Department of Mathematics
Western Kentucky University
Bowling Green, KY 42101
Member, WKU Applied Physics Institute
|Email:||mikhail.khenner AT wku dot edu|
Published research (1998-2012) <----- updated 08/01/2012
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)
Pulsed laser dewetting of Au films: Experiments and modeling of nanoscale behavior,
with Sagar Yadavali and Ramki Kalyanaraman (UTK), ACCEPTED for publication in the Focus Issue "Frontiers in Thin-Film Epitaxy and Nanostructured Materials"
of the Journal of Materials Research (JMR), publication date July 2013;
Analysis of a combined influence of substrate wetting and surface electromigration on a thin film stability and dynamical morphologies,
ACCEPTED for publication in the special issue "Nanoscale wetting of solids on solids" of the journal Comptes Rendus Physique (O. Pierre-Louis, Ed.; invited paper);
Long-wave Marangoni convection in a thin film heated from below,
with Sergey Shklyaev (Caltech, U Puerto Rico) and Alexei Alabuzhev (Perm State U, Rus Acad Sci), Physical Review E 85, 016328 (2012);
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) (invited paper).
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
Stability analysis of pulsed laser-melted bilayer thin films : one-hour presentation for graduate students in Mathematics (2011)
Lubrication approximation-based model and computations of pulsed laser-induced dewetting in thin metallic films : presentation at 2011 Meeting of the Society of Engineering Sciences
Morphological evolution of single-crystal ultrathin solid films: one-hour presentation for undergraduate Physics majors (2010)
Analytical and Computational Modeling of the Stability and Dynamics of a Dewetting Ultrathin Solid Film : one-hour presentation for graduate students in Mathematics (2010)
Teaching Spring 2013: