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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 A front-tracking method for computation of interfacial flows with soluble surfactants(Academic Press Inc Elsevier Science, 2008) Tryggvason, Gretar; Department of Mechanical Engineering; Muradoğlu, Metin; Faculty Member; Department of Mechanical Engineering; College of Engineering; 46561A finite-difference/front-tracking method is developed for computations of interfacial flows with soluble surfactants. The method is designed to solve the evolution equations of the interfacial and bulk surfactant concentrations together with the incompressible Navier-Stokes equations using a non-linear equation of state that relates interfacial surface tension to surfactant concentration at the interface. The method is validated for simple test cases and the computational results are found to be in a good agreement with the analytical solutions. The method is then applied to study the cleavage of drop by surfactant-a problem proposed as a model for cytokinesis [H.P. Greenspan, On the dynamics of cell cleavage, J. Theor. Biol. 65(l) (1977) 79; H.P. Greenspan, On fluid-mechanical simulations of cell division and movement, J. Theor. Biol., 70(l) (1978) 125]. Finally the method is used to model the effects of soluble surfactants on the motion of buoyancy-driven bubbles in a circular tube and the results are found to be in a good agreement with available experimental data.Publication Open Access A note on a strongly damped wave equation with fast growing nonlinearities(American Institute of Physics (AIP) Publishing, 2015) Zelik, Sergey; Department of Mathematics; Kalantarov, Varga; Faculty Member; Department of Mathematics; College of Sciences; 117655A strongly damped wave equation including the displacement depending nonlinear damping term and nonlinear interaction function is considered. The main aim of the note is to show that under the standard dissipativity restrictions on the nonlinearities involved, the initial boundary value problem for the considered equation is globally well-posed in the class of sufficiently regular solutions and the semigroup generated by the problem possesses a global attractor in the corresponding phase space. These results are obtained for the nonlinearities of an arbitrary polynomial growth and without the assumption that the considered problem has a global Lyapunov function. (C) 2015 AIP Publishing LLCPublication Metadata only A note on the algebra of p-adic multi-zeta values(International Press of Boston, 2015) Department of Mathematics; Ünver, Sinan; Faculty Member; Department of Mathematics; College of Sciences; 177871We prove that the algebra of p-adic multi-zeta values, as defined in [4] or [2], are contained in another algebra which is defined explicitly in terms of series. The main idea is to truncate certain series, expand them in terms of series all of which are divergent except one, and then take the limit of the convergent one. The main result is Theorem 3.12.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 Analytical solution of a stochastic content-based network model(Iop Publishing, 2005) Mungan, M; Balcan, D; Erzan, A; Department of Physics; Kabakçıoğlu, Alkan; Faculty Member; Department of Physics; College of Sciences; 49854We define and completely solve a content-based directed network whose nodes consist of random words and an adjacency rule involving perfect or approximate matches for an alphabet with an arbitrary number of letters. The analytic expression for the out-degree distribution shows a crossover from a leading power law behaviour to a log-periodic regime bounded by a different power law decay. The leading exponents in the two regions have a weak dependence on the mean word length, and an even weaker dependence on the alphabet size. The in-degree distribution, on the other hand, is much narrower and does not show any scaling behaviour.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 Open Access Blume-Emery-Griffiths spin glass and inverted tricritical points(American Physical Society (APS), 2008) Özçelik, V. Ongun; Department of Physics; Berker, Ahmet Nihat; Faculty Member; Department of Physics; College of SciencesThe Blume-Emery-Griffiths spin glass is studied by renormalization-group theory in d=3. The boundary between the ferromagnetic and paramagnetic phases has first-order and two types of second-order segments. This topology includes an inverted tricritical point, first-order transitions replacing second-order transitions as temperature is lowered. The phase diagrams show disconnected spin-glass regions, spin-glass and paramagnetic reentrances, and complete reentrance, where the spin-glass phase replaces the ferromagnet as temperature is lowered for all chemical potentials.Publication Open Access Buckling of stiff polymers: influence of thermal fluctuations(American Physical Society (APS), 2007) Emanuel, Marc; Mohrbach, Herve; Schiessel, Helmut; Kulic, Igor M.; Department of Mechanical Engineering; Sayar, Mehmet; Faculty Member; Department of Mechanical Engineering; College of Engineering; 109820The buckling of biopolymers is a frequently studied phenomenon The influence of thermal fluctuations on the buckling transition is, however, often ignored and not completely understood. A quantitative theory of the buckling of a wormlike chain based on a semiclassical approximation of the partition function is presented. The contribution of thermal fluctuations to the force-extension relation that allows one to go beyond the classical Euler buckling is derived in the linear and nonlinear regimes as well. It is shown that the thermal fluctuations in the nonlinear buckling regime increase the end-to-end distance of the semiflexible rod if it is confined to two dimensions as opposed to the three-dimensional case. The transition to a buckled state softens at finite temperature. We derive the scaling behavior of the transition shift with increasing ratio of contour length versus persistence length.