Rouben Rostamian | Research

Research interests

I am an applied mathematician in a generic sense. I will attempt to tackle any interesting problem that comes along if it has some sort of connection to the “real world” and poses an interesting question. My technical tool bag includes functional analysis and the theories of ordinary and partial differential equations, numerical analysis and computing, and I am beginning to learn probability theory. I am particularly interested in problems that relate to classical physics, rigid body dynamics, and continuum mechanics of solids and fluids. For numerical computations I prefer writing my own programs from scratch in my favorite programming language, C, rather than appealing to higher-level software such as Matlab and Comsol. My book, Programming Projects in C, reflects my philosophy in that regard.

Doctoral students

I have been fortunate to have had the opportunity to be the doctoral dissertation mentor of some of the brightest graduate students at UMBC. In the chronological order of their graduation years they are:

Fethi Saidi, PhD 1988: Dissertation title: The large time behavior of solutions of a diffusion equation involving a nonlocal convective term
Current position: Professor of Mathematics, Kuwait University
Ping Wang, PhD 1990: Dissertation title: Homogenization of an inhomogeneous degenerate elastic material
Current position: Professor of Mathematics, Eberly College of Science, Pennsylvania State University, Schuylkill
Wen-Jong Shyong, PhD 1991: Dissertation title: Homogenization and symmetry in perforated elastic media
Current position: Scientist, Applied Physics Laboratory, The Johns Hopkins University
William Oberle, PhD 1997: Dissertation title: An analysis of traveling wave solutions for a laminar-flame combustion model in a stratified-reacting material
Current position: Program Manager, US Army, Aberdeen Proving Ground, Aberdeen, Maryland
Ana Maria Soane, PhD 2008: Dissertation title: Variational problems in weighted Sobolev spaces with applications to computational fluid dynamics
Current position: Associate Professor of Mathematics, US Naval Academy, Annapolis, Maryland
Alen Alexanerian, PhD 2010 [Dr. Muruan Rathinam: co-mentor]: Dissertation title: Random composite media: Homogenization, modeling, simulation, and material symmetry
Current position: Associate Professor of Mathematics, North Carolina State University, Raleigh, NC

Publications

Articles in journals and proceedings

Stephen A. Thau, Andrej Umek, and Rouben Rostamian, Seismic motion of buildings with buried foundations, Journal of the Engineering Mechanics Division 100 (1974), 919–933.
Rouben Rostamian, Internal constraints in boundary value problems of continuum mechanics, Indiana University Mathematics Journal 27 (1978), no. 4, 637–656.
Rouben Rostamian, The completeness of Maxwell's stress function representation, Journal of Elasticity 9 (1979), no. 4, 349–356.
Rouben Rostamian, Internal constraints in linear elasticity, Journal of Elasticity 11 (1981), no. 1, 11–31.
Rouben Rostamian, Continuity properties of stationary points of quadratic functionals in Hilbert space, Numerical Functional Analysis and Optimization 3 (1981), no. 2, 147–167.
Nicholas D. Alikakos and Rouben Rostamian, Large time behavior of solutions of Neumann boundary value problem for the porous medium equation, Indiana University Mathematics Journal 30 (1981), no. 5, 749–785.
Nicholas D. Alikakos and Rouben Rostamian, Stabilization of solutions of the equation ∂u/∂t = Δφ(u) − β(u), Nonlinear Analysis 6 (1982), no. 6, 637–647.
Nicholas D. Alikakos and Rouben Rostamian, Lower bound estimates and separable solutions for homogeneous equations of evolution in Banach space, Journal of Differential Equations 43 (1982), no. 3, 323–344.
Nicholas D. Alikakos and Rouben Rostamian, Gradient estimates for degenerate diffusion equations. I, Mathematische Annalen 259 (1982), no. 1, 53–70.
Nicholas D. Alikakos and Rouben Rostamian, Gradient estimates for degenerate diffusion equations. II, Proceedings of the Royal Society of Edinburgh. Section A 91 (1981/82), no. 3–4, 335–346.
Nicholas D. Alikakos and Rouben Rostamian, On the uniformization of the solutions of the porous medium equation in R^N, Israel Journal of Mathematics 47 (1984), no. 4, 270–290.
Nicholas D. Alikakos and Rouben Rostamian, Classification of initial data for the porous medium equation in R^N, Differential equations: Proceedings of the international conference held at the University of Alabama in Birmingham, Birmingham, Ala., March 21–26, 1983 (Ian W. Knowles and Roger T. Lewis, eds.), North-Holland Mathematics Studies, vol. 92, North-Holland, Amsterdam, 1984, pp. 19–24.
Nicholas D. Alikakos and Rouben Rostamian, Large time estimates for solutions to the porous medium equation with nonintegrable data via comparison, Proceedings of the Royal Society of Edinburgh. Section A 100 (1985), no. 1–2, 1–10.
Michiel Bertsch and Rouben Rostamian, The principle of linearized stability for a class of degenerate diffusion equations, Journal of Differential Equations 57 (1985), no. 3, 373–405.
Nilotpal Ghosh and Rouben Rostamian, An oscillating solution for the porous medium equation, Nonlinear Analysis 10 (1986), no. 4, 383–390.
William W. Hager and Rouben Rostamian, Optimal coatings, bang-bang controls, and gradient techniques, Optimal Control Applications & Methods 8 (1987), no. 1, 1–20.
Takao Nambu, Rouben Rostamian, and Thomas I. Seidman, Feedback stabilization of a marginally stable heat conduction problem, Applicable Analysis 24 (1987), no. 3, 215–238.
William W. Hager and Rouben Rostamian, Coating reflectivity, Control problems for systems described by partial differential equations and applications: Proceedings of the IFIP-WG 7.2 conference held at the University of Florida, Gainesville, Fla., February 3–6, 1986 (Irena Lasiecka and Roberto Triggiani, eds.), Lecture Notes in Control and Information Sciences, vol. 97, Springer, Berlin, 1987, pp. 247–258.
Rouben Rostamian, Thomas I. Seidman, and Takao Nambu, Feedback control for an abstract parabolic equation, Differential equations and mathematical physics: Proceedings of the international conference held at the University of Alabama in Birmingham, Birmingham, Ala., March 3–8, 1986 (Ian W. Knowles and Yoshimi Saito, eds.), Lecture Notes in Mathematics, vol. 1285, Springer, Berlin, 1987, pp. 408–416.
William W. Hager and Rouben Rostamian, Reflection and refraction of elastic waves for stratified materials, Wave Motion 10 (1988), no. 4, 333–348.
Alain Damlamian, William W. Hager, and Rouben Rostamian, Homogenization for degenerate equations of elasticity, Asymptotic Analysis 1 (1988), no. 4, 283–302.
William W. Hager and Rouben Rostamian, Invariant imbedding and the reflection of elastic waves, Control of partial differential equations: Proceedings of the IFIP WG 7.2 Working Conference on Optimal Control of Systems Governed by Partial Differential Equations held at the University of Santiago de Compostela, Santiago de Compostela, July 6–9, 1987 (A. Bermúdez de Castro, ed.), Lecture Notes in Control and Information Sciences, vol. 114, Springer, Berlin, 1989, pp. 144–155.
William W. Hager and Rouben Rostamian, Plane waves, optimization, and homogenization in elasticity, Smart Materials, Structures, and Mathematical Issues: Proceedings of the U.S. Army Research Office workshop on Smart Materials, Structures, and Mathematical Issues held in Blacksburg, Va., 1989 (Robert C. Rogers, ed.), Technomics Publishing Co., 1989, pp. 183–197.
William W. Hager and Rouben Rostamian, Total absorption in elastic media, Transactions of the Seventh Army Conference on Applied Mathematics and Computing: United States Military Academy, West Point, New York, June 6–9, 1989, ARO Reports, vol. 90–1, U.S. Army Research Office, Research Triangle Park, NC, 1990, pp. 85–103.
William W. Hager and Rouben Rostamian, Optimal nonreflective elastic coatings, Transactions of the Eighth Army Conference on Applied Mathematics and Computing: Ithaca, New York, June 19–22, 1990, ARO Reports, U.S. Army Research Office, Research Triangle Park, NC, 1991.
William W. Hager, Rouben Rostamian, and Dongxing Wang, The wave annihilation technique and the design of nonreflective coatings, SIAM Journal on Applied Mathematics 60 (2000), no. 4, 1388–1424,
William F. Oberle and Rouben Rostamian, Traveling waves in layered combustible media, Mathematical and numerical aspects of wave propagation: Proceedings of the 5th International Conference (WAVES2000) held in Santiago de Compostela, July 10–14, 2000 (Alfredo Bermúdez, Dolores Gómez, Christophe Hazard, Patrick Joly, and Jean E. Roberts, eds.), SIAM, Philadelphia, PA, 2000, pp. 354–358.
Rouben Rostamian, Prosper: A LaTeX documentclass for presentations, Statistical Computing & Graphics 15 (2004), no. 1, 2–9.
Ana Maria Soane and Rouben Rostamian, Free Boundary Problems in Fluid Mechanics, Women in Mathematics: The Legacy of Ladyzhenskaya and Oleinik: Proceedings of MSRI conference, May 2006 (Susan Friedlander, Barbara Keyfitz, Irene Gamba, and Krystyna Kuperberg, eds.), Mathematical Sciences Research Institute (MSRI), Berkeley.
Alan Marc Lefcourt, Priya Narayanan, Uri Tasch, Rouben Rostamian, Moon S. Kim, and Yud Ren Chen, Development of video technology to analyze dynamics of inertia-based apple orientation, Optics for Natural Resources, Agriculture, and Foods: Proceedings of Optics East, Boston, October 1–4, 2006 (Y. R. Chen, G. E. Meyer, and S. I. Tu, eds.), vol. 6381, SPIE, 2006.
Priya Narayanan, Alan Marc Lefcourt, Uri Tasch, Rouben Rostamian, Abraham Grinblat, and Moon S. Kim, Theoretical aspects of orienting fruit using stability properties during rotation, Proceedings of 2006 ASAE Annual Meeting, July 9–12, 2006, Portland, Oregon, 2006. Paper number 061144.
Priya Narayanan, Alan Marc Lefcourt, Uri Tasch, Rouben Rostamian, and Moon S. Kim, Tests of the ability to orient apples using their inertial properties, Proceedings of 2007 ASAE Annual Meeting, June 17–20, 2007, Minneapolis, Minnesota, 2007. Paper number 076246.
Priya Narayanan, Alan Marc Lefcourt, Uri Tasch, Rouben Rostamian, and Moon S. Kim, Orientation of apples using their inertial properties, Transactions of the ASABE 51 (2008), no. 6, 2073–2081.
Priya Narayanan, Alan Marc Lefcourt, Uri Tasch, Rouben Rostamian, Abraham Grinblat, and Moon S. Kim, Theoretical analysis of stability of axially-symmetric rotating objects with regard to orienting apples, Transactions of the ASABE 51 (2008), no. 4, 1353–1364.
Alan Marc Lefcourt, Priya Narayanan, Uri Tasch, Rouben Rostamian, Moon S. Kim, and Yud Ren Chen, Algorithms for parametrization of dynamics of inertia-based apple orientation, Applied Engineering in Agriculture 24 (2008), no. 1, 123–129.
Alan Marc Lefcourt, Priya Narayanan, Uri Tasch, Moon S. Kim, Dan Reese, Rouben Rostamian, and Y. Martin Lo, Orientating apples for imaging using their inertial properties and random apple loading, Biosystems Engineering 104 (2009), no. 1, 64–71.
Ana Maria Soane and Rouben Rostamian, Variational problems in weighted Sobolev spaces on non-smooth domains, Quarterly of Applied Mathematics 68 (2010), no. 3, 439–458.
Ana Maria Soane, Manil Suri, and Rouben Rostamian, The optimal convergence rate of a C¹ finite element method for non-smooth domains, Journal of Computational and Applied Mathematics 233 (2010), no. 10, 2711–2723.
Alen Alexanderian, Muruhan Rathinam, and Rouben Rostamian, Irreducibility of a symmetry group implies isotropy, Journal of Elasticity 102 (2011), no. 2, 151–174.
Payam Motabar, Alan Marc Lefcourt, Uri Tasch, Moon S. Kim, and Rouben Rostamian, Use of inertial properties to orient tomatoes, Transactions of the ASABE 54 (2011), no. 2, 517–525.
Alen Alexanderian, Muruhan Rathinam, and Rouben Rostamian, Homogenization, symmetry and periodization in diffusive random media, Acta Mathematica Scientia 32 (2012), no. 1, 129–154.
Rouben Rstamian, Ana Maria Soane, and José M. Tavares, Bouncing on a slope, American Journal of Physics 88 (February 2021), 143–146.
Rouben Rstamian, Wallyson Thomas, Attila Szilagyi, Dynamic Analysis of an Internal Turning Tool with Elastic Foundation (Winkler Model), Proceedings of the 10th ECCOMAS Thematic Conference on Multibody Dynamics, (József Kövecses, Gábor Stépán, and Ambrus Zelei, eds.), Budapest, Hungary, December 2021, pp. 126–135.

Book

Rouben Rostamian, Programming Projects in C, SIAM, 2014.

Book that I have reviewed

William Alan Day, Heat conduction within linear thermoelasticity, Springer Tracts in Natural Philosophy, vol. 30, Springer-Verlag, New York, 1985, viii+83. In SIAM Review 29 (June 1987), no. 2, 335–336. [read review]
Sergey A. Lurie and Valery V. Vasiliev, The biharmonic problem in the theory of elasticity, Gordon and Breach, Luxembourg, 1995, viii+265. In Mathematical Reviews 2000d:74007. [read review]
Haojiang Ding, Weiqiu Chen, and L. Zhang, Elasticity of transversely isotropic materials, Solid Mechanics and its Applications, vol. 126, Springer, Dordrecht, 2006, xii+435. In Mathematical Reviews 2007e:74001. [read review]
Richard B. Hetnarski and Józef Ignaczak, The mathematical theory of elasticity, 2nd ed., CRC Press, Boca Raton, FL, 2011, xxvi+800. In Mathematical Reviews 2012f:74001. [read review]
Petre P. Teodorescu, Treatise on classical elasticity Springer, Dordrecht, 2013. xii+802. In Mathematical Reviews [read review]

Unpublished material

Rouben Rostamian, The differential geometry of tube plots and computer graphics, 2000.
Ana Maria Soane and Rouben Rostamian, Incompressible fluid flow and C¹ finite elements, 2007 (book, 159 pages).
Priya Narayanan, Rouben Rostamian, Uri Tasch, Alan Marc Lefcourt, and Moon S. Kim, Rolling dynamics of an inhomogeneous ball on an inclined track, 2008. [This movie shows what this paper is about]