Roderick Melnik

The Dynamic World of Coupled Systems

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Many processes have components that interact in a complicated dynamic manner; they are "coupled." Certain materials, for example, can mimic biological systems by recovering their shapes after suffering an apparently permanent deformity. Understanding coupled processes has important implications for applications in such fields as medicine and biotechnology and many others as well. The problems that arise are intrinsically interdisciplinary and their solutions require the development of advanced mathematical tools.

Dr. Roderick Melnik is an outstanding researcher in the mathematical sciences, with a strong commitment to the development of mathematical models of coupled systems and the computational methods necessary to analyze them. His appointment as Canada Research Chair in Mathematical Modelling has provided him with the support necessary to advance and analyze theoretical and applied models. His work will involve significant collaboration with other researchers in Australia, Europe, and North America.

Dr. Melnik's research into coupled effects and the dynamics of coupled systems will lead to new mathematical and computational tools for the analysis of systems and effects that should prove useful in several other areas of application, yielding significant benefits to Canadian society by advancing environmental and energy-saving technologies, biomedicine and biotechnology, nanotechnology, and optoelectronics.

The major emphasis of Dr. Melnik's research is on the development of constructive mathematical procedures for solving simultaneously the partial differential equations related to coupled processes. These processes are intrinsically dependent on both position and time, and certain elements are sometimes subject to random fluctuations. The related systems of equations are not amenable to analytical treatment, and an essential part of his research includes the development of efficient computational procedures.