## Books

Blackmore, D., Prykarpatsky, A., Samoylenko, V., *Nonlinear Dynamical Systems of Mathematical Physics*: *Spectral and Symplectic Integrability Analysis*, World Scientific, Singapore, 2011

Blackmore, D. Bose, A., Petropoulos, P., eds., *Proceedings of FACM’08 Dedicated to D. S. Ahluwalia on his Seventy-Fifth Birthday*, World Scientific, Singapore, 2008. (Dec.)

Blackmore, D., Krause, E., Tung, C., eds., *Vortex Dominated Flows – A Volume Celebrating Lu Ting’s Eightieth Birthday*, World Scientific, Singapore, 2005.

Rosato, A. and Blackmore, D., eds., *IUTAM Symposium*: *Segregation in Granular Flows*, Kluwer, Dordrecht, 2000.

Kappraff, J. and Blackmore, D., *Mathematics for Design*, NJIT Publ., Newark, 1979.

## Book Chapters

Ratnaswamy, V., Rosato, A., Blackmore, D.,Tricoche, X., Ching, N. and Zuo, L., Evolution of solids fraction surfaces in tapping: Simulation and dynamical systems analysis, *Granular Matter* **14** (2012), 169-174. (May)

Blackmore, D. and Wang, C., Recent advances in periodicity in dynamical systems, *Advances in Mathematical Research*, Vol. 15, Nova Science Publ., NY, 2011, pp 1- 47. (June)

Wang, C., Blackmore, D. and Wang, X., Upper and lower solutions method for a superlinear Duffing equation,* Commun. Appl. Nonlin. Anal*. **16** (2009), 19-29. (July)

Blackmore, D. and Peters, T.J., Computational topology, *Open Problems in Topology II*, E. Pearl (ed.), Elsevier, Amsterdam, 2007, pp. 493-545. (March)

Blackmore, D., Mileyko, Y., Leu, M.C., Regli, W. and Sun, W., Computational topology and swept volumes, *Geometric and Algorithmic Aspects of Computer-Aided Design and Manufacturing*, R. Janardan, M. Smid and D. Dutta (eds.), DIMACS Series in Discrete Mathematics and Theoretical Computer Science, Vol. 67, American Mathematical Society, Providence, 2005, pp. 53-78. (Sept.)

Blackmore, D. and Champanerkar, J., Periodic and quasiperiodic motion of point vortices, *Vortex Dominated Flows*, D. Blackmore, E. Krause and C. Tung (eds.), World Scientific, Singapore, 2005, pp. 21-42.

Kappraff, J., Blackmore, D. and Adamson, G., Phyllotaxis as a dynamical system: a study in number, *Symmetry in Plants*, R. Jean and D. Barabé (eds.), World Scientific, Singapore, 1998, pp. 409-458.

Blackmore, D., Collaborated with authors on chapter five, *Algebraic Integrability of Nonlinear Dynamical Systems on Manifolds*, by A. Prykarpatsky and I. Mykytiuk, Kluwer, Dordrecht, 1998.

Blackmore, D. and Dave, R., Chaos in one-dimensional granular flows with oscillating boundaries, *Powders & Grains 97*, R. Behringer and J. Jenkins (eds.), Balkema, Rotterdam, 1997, pp. 409-412.

Jiang, H., Blackmore, D. and Leu, M.C., The flow approach to CAD/CAM modeling of swept volumes, *Advances in Manufacturing Systems: Design, Modeling and Analysis*, R. Sodhi (ed.), Elsevier, Amsterdam, 1994, pp. 341-346.

Blackmore, D., Topological characterization of isolated singularities of infinite-dimensional complex hypersurfaces, *General Topology and Applications*, S. Andima, R. Kopperman, P. Misra, J. Reichman and A. Todd (eds.), Marcel Dekker, New York, 1991, pp. 1-17.

## Refereed Journal Papers

Prykarpatsky, Y., Blackmore, D., Golenia, J. and Prykarpatsky, A., A vertex operator representation of solutions to a Gurevich—Zybin hydrodynamical system, *Opuscula Math.* (to appear)

Rahman, A. and Blackmore, D., Neimark—Sacker bifurcations and evidence of chaos in a discrete dynamical system model of walkers, *Chaos, Solitons & Fractals ***91 **(2016), 339-349.

Rosato, A., Zuo, L., Wu, H, Blackmore, D., Horntrop, D., Parker, D. Windows-Yule, C., Tapped Granular Particle Dynamics: Simulations, Experiments and Modeling, *J. Comput. Particle Mech*. **3** (2016), 333-348.

Bogolubov (Jr.), N.N., Blackmore, D. and Prykarpatski, A.P., The Lagrangian and Hamiltonian aspects of the electromagnetic vacuum-field theory models, *Boson J. Modern Phys.* **2** (2016) (92 pages, ISSN: 2454-8413,online open access).

Rohn, E. and Blackmore, D., The augmented unified localizable crisis scale*, Technological Forecasting and Social Change* **100** (2015), 186-197.

Blackmore, D., Prykarpatsky, A., Özçağ, E., and Soltanov, K., Integrability analysis of a two-component Burgers type hierarchy, *Ukr. Math. J*. **67** (2015), 167- 185.

Bogolubov (Jr.), N., Prykarpatski, A. and Blackmore, D., Maxwell–Lorentz electrodynamics models revisited via the Lagrangian formalism and the Feynman proper time paradigm, *Mathematics ***3 **(2015), 190 – 257; doi:10.3390/math 3020190.

Joshi, Y. and Blackmore, D., Strange attractors for asymptotically zero maps, *Chaos, Solitons & Fractals* **68** (2014), 123-138.

Blackmore, D. and Prykarpatsky, A., Dark equations and their light integrability, *J. Nonlin. Math. Phys*. **21** (2014), 407-428.

Blackmore, D., Rosato, A., Tricoche, X., Urban, K. and Zuo, L., Analysis, simulation and visualization of 1D tapping dynamics via reduced dynamical models, *Physica D* **273-274** (2014), 14-27.

Blackmore, D., Prykarpatsky, Y., Bogolubov (Jr.), N. and Prykarpatsky, A., Integrability of and differential-algebraic structures for spatially 1D hydrodynamics systems of Riemann type, *Chaos, Solitons & Fractals* **59 **(2014), 59-81

Prykarpatsky, Y., Blackmore, D., Golenia, J. and Prykarpatsky, A., Hidden symmetry analysis of Lax integrable nonlinear systems, *Applied Math. ***4** (2013), 96-116. ( online: doi: 10.423/am.2013.410A3013)

Blackmore, D., Prykarpatski, A., Bogolubov Jr., N. and Sławianowski, J., Mathematical foundations of the classical Maxwell-Lorentz electrodynamic model via canonical Lagrangian and Hamiltonian formalisms, *Univ. J. Phys. Appl. ***1 **(2) (2013), 160-178. (online: doi: 10.13189/ujpa.2013.010216)

Prykarpatsky, A. and Blackmore, D., New vortex invariants in magneto-hydrodynamics and a related helicity theorem, *Chaotic Modeling and Simulation ***2 **(2013), 239-245.

Blackmore, D. and Prykarpatsky, A., A new exactly solvable spatially one-dimensional quantum superradiance Fermi-medium model and its quantum solitonic states, *Condensed Matter Phys. ***16 **(2013), 23701: 1-9.

Prykarpatsky, Y., Blackmore, D., Golenia, J. and Prykarpatsky, A., Invariant measures for discrete dynamical systems and ergodic properties of generalized Boole type transformations, *Ukr. Math. J*. **65 **(1) (2013), 44-57.

Prykarpatsky, Y., Blackmore, D., Golenia, J. and Prykarpatsky, A., A vertex operator representation of solutions to a Gurevich–Zybin hydrodynamical system, *Opuscula Math. ***33** (1) (2013), 139-149.

Ratnaswamy, V., Rosato, A., Blackmore, D.,Tricoche, X., Ching, N. and Zuo, L., Evolution of solids fraction surfaces in tapping: Simulation and dynamical systems analysis, *Granular Matter* **14** (2012), 169-174.

Joshi, Y. and Blackmore, D., Exponentially decaying discrete dynamical systems, *Recent Patents on Space Tech.* **2 **(1) (2012), 37-48.

Blackmore, D. and Prykarpatsky, A., The AKNS hierarchy revisited: A vertex operator approach and its Lie-algebraic structure, *J. Nonlin. Math. Phys.* **19** (2012), 1250001 (15 pages).

Blackmore, D., Prykarpatsky A. and Prykarpatsky Y., Isospectral integrability analysis of dynamical systems on discrete manifolds, *Opuscula Math*. **32 **(1) (2012), 41-66.

Joshi, Y. and Blackmore, D., Exponentially decaying discrete dynamical systems, *Recent Patents on Space Tech.* **2 **(1) (2012), 37-48. (April).

Blackmore, D. and Prykarpatsky, A., The AKNS hierarchy revisited: A vertex operator approach and its Lie-algebraic structure, *J. Nonlin. Math. Phys.* (in press).

Blackmore, D., Prykarpatsky A. and Prykarpatsky Y., Isospectral integrability analysis of dynamical systems on discrete manifolds, *Opuscula Math*. **32 **(1) (2012), 41-66. (Jan)

Blackmore, D., Prykarpatsky, Y., Golenia, J. and Prykarpatsky, A., The AKNS hierarchy and the Gurevich–Zybin dynamical system integrability revisited, *Math. Bull. Shevchenko Scientific Soc.* **8 **(2011), 258-282. (Dec.)

Blackmore, D., Rosato, A., Tricoche, X., Urban, K. and Ratnaswamy, V., Tapping dynamics for a column of particles and beyond, *J. Mech. Materials & Structures* **6** (2011), 71-86 (June)

Blackmore, D., Urban, K. and Rosato, A., Integrability analysis of regular and fractional Blackmore-Samulyak-Rosato fields, *Condensed Matter Phys. ***13 **(2010), 43403: 1-7. (Dec.)

Joshi, Y. and Blackmore, D., Bifurcation and chaos in higher dimensional pioneer-climax systems, *Int’l. Electronic J. Pure and Appl.* *Math.* **1 **(3) (2010), 303-337. (August)

Zhou, J., Vas, A. and Blackmore, D., Fractal geometry surface modeling and measurement for musical cymbal surface texture design and rapid manufacturing, *Periodical of Key Engineering Materials* **437**, *Measurement Technology and Intelligent Instruments IX*, (2010), 145-149. (March)

Prykarpatsky, A. and Blackmore, D., A solution set analysis of a nonlinear operator equation using a Leray-Schauder type fixed point approach, *Topology ***48** (2009), 182-185. (Dec.)

Rohn, E. and Blackmore, D., A unified localizable emergency events scale*, Int. J. Information Sys. for Crisis Response & Management* (*IJISCRAM*) **1** (2009), 1-14. (Oct.)

Wang, X., Blackmore, D., and Wang, C., The ω-limit sets of a flow and periodic orbits, *Chaos, Solitons and Fractals ***41** (2009), 2690-2696. (Sept.)

Blackmore, D., Rahman, A. and Shah, J., Discrete dynamical modeling and analysis of the R-S flip-flop circuit, *Chaos, Solitons and Fractals ***42 **(2009), 951-963. (May)

Gafiychuk, V., Datsko, B., Meleshko, V. and Blackmore, D., Analysis of the solutions of coupled nonlinear fractional reaction-diffusion equations, *Chaos, Solitons and Fractals ***41** (2009), 1095-1104 (June).

Blackmore, D., Brøns, M. and Goullet, A., A coaxial vortex ring model for vortex breakdown, *Physica D ***237** (2008), 2817-2844. (Nov.)

Bogolubov (Jr.), N., Blackmore, D., Samoylenko, V. and Prykarpatsky, A., On kinetic Boltzmann equations and related hydrodynamic flows with dry viscosity, *Opuscula Mathematica* **27 **(2007), 187-195. (Nov.)

Pillapakkam, S., Singh, P., Blackmore, D., and Aubry, N., Transient and steady state motion of rising bubble in a viscoelastic fluid, *J. Fluid Mech*. **589** (2007), 215-252. (Nov.)

Blackmore, D., Ting, L. and Knio, O., Studies of perturbed three vortex dynamics,* J. Math. Phys*. **48** (2007), 065402 (30 pages). (June)

Blackmore, D. and Mileyko, Y., Computational differential topology, *Appl. Gen. Topology* **8**, No. 1 (2007), 35-92. (May).

Champanerkar, J. and Blackmore, D., Pitchfork bifurcations of invariant manifolds, *Topology and Its Applications ***154** (2007), 1650-1663. (April)

Blackmore, D., Prykarpatska, N., Samoilenko, V., Wachnicki, E. and M. Pytel-Kudela, The Cartan-Monge geometric approach to the characteristic method for nonlinear partial differential equations of the first and higher orders, *Nonlinear Oscillations* **10** (2007), 22 -31. (Jan.)

Abdel-Malek, K., Yang, J., Blackmore, D. and Joy, K., Swept volumes: foundations, perspectives and applications, *Int. J. Shape Modeling* **12** (2006), 87-127. (July)

Blackmore, D., Prykarpatsky, Y., Samoilenko, A., and Prykarpatsky, A., The ergodic measures related to nonautonomous Hamiltonian systems and their homology structure. Part 1, *CUBO* **7** (2005), 49-63. (Dec.)

Prykarpatsky, Y., Samoilenko, A., Blackmore, D. and Prykarpatsky, A., Integrability by quadratures of Hamiltonian systems and Picard-Fuchs type equations: the modern differential-geometric aspects, *Miskolc Math. Notes* **6** (2005), 65-103. (July)

Blackmore, D., New models for chaotic dynamics, *Regular & Chaotic Dynamics* (Special Poincaré 150th Anniversary Issue) **10** (2005), 307-321. (July)

Aboobaker, N., Blackmore, D. and Meegoda, J., Mathematical modeling of the movement of suspended particles subjected to acoustic and flow fields, *Applied Math. Modeling* **29** (2005), 515-532 (June)

Zhou, Y., Wang, C. and Blackmore, D., The uniqueness of limit cycles for Liénard system,* J. Math. Anal. Appl.* **304** (2005), 473-489. (May)

Blackmore, D., Wang, C. and Champanerkar, J., A generalized Poincaré-Birkhoff theorem with applications to coaxial vortex ring motion, *Discrete and Continuous Dyn. Systems B* **5 **(2005), 15-33. (Feb.)

Samoilenko, A., Prykarpatsky, Y., Taneri, U., Prykarpatsky, A. and Blackmore, D., A geometrical approach to quantum holonomic computing algorithms, *Math. & Computers in Simulation* **66** (2004), 1-20. (July)

Blackmore, D., Prykarpatsky, A., and Prykarpatsky, Y., Symplectic field theory approach to studying ergodic measures related with nonautonomous Hamiltonian systems,” *CUBO Math. J.* **6** (2004), 19-28.

Samoilenko, A., Prykarpatsky, Y., Blackmore, D. and Prykarpatsky, A., On Liouville-Arnold integrable flows related to quantum algebras and their Poissonian representations, *Proc. Ukr. Acad. Sciences ***50 **(2004), 1184-1191. (Mar.)

Prykarpatsky, A., Samoilenko, A. and Blackmore, D., The Hopf algebras and the Heisenberg-Weil Coalgebra related integrable flows, *Ukr. J. Math*. 56 (2004), 88-96. (Feb.)

Rosato, A., Blackmore, D., Buckley, L., Johnson, M. and Oshman, C., Experimental, simulation and nonlinear dynamics analysis of Galton’s board, *Int. J. Nonlinear Science and Numerical Simulation *5 (2004), 289-312. (Nov.)

Blackmore, D. and Prykarpatsky, A., On a class of factorized operator dynamical systems and their integrability, *Math. Methods and Phys. Mech. Fields *46 (2003), 120-134. (Dec)

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

Prykarpatsky, N., Blackmore, D., Prykarpatsky, A. and Pytel-Kudela, M., On the inf-type extremality solutions to the Hamilton-Jacobi equations, their regularity properties, and some generalizations, *Miskolc Math. Notes* 4 (2003), 157-180. (Nov.)

Aboobaker, N., Meegoda, J. and Blackmore, D., Fractionation and segregation of suspended particles using acoustic and flow fields, *ASCE J. Environmental Eng.* 129 (2003), 427-434 (May)

Chen, J. and Blackmore, D., On the exponentially self-regulating population model, *Chaos, Solitons and Fractals* 14 (2002), 1433-1450. (Dec.)

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

Zhou, G. and Blackmore, D., Analysis and modeling of engineering surfaces and their interactions using fractal geometry, *Int.* *J. Smart Eng. Sys. Design Des*. 3 (2001), 159-173.

Rosato, A., Blackmore, D., Zhang, N. and Lan, Y., A perspective on vibration-induced size segregation of granular materials, *J.* *Chem. Eng. Science.* 57 (2002), 265-275. (Jan)

Prykarpatsky, A., Mykytiuk, I. and Blackmore, D., On the Lax solution to a Hamilton-Jacobi equation and its generalizations. Part 2, *Nonlin. Anal.* 55 (2003), 629-640. (Nov.)

Prykarpatsky, A., Blackmore, D. and Bogolubov (Jr.), N., Hamiltonian structure of Benney type hydrodynamic and Boltzmann-Vlasov kinetic equations on an axis and some applications to manufacturing science, *J*. *Open Systems & Information Dynamics* 6 (1999), 335-373.

Blackmore, D. and Knio, O., Hamiltonian structure for vortex filament flows, *ZAMM* 81S (2001), 145 – 148.

Leu, M.C., Maiteh, B., Blackmore, D. and Fu, L., Creation of freeform solid models in virtual reality, *Annals of CIRP* 50 (2001), 73-76.

Abdel-Malek, K., Yang, J. and Blackmore, D., On swept volume formulations: implicit surfaces, *Computer-Aided Design *33 (2001), 113-121.

Prykarpatsky, A., Stochel, J. and Blackmore, B., On versal deformation of a Sturm-Liouville type super-differential operator via Marsden-Weinstein reduction, *Math. Methods & Physicomechanical Fields* 43 (2000), 7-11.

(40)Wang, W., Hsu, C.T. and Blackmore, D., Geometrical formulation for strip yielding model with variable cohesion and its analytical solution, *Int. J. Solids Struc*. 37 (2000), 7533-7546.

Blackmore, D., Samulyak, R. and Leu, M.C., A singularity theory approach to swept volumes, *Int. J*. *Shape Modeling* 6 (2000), 105-129.

Blackmore, D. and Knio, O., Transition from quasiperiodicity to chaos for three coaxial vortex rings, *ZAMM* 80 S (2000), 173-176.

Blackmore, D. and Knio, O., KAM theory analysis of the dynamics of three coaxial vortex rings, *Physica* *D* 140 (2000), 321-348.

Bogolubov (Jr.), N., Prykarpatsky, A. and Blackmore, D., Swept volume dynamical systems and their kinetic models, *Comm. Math. Mech*. *Ukr. Acad. Sci*. 2 (1999), 291-305.

Maiteh, B., Leu, M.C., Blackmore, D. and Abdel-Malek, L., Swept volume computation for machining simulation and virtual reality application*, J. Materials Processing & Manufacturing Science* 7 (1999), 380-390.

Prykarpatsky, A. and Blackmore, D., Versal deformation of a Dirac type differential operator, *J. Nonlin. Math. Phys*. 6 (1999), 246-254.

Prykarpatsky, Y., Samoilenko, A.M. and Blackmore, D., Imbeddings of integral submanifolds and associated adiabatic invariants of slowly perturbed integrable Hamiltonian systems, *Rep. Math. Phys*. 44 (1999), 171-182.

Blackmore, D., Samulyak, R. and Leu, M.C., Trimming swept volumes, *Computer-Aided Design* 31 (1999), 215-223.

Blackmore, D., Samulyak, R. and Rosato, A., New mathematical models for particle flow dynamics, *J. Nonlin. Math. Phys*. 6 (1999), 198-221.

Blackmore, D. and Zhou, G., Fractal analysis of height distributions of anisotropic rough surfaces, *Fractals *6 (1998), 43-58.

Blackmore, D. and Zhou, G., A new fractal model for anisotropic surfaces, *Int. J. Mach. Tools Manufact*. 38 (1998), 551-557.

Blackmore, D., Prykarpatsky, Y. and Samulyak, R., The integrability of Lie-invariant geometric objects generated by ideals in the Grassmann algebra, *J. Nonlin. Math. Phys*. 5 (1998), 54-67.

Leu, M.C., Lu, F. and Blackmore, D., Simulation of NC machining with cutter deflection by modelling deformed swept volume, *Annals of CIRP* 47 (1998), 441-446.

Hentosh, O., Prykarpatsky, Y. and Blackmore, D., Geometric structure of integrable flows on Grassmann manifolds, *Math. Studies* 24 (1997), 202-218,

Prykarpatsky, A., Zagrodzinski, J. and Blackmore, D., Lax type flows on Grassmann manifolds and dual momentum maps, *Rep. Math. Phys*. 40 (1997), 539-549.

Leu, M.C., Wang, L.P. and Blackmore, D., A verification program for 5-axis NC machining with general APT tools, *Annals of CIRP* 46 (1997), 419-424.

Blackmore, D., Leu, M.C. and Wang, L.P., The sweep-envelope differential equation algorithm and its application to NC machining verification, *Computer-Aided Design* 29 (1997), 629-637.

Prykarpatsky, A., Hentosh, O. and Blackmore, D., The finite-dimensional Moser type reduction of modified Boussinesq and super-KdV Hamiltonian systems, *J. Nonlin. Math. Phys.* 4 (1997), 455-469.

Blackmore, D., Leu, M.C., Wang, L.P. and Jiang, H., Swept volumes: a retrospective and prospective view, *Neural*, *Parallel & Scientific Computations* 5 (1997), 81-102.

Deng, Z., Leu, M.C., Wang, L.P. and Blackmore, D., Determination of flat-end cutter orientation in 5-axis machining, *ASME J. Manufacturing Science & Engineering MED* 6 (1996), 73-80.

Blackmore, D., Prykarpatsky, A., Prytula, M. and Kopych, M., Transversal splitting of the separatrix manifolds of a generalized Henon-Heiles Hamiltonian system, *Proc. Nat. Acad. Sci. Ukr*. 11 (1996), 52-54.

Prykarpatsky, A., Blackmore, D. and Bogolubov (Jr.), N., Swept volume dynamical systems and their kinetic models, *Ukr. Math. J*. 48 (1996), 1620-1627.

Blackmore, D. and Zhou, G., A general fractal distribution function for rough surface profiles, *SIAM J. Appl. Math*. 56 (1996), 1694-1719.

Blackmore, D. and Kappraff, J., Integrable discrete dynamics and Fibonacci sequences, *ZAMM* 76 S (1996), 49-52.

Prykarpatsky, A., Blackmore, D., Strampp, W., Sydorenko, Yu. and Samulyak, R., Some remarks on Lagrangian and Hamiltonian formalisms for infinite-dimensional dynamical systems with symmetries, *Condensed Matter Phys*. 6 (1995), 79-104.

Blackmore, D., Leu, M.C. and Shih, F., Analysis and modelling of deformed swept volume, *Computer-Aided Design* 26 (1994), 315-326.

Blackmore, D., Simple dynamical models for vortex breakdown of B-type, *Acta Mech*. 102 (1994), 91-101.

Zhou, G., Leu, M.C. and Blackmore, D., Fractal geometry model for wear prediction, *Wear* 170 (1993), 91-101.

Leu, M.C., Blackmore, D. and Wang, K.K., Applications of flows and envelopes to NC machining, *Annals of CIRP* 41 (1992), 493-496.

Blackmore, D. and Leu, M.C., Analysis of swept volume via Lie groups and differential equations, *Int. J.* *Robot. Res*. 11 (1992), 516-537.

Kristol, D., Stackhouse, J., Blackmore, D. and Odak, S., Development of a dentin bonding agent: correlation of bond strength to microleakage, *Innov. Tech. Med*. 10 (1989), 210-219.

Blackmore, D., The mathematical theory of chaos, *J. Comp. and Maths. with Appls*. 12B (1986), 1039-1045.

Blackmore, D. and Ting, L., Surface integral of its mean curvature, *SIAM Rev*. 27 (1985), 569-572.

Blackmore, D., Chaos in a simple counter/identification model, *J. Franklin Inst*. 325 (1988), 95-105.

Blackmore, D., The describing function for bounded nonlinearities, *IEEE Trans. Circuits Syst*. 28 (1981), 442-447.

Blackmore, D., On the index sum of a vector field, *Topology* 4 (1980), 401-415.

Blackmore, D., An example of a local flow on a manifold, *Proc. Amer. Math. Soc*. 42 (1974), 208-213.

Blackmore, D., On the local normalization of a vector field at a degenerate critical point, *J. Diff. Eqs*. 14 (1973), 338-359.

Blackmore, D., Flows about a critical point with a single zero characteristic root, *J. Diff. Eqs*. 13 (1973), 403-431.

## Refereed Conference Papers

Blackmore, D., Tricoche, X. and Rosato, A., Dynamical Systems-Simulation-Visualization Approach to Tapping and Other Granular Flow Phenomena: First Steps, *Proc. NSF CMMI Grantees Conference*, Atlanta, Georgia, Jan. 4-7, 2011, 10 pages.

Prykarpatsky, A. and Blackmore, D., On new invariants in MHD and a related helicity theorem, *Proc.Dubrovin Int. Conf. on Geometrical Methods in Math. Phys.*, Moscow State University, Russia, 12-17 Dec., 2011, *SIGMA* (online), pp 46-50. (58)

Prykarpatsky, A. and Blackmore, D., Analysis of a nonlinear operator equation using a Leray-Schauder type theorem point approach, *Proc. Workshop on Infinite Dimensional Functional Analysis and Topology (IDAT)*, Yaremczha City, Ukraine, Sept., 2009, pp 46-50.

Blackmore, D., Brøns, M. and Goullet, A., Two-vortex models for vortex breakdown, *Proc. ASME 2008 Dynamics Systems and Control Conf*., Oct. 20-22, 2008, Ann Arbor, Michigan, 2008. Paper No. DSCC2008-180. (to appear).

Knio, O., Ting, L. and Blackmore, D., Simulation of dynamics of binary and ternary vortex clusters, *Proc. ICCES’08*, Honolulu, Hawaii, March 2008, Tech Science Press (online), pp. 120-121.

Zhou, G., Vas, A., Blackmore, D., Mulero, R., Tan, J., Lyman, J., and Roukous, D., CAD/CAM for a musical cymbal generated from a fractal geometry model, *Proc. ASME MSEC Sympos. On Advances in Rapid Manufacturing Technologies for Metal Parts*, June 25-29, 2007, Honolulu, Hawaii, *CAD & Appl.* 4 (2007), pp. 53-60.

Blackmore, D., Ting, L. and Knio, O., Invariant tori in perturbed three vortex motion, *Proc. ICIAM’07, *Zurich, Switzerland, *PAMM *7 (2008), pp. 1101507-1101508 (online) (Dec.)

Ting, L., Knio, O. and Blackmore, D., Dynamics of planar vortex clusters with binaries, *Proc. ICIAM’07, *Zurich, Switzerland, *PAMM* 7 (2008), pp. 1101501-1101502 (online) (Dec.)

Blackmore, D., Nonintegrable perturbations of two vortex dynamics, *Proc. IUTAM Sympos. on Hamiltonian Dynamics, Vortex Structures and Turbulence,* Moscow, Aug. 2006, A. Borisov, V. Koslov, I. Mamaev, and M. Sokolovsky (eds.), Springer, Berlin, 2007, pp. 202-212. (Dec.)

Pillapakkam, S., Singh, P., Blackmore, D. and Aubry, N., Analysis of the motion and deformation of a bubble rising in a viscoelastic fluid, *Proc. FEDSM2006*, July 2006, Miami, FL, 2006, pp. 67-72.

Zhang, W., Leu, M.C., Peng, X. and Blackmore, D., Accuracy and computational complexity analysis of design model created by virtual scuplting,* Proc. of 2005 IMECE*, Orlando, FL, Nov. 5-11, 2005, pp. 63-69.

Ting, L. and Blackmore, D., Bifurcations of motions of three vortices and applications, *ICTAM04 Abstracts and CD-ROM Proceedings,* W. Gutkowski and T. Kowalewski, eds., Aug. 15-21, 2004, Warsaw, Poland, IPPT PAN, Warsaw, 2004, p. 189.

Blackmore, D., Champanerkar, J. and Levandowsky, M., Complexity measures for ecological assemblages, *Proc. Int. Conf. on Complex Systems* (ICCS’04), Boston, May 16-21, 2004, pp. 220-228.

Blackmore, D. and Champanerkar, J., Some new extensions of the Poincaré-Birkhoff theorem, *Proc. Conf. on Dynamical* *Systems – Theory and Applications*, Łódź, Poland, Dec. 8-11, 2003, pp. 13-24.

Prykarpatsky, A., Taneri, U. and Blackmore, D., Quantum holonomic computing via Lax type flows on Grassmanian manifolds and the dual momentum mappings, *Proc. Symmetry in Nonlinear Mathematical* *Physics*, Kyiv, Ukraine, June 23-29, 2003, pp. 128-135.

Blackmore, D. and Ting, Vorticity jumps across shock surfaces, *Proc. 2**nd** MIT Conf. on Computational Fluid* *and Solid Mechanics*, Vol. 1, K.J. Bathe, ed., Elsevier, Amsterdam, 2003, pp. 847-849.

Blackmore, D., Basiura, R., Prykarpatsky, A. and Soroka, O., On a class of factorized operator dynamical systems and their integrability, *Proc. SCI 2002*, Orlando, Florida, Aug. 2002, pp. 406-501.

Blackmore, D., Taneri, U. and Prykarpatsky, A., Quantum coherent transform of Lax-integrable Hamiltonian systems: quantum computing, *Proc. SCI 2002*, Orlando, Florida, Aug. 2002, pp. 350-360.

Blackmore, D., Hamiltonian analysis of vortex filaments, *Proc. Fourth Int. Conf. on Nonlinear* *Mechanics*, Shanghai, China, Aug. 2002, pp. 807-813.

Ting, L. and Blackmore, D., Higher order shock conditions for curved shocks in unsteady flows, *Proc. Fourth Int. Conf. on Nonlinear Mechanics, *Shanghai, China, Aug. 2002, pp. 160-164.

Blackmore, D. and Ting, L., Interaction of shocks and weak vorticity fields, *Proc. Fifth World Cong. on Comp. Mech*., Vienna, Austria, July 2002 (online).

Blackmore, D. and Knio, O., A Hamiltonian approach to vortex breakdown, *Proc. Euromech Colloquium* *No. 433: Dynamics of Trailing Vortices*, Aachen, Germany, March 2002 (online).

Blackmore, D. and Ting, L., Higher order conditions for weak shocks: modified Prandtl relation, *PAMM *1, 2002, pp. 397-398. (online)

Blackmore, D., Samulyak, R. and Rosato, A., Chaos in vibrating granular flows, *Proc. Dynamic. Systems and* *Applications* 3 , G. Ladde, N. Medhin and M. Sambandham (eds.), Dynamic Publ., Inc., Atlanta, 2001, pp. 77-84.

Aboobaker, N., Meegoda, J. and Blackmore, D., Analysis of fractionation of sediments caused by an acoustic field, *Proc. Int. Conf. on Computer Methods and Advances in Geomechanics*, C. Desai (ed.), Balkema, Rotterdam, Vol.1, 2001, pp. 775-780.

Aboobaker, N., Meegoda, J. and Blackmore, D., Fractionation and segregation of suspended particles using acoustic and flow fields, *Proc. 32**nd** Mid-Atlantic Industrial and Hazardous Waste Conf*., Technomic, 2000, pp. 659-668.

Abdel-Malek, K., Yang, J. and Blackmore, D., Closed form-swept volume of implicit surfaces, *Proc. 26**th* *ASME Design Eng. Tech. Conf*., Johns Hopkins University, Sept., 2000, pp. 1-6.

Blackmore, D., Samulyak, R., Rosato, A. and Dave, R., Dynamics of a two species oscillating particle system, *Segregation in Granular Flows*, A. Rosato and D. Blackmore, eds., Kluwer, Dordrecht, 2000, pp. 255-268.

Maiteh, B., Leu, M.C., Blackmore, D., Liu, G. and Abdel-Malek, L., Swept volume computation for virtual reality application of NC machining, *Proc. ASME Sympos. on Virtual Environments for Manufacturing, *University of Illinois at Chicago, Nov. 1-2, 1999, pp. 1-9.

Prykarpatsky, A., Blackmore, D., Bogolubov (Jr.), N. and Samoilenko, V., On the Hamiltonian structure of Benney type hydrodynamic and Boltzmann-Vlasov axial kinetic equations, *Proc. Conf. on Diff. Eqs. in* *Honor of N. N. Bogolubov*, Kyiv, 1999, pp. 59-82.

Blackmore, D., Quasi-optimal paths in automated assembly, *Int. Conf. on Quality Manufacturing*, Stellenbosch, South Africa, Jan. 13-15, 1999, pp. 23-27.

Leu, M.C., Blackmore, D. and Maiteh, B., Deformed swept volume analysis of NC machining with cutter deflection, *Machining Impossible Shapes*, B.K. Choi and R. Jerard, eds., Kluwer, Boston, 1999, pp. 158-166.

Prykarpatsky, A. and Blackmore, D., On the Lax solution to a Hamilton-Jacobi equation and its generalizations. Part 1, *Proc. Int. Conf. on Partial Differential Equations*, Praha, Czech Republic, 1998, pp. 234-242.

Blackmore, D., Samulyak, et al. (1998). Granular flow in hoppers and vibrating beds: Mathematical models, numerical solutions and computer simulations. *Proc. of the 1998 AIChe Annual Meeting*, Miami, FL, American Institute of Chemical Engineers, 1998.

Prykarpatsky, A., Stochel, J. and Blackmore, D., Versal deformations of a Sturm-Liouville type super-differential operator, *Proc. Int. Res. Conf. on Modern Problems of Math*., Chenivtsi, Ukraine, 1998, pp. 232-237.

Zhou, G. and Blackmore, D., Fractal geometry modeling and simulation for engineering surfaces, *Proc*. *Young Scientists Conf. on Manufacturing Science*, Wuhan, China, 1998, pp. 429-433.

Prykarpatsky, A., Blackmore, D. and Bogolubov (Jr.), N., A new integrable nonlinear Schrödinger type dynamical system, *Proc. 7**th** Int. Scientific Kravchuk Conf*., Kyiv, Ukraine, 1998, pp. 414-415.

Wang, L.P., Leu, M.C. and Blackmore, D., Generating swept solids for NC verification using the SEDE method, *Proc. Fourth ACM Sympos. on Solid Modeling and Applications*, Atlanta, May 14-16, 1997, pp. 267-276.

Wang, L.P., Leu, M.C. and Blackmore, D., Swept volume approach as an integral part of a 5-axis NC milling CAD/CAM system, *Proc. Int. Conf. on Manufacturing Automation*, Hong Kong, April 28-30, 1997, pp. 402-409.

Wang, L.P., Leu, M.C. and Blackmore, Kinematics analysis of 5-axis milling machine and its application to NC verification, *Proc. Int. Conf. on Manufacturing Automation*, Hong Kong, April 28-30, 1997, pp. 327-333.

Prykarpatsky, A.K., Blackmore, D. and Hentosh, O., The finite-dimensional Moser type reductions of modified Boussinesq and super Korteweg-de Vries Hamiltonian systems via the gradient holonomic algorithm and dual momentum map, in T. Gill (ed.), *Proc. Int’l. Conf. on New Frontiers in Physics*, vol. 11, Institute for Basic Research, Monteroduni, Italy, Hadronic Press, 1996, pp. 271-292

Deng, Z., Leu, M.C. and Blackmore, D., Application of SDE to 5-axis sculptured surface machining, *Proc. 3**rd** Int. Conf. on Automation Technology*, 1996, pp. 104-112.

Drobotska, I., Prykarpatsky, A. and Blackmore, D., Functionally constrained variational analysis in nonlinear dynamical systems theory, *Proc. Conf. on Nonlinear Analysis Problems*, 1996, pp. 31-35.

Deng, Z., Leu, M.C., Wang, L.P. and Blackmore, D., Determination of flat-end cutter orientation in 5-axis machining, *Proc. ASME Symp. on Rapid Response Manufacturing*, 1996, pp. 21-29.

Leu, M.C., Blackmore, D., Pak, K. and Wang, L.P., Implementation of the SDE method to represent cutter swept volumes in 5-axis NC milling, *Proc. Int. Conf. on Intelligent Manufacturing*, Wuhan, China, 1995, pp. 212-220.

Deng, Z., Leu, M.C. and Blackmore, D., Application of sweep differential equation approach to nonholonomic motion planning, *Proc. 1994 Japan-USA Sympos. on Flexible Automation*, 1994, pp. 1025-1034.

Shih, F., Blackmore, D. and Gaddipati, V., Error analysis of surface fitting for swept volumes, *Proc. 1994* *Japan-USA Sympos. on Flexible Automation*, 1994, pp. 733-738.

Blackmore, D., Leu, M.C. and Qin, D., Improved flow approach for swept volumes, *Proc. 1994 Japan-USA Sympos. on Flexible Automation*, 1994, pp. 1191-1198.

Leu, M.C. and Blackmore, D., Application of the sweep differential equation method to multiaxis NC machining, *Proc. Sino-German Sympos. on Precision and High-Speed Manufacturing Technology*, 1993, pp. 159-169.

Blackmore, D., Leu, M.C. and Jiang, H., Modeling swept solids using sweep differential techniques, *Proc*. *Conf. on Solid Modeling*, 1993, pp. 46-55.

Blackmore, D., Infinite-dimensional deformations and Milnor fibrations, *Proc. 1992 Summer Conf. on* *Topology*, 1992, pp. 15-24.

Blackmore, D., Leu, M.C. and Wang, W., Classification and analysis of robot swept volumes, *Proc. 1992* *Japan-USA Sympos. on Flexible Automation*, 1992, pp. 69-75.

Blackmore, D. and Leu, M.C., A differential equations approach to swept volumes, *Proc. Rennselaer’s 2**nd* *Int. Conf. on Computer Integrated Manufacturing*, SME, 1990, pp. 143-149.

Rajaram, L. and Blackmore, D., Deconvolution techniques in cardiovascular system analysis, *Proc. IEEE* *Engineering and Biology Society Conf.*, 1985, p. 1271.

Blackmore, D. and Cooper, M., Normal forms for isolated hypersurface singularities, *Proc. Princeton* *Conf. on Several Complex Variables*, E. Fornaess (ed.), Springer-Verlag, Berlin, 1982, pp. 321-338.

Blackmore, D., A singularity theory approach to describing functions, *Proc. 50**th** Annual Meeting Soc. Nat*. *Philos*., 1979, pp. 313-319.

Blackmore, D., On local normal forms for diffeomorphisms, *Proc. Warwick Conf. on Dynamical Systems*, *Vol. 2*, Springer-Verlag, 1977, pp. 102-106.

Blackmore, D., Sufficient conditions for structural stability of diffeomorphisms, *Proc. Warwick Conf. on* *Dynamical Systems*, *Vol. 1*, Springer-Verlag, Berlin, 1976, pp. 215-218.

## Non-Refereed Conference Papers

Blackmore, D., Tricoche, X. and Rosato, A., Dynamical Systems-Simulation-Visualization Approach to Tapping and Other Granular Flow Phenomena: First Steps, *Proc. NSF CMMI Grantees Conference*, Atlanta, Georgia, Jan. 4-7, 2011, 10 pages.

Blackmore, D., Leu, M.C., Regli and Sun, W., Accuracy and stability of swept volume representations, *Proc. NSF/DARPA CARGO Grantees Workshop*, June, 2003, Santa Rosa, CA (online).

Blackmore, D., A new method for computing swept volumes, *Proc. 1998 NSF Design and Manufacturing* *Grantees Conf*., 1998, pp. 485-486.

Blackmore, D., Extensions and generalizations of the SDE method, *Proc. 1997 NSF Design and* *Manufacturing Grantees Conf*., 1997, pp. 120-121.

Blackmore, D. and Leu, M.C., Further developments of the SDE approach, *Proc. 1994 NSF Design and* *Manufacturing Grantees Conf*., 1994, pp. 63-64.

Blackmore, D. and Leu, M.C., Application and implementation of the sweep differential equation method, *Proc. 1993 NSF Design and Manufacturing Grantees Conf*., 1993, pp. 1411-1418.

Blackmore, D. and Leu, M.C., Representation of sweeps and swept volumes via differential equations, *Proc. 1992 NSF Design and Manufacturing Grantees Conf*., 1992, pp. 731-735.

## Reports (selected examples)

Lustyk, M., Bogolubov (Jr.), Blackmore, D. and Prykarpatsky, A., Analysis of the Calogero Projection-Algebraic Scheme for Differential Operators, Abdus Salam International Centre for Theoretical Physics, Trieste, Italy, Preprint #IC/2010/097. (August, 2011)

Competing Portfolio Market with a Polyvariant Profit Function, Abdus Salam International Centre for Theoretical Physics, Trieste, Italy, Preprint #IC/2010/098. (August, 2011)

Bogolubov (Jr.), Kyshakevych, B., Blackmore, D. and Prykarpatsky, A., Optimal Strategy Analysis of

Analysis of Infinite-dimensional Dynamical Systems, Abdus Salam International Centre for Theoretical Physics, Trieste, Italy, Preprint #IC/2010/090. (July, 2011)

Bogolubov (Jr.), Prykarpatsky, Y., Blackmore, D. and Prykarpatsky, A., Lagrangian and Hamiltonian

Blackmore, Notes on the Tittel-Berndt Filter Fabric Model, Prepared for Unique Wire Weaving Co. and Published in ASTM WK23197 – New Guide for Industrial Woven Wire Filter Cloth, 2010.

Ting. L., Knio, O. and Blackmore, D., Critical solution of three vortex motion in the parabolic case, arXiv:0807.0454v1 (2008) (July)

Prykarpatsky, Y., Samoilenko, A., Prykarpatsky, A., Bogolubov (Jr.), N. and Blackmore, D., The Differential-Geometric Aspects of Integrable Dynamical Systems, Abdus Salam International Centre for Theoretical Physics, Trieste, Italy, Preprint #IC/2007/030.

Prykarpatsky, A., Blackmore, D. and Bogolubov (Jr.), N., The Lie-Algebraic Structures and Integrability of Differential and Differential-Difference Nonlinear Dynamical Systems, Abdus Salam International Centre for Theoretical Physics, Trieste, Italy, Preprint #IC/2007/029

Bogolubov (Jr.), N, Prykarpatsky, A. and Blackmore, D., On Benney Type Hydrodynamical Systems and Their Boltzmann-Vlasov Equations Kinetic Models, Abdus Salam International Centre for Theoretical Physics, Trieste, Italy, Preprint #IC/2006/006

Blackmore, D. and Leu, M.C., Analysis of Sweep Classes: an Application of Differential Topology to Manufacturing Science, CAMS Tech. Rep., 1997.

Prykarpatsky, A., Blackmore, D., Strampp, W., Sydorenko, Yu. and Samulyak, R., On Lagrangian and Hamiltonian Formalisms for Infinite-Dimensional Dynamical Systems with Symmetries, CAMS Tech. Rep., 1997.

Leu, M.C. and Blackmore, D., Analysis and Representation of Swept Volume via Lie Groups and Differential Equations, Robotics and Automation Research Tech. Rep.-021, 1990.

Blackmore, D. and Ting, L., Minimal Geodesic Triangulations of the n-Sphere, CAMS Tech. Rep., 1989.

Blackmore, D., Describing Function Analysis of Bounded Discontinuous Autonomous Systems, CAMS Tech. Rep., 1988.

Blackmore, D., Exceptional Minimal Sets for Diffeomorphisms and Flows, CAMS Tech. Rep., 1987.

## Professional Presentations (selected examples)

*Infinite-dimensional Flow Field Models: Integrability, Wave Propagation, Vortex Invariants and Helicity Theorems* (invited), Mathematics Seminar, AGH University of Science and Technology, Kraków, Poland, June 6, 2012.

*Integrability of a New Class of Infinite-Dimensional Hamiltonian Systems* (invited), Math. Division of Shevchenko Scientific Soc. Jubilee Workshop on Nonlinear Dynamical Systems and Lax Integrability, Ivan Franko University, Drohobych, Ukraine, June 4, 2012.

*Infinite-Dimensional Dynamical System Approximation of Granular Flow* (invited plenary talk), Int’l. Conf. on Theory of Approximation of Functions and Its Applications, Ivan Ohienko National University, Kamianets-Podilsky, Ukraine, May 28-June 3, 2012.

*Hamiltonian Dynamical Systems: Applications to Vortex and Granular Dynamics *(invited), Mathematical Fluid Dynamics Seminar, New Mexico State University, Las Cruces, New Mexico, Dec. 2, 2011.

*Infinite-dimensional Dynamics and Granular Flow*, NJIT Summer Math. Science Seminar Series, June 27, 2011.

*New Applications of Infinite-dimensional Dynamics to Granular Flows *(invited), Mathematics Lecture Series, Wichita State University, Wichita, Kansas, April 1, 2011.

*Swept Volumes and Computational Topology *(invited), Texas Tech Mechanical Engineering Seminar, Texas Tech University, Lubbock, Texas, Oct. 22, 2010.

*Approximations to Granular Relaxation Flows: Lattices, Limits, Infinite-dimensional Dynamical Systems and Solitons* (invited), NJIT Applied Mathematics Colloquium, Feb. 5, 2010.

*A Planar Hamiltonian Model for Vortex Breakdown *(invited), NJIT Summer Mathematical Sciences Seminar, June 25, 2009.

*Dynamical Properties of Planar Point Vortex Clusters* (invited), SIAM Snowbird Applied Dynamical Systems Conf., Snowbird, Utah, May 17-21, 2009.

*Bifurcation of Invariant Manifolds in Discrete and Continuous Dynamical Systems* (invited), Second Annual George Bachman Memorial Conference, St. Johns University, June 6, 7, 2009.

*A New Hamiltonian Dynamical Paradigm for Vortex Breakdown* (invited), Joint Mathematics and Mechanical Engineering Colloquium, Carnegie Mellon University, February 13, 2009.

*Two-Vortex Models for Vortex Breakdown *(invited), ASME 2008 Dynamic Systems and Control Conf., University of Michigan, Oct. 20-23, 2008.

*Invariant Tori in Perturbed Three Vortex Motion* (invited), Minisymposium on Recent Advances in Vortex Dynamics, ICIAM’07, ETH, Zürich, Switzerland, July 18, 2007.

*Recent Results on Perturbed Three Vortex Dynamics* (invited), Aerodynamisches Institüt, RWTH-Aachen, Aachen, Germany, May 10, 2007.

*Stability and Chaos in Vortex Dominated Flow Models *(invited), Fluid Dynamics Seminar, Technical University of Denmark, Lyngby, Denmark, May 8, 2007.

*Computable Topological Consistency of Non-manifold Objects* (invited), General Mathematics Seminar, Technical University of Denmark, Lyngby, Denmark, April 25, 2007.

*Perturbations of Integrable Vortex Dynamics *(invited), Mathematics Colloquium, University of South Alabama, Mobile, Alabama, March 22, 2007.

*Adventures in Applied Mathematics* (invited), Science Colloquium, Essex County Community College, Newark, NJ, March 7, 2007

*Effective Computability of Equivalence of Stratified Varieties* (invited), Computer Science Colloquium, University of Connecticut, Dec. 1, 2006.

*Equivalence of Computational Geometric Objects *(invited), Topology Seminar, City College of New York, Nov. 16, 2006.

*Neighborhoods for Computational Geometric Objects* (invited), Special Session on Topology and Computing, AMS Meeting #1021, University of Connecticut, Oct. 28, 2006.

*Categories and Structures for Computational Topology* (invited), Algorithms Seminar, Duke University, Oct. 23, 2006.

*Nonintegrable Perturbations of Two Vortex Dynamics *(invited), IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, and Turbulence, Aug. 27, 2006, Steklov Institute, Moscow, Russia.

*Recurrent Motions for Perturbed Three Vortex Dynamics *(invited), Special Session on Theoretical Studies and Engineering Applications of Vortical Flows, GAMM Annual Meeting, March 27-31, 2006, Berlin, Germany.

*Chaos and Mixing in Vortex Dominated Flows* (invited), Feb. 27, 2006, Chemical Engineering Graduate Seminar, NJIT.

*Simple Dynamical Models of Complex Granular Flow, *(invited), Oct. 31, 2005, Colloquium Series: Granular and Multiphase Flows, Sponsored by MRC and Granular Science Laboratory, Mechanical Engineering, NJIT.

*Computational Topology of Projected Objects* (invited), Oct. 24, 2005, Minisymposium on Computational Topology in Bioscience and Industry, SIAM Conference on Mathematics for Industry: Challenges and Frontiers, Detroit, Michigan,.

*Differential Computational Topology*, (invited plenary speaker), July 14, 2005, NSF Workshop on Computational Topology, Denison University.

*Perturbed Three Point Vortex Problems* (invited), June 2005, Minisymposium on Vortex Dominated Flows, Third MIT Conf. on Computational Fluid and Solid Mechanics.

*Opportunities for Computer Science and Mathematics Synergy in the Representation of Geometric Objects* (invited), Dec. 2004, Computer Science Colloquium, CUNY Graduate Center.

*Computational Topology: Where’s the Topology? *(invited), Nov. 2004, Topology and Group Theory Seminar, CUNY.

*Vortex Dynamics: Past Present and Future* (invited), Oct. 2004, Physics Seminar, Wesleyan University, New Haven, CT.

*Perturbations of Point and Ring Vortex Dynamics* (invited; joint work with L. Ting), ICTAM Conf. on Fluid Mechanics, Warsaw, Poland, Aug., 2004.

*Stability of Coaxial Vortex Ring Motions* (invited; joint work with L. Ting)), AIMS Conf., Cal Poly, Pomona, June 16-19, 2004.

*Swept Volumes from the Computational Topology Viewpoint* (invited), April 22, 2004, University of Missouri-Rolla.

*Computing the Shape of Swept Volumes and Their Intersections* (invited), Nov. 20, 2003, Drexel University Computer Science Seminar Series.

*Some New Extensions of the Poincaré-Birkhoff Theorem and Their Applications* (invited plenary lecture), Int. Conf. on Dynamical Systems-Theory and Applications, Dec. 8-11, 2003, Łódź, Poland.

*Applications of the Computational Topology of Swept Volumes*, DIMACS Workshop on Computational Geometry and Manufacturing, Oct. 2003, New Brunswick, NJ.

*Vorticity Jumps Across Shock Surfaces* (invited), 2nd MIT Conf. on Computational Fluid and Solid Mechanics, June, 2003.

*Periodic Motion for Coaxial Vortex Ring Configurations* (invited), SIAM Snowbird Conference on Dynamical Systems, May, 2003.

*Hamiltonian Analysis of Vortex Filament Dynamics* (invited), Fourth International Congress on Nonlinear Mechanics and IUTAM Symposium on Duality-Complementarity-Symmetry in Nonlinear Mechanics, Shanghai, China, Aug. 14-17, 2002.

*Shock-Weak Vortex Filament Interaction* (invited), Fifth World Congress on Computational Mechanics, Vienna, Austria, July 7-11, 2002.

*A Hamiltonian Approach to Vortex Breakdown* (invited), Euromech Colloquium on Dynamics of Trailing Vortices, Aachen, Germany, March 21-22, 2002.

*Higher Order Conditions for Weak Shocks: Modified Prandtl Relation, *GAMM 2001, Zurich, Switzerland, Feb. 12 -15, 2001.

*A Hamiltonian Approach to Vortex Filament – Obstacle Interactions* (invited), Joint Mechanical Engineering – Mathematical Sciences Colloquium, NJIT, Oct. 18, 2000.

*Hamiltonian Formulation of the Interaction between a Vortex Ring and a Sphere* (invited), ECCOMAS 2000, Barcelona, Spain, Sept. 11-14, 2000.

*Hamiltonian Structure for Vortex Filament Flows* (invited), Annual Meeting of GAMM, Göttingen, Germany, April 2-7, 2000.

*Dynamics of Coaxial Vortex Rings* (invited), Rensselaer Polytechnic Institute, Oct. 18, 1999.

*Regular and Chaotic Motions of Coaxial Vortex Rings *(invited), The Johns Hopkins University, 1999.

*Chaos in Granular Flows* (invited), Third Int. Conf. on Dynamic Systems and Applications, Atlanta, 1999.

*Characterization of Versal Deformations of the Dirac Differential Operator*, SIAM Annual Mtg., Stanford University, 1997.

*New Fractal Models for Engineering Surfaces* (invited), Int. Conf. on Engineering Surfaces and Metrology, Göteborg, Sweden, 1996.

*Engineering Applications of Chaos Theory* (invited), Civil and Environ. Eng. Seminar, NJIT, 1994.

*Fractals with some Applications to Surface Mechanics* (invited), Mech. and Indust. Eng. Colloquium, NJIT, 1992.

*Applications of Differential Topology to Manufacturing Engineering* (invited), Rutgers University, 1991.

*Global Vortex Breakdown Solutions*, 2nd Int. Congress of Industrial and Appl. Math., Washington, D.C., 1991.

*An Analysis of Vortex Breakdown*, 1st Int. Congress of Industrial and Appl. Math., Paris, France, 1987.

*Topological Equivalence of Real Singularities* (invited), Special Session talk at 819th Meeting of AMS, College of Holy Cross, 1985.

*Topological Type of Nonisolated Singularities* (invited), Special Session talk at 784th Meeting of the AMS, University of Notre Dame, 1981.

*Normal Forms for Isolated Singularities* (invited), Princeton University, 1979.

*Pseudo-linearization of Diffeomorphisms* (invited), Graduate Center of CUNY, 1977.

*Structural Stability Theorems* (invited), Northwestern University, 1975.

*Nongenericity in Dynamical Systems*, Int. Congress of Mathematicians, Vancouver, B. C., Canada, 1974.

## Posters

Blackmore, A. Rosato and X. Tricoche, A Dynamical Systems-Simulation-Visualization Approach to Tapping and Other Granular Flow Phenomena: First Steps, NSF CMMI Grantees Conference, Atlanta, Georgia, Jan. 4-7, 2011.

Blackmore, A. Rosato, X. Tricoche and K. Urban, Tapping Dynamics: Theory and Applications, Gordon Research Conference on Granular Dynamics, Colby College, Maine, June 20-25, 2010.

Rahman and D. Blackmore, Dynamics of Logical Circuits, FACM’10, May 21-23, NJIT, 2010.

Joshi and D. Blackmore, Bifurcation and Chaos in Discrete Dynamical Hierarchical Pioneer-Climax Models , FACM’09, June 5-7, NJIT, 2009.

Kaur and D. Blackmore, Acoustic and Fluid Flows on Perturbed Spherical Objects, FACM’08, May 19-21, NJIT, 2008.

Joshi and D. Blackmore, Dynamics of Discrete Population Models: Higher Dimensional Pioneer-Climax Models, FACM’08, May 19-21, NJIT, 2008.

Blackmore, A. Rahman and J. Shah, Discrete Dynamical Modeling and Analysis of the R-S Flip-Flop Circuit, FACM’08, May 19-21, NJIT, 2008.

Blackmore and J. Champanerkar, Quasiperiodic Dynamics of Point Vortices, FACM’05, May 13-15, 2005.

Blackmore and L. Ting, Bifurcation of Motion of Three Vortices, ICTAM’04, Aug. 15-21, 2004, Warsaw University of Technology, Warsaw, Poland.

Mileyko and D. Blackmore, Intersections of Swept Manifolds, FACM’04, May 21-22, 2004, New Jersey Institute of Technology, Newark, NJ.

Champanerkar and D. Blackmore, Pitchfork Bifurcation of Submanifolds, FACM’04, May 21-22, 2004, New Jersey Institute of Technology, Newark, NJ.

Rosato, D. Blackmore, L. Buckley, C. Oshman and M. Johnson, Galton’s Board Dynamics, FACM’04, May 21-22, 2004, New Jersey Institute of Technology, Newark, NJ.

Levandowsky, D. Blackmore, J. Champanerkar *et al., *Three Approaches to Biocomplexity Measures. Application to Protistan Data from the Meadowlands, Meadowlands Symposium, Oct. 9-10, 2003, Meadowlands Environmental Center, Lyndhurst, NJ.

## Patents

B. Maiteh, M.C. Leu and D. Blackmore: *Virtual Reality System for Creation of Design Models and Generation of Numerically Controlled Machining Trajectories*, NJIT, Sept. 19, 2002 – # US 20020133264.