Mikhail Khenner

Department of Mathematics
Western Kentucky University                              
Bowling Green, KY 42101

Member, WKU Applied Physics Institute

  Office: 4104 COHH
Phone: 270-745-2797
Email: mikhail.khenner AT wku dot edu
Home Page: http://people.wku.edu/mikhail.khenner/

PhD : Université de la Mediterranée, Aix-Marseille II, France   PhD Thesis in French    Figures    Journal article
          Perm State University, Russia                                                    
Advisors: Prof. Dmitrii V. Lyubimov
                Dr. Bernard Roux

CV    <----- updated April 2022

I 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
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 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.

Resent publications:

Vacancy-mediated suppression of phase separation in a model two-dimensional surface alloy by the difference of the atomic jump rates , Surface Science 722, 122100 (2022)      ArXiv

A mesoscopic model of nanoclusters self-assembly on a graphene Moiré, with Lars Hebenstiel, Journal of Applied Physics 130, 124301 (2021)      ArXiv

Directed long-range transport of a nearly pure component atom clusters by the electromigration of a binary surface alloy, Physical  Review Materials 5, 024001 (2021)      ArXiv

Modeling evolution of composition patterns in a binary surface alloy, with Victor Henner, Modelling and Simulation in Materials Science and Engineering 29, 015002 (2020)        ArXiv

Electromigration-guided composition patterns in thin alloy films: a computational study, Surface Science 698, 121611 (2020)        ArXiv

Morphology and structure of Pb thin films grown on Si(111) by pulsed laser deposition, with Bektur Abdisatarov, Saidjafarzoda Ilhom, Khomidkhodzha Kholikov, Devon Loomis, Vladimir Dobrokhotov, and Ali Oguz Er, Applied Physics A 126, 237 (2020)

Morphologies, metastability and coarsening of quantum nanoislands on the surfaces of the annealed  Ag(110) and Pb(111) thin films, with Donald Price and Victor Henner, Journal of Applied Physics 124, 174302 (2018)       ArXiv

Kinetics of nanorings formation on surfaces of stressed thin films, with Lin Du and Dimitrios Maroudas, Physical  Review Materials 2, 083403 (2018)  (Lin and Dimitrios take most credit for this insightful work)

Modeling solid-state dewetting of a single-crystal binary alloy thin films, Journal of Applied Physics 123, 034302 (2018)       ArXiv

Height transitions, shape evolution, and coarsening of equilibrating quantum nanoislands, Modelling and Simulation in Materials Science and Engineering 25, 085003 (2017)       ArXiv

Interplay of quantum size effect, anisotropy and surface stress shapes the instability of thin metal films, Journal of Engineering Mathematics 104(1), 77-92 (2017)       ArXiv

Model for computing kinetics of the graphene edge epitaxial growth on copper , Physical Review E 93, 062806 (2016)     ArXiv

More published research (1998-2020)    


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 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 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:

Morphologies and Coarsening of Quantum nanoislands on Annealed Metal Surfaces

Formation of Core-Shell Particles by Solid-State Dewetting of a Binary Alloy Thin Film

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 

Modeling formation of pits in the Si thin film on the quartz or sapphire substrate 

Research interests:

Mathematical modeling in materials science, crystal growth, and fluid dynamics

Numerical methods for evolving surfaces and interfaces

Pattern formation on surfaces and stability of surfaces and interfaces

Dynamics of thin solid and liquid films

Engineering mathematics

 Teaching Spring 2022:

MATH 136, Calculus I 
MATH 137, Calculus II (two sections)

(C) Mikhail Khenner
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