Wednesday, April 4, 2012

1:00 pm - 3:00 pm (Carleton 104)

**An application of the nonlinear Crank-Nicholson method:solving the Cahn-Hillard Equation**

Kathleen Alexander

Kathleen Alexander

The Cahn-Hillard equation was proposed as a model for phase separation in binary mixtures. It is a fourth-order, nonlinear, partial differential equation that can be generalized to n spatial dimensions. In this study, a finite difference approach has been used to solve the Cahn-Hillard equation in 1 and 2 spatial dimensions using the nonlinear Crank-Nicholson method.

**The Farley-Buneman problem in the auroral E-Region turbulence**

Kaddour Chelabi

We attempt to understand the Farley-Buneman problem in the E-region auroral turbulence by solving a nonlinear elliptic partial differential equation. The solution of the PDE can be used to predict the ion density.

**Numerical solutions to the geometric flow of wormhole geometries**

Andrew Day

Andrew Day

In Einstein's general theory of relativity there exist equations describing the behaviour of wormholes. In this talk, we will describe the numerical solutions of the equations that arise from DeTurck-Ricci flow of such wormhole geometries using the forward-time centered space (FTCS) and Dufort-Frankel methods. We find that there are two types of solutions to these equations. One where the wormhole throat pinches off in finite flow time, and another where the wormhole throat expands indefinitely.

**Radio wave scintillation in the ionosphere: solving the wave equation for the propagating electric field in the ionospheric regions**

Hichem Mezaoui

Irregularities in the electron density in the ionosphere cause amplitude fluctuations of the electric field. This can be a problem to communication and navigation system in the very-high frequency-ultra-high frequency (VHF-UHF) range. A good knowledge of the behavior of the phase and the amplitude in this region will help for preventing these problems.

**Chaos in nonlinear four-wave interaction**

Adnane Osmane

Wave-wave-interactions are commonly studied in plasmas, optics and geophysics where they can become dominant energy-momentum carriers. Studying a dynamical system representing the nonlinear interaction of four waves, we will demonstrate, that similarly to the three wave-interactions, the four wave-interactions can also result in chaotic orbits.

**Modelling non-linear field line resonances in the Earth's magnetosphere**

Chris Watson

Low frequency plasma waves play an important role in energy transfer within the Earth's magnetosphere and ionosphere. The evolution of magnetic field and density perturbations in magnetospheric plasma can be described by two coupled differential equations: a non-linear Schrodinger equation for the magnetic field and an equation for the plasma response driven by the magnetic field fluctuation. This system can be numerically solved using the split-step Fourier method.

Thursday, April 5 2012

1:00 pm - 2:30 pm (Carleton 104)

**Meter-Scale E-Region Irregularities**

Francis Bischoff

This project will deal with plasma density meter-scale irregularities in the auroral atmosphere's electroject. In particular, I will try to model the interaction between three coupled modes and try to determine the existence of saturated states.

**Modelling vibrations of a two link flexible manipulatorusing finite element analysis**

Jason Elliott

Jason Elliott

When designing a controller for a system, it is necessary to know how the system will response to uncontrolled inputs, otherwise known as the system's open loop response. Once the system’s open loop response has been identified, a controller can then be designed to modify inputs to a system such that it will provide a desired response. However, in many cases it can be impractical or even impossible to obtain an open loop response of a system through testing. As such, it is advantageous to have a model around which the controller can be designed. For the application of controlling vibrations in a two link flexible manipulator, finite element analysis provides a means of creating such a model capable of predicting the induced vibration within each link for known inputs from motors at the manipulators base and elbow joints.

**Numerical solution of the linear Black–Scholes equation**

Mohammed AL Humaidi

We solve the linear Black-Scholes equation arising in mathematical finance using several different numerical methods and compare the results.

**Charged particle orbits in steep field gradients with a multiplicative noise**

Karim Meziane

Karim Meziane

The project describes a particle trajectory in a nonuniform magnetic field in which random fluctuations are added. The purpose is to examine how the orbits are affected by the magnetic field fluctuations. Two numerical schemes have been used: The standard Euler scheme and a method based on Taylor expansion adapted to stochastic differential equations found in the literature [exp. Mannella & Palleschi, Phys. Rev. A, Vol. 40, p3381, 1989].