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The role of complex singularities in geometric flows

A popular topic in differential geometry involves studying the singularity structure of geometric flows. The most well-known example is mean curvature flow. In this example, surfaces evolve according to a flow rule that relates the speed of the surface to its curvature. Certain surfaces will evolve until singularities occur in finite time, and these singularities can be studied using similarity solutions and asymptotic analysis.In this project, a different perspective is applied to these problems, namely the use of complex variable …

Study level
Master of Philosophy, Honours, Vacation research experience scheme
Faculty
Faculty of Science
School
School of Mathematical Sciences

Separating nonlinear optical effects in optical limiters

Optical limiting uses a medium’s nonlinear response to allow light at low intensities to be transmitted, but restricts transmission at high intensities so as to safeguard sensitive detectors including the eye. A popular nonlinear process used in optical limiters is two photon absorption where two high intensity light photons are simultaneously absorbed thereby reducing the light transmission through the medium. Unfortunately, in gold nanoparticle optical limiters a second nonlinear process can arise – saturated absorption which leads to an increase …

Study level
Honours, Vacation research experience scheme
Faculty
Faculty of Science
School
School of Chemistry and Physics
Research centre(s)
Centre for Materials Science

Nonlinear water waves and signal analysis

When a ship moves through water, it generates waves. These waves propagate through the medium and their effect can be detected many kilometres away from the initial disturbance.Supposing that a sensor is placed in the water which can measure the height of the free surface at a single point over time, somewhere close to the shore perhaps, it is of considerable interest to know how much information about the disturbance can be recovered from that signal, such as the size, …

Study level
Vacation research experience scheme
Faculty
Faculty of Science
School
School of Mathematical Sciences
Research centre(s)
Centre for Data Science

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