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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February 4, 2011

Speaker: Nicolas Perinet, Faculty of Science, Ontario Tech University

Title: Numerical investigation of Faraday instability

Abstract: In 1831, Farday discovered that when two immiscible fluid layers were subjected to vertical vibration, standing waves would appear at the interface if the oscillation amplitude was sufficiently large. Recent work has shown an astonishing variety of patterns, which has contributed to the current interest in the Faraday problem. We have carried out the first complete three-dimensional simulation of Faraday waves. The algorithm we use combines a projection method to solve the Navier-Stokes equations with a Front-Tracking method to treat the interface. \r\n\r\nThe neutral curves and temporal modes agree with Floquet theory. We then simulated the Faraday problem under the conditions in which square and hexagonal patterns appear. The spatio-temporal spectra of the simulated patterns agree with experiment. Nevertheless, the hexagons destabilize in favour of a an alternating sequence of patterns with different symmetries, suggesting the presence of a homoclinic orbit. We have developed an algorithm which forces the hexagonal symmetry in order to calculate the fixed point of this orbit. Finally, we have carried out a numerical study of the drift instability in the Faraday experiment. A horizontal displacement of initially stationary patterns has been experimentally observed when the oscillation amplitude exceeds a secondary threshold. Our numerical simulations have confirmed this result. Bifurcation diagrams displaying additional instabilities have been constructed, as well as a complementary spatio-temporal spectral analysis.

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