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1. Short Bio
2. Research Interests
3. Teaching Portfolio
4. CV
Roderick Melnik is a Full Professor at the Wilfrid Laurier University in Waterloo, Canada. It is the older of the two universities in the city of Waterloo. He is a Tier I Canada Research Chair in Mathematical Modelling. He is affiliated also with the University of Waterloo and the University of Guelph, as well as with the Guelph-Waterloo Institute of Physics. Before joining Laurier, Professor Melnik held senior professorial and research positions in the USA, Europe, and Australia. He remains associated with Syddansk University in Denmark where he served as Head of Mathematical Modelling and Engineering Mathematics at the Mads Clausen Institute for a number of years. Later, he was a Full Professor in the Computational Analysis and Modelling Program at the Louisiana Tech University in the USA from where he moved to Canada in 2004. Dr Melnik has also experience in working as a scientist outside of academia. In the late 1990s, he held the position of senior mathematician at the Commonwealth Scientific and Industrial Research Organisation in Sydney, Australia, working in the Division of Mathematical and Information Sciences until he joined the Syddansk University in Denmark as full professor. Dr Melnik received his M.Sc. degree in Applied Mathematics and Ph.D. degree in Computational Mathematics from the Kiev State University in 1985 and 1989, respectively. Since 1989 Professor Melnik held academic tenures in Europe, Australia, and North America and has published extensively, as a sole author and with his collaborators from around the world, in the field of applied mathematics, computational sciences, and mathematical modelling in sciences and technology.
Professor Melnik's major results are in the development, analysis and applications of mathematical models based on partial differential equations and computational mathematics, focusing on coupled dynamic phenomena, systems, and processes. The areas of his research contributions include computational physics, applied numerical analysis, chemistry, and biology, non-smooth control, and stochastic differential equations. Over the past years, some of his main contributions have been to the development and applications of mathematical models in the area nano- and bionano- sciences with particular emphasis on the analysis of coupled multiscale phenomena, processes, and systems. This includes his contributions to the analysis of coupled effects in low-dimensional nanostructures, such as quantum dots, in bio-inspired and in biological systems. As an active researcher and academic, he is involved in numerous editorial duties and professional services in the applied mathematics and a larger scientific community. Dr Melnik is an Associate Editor of Advances in Difference Equations and is on editorial boards of several other research journals. He is an active member in major professional societies, including the American Society of Mechanical Engineers, American Mathematical Society, Canadian Applied and Industrial Mathematics Society and its analogue in Australia (ANZIAM), and the New York Academy of Sciences. Since 1998 he is an Elected Fellow of the Institute of Mathematics and its Applications in the United Kingdom. Dr Melnik was the recipient of the Hans Christian Andersen Academy Fellowship Award in Denmark with only two such awards given annually to researchers worldwide. He was also a visiting fellow at the Isaac Newton Institute of the University of Cambridge in England, at the Institute for Mathematics and its Applications of the University of Minnesota in the USA, the Center of Excellence in Applied Mathematics BCAM in Spain, and other research institutions in Europe, North America, and Australia.
Professor Roderick Melnik is an applied mathematician with major research interests in computational and engineering mathematics and its enrichments in sciences and technology, focusing on models based on partial differential equations and the analysis of complex dynamic systems. Dr Melnik's research program covers the areas from constructing mathematical models to their mathematical analysis, through to the development of algorithms, numerical analysis, and computations, providing further insight into mathematical problems and methodologies for their solution with an ultimate goal of
a better understanding of new phenomena and processes in studying physical, biological, and engineering systems.
Professor Melnik's early results were in applying pure mathematics tools to solving an applied problem in smart materials and structures technology. Dr Melnik was the first to prove well-posedness of coupled hyperbolic-elliptic systems of partial differential equations with coupling conditions at boundaries, as applied in dynamic piezoelectricity theory, in classes of generalized (Sobolev's) solutions. He was the first to analyze regularity of such solutions for an important class of models. Such models, originally proposed by W. Voigt in 1910, have found many interesting applications, and in the late 1980ies Dr Melnik succeeded in giving a rigorous mathematical proof of such models well-posedness. Since that time, Professor Melnik's research has taken him to several different avenues of applied research where he has successfully developed, analyzed, and applied tools of mathematical modelling and computational experiments to provide a better understanding of phenomena and processes described by mathematical models. He has been fortunate enough to work on a wide range of fascinating mathematical problems in sciences and engineering, including semiconductor device theory, climate systems modelling, financial engineering, analysis of complex biomolecules, polymers, and materials with memory, phase transformations, and modelling quantum structures, to name just a few.
Although diverse in the areas of applicability, ranging from domestic goods to high-tech applications and to bioengineering and nanotechnology, the unity in Dr Melnik's research is achieved through the tools which he uses to study these problems. Among these tools are mathematical and numerical analysis, mathematical modelling and computational experiments. Much (if not most) of the mathematics of science and technology involves the development and analysis of mathematical models written in the language of differential (partial differential, ordinary differential, stochastic), difference, integral, and integro-differential equations. Professor Roderick Melnik's primary research interests center around analysis & applications of such equations, and modelling complex systems in nature, technology, and society.
You'll find here links to some of the projects of Dr Melnik's continuing interest. If you are a student, postdoctoral fellow, or a potential collaborator who would like to work on one of these or related projects, you are encouraged to contact Professor Roderick Melnik directly.
Go to Melnik Research Group Research Overview
Follow this link.
Curriculum Vitae can be found here. For the list of publications follow this link.
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