We are thankful to be welcome on these lands in friendship. The lands we are situated on are covered by the Williams Treaties and are the traditional territory of the Mississaugas, a branch of the greater Anishinaabeg Nation, including Algonquin, Ojibway, Odawa and Pottawatomi. These lands remain home to many Indigenous nations and peoples.

We acknowledge this land out of respect for the Indigenous nations who have cared for Turtle Island, also called North America, from before the arrival of settler peoples until this day. Most importantly, we acknowledge that the history of these lands has been tainted by poor treatment and a lack of friendship with the First Nations who call them home.

This history is something we are all affected by because we are all treaty people in Canada. We all have a shared history to reflect on, and each of us is affected by this history in different ways. Our past defines our present, but if we move forward as friends and allies, then it does not have to define our future.

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March 21, 2014

Speaker: Jamil Jabbour

Title: Towards Matrix-Free Methods Towards Annular Electroconvection

Abstract: The flow of a smectic liquid crystal in annular geometry, when an electrical potential is applied between the boundaries, is investigated using a dynamical systems approach. In particular, matrix-free continuation methods are implemented to trace branches of solutions as a parameter of the nonlinear system is changed. Nonlinear systems of this type are generally solved using a Newton-type solver. The methods are called matrix-free methods if the Jacobian is not calculated explicitly but is approximated by its action on a vector with function evaluation, thus the corresponding linear systems may be solved using an iterative method. In this presentation, we discuss the matrix-free methods, and show results of their implementation on a model problem, specifically, the one dimensional K-S equation with periodic boundary. The stability and the bifurcation points of steady states in the K-S equation are examined for the parameter $\alpha$ between 0 and 40. Further we discuss the implementation of the continuation code to the electroconvection time stepper.