Mikhail
Khenner Associate Professor Department of Mathematics Western Kentucky University Bowling Green, KY 42101 Member, WKU Applied Physics Institute 

Office:  4104 COHH 
Phone:  2707452797 
Email:  mikhail.khenner AT wku dot edu 
Home Page:  http://people.wku.edu/mikhail.khenner/ 
ResearchGate:  https://www.researchgate.net/profile/Mikhail_Khenner/ 
Published research (19982015)
I
am the applied mathematician, working in the fields of PDEbased
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.
The
common thread through my work is modeling and analysis of a thin
film phenomena, such as the free surface/interface instability,
wetting/dewetting,
micro/nanostructure selfassembly and film
patterning. Models of these phenomena usually result in a highly
nonlinear, highorder parabolic PDE(s) for the
shape of the
film free surface or interface, which are derived from a governing
freeboundary 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
differencesbased fronttracking methods.
Research news:
Model for computing kinetics of the graphene edge epitaxial growth on copper , Physical Review E 93, 062806 (2016); ArXiv
Interplay of quantum size effect, anisotropy and surface stress shapes the instability of thin metal films; to appear in the Journal of Engineering Mathematics (accepted) 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 94 (2016), 623638;
Step growth and meandering in a precursormediated epitaxy with anisotropic attachment kinetics and terrace diffusion, Mathematical Modelling of Natural Phenomena 10(4), 97110 (2015); ArXiv
Electromigrationdriven evolution of the surface morphology and composition for a bicomponent solid film, with Mahdi Bandegi, Mathematical Modelling of Natural Phenomena 10(4), 8396 (2015); ArXiv
Preface (1st to read if you are thinking about adopting or using this textbook)
"Ordinary and Partial Differential Equations provides
collegelevel readers with a comprehensive textbook covering both
ordinary
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 indepth
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 secondorder PDEs."
 Joe Latulippe, MAA Reviews, June 2013.
Selected recent presentations:
Mathematical model of electromigrationdriven evolution of the surface morphology and composition for a bicomponent solid film
Experiments, Modeling and Computations of Pulsed Laser Induced Dewetting in Thin Metallic Films
Teaching Fall 2016:
(C) Mikhail
Khenner
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