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Full Text: NoSubject: search.filters.subject.Mathematical physics

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Now showing 1 - 10 of 28
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    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; 46561
    A 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.
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    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; 46561
    A 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.
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    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; 177871
    We 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.
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    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/A
    A 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.
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    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; 49854
    We 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.
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    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; 179940
    This 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.
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    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; 232890
    We 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.
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    Can Nth order Born approximation be exact?
    (IOP Publishing Ltd, 2024) Loran, Farhang; Department of Mathematics; Mostafazadeh, Ali; Department of Mathematics; College of Sciences
    For the scattering of scalar waves in two and three dimensions and electromagnetic waves in three dimensions, we identify a condition on the scattering interaction under which the Nth order Born approximation gives the exact solution of the scattering problem for some N >= 1.
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    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; 254225
    We 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.
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    Dynamical theory of scattering, exact unidirectional invisibility, and truncated z e(-2ik0x) potential
    (Iop Publishing Ltd, 2016) N/A; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231
    The dynamical formulation of time-independent scattering theory that is developed in (2014 Ann. Phys., NY 341 70-85) offers simple formulas for the reflection and transmission amplitudes of finite-range potentials in terms of the solution of an initial-value differential equation. We prove a theorem that simplifies the application of this result and use it to give a complete characterization of the invisible configurations of the truncated z e(-2ik0x) potential to a closed interval, [0, L], with k(0) being a positive integer multiple of pi/L. This reveals a large class of exact unidirectionally and bidirectionally invisible configurations of this potential. The former arise for particular values of z that are given by certain zeros of Bessel functions. The latter occur when the wavenumber k is an integer multiple of pi/L but not of k(0). We discuss the optical realizations of these configurations and explore spectral singularities of this potential.