biology.
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    Balancing the inverted pendulum using position feedback
    (Pergamon-Elsevier Science Ltd, 1999) Department of Mathematics; Department of Mathematics; Atay, Fatihcan; Faculty Member; College of Sciences; 253074
    It is shown how to obtain asymptotic stability in second-order undamped systems using time-delay action in the feedback of position. The effect of the delay is similar to derivative feedback in modifying the behavior of the system. Results are given on the selection of the controller parameters both in the absence and the presence of additional delay ill the feedback path. The timelag position feedback is shown to compare favorably with the conventional PD controller in terms of stability. (C) 1999 Elsevier Science Ltd. All rights reserved.
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    Laser beam propagation in a saturable absorber
    (Optical Soc Amer, 1997) Department of Physics; Department of Mathematics; Department of Mathematics; Department of Physics; Department of Mathematics; Sennaroğlu, Alphan; Atay, Fatihcan; Aşkar, Attila; Faculty Member; Faculty Member; Faculty Member; College of Sciences; College of Sciences; College of Sciences; 23851; 253074; 178822
    The effects of the saturation of absorption on the propagation of Gaussian laser beams in an absorber are investigated analytically. Using a dimensionless parameter quantifying the level of saturation, we calculate the modifications in the beam parameters as perturbations from known solutions. are carried out in two directions, covering both low-and high-saturation cases. mates the power transmission for all saturation levels. Numerical results are provided showing the effects of saturation on the spatial beam-spot size variation and the power transmission.
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    Van der Pol's oscillator under delayed feedback
    (Academic Press Ltd, 1998) Department of Mathematics; Department of Mathematics; Atay, Fatihcan; Faculty Member; College of Sciences; 253074
    The effect of delayed feedback on oscillatory behaviour is investigated for the classical van der Pol oscillator. It is shown how the presence of delay can change the amplitude of limit cycle oscillations, or suppress them altogether. The result is compared to the conventional proportional-and-derivative feedback. The derivative-like effect of delay is also demonstrated in a modified equation where a delayed term provides the damping. (C) 1998 Academic Press.