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Publication Metadata only Large deformations of helices(İstanbul Technical University (İTÜ) / İstanbul Teknik Üniversitesi (İTÜ), 1992) Aköz, Yalçın; Department of Mathematics; Aşkar, Attila; Faculty Member; Department of Mathematics; College of Sciences; 178822N/APublication Open Access Long time scale molecular dynamics subspace integration method applied to anharmonic crystals and glasses(American Institute of Physics (AIP) Publishing, 1993) Space B.; Rabitz H.; Department of Mathematics; Aşkar, Attila; Faculty Member; Department of Mathematics; College of Sciences; 178822A subspace dynamics method is presented to model long time dynamical events. The method involves determining a set of vectors that span the subspace of the long time dynamics. Specifically, the vectors correspond to real and imaginary low frequency normal modes of the condensed phase system. Most importantly, the normal mode derived vectors are only used to define the subspace of low frequency motions, and the actual time dependent dynamics is fully anhannonic. The resultant projected set of Newton's equations is numerically solved for the subspace motions. Displacements along the coordinates outside the subspace are then constrained during the integration of the equations of motion in the reduced dimensional space. The method is different from traditional constraint methods in that it can systematically deduce and remove both local and collective high frequency motions of the condensed phase system with no a priori assumptions. The technique is well suited to removing large numbers of degrees of freedom, while only keeping the very low frequency global motions. The method is applied to highly anhannonic Lennard-Jones crystal and glass systems. Even in these systems with no intramolecular degrees of freedom or obvious separation of time scales, the subspace dynamics provides a speed up of approximately a factor of 5 over traditional molecular dynamics through use of a larger integration time step. In the cases illustrated here a single set of subspace vectors was adequate over the full time interval, although this is not expected to be true for all systems.Publication Open Access Molecular dynamics with Langevin equation using local harmonics and Chandrasekhar’s convolution(American Institute of Physics (AIP) Publishing, 1993) Owens, R.G.; Rabitz, H.A.; Department of Mathematics; Aşkar, Attila; Faculty Member; Department of Mathematics; College of Sciences; 178822A numerical method for studying molecular systems subject to a random force field leading to a Gaussian velocity distribution and described by the Langevin equation is presented. Two basic elements constitute the formulation: local harmonic modes and Chandrasekhar's formula for the distribution function for a convolution involving a random function. First, by linearizing the governing Langevin equations locally and employing an orthogonal change of coordinates, an explicit solution for the displacement and velocity is constructed. Second, Chandrasekhar's formula is employed in deriving the probability distribution function of the displacements and the velocities coming from the random forces. The local mode analysis is essential for the use of the Chandrasekhar's formula, since we need the formal solution as a convolution of the random forces and the local Green's function. For an illustration of the method in a significant case representative of real problems, we study a one dimensional idealization of a long chain molecule possessing internal energy barriers and subjected to an applied tension. The results are compared with the predictions of a conventional approximate method where a finite number of random realizations are generated in each time step. This truncation constitutes an approximation to obtain the desired Gaussian probability distribution function for the velocities which is reached in the limit of an infinity of random realizations. The calculations show that the conventional approximations may be acceptable only for short times, small temperatures, and average values over very long times. In particular, these approximations fail to give accurate results for transient phenomena, show slow convergence with the increase in the number of random realizations, and predict large values for the variance even in the steady regime. The new proposed method on the other hand, (i) incorporates the mathematically and conceptually correct limit for the distribution function, (ii) is quite stable with respect to increases in the value of the time increment as well as in terms of fluctuations characterized by the variance, (iii) leads to considerable savings in computer time over the approximate method, and (iv) has the proper description during the transient regime, which is usually the most interesting phase of dynamical processes.Publication Metadata only Finite-element method for quantum scattering(Kluwer Academic Publ, 1993) Department of Mathematics; Aşkar, Attila; Faculty Member; Department of Mathematics; College of Sciences; 178822The finite element method is introduced and applied to quantum mechanical scattering problems. In this procedure the space is discretized on a grid with the unknown quantities being the wavefunction values. Local polynomials approximate the wave function and no global basis set expansion is required. The scattering solution is constructed by a suitable combination of independent standing wave solutions. These latter solutions are generated numerically by using real, not complex, arithmetic. A one-dimensional barrier crossing is studied as a first example to illustrate finite element discretization and the construction of the scattered wave forms in an uncomplicated situation. A two variable generalization is given next. The method is then sucessfully applied to a model collinear problem which is analytically soluble and to the collinear H + H2 system. Next, a three variable formulation of the co-planar A + BC system is discussed with specific reference to co-planar H + H2 . Some comments on the generalization of the technique complete the discussion.Publication Metadata only The continuum solid and compliance functions in gas-surface low-energy collisions(Elsevier, 1994) Department of Mathematics; Aşkar, Attila; Faculty Member; Department of Mathematics; College of Sciences; 178822The paper presents a model and calculations for the scattering of atomic and molecular beams from solid surfaces at low energies. The formulation permits the study of momentum and energy exchange phenomena including multiple collisions and the capture, i.e. adsorption of the projectile. The model uses a hybrid continuum-discrete representation for the system. An elastic continuum is used for the representation of the generation of phonons in the solid through collisions and the resulting momentum and energy exchange processes. on the other hand, the particulate nature of the lattice, as manifested in the corrugation is retained. This hybrid continuum-discrete representation of the solid is a suitable description for relaxation dynamics of adsorbates on surfaces and low energy collisions of gas particles with surfaces. For high energy collisions, the collision time is too short for the phonons created at the target to reach other lattice points. Therefore, the representation of the target solid by a relatively small cluster is an adequate model and there is no need to include the collaborative response of the lattice as a whole. For the low energy collisions on the other hand, the collision time is long enough such that the phonons have sufficient time to propagate over a substantial region in the lattice. Consequently, the collaborative response of the solid as a collection of a large number of lattice particles is essential. The present model uses a continuum model for the response of the solid as an accurate and convenient representation. The continuum hypothesis is validated by the predominance of long or equivalently, low frequency waves among the phonons generated during the collision. The formulation is presented for an atomic particle as projectile. Possible extensions to cover projectiles like molecules or clusters are briefly indicated. The phonons generated by the projectile are described in terms of compliance functions. These are basically Green's functions for the response of a semi-infinite solid to forces acting on its boundary. In physical terms, the compliance functions can be viewed as a frequency dependent effective spring with damping coefficients for the motion of the target point embedded in the solid. This makes the handling of the solid extremely practical by reducing the representation of its collaborative response to that of one point. The full set of compliance coefficients for all possible surface forces and moments are available. Within this picture, the discreteness of the lattice enters through the corrugated gas particle-surface interaction potential. As applications, both exact numerical integration of the equations as well as perturbation calculations are presented within a classical framework, although the formulation and calculations presented here are all within a classical context. Specific results are given for the projectile trajectories as well as momentum and energy exchange. The numerical, i.e. exact, trajectory calculations show the capability of the model in allowing realistic simulations for phenomena that involve rather complicated dynamics, including multiple collisions, skidding along the surface and eventual capture of the projectile. The perturbation solutions on the other hand, while limited to single collisions, provide attractive analytical expressions that capture basic features of the physics in the energy exchange through collision Particularly, the availability of thermal averages through simple quadratures is a valuable asset considering the gigantic computational tasks involved in exact simulations. The quadratures involved can be evaluated in closed form for both the exponential repulsive and Morse potentials. The specific results presented use the parameters of the He + LiF system as well as models with deeper wells and softer solids.Publication Open Access Optimal-control of laser-generated acoustic-waves in solids(American Physical Society (APS), 1994) Kim, Y. S..; Tadi, M.; Rabitz, H.; Mcmanus, J. B.; Department of Mathematics; Aşkar, Attila; Faculty Member; Department of Mathematics; College of Sciences; 178822This paper is concerned with the design of optimal surface-heating patterns that result in focusing acoustic energy inside a subsurface target volume at a specified target time. The surface of the solid is heated by an incident laser beam which gives rise to shear and compressional waves propagating into the solid. The optimal heating design process aims to achieve the desired energy focusing at the target with minimal laser power densities and minimal system disturbance away from the target. Due to the slow motion of the thermal conduction process relative to the propagation of acoustic waves, a general formulation is derived which is the limiting case for a heat-absorbing nonconducting solid. This is consistent with the laser heating of the surface where, for the time duration of interest, thermal effects are confined to a thin layer at the surface. This simplification allows for the solution of the problem through the use of the system Greens function for the purely elastic medium where thermal expansion enters as an external force. The problem is then posed as an optimal control problem, the solution of which is the required heating pattern at the surface. The optimality conditions are secured via the conjugate gradient method and the mechanics of the elastic medium is treated by the finite element method along with using the half-space Greens function matrix. Good quality energy focusing is achieved, with the optimal designs reflecting the high directivity of the photothermally generated shear-wave patterns. © 1994 The American Physical Society.Publication Metadata only A direct method for the inversion of physical systems(Institute of Physics (IOP) Publishing, 1994) Caudill, Lester F.; Rabitz, Herschel; Department of Mathematics; Aşkar, Attila; Faculty Member; Department of Mathematics; College of Sciences; 178822A general algorithm for the direct inversion of data to yield unknown functions entering physical systems is presented. of particular interest are linear and non-linear dynamical systems. The potential broad applicability of this method is examined in the context of a number of coefficient-recovery problems for partial differential equations. Stability issues are addressed and a stabilization approach, based on inverse asymptotic tracking, is proposed. Numerical examples for a simple illustration are presented, demonstrating the effectiveness of the algorithm.Publication Metadata only Modeling of biological polymers - discrete and continuum-mechanics formulations(Springer-Verlag Berlin, 1994) Department of Mathematics; Aşkar, Attila; Faculty Member; Department of Mathematics; College of Sciences; 178822N/APublication Metadata only Interval algebra to deal with pattern loading and structural uncertainties(Asce-Amer Soc Civil Eng, 1995) Çakmak, Ahmet Ş.; Nielsen, Søren R.K.; Department of Mathematics; Köylüoğlu, Hasan Uğur; Teaching Faculty; Department of Mathematics; College of Sciences; N/AStructural and loading uncertainties, bounded from above and below, are considered within a finite-element formulation to determine conservative bounds for the displacement and force response quantities. Discretization of a continuum with material uncertainties is illustrated using a linear elastic beam. This yields the elements of the stiffness matrix with uncertainties and the components of the force vector with uncertainties, to be defined in bounded intervals. Then, the response quantities become uncertain, yet bounded, in-a multidimensional rectangular prism. The discretized linear static interval equation is solved using the triangle inequality and linear programming to determine the conservative bounds for the response quantities. For the case when only loading uncertainties are considered, the problem reduces to the pattern loading problem of structural design. The proposed formulation is applied to the structural analysis of frames with material uncertainty under static loads with uncertainties.Publication Metadata only Turkish adaptation of the need for cognition scale and its correlation with performance measures(Turkish Psychologists Assoc, 1995) Sadowski, CJ; Department of Psychology; Gülgöz, Sami; Faculty Member; Department of Psychology; College of Social Sciences and Humanities; 49200The need for cognition scale has been devised by Cacioppo and Petty (1984) in an attempt to measure people's tendency to think and enjoy thinking. In the Turkish adaptation of this scale significant test-retest reliability and internal consistency were found but these were lower than the coefficients obtained with the original scale. Factor analysis indicated that the same factor structure was maintained to a large extent. There was no relationship between need for cognition scale scores and performance measures such as university entrance subtest scores and course grades. The results were discussed for their implications about whether need for cognition is a cognitive or attitude scale.Publication Metadata only Generation of controlled acoustic-waves by optimal-design of surface loads with constrained forms(Pergamon-Elsevier Science Ltd, 1995) Kim, Ys; Rabitz, H; Tadi, M; Mcmanus, Jb; Department of Mathematics; Aşkar, Attila; Faculty Member; Department of Mathematics; College of Sciences; 178822Model calculations are presented for the optimal design of surface force patterns to generate acoustic waves that come to a focus within the bulk of a homogeneous elastic solid. The optimal design consists of achieving a high level of energy at the target at a prescribed time by applying a relatively minimal surface force while aiming for a minimal system disturbance away from the focal target. Such optimal designs were derived in an earlier paper, in which no restriction was imposed on the functional form of the applied stress. In this paper we examine the importance of the fine detail in the earlier derived forcing functions in achieving efficient acoustic focusing. We repeat the optimal design calculations with the surface stress constrained to be in the form of rings of variable radius, with cross sectional profiles made by the superposition of two Gaussians. The optimality conditions are secured via the conjugate gradient algorithm (CGA) and the mechanics of the elastic medium are treated by the finite element method along with using the half space Green's function matrix. We use a criterion for focusing efficiency of the ratio of acoustic energy in the target volume to the total work done on the surface, at a prescribed time. The calculations show the high levels of focusing efficiency derived in earlier work with unconstrained force patterns also can be achieved with constrained and simplified force patterns. This observation is encouraging in terms of the robustness of the optimal solution as well as the possibility of laboratory realizations of the designed force patterns for generating focused acoustic waves.Publication Metadata only Subspace method for long time scale molecular dynamics(Amer Chemical Soc, 1995) Space, Brian; Rabitz, Herschel; Department of Mathematics; Aşkar, Attila; Faculty Member; Department of Mathematics; College of Sciences; 178822This article presents the dual foundations of an approach to the long time integration of molecular dynamics equations. This work demonstrates that the long time scale molecular dynamics takes place in a relatively low dimensional subspace spanned by a set of collective eigenmodes and that the molecule remains in this subspace for long spans of time, at least on the order of picoseconds or greater. Both of these points are central to constructing an efficient numerical algorithm for long time scale dynamics. The first point allows for automatic filtering of the high frequency components of the dynamics and thus enables the stable use of very large time steps. The second observation allows for possibly using the same basis set for a long time span. Calculations are presented to substantiate these points. The model molecule consists of a 32 atom chain for which the equilibrium configuration is a helix. The chain interactions are of a two, three, and four body nature, allowing respectively for stretch, bending, and torsional motions. The molecule is intentionally chosen to undergo extreme dynamical changes for a severe test of both assertions 1 and 2 and the resulting algorithm. Moreover, one initial state is chosen very far from thermal equilibrium, with all of the energy of the molecule residing in a single local normal mode of the equilibrium configuration. Another initial condition, with a thermal distribution of kinetic energy, is explored. The methods presented are shown to be capable of handling both diverse initial conditions. The dynamical results permit a detailed analysis of the spectral aspects of the problem and provide further support for the subspace concept and the methodology based on it. Stable subspace dynamic integration for time steps of delta t = 100 fs were executed, and the results agree well with the full dynamics (for which the maximum allowable time step using standard molecular dynamics would be delta t approximate to 1 fs); the dynamics included torsional barrier crossings.Publication Metadata only Faster simulation methods for the non-stationary random vibrations of non-linear mdof systems(A A Balkema, 1995) Department of Mathematics; Department of Mathematics; N/A; N/A; Aşkar, Attila; Köylüoğlu, Hasan Uğur; Çakmak, Ayşe Selin; Nielsen, Susanne Ramtung; Faculty Member; Teaching Faculty; Other; Other; Department of Mathematics; College of Sciences; College of Sciences; N/A; N/A; 178822 N/A; N/A; N/AN/APublication Metadata only Strangers' disease - determinants of yellow-fever mortality during the New Orleans epidemic of 1853(Elsevier, 1995) Pritchett, Jonathan B; Department of Economics; Tunalı, Fehmi İnsan; Faculty Member; Department of Economics; College of Administrative Sciences and Economics; 105635During the summer of 1853, New Orleans experienced one of the worst epidemics in the history of the United States. Immigrants accounted for a vast majority of the deaths. In this paper, we analyze differential mortality risk from yellow fever using microdata from interment records. Using a legit model, we sort out the influence of demographic and socioeconomic factors on mortality risk. We establish that the strong relationship between nativity and yellow fever mortality disappears once we control for poverty. status and immunization as measured by duration of residence in New Orleans. (C) 1995 Academic Press, Inc.Publication Metadata only Notes on manuscripts submitted to Turk-Psikoloji-Dergisi(Turkish Psychologists Assoc, 1995) DURAK, A; Department of Psychology; Gülgöz, Sami; Faculty Member; Department of Psychology; College of Social Sciences and Humanities; 49200N/APublication Metadata only Derivatives and stock market volatility: is additional government regulation necessary?(Kluwer Academic Publ, 1995) Department of Business Administration; Tiniç, Mehmet Seha; Faculty Member; Department of Business Administration; College of Administrative Sciences and Economics; N/AN/APublication Metadata only Generation of controlled acoustic waves by optimal design of surface loads with constrained forms(Elsevier, 1995) Young Sik, Kim; Rabitz, Herschel; Tadi, Mohsen; McManus, John B.; Department of Mathematics; Aşkar, Attila; Faculty Member; Department of Mathematics; College of Sciences; 178822Model calculations are presented for the optimal design of surface force patterns to generate acoustic waves that come to a focus within the bulk of a homogeneous elastic solid. The optimal design consists of achieving a high level of energy at the target at a prescribed time by applying a relatively minimal surface force while aiming for a minimal system disturbance away from the focal target. Such optimal designs were derived in an earlier paper, in which no restriction was imposed on the functional form of the applied stress. In this paper we examine the importance of the fine detail in the earlier derived forcing functions in achieving efficient acoustic focusing. We repeat the optimal design calculations with the surface stress constrained to be in the form of rings of variable radius, with cross sectional profiles made by the superposition of two Gaussians. The optimality conditions are secured via the conjugate gradient algorithm (CGA) and the mechanics of the elastic medium are treated by the finite element method along with using the half space Green's function matrix. We use a criterion for focusing efficiency of the ratio of acoustic energy in the target volume to the total work done on the surface, at a prescribed time. The calculations show the high levels of focusing efficiency derived in earlier work with unconstrained force patterns also can be achieved with constrained and simplified force patterns. This observation is encouraging in terms of the robustness of the optimal solution as well as the possibility of laboratory realizations of the designed force patterns for generating focused acoustic waves. © 1995.Publication Metadata only Development of psychology in developing countries: factors facilitating and impeding its progress - introduction(Wiley, 1995) Adair, John G.; Department of Psychology; Kağıtçıbaşı, Çiğdem; Faculty Member; Department of Psychology; College of Social Sciences and Humanities; N/AThis special issue focuses on the factors facilitating and impeding discipline development in developing countries. Eight articles, originally presented in two IUPsyS-sponsored symposia at the International Congress of Applied Psychology in Madrid, Spain in July 1994, articulate the conditions under which research is conducted and which influence discipline progress in developing countries. This introduction summarizes the commonalities among these papers and their implications for the future of the discipline.Publication Metadata only Fast cell-to-cell mapping (path integration) for nonlinear white noise and Poisson driven systems(Elsevier Science Bv, 1995) Nielsen, SRK; Cakmak, AS; Department of Mathematics; Köylüoğlu, Hasan Uğur; Teaching Faculty; Department of Mathematics; College of Sciences; N/AThe stochastic response of nonlinear nonhysteretic single-degree-of-freedom oscillators subject to random excitations with independent increments is studied, where the state vector made up of the displacement and the velocity components becomes a Markov process. Random stationary white noise excitations and homogeneous Poisson driven impulses are considered as common examples of random excitations with independent increments. The applied method for the solution of the joint probability density function (jpdf) of the response is based on the cell-to-cell mapping (path integration) method, in which a mesh of discrete states of the Markov vector process is initially defined by a suitable distribution throughout the phase plane and the transition probability matrix related to the Markov chain originating from this discretization is approximately calculated. For white noise driven systems, transitions are assumed to be locally Gaussian and the necessary conditional mean values and covariances for only the first time step are obtained from the numerical integration of the differential equations for these quantities in combination with a Gaussian closure scheme, For Poisson driven systems, the transition time interval is taken sufficiently small so that at most one impulse is likely to arrive during the interval. The conditional transitional jpdf for exactly one impulse occurrence in the transition time interval is obtained by a new technique in which a convection expansion in terms of pulse intensities is employed. Next, the time dependent jpdf of the response is obtained by passing the system through a sequence of transient states. The formulation allows for a very fast and very accurate calculation of the stationary jpdf of the displacement and velocity by solving an eigenvector problem of the transition probability matrix with eigenvalue equal to 1. The method has been applied to the Duffing oscillator and the results for the stationary jpdf and extreme values have been compared to analytically available results for white noise driven systems acid to those obtained from extensive Monte Carlo simulations for Poisson driven systems.Publication Metadata only Subspace molecular dynamics for long time phenomena(Kluwer Academic Publ, 1995) Department of Mathematics; Aşkar, Attila; Faculty Member; Department of Mathematics; College of Sciences; 178822N/A