I work in the area of interdisciplinary applied mathematics, also often referred to
as physical applied mathematics and modeling. More specifically, my area of work is the
partial differential equations (PDE)-based modeling in materials science, crystal growth,
and fluid dynamics. This work requires insights into the real-world physical phenomena.
Correspondingly, research is disseminated through the materials science, physics and
engineering journals. Applied mathematics is used (i) to formulate sets of governing PDEs
and boundary conditions, and (ii) in the analytical solutions of simplified models. 

For the problems that do not allow analytical treatment, I had developed sophisticated
marker-particle methods for tracking surfaces in 2D and 3D. 

Research keywords: Applied mathematical modeling in materials science, crystal growth,
and fluid dynamics; Numerical methods for problems with surfaces and interfaces; Pattern
formation on surfaces and stability; Thin solid and liquid films.

All publications (1998 - present)

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Full text (PDF) of most papers I published to-date, (all journals) (2011)
 

Presentations

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Modeling diverse physics of nanoparticle self-assembly in pulsed laser-irradiated metallic films, WKU Physics Colloquium (2011)
 

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Morphological evolution of single-crystal ultrathin solid films, WKU Physics Colloquium (2010)
 

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Thermocapillary effects in driven dewetting and self-assembly of pulsed laser-irradiated metallic films, 2009 Fall Meeting of the Materials Research Society (2009)
 

Selected recent publications

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Controlling nanoparticles formation in molten metallic bilayers by pulsed-laser interference heating (with Sagar Yadavali and Ramki Kalyanaraman), Mathematical Modeling of Natural Phenomena (2012)
 

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Formation of organized nanostructures from unstable bilayers of thin metallic liquids (with Sagar Yadavali and Ramki Kalyanaraman), Physics of Fluids (2011)
 

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Stability of a strongly anisotropic thin epitaxial film in a wetting interaction with elastic substrate (with Wondimu T. Tekalign and Margo S. Levine), Eur. Phys. Lett. (2011)
 

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A tangent-plane, marker-particle method for the computation of three-dimensional solid surfaces evolving by surface diffusion on a substrate (with Ping Du and Harris Wong), Journal of Computational Physics (2010)
 

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Oscillatory and monotonic modes of long-wave Marangoni convection in a thin film (with Sergey Shklyaev and Alexei Alabuzhev), Physical Review E (2010)
 

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