Department of Mathematics
Western Kentucky University
Bowling Green, KY 42101
Member, WKU Applied Physics Institute
|Email:||mikhail.khenner AT wku dot edu|
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 or a system
of such PDEs 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).
Height transitions, shape evolution, and coarsening of equilibrating quantum nanoislands, submitted (January 2017). Abstract: Morphology evolution and coarsening of metal nanoislands during the constant-temperature annealing phase of a two-stage heteroepitaxial growth is computed within the framework of a surface diffusion-type model that includes the effects of the electron energy confinement within the film, the charge spillage at the film/substrate interface, the energy anisotropy of the film surface and the surface stress. The conditions that result in large islands with flat tops, steep edges, and strongly preferred heights are determined. A strong influence of the film height on the coarsening dynamics and final morphologies is found; the conditions leading to interrupted coarsening are highlighted. The dependence of the geometric parameters of the equilibrium island on the film height and on the island initial volume is computed.
Model for computing kinetics of the graphene edge epitaxial growth on copper , Physical Review E 93, 062806 (2016); ArXiv
of quantum size effect, anisotropy and surface stress shapes
the instability of thin metal films, in press;
Journal of Engineering Mathematics ..., ... (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;
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
More published research (1998-2016)
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)
"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:
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 2017: