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Publication Metadata only A front tracking method for direct numerical simulation of evaporation process in a multiphase system(Academic Press Inc Elsevier Science, 2017) N/A; N/A; Department of Mechanical Engineering; Irfan, Muhammad; Muradoğlu, Metin; PhD Student; Faculty Member; Department of Mechanical Engineering; Graduate School of Sciences and Engineering; College of Engineering; N/A; 46561A front-tracking method is developed for the direct numerical simulation of evaporation process in a liquid-gas multiphase system. One-field formulation is used to solve the flow, energy and species equations in the framework of the front tracking method, with suitable jump conditions at the interface. Both phases are assumed to be incompressible; however, the divergence-free velocity field condition is modified to account for the phase-change/mass-transfer at the interface. Both temperature and species gradient driven evaporation/phase-change processes are simulated. For the species gradient driven phase change process, the Clausius-Clapeyron equilibrium relation is used to find the vapor mass fraction and subsequently the evaporation mass flux at the interface. A number of benchmark cases are first studied to validate the implementation. The numerical results are found to be in excellent agreement with the analytical solutions for all the studied cases. The methods are then applied to study the evaporation of a static as well as a single and two droplets systems falling in the gravitational field. The methods are demonstrated to be grid convergent and the mass is globally conserved during the phase change process for both the static and moving droplet cases.Publication Metadata only An auxiliary grid method for computations of multiphase flows in complex geometries(Academic Press Inc Elsevier Science, 2006) N/A; Department of Mechanical Engineering; N/A; Muradoğlu, Metin; Kayaalp, Arif Doruk; Faculty Member; Master Student; Department of Mechanical Engineering; College of Engineering; Graduate School of Sciences and Engineering; 4656; N/AA method is developed for computations of interfacial flows in complex geometries. The method combines a front-tracking method with a newly developed finite volume (FV) scheme and utilizes an auxiliary grid for computationally efficient tracking of interfaces in body-fitted curvilinear grids. The tracking, algorithm reduces particle tracking in a curvilinear grid to tracking on a uniform Cartesian grid with a look up table. The algorithm is general and can be used for other applications where Lagrangian particles have to be tracked in curvilinear or unstructured grids. The spatial and temporal errors are examined and it is shown that the method is globally second order accurate both in time and space. The method is implemented to solve two-dimensional (planar or axisymmetric) interfacial flows and is validated for a buoyancy-driven drops in a straight tube and the motion of buoyancy-driven drops in a periodically constricted channel.Publication Metadata only Application of proportional velocity feedback control to attenuate the vibrations of a flexible plate using piezoceramic patch actuators(Springer-Verlag Berlin, 2011) N/A; N/A; N/A; Department of Mechanical Engineering; Külah, Serkan; Boz, Utku; Başdoğan, İpek; Master Student; PhD Student; Faculty Member; Department of Mechanical Engineering; Graduate School of Sciences and Engineering; Graduate School of Sciences and Engineering; College of Engineering; N/A; N/A; 179940This paper presents a theoretical and experimental study on the control performance of proportional velocity feedback control with rectangular piezoceramic patch actuators to attenuate the vibrations of a thin flexible plate. For this purpose, first, frequency response funciton of the plate is obtained based on the experimental frequency sweep data. Then, a state space model was fitted to the measured frequency response to be used in the simulations to represent the plant dynamics. The controlled response of the plate is investigated via simulations using MATLAB/SIMULINK. Control performance of the controller is investigated and discussed for various feedback gains.Publication Metadata only Application of pseudo-Hermitian quantum mechanics to a complex scattering potential with point interactions(Iop Publishing Ltd, 2010) Mehri-Dehnavi, Hossein; Department of Mathematics; N/A; Mostafazadeh, Ali; Batal, Ahmet; Faculty Member; Master Student; Department of Mathematics; College of Sciences; Graduate School of Sciences and Engineering; 4231; 232890We present a generalization of the perturbative construction of the metric operator for non-Hermitian Hamiltonians with more than one perturbation parameter. We use this method to study the non-Hermitian scattering Hamiltonian H = p(2)/2m + zeta(-)delta(x + alpha) + zeta(+)delta(x - alpha), where zeta(+/-) and alpha are respectively complex and real parameters and delta(x) is the Dirac delta function. For regions in the space of coupling constants zeta(+/-) where H is quasi-Hermitian and there are no complex bound states or spectral singularities, we construct a (positive-definite) metric operator eta and the corresponding equivalent Hermitian Hamiltonian h. eta turns out to be a (perturbatively) bounded operator for the cases where the imaginary part of the coupling constants have the opposite sign, (sic)(zeta(+)) = -(sic)(zeta(-)). This in particular contains the PT-symmetric case: zeta(+) = zeta*. We also calculate the energy expectation values for certain Gaussian wave packets to study the nonlocal nature of h or equivalently the non-Hermitian nature of H. We show that these physical quantities are not directly sensitive to the presence of the PT - symmetry.Publication Metadata only Constraining scalar-tensor theories using neutron star mass and radius measurements(American Physical Society (APS), 2022) Tuna, Semih; N/A; Department of Physics; Ünlütürk, Kıvanç İbrahim; Ramazanoğlu, Fethi Mübin; PhD Student; Faculty Member; Department of Physics; Graduate School of Sciences and Engineering; College of Sciences; N/A; 254225We use neutron star mass and radius measurements to constrain the spontaneous scalarization phenomenon in scalar-tensor theories using Bayesian analysis. Neutron star structures in this scenario can be significantly different from the case of general relativity, which can be used to constrain the theory parameters. We utilize this idea to obtain lower bounds on the coupling parameter ?? for the case of massless scalars. These constraints are currently weaker than the ones coming from binary observations, and they have relatively low precision due to the approximations in our method. Nevertheless, our results clearly demonstrate the power of the mass-radius data in testing gravity, and can be further improved with future observations. The picture is different for massive scalars, for which the same data is considerably less effective in constraining the theory parameters in an unexpected manner. We identify the main reason for this to be a large high-likelihood region in the parameter space where deviations from general relativity are relatively small. We hope this initial study to be an invitation to use neutron star structure measurements more commonly to test alternative theories in general.Publication Metadata only Linearization of one-dimensional nonautonomous jump-diffusion stochastic differential equations(World Scientific Publ Co Pte Ltd, 2007) Unal, Gazanfer; Khalique, C. Masood; N/A; İyigünler, İsmail; Master Student; Graduate School of Sciences and Engineering; N/ANecessary and sufficient conditions for the linearization of one-dimensional nonautonomous jump-diffusion stochastic differential equations are given. Stochastic integrating factor is introduced to solve the linear jump-diffusion stochastic differential equations. Closed form solutions to certain linearizable jump-diffusion stochastic differential equations are obtained.Publication Metadata only Physical aspects of pseudo-Hermitian and PT-symmetric quantum mechanics(IOP Publishing Ltd, 2004) NA; Department of Mathematics; N/A; Mostafazadeh, Ali; Batal, Ahmet; Faculty Member; Master Student; Department of Mathematics; College of Sciences; Graduate School of Sciences and Engineering; 4231; 232890For a non-Hermitian Hamiltonian H possessing a real spectrum, we introduce a canonical orthonormal basis in which a previously introduced unitary mapping of H to a Hermitian Hamiltonian h takes a simple form. We use this basis to construct the observables O-alpha, of the quantum mechanics based on H. In particular, we introduce pseudo-Hermitian position and momentum operators and a pseudo-Hermitian quantization scheme that relates the latter to the ordinary classical position and momentum observables. These allow us to address the problem of determining the conserved probability density and the underlying classical system for pseudo-Hermitian and in particular PT-symmetric quantum systems. As a concrete example we construct the Hermitian Hamiltonian h, the physical observables O-alpha, the localized states and the conserved probability density for the non-Hermitian PT-symmetric square well. We achieve this by employing an appropriate perturbation scheme. For this system, we conduct a comprehensive study of both the kinematical and dynamical effects of the non-Hermiticity of the Hamiltonian on various physical quantities. In particular, we show that these effects are quantum mechanical in nature and diminish in the classical limit. Our results provide an objective assessment of the physical aspects of PT-symmetric quantum mechanics and clarify its relationship with both conventional quantum mechanics and classical mechanics.