Research Interests

  • Computational Fluid Dynamics (CFD)
  • Parallel Computing
  • Level Set Methods and Applications In CFD
  • Quantum Computation
  • Fractional Calculus and Its Applications in Quantum Mechanics
  • Heat and Mass Transfer
  • Applied Computational Mathematics
  • Computational Quantum Mechanics

Publications

  1. A. Kaboudian, V. Kulish, “The Modified Fractional Order Schrödinger Equation With Relativistic Limits ”, Under Preparation.
  2. A. Kaboudian, P. Tavallali, V. Kulish, “ Derivation of The Phase-Lagged Schrödinger Equation from Brownian Motion”, Under Preparation.
  3. P. Tavallali, A. Kaboudian, V. Kulish, “ Exact Solution for Phase-Lagged Heat Equation in One Dimensional Domain”, International Journal of Heat and Mass Transfer, Submitted.

Research Experiences

  1. Phase-lagged Formulation of Quantum Mechanics: Application to Ultra-Fast Processes of Energy and Information Transport (Current Research Topic in NTU)

    The Schrödinger equation, the corner stone in quantum mechanics, gives rise to the paradox of instantaneous propagation of energy. The Schrödinger equation is not a relativistic formula. Despite of all the attempts, there is no unique and general formulation which removes the paradox and gives relativistic results in all cases has been proposed.

    Three possible phased-lagged derivations of the Schrödinger equation have been proposed, based on the assumption that there exists a finite time lag between the onset of gradients and the corresponding flux. The extended version of the Schrödinger equation, therefore, has been proposed to eliminate the paradox of instantaneous propagation, intrinsic to the classical Schrödinger equation.

    Furthermore, based on the theory of fractional calculus a fractional order PDE is proposed to modify the classical Schrödinger equation. The proposed equation has relativistic limits. New concepts such as quantum information wave speed has been proposed to further extend the idea of the Lorentz invariant.


  2. Solving Partial Differential Equations Using scilab (B. Sc theses in IUT)

    In this project, we tried to solve PDEs, specifically heat equation, using scilab. Scilab is an open source software developed by INREA which has several matrix calculation abilities comparable to MATLAB. In the end of the project, a toolbox was designed for scilab which was named the PDE- toolbox.

    This project consisted of several programming stages:

    The first stage was to develop an engine to generate mesh, apply boundary conditions and solve the corresponding PDE. This stage was implemented using the MODULEF which is a library of 3000 procedures written in FORTRAN 77. This part of the engine reads and write all the input-output data to files, so that all the data can be used for future reference and use. It also, performs all the computations to generate mesh, and solve the PDEs.

    The second step was to interface the engine with the scilab engine so that the engine can be called inside scilab. This steps consisted of several steps of interfacing and calling either FORTRAN procedures or linux external programs inside scilab.

    The third step was to develop a graphical user interface for the toolbox. This graphical user interface was developed using Tcl/Tk programming. The Tcl/Tk programs was later interfaced with scilab to facilitate input-output procedures.

    The fourth step was to develop some tools for drawing the geometry or the domain of the solution. This step was done using the graphical properties of scilab. All drawing tools were designed within the scope of the project.The last stage was developing the post processing tool. In order to do so, post processing facilities and programs were developed using MODULEF library and were interfaced with the scilab engine.

  3. Honeycomb design for low speed wind tunnel in IUT

    Honeycombs are used in wind tunnels, to reduce the longitudinal components of turbulence as well as the lateral components of mean velocity and turbulent eddies. The mode of action of a honeycomb with cells elongated in the flow direction, is qualitatively clear but few tests have actually been made, and all that is certain is that the cell length of the honeycomb should be at least six or eight times the cell diameter. Stacking two honeycombs together to get a larger effective length-to-diameter ratio is acceptable if the two are tightly laced together.

    In this project, a honeycomb cell size and length had to be designed such that it meets both research and educational requirements in a economical and practical way. Deciding between a honeycomb with large longitudinal length and two honeycombs of smaller size was crucial, as two honeycombs can produce turbulence but would be much more economical.



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