Research with Graduate and Undergraduate Students

Spring 2012

Chua's Circuit and Conditions of Chaotic Behavior
This research investigates the chaos conditions of Chua's circuits with an untraditional way.

Finding Global Minimum / Maximum
This research explores how two different approaches, simulated annealing and genetic algorithm to find a global minimum or maximum with some functions.

Nash Equilibrium Trends (Game Theory Analysis)
This is the research of trends we can find Nash equilibra with random parameters for certain games.

Heart Physiology and the Pacemaker (Comparison of voltage change data sets made by the heart with and without an artificial pacemaker)
This research shows that simulated properties of heat motions and the motions aided by artificial pace makers.

Maximum Entropy and Fourier Transformation
This explains the concept of entropy and shows the comparison between maximum entropy method and Fourier transformation.

Time Dilation and Determining Eigen Values
The main topics from modern physics are relativity and quantum physics. This explores a problem of general relativity in terms of special relativity. In addition, PT-symmetric quantum systems are invastigated computationally.

Object Oriented Programming for Beginners
This is an untraditional pedagogy of object oriented programming.

Approximation of Percolation Thresholds
This research introduces a new way of finding the threshold of two dimensional percolation.

Effective Hamiltonian Operations (Considering Physics to Conserve Over Time)
This research investigates the hamiltonian systems with a symplectic algorithm. For the comparison, Euler and Runge-Kutta methods are used.

Spring 2011

Computational Error Analyses for Euler's Method, Runge-Kutta 4th and 6th Methods
This research investigates the errors of differential equation solvers.

Various Random Number Generators and the Applications
This research explores how various random number generators are used for physical and mathematical problems.

Fourier Analysis and its Applications
This is the research of Fourier transformation of one and two dimensional.

Simulation of the Electromagnetic Fields and its Properties (With Free-space and Dielectrics Using the FDTD Method)
This research shows that simulated properties of electromagnetic waves for various conditions.

The Use of Bayesian Statistics in Court
This explains the basics of Bayesian statistics and its application to a court room.

Some Aspects of Numerical Solutions for Partial Differential Equations
The main topics from partial differential equations. This explores a problem of poisson equations and nonlinear partial differential equations.

Spring 2010

Equipotentials and Electric Field Lines
The research investigates the electric fields and potentials.

Finding the Popular Frequency
This explains the Fourier Transformation and its applications.

Fourier Series
This is the introduction to Fourier series by showing how they approximate periodic functions.

Introduction to Object Oriented Programming
The basic ideas of OOP is presented.

RC Circuits and its Physical Simulations
This shows the computational experiment on RC circuits.

With Graduate Students

Fokker-Planck Equation and its Related Topics
The summery of Fokker-Planck equation and related applications.

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