Full Professor

Education

PhD, Mathematics, Polytechnic University
MS, Mathematics, Polytechnic University
BS, Aerospace Engineering, Polytechnic University

Areas of Research

Dynamical systems (nonlinear dynamics) theory is a rich amalgam of techniques from algebra, analysis, chaos theory, differential equations, differential geometry, differential topology, fractals, geometry, singularity theory, and topology, and has important applications in every branch of science and engineering. Denis Blackmore's research is primarily in the theory and applications of dynamical systems and closely related fields. He has studied a plethora of applications in such areas as acoustics, automated assembly, biological populations, computer aided geometric design, fluid mechanics, granular flows, plant growth (phyllotaxis), relativistic and quantum physics, and rough surface analysis. His theoretical work includes fundamental results on solution properties and integrability of differential equations, and analysis of hypersurface singularities. Among his current projects are acoustically generated particle flows, biocomplexity of marshes, competing species dynamics, dynamical models in economics, integrability of infinite-dimensional dynamical systems (PDEs), particle dynamics, phyllotaxis, virtual reality systems, vortex dynamics, and weak shock waves. 

Selected Publications  

"Morse index for autonomous linear Hamiltonian systems," (with C. Wang), Int. J. Diff. Eqs. and Appl. 7 (2003), 295-309.

"The Lax solution to a Hamilton-Jacobi equation and its generalizations: Part 2," (with Ya V. Mykytiuk and A. Prykarpatsky), Nonlin. Anal. 55 (2003), 629-640.

"Vorticity jumps across shock surfaces," (with L. Ting), Proc. 2nd MIT Conf. on Computational Fluids and Solid Mechanics, Vol. 1, K. J. Bathe, ed., Elsevier, Amsterdam, 2003, pp. 847-849.

"Fractionation and segregation of suspended particles using acoustic and flow fields," (with N. Aboobaker and J. Meegoda), ASCE J. Environ. Eng. 129 (2003), 427-434.

" Higher order conditions for weak shocks: modified Prandtl relation," (with L. Ting), PAMM 1 (2002), 397-398.

"A perspective on vibration-induced size segregation of granular materials," J. Chem. Eng. Sci. 57 (2002), 265-275.

"On the exponentially self-regulating population model," (with J. Chen), Chaos, Solitons and Fractals 14 (2002), 1433-1450.

"Hamiltonian structure for vortex filament flows," (with O. Knio),  ZAMM  81S  (2001), 45-48.

''Dynamical properties of discrete Lotka-Volterra equations,'' (with J. Chen, J. Perez and M. Savescu), Chaos, Solitons and Fractals 12 (2001), 2553-2568.

''New mathematical models for particle flow dynamics,'' (with R. Samulyak and A. Rosato), J. Nonlinear Math. Physics 6, (1999), 198-221. 4. ''KAM theory analysis of the dynamics of three coaxial vortex rings''(with O. Knio), Physica D 140, (2000), 321-348.