Department of Mathematics
Western Kentucky University
Bowling Green, KY 42101
Member, WKU Applied Physics Institute
|Email:||mikhail.khenner AT wku dot edu|
Published research (1998-2015)
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
mathematical 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.
NEW 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)
"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.
Insights into the kinetics of a graphene edge epitaxial growth on copper from a one-dimensional PDE model; submitted ArXiv
The interplay of quantum size effect, anisotropy and surface stress defines stability of metal thin films on semiconductor substrate; submitted
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; in press
Step growth and meandering in a precursor-mediated epitaxy with anisotropic attachment kinetics and terrace diffusion, Mathematical Modelling of Natural Phenomena 10(4), 97-110 (2015); ArXivElectromigration-driven evolution of the surface morphology and composition for a bi-component solid film, with Mahdi Bandegi, Mathematical Modelling of Natural Phenomena 10(4), 83-96 (2015); ArXiv
Selected recent presentations:
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
Experiments, Modeling and Computations of Pulsed Laser Induced Dewetting in Thin Metallic Films
Modeling and computational studies of surface shape dynamics of ultrathin single-crystal films with anisotropic surface energy
Modeling impacts of surface electromigration on stability and dynamical morphologies of a wetting, homoepitaxial solid film
Teaching Spring 2016: