Department of Mathematics
Western Kentucky University
Bowling Green, KY 42101
Member, WKU Applied Physics Institute
|Email:||mikhail.khenner AT wku dot edu|
Published research (1998-2018)
am the applied mathematician, working in the fields of PDE-based
modeling and computation in materials science, crystal growth,
and fluid dynamics.
This is also often referred to as physical applied mathematics and modeling. Correspondingly, the dissemination of the results is primarily through the
physics, materials science and engineering journals. I have collaborators among researchers who work in these areas.
common thread through my work is modeling and analysis of a thin
film phenomena, such as the free surface/interface instability,
micro/nanostructure self-assembly and film patterning. Models of these phenomena usually result in a highly nonlinear, high-order parabolic PDE(s) for the
shape of the film free surface or interface, which are derived from a governing free-boundary problem. I employ methods of the stability theory, perturbation
theory, nonlinear dynamics, and the numerical simulations. Analyses range from the more theoretical to more applied (where direct quantitative matching of
the model to the experiment is sought). As needed for modeling, I develop the 2D and 3D finite differences-based front-tracking methods.
Kinetics of nanorings formation on surfaces of stressed thin films, with Lin Du and Dimitrios Maroudas, Physical Review Materials 2, 083403 (2018) (Lin and Dimitrios take most credit for this insightful work)
Modeling solid-state dewetting of a single-crystal binary alloy thin films, Journal of Applied Physics 123, 034302 (2018) ArXiv
Height transitions, shape evolution, and coarsening of equilibrating quantum nanoislands, Modelling and Simulation in Materials Science and Engineering 25, 085003 (2017) ArXiv
Interplay of quantum size effect, anisotropy and surface stress shapes the instability of thin metal films, Journal of Engineering Mathematics 104(1), 77-92 (2017) ArXiv
Model for computing kinetics of the graphene edge epitaxial growth on copper , Physical Review E 93, 062806 (2016); ArXiv
Mathematical modeling of a surface morphological instability of a thin monocrystal film in a strong electric field, with Aaron Wingo, Selahittin Cinar, and Kurt Woods, Involve, a Journal of Mathematics 9-4 (2016), 623-638;
Textbook: Ordinary and Partial Differential Equations, by Victor Henner, Tatyana Belozerova, and Mikhail Khenner
Preface (1st to read if you are thinking about adopting or using this textbook)
"Ordinary and Partial Differential Equations provides
college-level readers with a comprehensive textbook covering both
differential equations and partial differential equations, offering a complete course on both under one cover, which makes this a unique
contribution to the field. Examples and exercises accompany software supporting these and a text that covers all the basics any undergraduate
or beginning graduate course will cover in differential equations. This doesn't require programmer knowledge nor any special computer software
outside the disc provided here, and provides in-depth detail for students in the physical, engineering, biological, and math sciences using examples
throughout. Very highly recommended for any college collection supporting these disciplines."
—Midwest Book Review
"Henner, Belozerova, and Khenner cover most of the fundamental topics found in introductory ODEs and PDEs courses,
nicely balancing scope without sacrificing content. … The authors have managed to provide the right amount of details
and have outlined the text in such a way that all material needed to solve the PDEs discussed in Part II can be referenced
within the text. This, in my opinion, is the main strength of the book. … this single book could be used successfully for a
series of differential equations courses that covered both ODEs and PDEs if the same students took the courses. … This
text finds a nice balance between general topics of ODEs and second-order PDEs."
- Joe Latulippe, MAA Reviews, June 2013.
Selected recent presentations:
Morphologies and Coarsening of Quantum nanoislands on Annealed Metal Surfaces
Formation of Core-Shell Particles by Solid-State Dewetting of a Binary Alloy Thin Film
Mathematical model of electromigration-driven evolution of the surface morphology and composition for a bi-component solid film
Problems in growth and instabilities of microscopic steps on monocrystalline surfaces: The effects of anisotropic step energy
Modeling formation of pits in the Si thin film on the quartz or sapphire substrate
Teaching Fall 2018: