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Welcome to the Melnik Group Website
By developing tools and methods of mathematical modeling and by applying them along with two other research methodologies based on theory and experiment, we seek a better understanding of new phenomena and processes in studying engineering, physical, and biological systems. Our focus is on coupled multiscale phenomena and processes.
Coupled Multiscale Phenomena and Processes
Some of the most important and challenging problems in science and engineering are coupled problems. The coupling is pronounced at three basic levels: (i) the level of field coupling as it is the case in thermo-elasticity, electro-elasticity and in many other areas of applications, (ii) the level of coupled effects between different parts of the system, and/or (iii) the level of coupling between different spatial/spatio-temporal scales at which the natural or man-made system, that is being studied, operates. This coupling brings to life new phenomena, the phenomena which are not amenable to an adequate description with conventional mathematical models, traditionally developed without accounting for the coupled nature of the problem. An early observation that the coupling in nature plays a profound role was made by Aristotle who noted that "the whole is more than the sum of its parts." The development of coupled mathematical models has an interesting history with one of the first examples attributed to Pierre Simon Laplace who corrected Newton's purely mechanical theory of sound propagation by accounting for thermal field effects. Another important example includes the development of a dynamic model of coupled electro-magnetic interactions by James Clerk Maxwell. At the M²NeT Lab, we focus on the development of coupled mathematical models for addressing fundamental questions of science and solving new problems in science and engineering. We study coupled phenomena, effects, and processes that are becoming increasingly important in the areas of nano- and bio-nano technologies, in new technologies based on smart materials and structures, biocompatible materials and bio-inspired systems, and in other areas.
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