Attila Askar - Academia.edu (original) (raw)

Papers by Attila Askar

Harmonic generation in nonlinear dielectrics

Journal of Applied Physics, Oct 1, 1975

A method based on Poincaré perturbation is presented for finding the various order harmonics in a... more A method based on Poincaré perturbation is presented for finding the various order harmonics in a nonlinear dielectric. The method is an extension of the ideas utilized by this author for finding spatial and temporal periodic solutions for elastic waves in an anharmonic lattice. The method is applied here to find the generation of the first and second harmonics by a fundamental mode in a dielectric where the relationship between the electric field and electric displacement contains linear, quadratic, and cubic terms.

One-Dimensional Nonsimple Lattices and Special Continuum Theories

An assessment of the poincare scheme for non-linear oscillators and an improvement of its range of validity

International Journal of Non-linear Mechanics, 1979

Abstract The range of validity of the Poincare method is studied by comparison with the exact sol... more Abstract The range of validity of the Poincare method is studied by comparison with the exact solution for the anharmonic and Morse oscillators. The exact solutions for these cases are expressible respectively in terms of elliptic and inverse trigonometric functions. The oscillation frequency is taken as the basis for the comparison. It is seen that the Poincare perturbation gives fairly accurate results up to amplitudes that are 20–30 per cent of the maximum value allowed for periodic solutions depending on the form of the potential energy. A new method is presented as a slight variation over the standard Poincare method. This method differs from the former only by a rearrangement of the differential equation through a collocation approximation for the potential. In spite of its simplicity, the method proves to be a better approximation than the standard Poincare method and gives remarkably accurate results for amplitudes up to 60–70 per cent of the maximum value allowed for periodic solutions.

Journal of Chemical Physics, Sep 15, 2003

An optimal reduced space method for capturing the low-frequency motion in classical molecular dyn... more An optimal reduced space method for capturing the low-frequency motion in classical molecular dynamics calculations is presented. This technique provides a systematic means for carrying out reduced-dimensional calculations in an effective set of reduced coordinates. The method prescribes an optimal reduced subspace linear transformation for the low frequency motion. The method is illustrated with a dynamics calculation for a model potential, where the original six-dimensional space is reduced to two ͑three͒ dimensions, depending on the desired frequency cutoff value.

Quantum Fluid Dynamics (QFD) or Bohmian Representation of Schrödinger Equation with Navier - Stokes Type Dissipation Attila Askar Koc University, Sariyer, Istanbul 34450, Turkey

APS March Meeting Abstracts, 2019

Lattice Dynamics Approach to the Theory of Elastic Dielectrics with Polarization Gradient: The Continuum Limit of the Optical Branch

Explicit Integration of Boundary Integral Equations in the Frequency Domain for Wave Scattering Problems

ASCE eBooks, 1986

The goals of this article are: (1) to present an efficient method for the integration of the boun... more The goals of this article are: (1) to present an efficient method for the integration of the boundary integral equations for wave scattering problems and (2) to apply this method to the study of scattering of elastic waves by surface topographies and underground structures. The explicit integration scheme of the boundary integral equations is shown to be stable and the computational effort is seen to be of the order of constructing the matrix of coefficients since no matrix inversions are involved. The computer memory requirements are also quite minimal since the coefficient matrices are not needed.

Probabilistic Engineering Mechanics, Apr 1, 1996

In this paper semi-analytical forward-difference Monte Carlo simulation procedures are proposed f... more In this paper semi-analytical forward-difference Monte Carlo simulation procedures are proposed for the determination of the lower order statistics and the Joint Probability Density Function (JPDF) of the stochastic response of geometrically nonlinear multi-degree-of-freedom structural systems subject to nonstationary Gaussian white noise excitation, as an alternative to conventional direct simulation methods. These alternative simulation procedures rely on an assumption of local Gaussianity during each time step. This assumption is tantamount to various linearizations of the equations of motion. All of the proposed procedures yield the exact results as the time step goes to zero. The proposed procedures are based on analytical convolutions of the excitation process, hereby, reducing the generation of stochastic processes and numerical integration to the generation of random vectors only. Such a treatment offers higher rates of convergence, faster speed and higher accuracy. These procedures are compared to the direct Monte Carlo simulation procedure, which uses a fourth order Runge-Kutta scheme with the white noise process approximated by a broad band Ruiz-Penzien broken line process. The comparisons show that the so-called Ermark-Allen algorithm developed for simulation applications in molecular dynamics is the most favourable procedure for MDOF structural systems.

International Journal of Engineering Science, May 1, 1995

Earthquake Engineering & Structural Dynamics, 1981

An approximate method is proposed for the scattering of SH-waves by foundations of irregular shap... more An approximate method is proposed for the scattering of SH-waves by foundations of irregular shape and the resulting soil-structure interaction problems. The scattering of elastic waves by the rigid foundation embedded in half-space is solved approximately by using integral representation of the wave equation. The procedure is the Born approximation which has been widely used in quantum mechanics for collision and scattering theory though not well-known in elastodynamics. This paper extends the previous work of the authors on the scattering of waves to account for soil-structure interaction. The motion ofthe foundation is evaluated by the balance of momentum under stresses due to the incident waves as well as the waves generated by its own motion and the forces coming from the superstructure. The model investigated consists of an infinitely long elastic shear wall of height H and thickness h erected on a rigid infinitely long foundation. Results are Pesented for the cases with circular, elliptical and rectangular foundations. For a circular foundation, excellent agreement is found with the exact solutions for the foundation displacement and the relative displacement between the top and bottom of the structure for the entire range of wave numbers. For an elliptical foundation, accuracy decreases with increasing wave numbers. Foundation displacements are compared for foundation shapes that are shallow elliptical, deep elliptical, rectangular and circular. It is observed that foundation displacements are dependent on the angle ofincidence except for a semicircle. The results on the details of the scattered field are, however, not as accurate.

Designing Coherent Acoustic Waves by Optimal Control Theory

Springer eBooks, 1992

There exists an intensive effort to design specific wave patterns in classical fields as well as ... more There exists an intensive effort to design specific wave patterns in classical fields as well as in quantum chemistry 1–9. In particular, there are a number of physical situations such as internal material diagnostics and modifications10 where it would be useful to produce a specified acoustic wave structure within a solid by applying a pattern of forces on the solid’s surface. The surface loads are created by using lasers, electron beams as well as through transducer arrays 11–15, Waves in a solid are of two types as compressional and shear waves with respectively longitudinal and transverse propagation character. This added complexity offers in fact an additional flexibility for achieving a desired output. The design of a surface load pattern in both space and time for the coherent focusing of waves at a prescribed target volume at a prescribed time is studied in this paper. Posed in this manner, such a design is an inverse problem. In general, the guessing of the input surface load to achieve a prescribed wave pattern as output is very complicated and relies heavily on experience and intuition in the absence of a rational design procedure. The proposed scheme provides a rational design procedure to substitute intuition and to achieve constructions where intuition would fail. This is particularly true for generating coherent waves that interfere constructively as well as destructively in specific regions of space.

Energy Loss Mechanisms and Viscoelasticity

WORLD SCIENTIFIC eBooks, Jul 1, 1986

Polarizable Lattices and Piezoelectricity

Laser Beam Propagation in a Thermally Loaded Absorber

Beam propagation in a thermally loaded absorber is analyzed by a novel method. The formulation id... more 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.

Interior energy focusing within an elasto-plastic material

International Journal of Solids and Structures, May 1, 1996

ABSTRACT

A finite element method with local trigonometric basis for close coupling equations

Journal of Chemical Physics, Jun 1, 1981

A method is presented for the solution of close coupling equations. The method formulates the sca... more A method is presented for the solution of close coupling equations. The method formulates the scattering problem (i) as a set of boundary value problems, (ii) uses a variational principle, and (iii) used local trigonometric basis within the spirit of the finite element method. The use of local trigonometric basis as compared with the traditional polynomial basis in finite elements offers a distinct superiority in approximating oscillary wave functions.

Physical Review A, Mar 16, 2000

A quantum fluid dynamic(QFD) control formulation is presented for optimally manipulating atomic a... more A quantum fluid dynamic(QFD) control formulation is presented for optimally manipulating atomic and molecular systems. In QFD the control quantum system is expressed in terms of the probability density ρ and the quantum current j. This choice of variables is motivated by the generally expected slowly varying spatial-temporal dependence of the fluid dynamical variables. The QFD approach is illustrated for manipulation of the ground electronic state dynamics of HCl induced by an external electric field.

Computers & mathematics with applications, Feb 1, 2002

This paper proposes a new numerical technique for solving the quantum fluid dynamical equations w... more This paper proposes a new numerical technique for solving the quantum fluid dynamical equations within the Lagrangian description. An efficient and accurate numerical scheme is achieved by taking advantage of the smooth field variables obtained via the Madelung transformation combined with the radial basis function interpolation. Applications to the 2D coherent state and a 2D model of NO2 photodissociation dynamics show that the present method rivals the split-operator method in both efficiency and accuracy. The advantage of the new algorithm as a computational tool is expected to prevail for high-dimensional systems.

The use of global wavefunctions in scattering theory

Chemical Physics, Mar 1, 1978

Abstract This paper considers the potential savings associated with the use of global wavefunctio... more Abstract This paper considers the potential savings associated with the use of global wavefunctions in scattering theory. The normal close coupling approach exp