Department of Mathematics
Western Kentucky University
Bowling Green, KY 42101
Member, WKU Applied Physics Institute
|Email:||mikhail.khenner AT wku dot edu|
Published research (1998-2013) <----- updated 11/10/2013
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.
Long-wave model for strongly anisotropic growth of a crystal step, Physical Review E 88, 022402 (2013);
Pulsed laser dewetting of Au films: Experiments and modeling of nanoscale behavior,
with Sagar Yadavali and Ramki Kalyanaraman (UTK), Journal of Materials Research (JMR), 28(13), 1715-1723 (2013)
(the focus issue "Frontiers in Thin-Film Epitaxy and Nanostructured Materials");
Analysis of a combined influence of substrate wetting and surface electromigration on a thin film stability and dynamical morphologies,
Comptes Rendus Physique 14, 607-618 (2013) (the special issue "Trends and perspectives in solid-state wetting" , Ed. O. Pierre-Louis);
Controlling nanoparticles formation in molten metallic bilayers by pulsed-laser interference heating,
with Sagar Yadavali and Ramki Kalyanaraman (UTK), Mathematical Modeling of Natural Phenomena 7(4), 20-38 (2012)
(the special issue ``Modeling Phenomena on Micro- and Nanoscale”, Ed. Alexander A. Nepomnyashchy).
Selected recent presentations:
Experiments, Modeling and Computations of Pulsed Laser Induced Dewetting in Thin Metallic Films : poster from 2011 Fall Meeting of the Materials Research Society
Modeling and computational studies of surface shape dynamics of ultrathin single-crystal films with anisotropic surface energy: presentation at Perm State University, Russia (2013)
Modeling impacts of surface electromigration on stability and dynamical morphologies of a wetting, homoepitaxial solid film: presentation at Perm State University, Russia (2013)
Teaching Fall 2013: