Researcher:
Aşkar, Attila

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Attila

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Aşkar

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Researcher Of Publications: search.filters.isAuthorOfPublication.0efdd9c6-dbb3-4d55-9022-2408d1d5b499

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Now showing 1 - 10 of 28
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    Interior energy focusing within an elasto-plastic material
    (Pergamon-Elsevier Science Ltd, 1996) Tadi, M; Rabitz, H; Kim, YS; Prevost, JH; McManus, JB; Department of Mathematics; Aşkar, Attila; Faculty Member; Department of Mathematics; College of Sciences; 178822
    In this paper we consider the problem of focusing acoustic energy within a subsurface volume in a solid by means of a designed surface pattern, and ask how that focusing is affected by plastic yield of the material. Surface force patterns that yield efficient subsurface acoustic focusing have been designed using optimal control theory, based on a linear elastic model of a solid. The acoustic waves generated by these forces then are propagated, via numerical algorithms, in a model solid that exhibits plastic yield. Numerical results indicate that as the amplitude of the force increases, yield begins to develop at the focus, with the formation of an expanding region of permanent plastic deformation. Despite the occurrence of yield near the focus, acoustic energy still can be delivered to the focal volume with good efficiency.
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    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; 178822
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    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; 178822
    Model 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.
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    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/A
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    Finite-element method for quantum scattering
    (Kluwer Academic Publ, 1993) Department of Mathematics; Aşkar, Attila; Faculty Member; Department of Mathematics; College of Sciences; 178822
    The 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.
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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; Sennaroğlu, Alphan; Aşkar, Attila; Atay, Fatihcan; Faculty Member; Faculty Member; Faculty Member; Department of Physics; Department of Mathematics; 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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    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; 178822
    The 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.
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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; Sennaroğlu, Alphan; Aşkar, Attila; Atay, Fatihcan; Faculty Member; Faculty Member; Faculty Member; Department of Physics; Department of Mathematics; 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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    Nonlinear Schrödinger and gross - Pitaevskii equations in the Bohmian or Quantum Fluid Dynamics (QFD) representation
    (Springer, 2018) Department of Mathematics; Aşkar, Attila; Faculty Member; Department of Mathematics; College of Sciences; 178822
    The Quantum Fluid Dynamics (QFD) representation has its foundations in the works of Madelung (1929), De Broglie (1930 - 1950) and Bohm (1950 - 1970). It is an interpretation of quantum mechanics with the goal to find classically identifiable dynamical variables at the sub-particle level. The approach leads to two conservation laws, one for "mass" and one for "momentum", similar to those in hydrodynamics for a compressible fluid with a particular constitutive law. The QFD equations are a set of nonlinear partial differential equations. This paper extends the QFD formalism of quantum mechanics to the Nonlinear Schrödinger and the Gross-Pitaevskii equation.
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    Subspace molecular dynamics for long time phenomena
    (Kluwer Academic Publ, 1995) Department of Mathematics; Aşkar, Attila; Faculty Member; Department of Mathematics; College of Sciences; 178822
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