About Me
Denis Blackmore is a Professor of Mathematical Sciences at the NJIT. He is a founding member of the Center for Applied Mathematics and Statistics, a member of the Center for Manufacturing Systems and a member of the Particle Technology Center, all at NJIT. While conducting his own research in dynamical systems and differential topology, he has also devoted considerable time to collaborative research in various engineering and science disciplines.
Education
Ph.D.; Polytechnic Institute of Brooklyn; Mathematics; 1971
M.S.; Polytechnic Institute of Brooklyn; ; 1966
B.S.; Polytechnic Institute of Brooklyn; ; 1965
M.S.; Polytechnic Institute of Brooklyn; ; 1966
B.S.; Polytechnic Institute of Brooklyn; ; 1965
Website
Teaching Interests
Differential Equations, Analysis, Algebra
Past Courses
MATH 111: CALCULUS I
MATH 211: CALCULUS IIIA
MATH 222: DIFFERENTIAL EQUATIONS
MATH 331: INTRO PARTIAL DIFF EQ
MATH 332: INTRO COMPLEX VARIABLES
MATH 335: VECTOR ANALYSIS
MATH 337: LINEAR ALGEBRA
MATH 388: INTRO CHAOS THEORY
MATH 473: INTERMED DIFFEREN EQUATN
MATH 473: INTERMEDIATE DIFFERENTIAL EQUATIONS
MATH 480: INTRO MATH ANALYSIS
MATH 480: INTRODUCTORY MATHEMATICAL ANALY
MATH 481: ADVANCED CALCULUS
MATH 545: INTRO MATH ANALYSIS
MATH 545: INTRODUCTORY MATHEMATICAL ANALY
MATH 546: ADVANCED CALCULUS II
MATH 573: INTERMED DIFF EQUATIONS
MATH 573: INTERMEDIATE DIFFERENTIAL EQUATIONS
MATH 631: LINEAR ALGEBRA
MATH 645: ANALYSIS
MATH 656: COMPLEX VARIABLES
MATH 656: COMPLEX VARIABLES I
MATH 676: ADV ORDINARY DIFFE EQ
MATH 707: ST: APPL OF ABSTRACT ALGEBRA
MATH 745: MATHMATICAL ANALYSIS II
MATH 756: COMPLEX VARIABLES II
MATH 211: CALCULUS IIIA
MATH 222: DIFFERENTIAL EQUATIONS
MATH 331: INTRO PARTIAL DIFF EQ
MATH 332: INTRO COMPLEX VARIABLES
MATH 335: VECTOR ANALYSIS
MATH 337: LINEAR ALGEBRA
MATH 388: INTRO CHAOS THEORY
MATH 473: INTERMED DIFFEREN EQUATN
MATH 473: INTERMEDIATE DIFFERENTIAL EQUATIONS
MATH 480: INTRO MATH ANALYSIS
MATH 480: INTRODUCTORY MATHEMATICAL ANALY
MATH 481: ADVANCED CALCULUS
MATH 545: INTRO MATH ANALYSIS
MATH 545: INTRODUCTORY MATHEMATICAL ANALY
MATH 546: ADVANCED CALCULUS II
MATH 573: INTERMED DIFF EQUATIONS
MATH 573: INTERMEDIATE DIFFERENTIAL EQUATIONS
MATH 631: LINEAR ALGEBRA
MATH 645: ANALYSIS
MATH 656: COMPLEX VARIABLES
MATH 656: COMPLEX VARIABLES I
MATH 676: ADV ORDINARY DIFFE EQ
MATH 707: ST: APPL OF ABSTRACT ALGEBRA
MATH 745: MATHMATICAL ANALYSIS II
MATH 756: COMPLEX VARIABLES II
Research Interests
Dynamical systems, differential topology, computational topology, manufacturing science, fractal surface characterization, vortex breakdown, granular flow dynamics, metrology, biomathematics and his work in swept volumes reflects his interests in applications of mathematics.
In Progress
Application of Machine Learning to Discrete Interacting Particle Systems
Density Relaxation in Granular Systems
One of the principal findings in the tapped density relaxation study (that involved both stochastic and deterministic simulations) was the discovery of a dynamical process responsible for the phenomenon, namely, the upward progression of self-organized layers induced by a plane boundary. Indeed, its occurrence in both simulation models suggests the universality of this mechanism in density relaxation which, to our knowledge, had not been previously reported in the literature. An equally striking result was the identification of the existence of critical tap amplitude which optimizes the evolution process. This work has spurred the development of dynamical systems models by my colleague (Prof. D. Blackmore), using a first principals approach, which in turn enabled us to initiate a collaboration with Prof. Tricoche, a computer scientist at Purdue University with expertise in identifying and characterizing dynamically evolving structures in large data sets.
Our collaboration has resulted in the publication of several peer-reviewed journal papers, conference papers and presentations.
Wave Propagation in Granular Systems
Validation of Continuum model in the propagation of wave phenomena in one-dimensional systems.
Density Relaxation in Granular Systems
One of the principal findings in the tapped density relaxation study (that involved both stochastic and deterministic simulations) was the discovery of a dynamical process responsible for the phenomenon, namely, the upward progression of self-organized layers induced by a plane boundary. Indeed, its occurrence in both simulation models suggests the universality of this mechanism in density relaxation which, to our knowledge, had not been previously reported in the literature. An equally striking result was the identification of the existence of critical tap amplitude which optimizes the evolution process. This work has spurred the development of dynamical systems models by my colleague (Prof. D. Blackmore), using a first principals approach, which in turn enabled us to initiate a collaboration with Prof. Tricoche, a computer scientist at Purdue University with expertise in identifying and characterizing dynamically evolving structures in large data sets.
Our collaboration has resulted in the publication of several peer-reviewed journal papers, conference papers and presentations.
Wave Propagation in Granular Systems
Validation of Continuum model in the propagation of wave phenomena in one-dimensional systems.
Journal Article
Benouaguef, Islam, & Musunuri, N, & Amah, E, & Blackmore, Denis, & Fischer, Ian, & Singh, Pushpendra (2021). Solutocapillary Marangoni flow induced in a waterbody by a solute source. Journal of Fluid Mechanics, Volume 922,
Blackmore, Denis, & Benouaguef, Islam, & Musunuri, Naga, & Amah, Edison, & Fischer, Ian, & Singh, Pushpendra (2021). Solutocapillary Marangoni flow induced in a waterbody by a solute source. Journal of Fluid Mechanics, 922, A23 15 pgs..
Blackmore, Denis, & Murthy, Karthik, & Jordan, Ian, & Sojitra, Parth, & Rahman, Aminur (2020). Generalized attracting horseshoe in the Rössler attractor. Symmetry, 13, 12 pgs..
Blackmore, Denis, & Rahman, Aminur (2020). Interesting bifurcations in walking droplet dynamics. Commun. Nonlinear. Sci. Numer. Simulat., 90, 105348, 13 pgs..
Blackmore, Denis, & Rahman, Aminur (2020). Walking droplets through the lens of dynamical systems. Modern Phys. Lett. B, 34, 20320009, 22 pgs..
Blackmore, Denis, & Benouaguef, Islam, & Musunuri, Naga, & Amah, Edison, & Fischer, Ian, & Singh, Pushpendra (2021). Solutocapillary Marangoni flow induced in a waterbody by a solute source. Journal of Fluid Mechanics, 922, A23 15 pgs..
Blackmore, Denis, & Murthy, Karthik, & Jordan, Ian, & Sojitra, Parth, & Rahman, Aminur (2020). Generalized attracting horseshoe in the Rössler attractor. Symmetry, 13, 12 pgs..
Blackmore, Denis, & Rahman, Aminur (2020). Interesting bifurcations in walking droplet dynamics. Commun. Nonlinear. Sci. Numer. Simulat., 90, 105348, 13 pgs..
Blackmore, Denis, & Rahman, Aminur (2020). Walking droplets through the lens of dynamical systems. Modern Phys. Lett. B, 34, 20320009, 22 pgs..
SHOW MORE
Blackmore, Denis, & Balinsky, Alexander, & Kycia, Radoslaw, & Prykarpatski, Anatolij (2020). Geometric aspects of isentropic liquid dynamics and vorticity invariants. Entropy, 22, 1241, 26 pgs..
Blackmore, Denis, & Byszewski, Ludwik, & Balinsky, Alexander, & Prykarpatski, Anatolij, & Lustyk, M. (2020). Solvability, completeness and computational analysis of a perturbed control system with delays. Mathematics and Statistics , 8, 187-200.
Blackmore, Denis, & Artemovych, Orest, & Prykarpatski, Anatolij (2020). Non-associative structure of commutative algebras related with quadratic Poisson brackets. European Journal of Mathematics, 6, 21 pages.
Blackmore, Denis, & Samoilenko, Anatoliy, & Prykarpatsky, Yarema, & Prkarpatski, Anatolij (2019). Theory of multidimensional Delsarte--Lions transmutation operators. II. Ukranian Mathematics Journal, 71, 921-955.
Blackmore, Denis, & Hentosh, Oksana, & Prykarpatsky, Yarema, & Prykarpatski, Anatolij (2019). Dispersionless multi-dimensional integrable systems and related conformal structure generating equations of mathematical physics. SIGMA, 15, 20.
Blackmore, Denis, & Addabbo, Raymond (2019). A Dynamical Systems-Based Hierarchy for Shannon, Metric and Topological Entropy. Entropy, 21, 14 pages.
Blackmore, Denis, & Samoilenko, Anatoliy, & Prykarpatsky, Yarema, & Prykarpatski, Anatolij (2019). Theory of multidimensional Delsarte--Lions transmutation operators. I. Ukrainian Mathematical Journal, 70, 1913-1952.
Blackmore, Denis, & Hentosh, Oksana, & Kyshakevych, Bohdan, & Prykarpatski, Anatolij (2019). New Fractional Nonlinear Integrable Hamiltonian Systems. Applied Mathematics Letters, 88, 41-49.
Blackmore, Denis, & Artemovych, Orest, & Balinsky, Alexander, & Prykarpatski, Anatolij (2018). Reduced Pre-Lie Algebraic Structures, the Weak and Weakly Deformed Balinsky--Novikov Type Symmetry Algebras and Related Hamiltonian Operators. Symmetry, 10, 28 pages.
Blackmore, Denis, & Samoilenko, Anatoliy, & Prykarpatsky, Yarema, & Prykarpatski, Anatolij (2018). A novel integrability analysis of a generalized Riemann type hydrodynamic hierarchy. Miskolc Math. Notes, 27,
Blackmore, Denis, & Hentosh, Oksana, & Prykarpatsky, Yarema, & Prykarpatski, Anatolij (2018). Generalized Lie-algebraic structures related to integrable dispersionless dynamical systems and their application. Journal of Mathematical Science and Modelling, 1, 105-130..
Blackmore, Denis, & Artemovych, Orest, & Prykarpatski, Anatolij (2018). Examples of Lie and Balinsky--Novikov algebras related to Hamiltonian operators. Topological Algebra and Its Applications/de Gruyter, 6, 43-52.
Blackmore, Denis, & Rahman, Aminur, & Jordan, Ian (2018). Qualitative models and experimental investigation of chaotic NOR gates and set/reset flip-flops. Proceeding of the Royal Society A, 474, 18 pages.
Blackmore, Denis, & Rahman, Aminur, & Joshi, Yogesh (2017). Sigma Map Dynamics and Bifurcations. Regular & Chaotic Dynamics, 22, 740-749.
Blackmore, Denis, & Prykarpatski, Anatolij, & Vovk, M., & Pukach, P., & Prykarpatsky, Yarema (2017). The Pfeiffer-Lax-Sato vector field equations and related integrable versal deformations. Matematychni Studii, 48(2), 124-133.
Singh, Pushpendra, & Benouaguef, I. , & Musunuri, N., & Amah, E., & Blackmore, Denis, & Fischer, Ian (2017). Flow induced on a salt waterbody due to the impingement of a freshwater drop or a water source. Mechanics Research Communications, 85, 89–95.
Blackmore, Denis, & Rahman, Aminur (2017). Threshold voltage dynamics of chaotic RS flip-flops. Chaos, Solitons & Fractals , 103, 555-566.
Blackmore, Denis, & Windows-Yule, C.R.K., & Rosato, Anthony (2017). Energy decay in a tapped granular column: Can a one-dimensional toy model provide insight into fully three-dimensional systems?. Phys. Rev. E, 96, 11.
Blackmore, Denis, & Hentosh, Oksana, & Prykarpatsky, Yarema, & Prykarpatski, Anatolij (2017). Lie-algebraic structure of Lax—Sato integrable heavenly equations and the Lagrange—d’Alembert principle. J. Geometry & Phys. , 120, 208-227.
Blackmore, Denis, & Soltanov, Kamal, & Prykarpatski, Anatolij (2017). Long-time behavior of solutions and chaos in reaction-diffusion equations . Chaos, Solitons & Fractals, 99, 91-100.
Blackmore, Denis, & Artemovych, Orest, & Prykarpatski, Anatolij (2017). Hamiltonian operators and related integrable differential-algebraic Novikov—Leibniz type structures . Asian Journal of Mathematical and Computational Research, 17, 184-203.
Blackmore, Denis, & Rosato, Anthony, & Sen, Surajit, & Wu, Hao (2017). Simulation, modeling and dynamical analysis of multibody flows. International Journal of Modern Physics B, 31, 14 pages.
Blackmore, Denis, & Artemovych, Orest, & Prykarpatski, Anatolij (2017). Poisson brackets, Novikov—Leibniz structures and integrable Riemann hydrodynamic systems. Journal of Nonlinear Mathematical Physics , 24, 41-72.
Blackmore, Denis, & Hentosh, Oksana, & Prykarpatski, Anatolij (2017). The novel Lie-algebraic approach to studying integrable heavenly type equations. Journal of Generalized Lie Theory and Applications , 11(3), 19 pages.
Blackmore, Denis, & Rahman, Aminur (2016). Neimark—Sacker bifurcations and evidence of chaos in a discrete dynamical system model of walkers. Chaos, Solitons & Fractals, 91, 339-349.
Rosato, Anthony, & Zuo, Luo, & Blackmore, Denis, & Wu, Hao, & Horntrop, David, & Parker, David, & Windows-Yule, Christopher (2016). Tapped granular column dynamics: simulations, experiments and modeling. Computational Particle Mechanics, 3(3), 333-348.
Blackmore, Denis, & Bogolubov Jr., Nikolai, & Prykarpatsky, Anatoliy (2016). The Lagrangian and Hamiltonian aspects of the electromagnetic vacuum-field theory models. Boson J. Modern Phys. , 2, 92 pages.
Blackmore, Denis, & Rohn, Eli (2015). The augmented unified localizable crisis scale . Technological Forecasting and Social Change , 100, 186-197.
Blackmore, Denis, & Prykarpatsky, Anatoliy, & Özçag, E. , & Soltanov, Kamal (2015). Integrability analysis of a two-component Burgers type hierarchy. Ukr. Math. J., 67, 167- 185.
Blackmore, Denis, & Bogolubov Jr., Nikolai, & Prykarpatsky, Anatoliy (2015). Maxwell--Lorentz electrodynamics models revisited via the Lagrangian formalism and the Feynman proper time paradigm. Mathematics, 3, 190-257.
Blackmore, Denis, & Joshi, Yogesh (2014). Strange attractors for asymptotically zero maps. Chaos, Solitons & Fractals, 68, 123-138.
Blackmore, Denis, & Prykarpatsky, Anatoliy (2014). Dark equations and their light integrability. Journal of Nonlinear Mathematical Physics, 21 , 407-428..
Blackmore, Denis, & Prykarpatsky, Yarema, & Bogolubov (Jr.), Nikolai, & Prykarpatsky, Anatoliy (2014). Integrability of and differential-algebraic structures for spatially 1D hydrodynamics systems of Riemann type. Chaos, Solitons & Fractals, 59, 59-81.
Blackmore, Denis, & Rosato, Anthony, & Tricoche, Xavier, & Urban, Kevin, & Zuo, Luo (2014). Analysis, Simulation, Visualizaiton of 1D Tapping via Reduced Dynamical Systems Models. Physica D, 273-74, 14-27.
Blackmore, Denis, & Prykarpatsky, Yarema, & Golenia, Jolanta, & Prykarpatsky, Anatoliy (2013). Hidden symmetry analysis of Lax integrable nonlinear systems. Applied Mathematics, 4, 96-116.
Blackmore, Denis, & Prykarpatsky, Anatoliy, & Bogolubov (Jr.), Nikolai, & Slawianowski, Jan (2013). Mathematical foundations of the classical Maxwell-Lorentz electrodynamic model via canonical Lagrangian and Hamiltonian. Universal Journal of Physics and Applications, 1(2), 160-178.
Blackmore, Denis, & Prykarpatsky, Anatoliy (2013). New vortex invariants in magneto-hydrodynamics and a related helicity theorem. Chaotic Modeling and Simulation , 2, 239-245.
Blackmore, Denis, & Prykarpatsky, Anatoliy (2013). A new exactly solvable spatially one-dimensional quantum superradiance Fermi-medium model and its quantum solitonic states. Condensed Matter Physics, 16, 1-9.
Blackmore, Denis, & Prykarpatsky, Yarema, & Golenia, Jolanta, & Prykarpatsky, Anatoliy (2013). Invariant measures for discrete dynamical systems and ergodic properties of generalized Boole type transformations. Ukrainian Mathematics Journal, 65(1), 44-57.
Blackmore, Denis, & Prykarpatsky, Yarema, & Golenia, Jolanta, & Prykarpatsky, Anatoliy (2013). A vertex operator representation of solutions to a Gurevich--Zybin hydrodynamical system. Opuscula Mathematica, 33(1), 139-149 .
Blackmore, Denis, & Ratnaswamy, Vish, & Rosato, Anthony, & Tricoche, Xavier, & Ching, Nathaniel, & Zuo, Luo (2012). Evolution of solids fraction surfaces in tapping: Simulation and dynamical systems analysis. Granular Matter, 14, 169-174.
Blackmore, Denis, & Joshi, Yogesh (2012). Exponentially decaying discrete dynamical systems. Recent Patents on Space Tech, 2(1), 37-48.
Ratnaswamy, Vishagan, & Rosato, Anthony, & Blackmore, Denis, & Tricoche, Xavier, & Ching, Nathaniel, & Zuo, Luo (2012). Evolution of Solids Fraction Surfaces in Tapping: Simulation and Dynamic Systems Analysis. Granular Matter, 14, 163-168.
Blackmore, Denis, & Prykarpatsky, Anatoliy (2012). The AKNS hierarchy revisited: A vertex operator approach and its Lie-algebraic structure. J. Nonlinear Math. Phys., 19, 15 pages.
Blackmore, Denis, & Prykarpatsky, Anatoliy, & Prykarpatsky, Yarema (2012). Isospectral integrability analysis of dynamical systems on discrete manifolds. Opuscula Math. , 32(1), 41-66.
Blackmore, Denis, & Prykarpatsky, Yarema, & Golenia, Jolanta, & Prykarpatsky, Anatoliy (2011). The AKNS hierarchy and the Gurevich--Zybin dynamical system integrability revisited. Math. Bull. Shevchenko Scientific Soc, 8, 258-282.
Blackmore, Denis, & Rosato, Anthony, & Tricoche, Xavier, & Urban, Kevin, & Ratnaswamy, Vishagan (2011). Tapping dynamics for a column of particles and beyond. J. Mech. Materials & Structures, 6, 71-86 .
Blackmore, Denis, & Urban, Kevin, & Rosato, Anthony (2010). Integrability analysis of regular and fractional Blackmore-Samulyak-Rosato fields. Condensed Matter Physics, 13, 43403: 1-7.
Blackmore, Denis, & Joshi, Yogesh (2010). Bifurcation and chaos in higher dimensional pioneer-climax systems. Int’l. Electronic J. Pure and Appl. Math., 1(3), 303-337.
Blackmore, Denis, & Zhou, J., & Vas, A. (2010). Fractal geometry surface modeling and measurement for musical cymbal surface texture design and rapid manufacturing. Periodical of Key Engineering Materials, 437, 145-149.
Blackmore, Denis, & Prykarpatsky, Anatoliy (2009). A solution set analysis of a nonlinear operator equation using a. Topology, 48, 182-185.
Blackmore, Denis, & Rohn, Eli (2009). A unified localizable emergency events scale. Int. J. Information Sys. for Crisis Response & Management (IJISCRAM), 1(1), 1-14.
Blackmore, Denis, & Wang, Xiaxia, & Wang, Chengwen (2009). The ω-limit sets of a flow and periodic orbits. Chaos, Solitons and Fractals, 41, 2690-2696.
Blackmore, Denis, & Wang, Chengwen, & Wang, Xiaoxia (2009). Upper and lower solutions method for a superlinear Duffing equation. Communications in Applied Nonlinear Analysis, 16, 19-29.
Blackmore, Denis, & Gafiychuk, V., & Datsko, B., & Meleshko, V. (2009). Analysis of the solutions of coupled nonlinear fractional reaction-diffusion equations. Chaos, Solitons and Fractals/Elsevier, 41, 1095-1104.
Blackmore, Denis, & Rahman, A., & Shah, J. (2009). Discrete dynamical modeling and analysis of the R-S flip-flop circuit. Chaos, Solitons and Fractals/Elsevier, 42, 951-963.
Blackmore, Denis, & Brons, Morten, & Goullet, Arnaud (2008). A coaxial vortex ring model for vortex breakdown. Physica D/Elsevier, 237, 2817-2844.
Rosato, Anthony, & Blackmore, Denis, & Buckley, Liam, & Oshman, Christopher, & Johnson, Mark (2004). Experimental, Simulation and Nonlinear Dynamics Analysis of Galton’s Board. International Journal of Nonlinear Sciences and Numerical Simulation , 5(4), 289-312.
Rosato, Anthony, & Blackmore, Denis, & Zhang, Ninghua, & Lan, Yidan (2002). A Perspective of Vibration-Induced Size Segregation of Granular Materials. Chemical Engineering Science, 57(2), 265-275.
Blackmore, Denis, & Samulyak, Roman, & Rosato, Anthony (2001). Chaos in Vibrating Granular Flows. Dynamic Systems and Applications, 3, 77-84.
Blackmore, Denis, & Samulyak, Roman, & Rosato, Anthony New Mathematical Models for Particle Flow Dynamics. Journal of Nonlinear Mathematical Physics, 6(2), 198-221.
Blackmore, Denis, & Byszewski, Ludwik, & Balinsky, Alexander, & Prykarpatski, Anatolij, & Lustyk, M. (2020). Solvability, completeness and computational analysis of a perturbed control system with delays. Mathematics and Statistics , 8, 187-200.
Blackmore, Denis, & Artemovych, Orest, & Prykarpatski, Anatolij (2020). Non-associative structure of commutative algebras related with quadratic Poisson brackets. European Journal of Mathematics, 6, 21 pages.
Blackmore, Denis, & Samoilenko, Anatoliy, & Prykarpatsky, Yarema, & Prkarpatski, Anatolij (2019). Theory of multidimensional Delsarte--Lions transmutation operators. II. Ukranian Mathematics Journal, 71, 921-955.
Blackmore, Denis, & Hentosh, Oksana, & Prykarpatsky, Yarema, & Prykarpatski, Anatolij (2019). Dispersionless multi-dimensional integrable systems and related conformal structure generating equations of mathematical physics. SIGMA, 15, 20.
Blackmore, Denis, & Addabbo, Raymond (2019). A Dynamical Systems-Based Hierarchy for Shannon, Metric and Topological Entropy. Entropy, 21, 14 pages.
Blackmore, Denis, & Samoilenko, Anatoliy, & Prykarpatsky, Yarema, & Prykarpatski, Anatolij (2019). Theory of multidimensional Delsarte--Lions transmutation operators. I. Ukrainian Mathematical Journal, 70, 1913-1952.
Blackmore, Denis, & Hentosh, Oksana, & Kyshakevych, Bohdan, & Prykarpatski, Anatolij (2019). New Fractional Nonlinear Integrable Hamiltonian Systems. Applied Mathematics Letters, 88, 41-49.
Blackmore, Denis, & Artemovych, Orest, & Balinsky, Alexander, & Prykarpatski, Anatolij (2018). Reduced Pre-Lie Algebraic Structures, the Weak and Weakly Deformed Balinsky--Novikov Type Symmetry Algebras and Related Hamiltonian Operators. Symmetry, 10, 28 pages.
Blackmore, Denis, & Samoilenko, Anatoliy, & Prykarpatsky, Yarema, & Prykarpatski, Anatolij (2018). A novel integrability analysis of a generalized Riemann type hydrodynamic hierarchy. Miskolc Math. Notes, 27,
Blackmore, Denis, & Hentosh, Oksana, & Prykarpatsky, Yarema, & Prykarpatski, Anatolij (2018). Generalized Lie-algebraic structures related to integrable dispersionless dynamical systems and their application. Journal of Mathematical Science and Modelling, 1, 105-130..
Blackmore, Denis, & Artemovych, Orest, & Prykarpatski, Anatolij (2018). Examples of Lie and Balinsky--Novikov algebras related to Hamiltonian operators. Topological Algebra and Its Applications/de Gruyter, 6, 43-52.
Blackmore, Denis, & Rahman, Aminur, & Jordan, Ian (2018). Qualitative models and experimental investigation of chaotic NOR gates and set/reset flip-flops. Proceeding of the Royal Society A, 474, 18 pages.
Blackmore, Denis, & Rahman, Aminur, & Joshi, Yogesh (2017). Sigma Map Dynamics and Bifurcations. Regular & Chaotic Dynamics, 22, 740-749.
Blackmore, Denis, & Prykarpatski, Anatolij, & Vovk, M., & Pukach, P., & Prykarpatsky, Yarema (2017). The Pfeiffer-Lax-Sato vector field equations and related integrable versal deformations. Matematychni Studii, 48(2), 124-133.
Singh, Pushpendra, & Benouaguef, I. , & Musunuri, N., & Amah, E., & Blackmore, Denis, & Fischer, Ian (2017). Flow induced on a salt waterbody due to the impingement of a freshwater drop or a water source. Mechanics Research Communications, 85, 89–95.
Blackmore, Denis, & Rahman, Aminur (2017). Threshold voltage dynamics of chaotic RS flip-flops. Chaos, Solitons & Fractals , 103, 555-566.
Blackmore, Denis, & Windows-Yule, C.R.K., & Rosato, Anthony (2017). Energy decay in a tapped granular column: Can a one-dimensional toy model provide insight into fully three-dimensional systems?. Phys. Rev. E, 96, 11.
Blackmore, Denis, & Hentosh, Oksana, & Prykarpatsky, Yarema, & Prykarpatski, Anatolij (2017). Lie-algebraic structure of Lax—Sato integrable heavenly equations and the Lagrange—d’Alembert principle. J. Geometry & Phys. , 120, 208-227.
Blackmore, Denis, & Soltanov, Kamal, & Prykarpatski, Anatolij (2017). Long-time behavior of solutions and chaos in reaction-diffusion equations . Chaos, Solitons & Fractals, 99, 91-100.
Blackmore, Denis, & Artemovych, Orest, & Prykarpatski, Anatolij (2017). Hamiltonian operators and related integrable differential-algebraic Novikov—Leibniz type structures . Asian Journal of Mathematical and Computational Research, 17, 184-203.
Blackmore, Denis, & Rosato, Anthony, & Sen, Surajit, & Wu, Hao (2017). Simulation, modeling and dynamical analysis of multibody flows. International Journal of Modern Physics B, 31, 14 pages.
Blackmore, Denis, & Artemovych, Orest, & Prykarpatski, Anatolij (2017). Poisson brackets, Novikov—Leibniz structures and integrable Riemann hydrodynamic systems. Journal of Nonlinear Mathematical Physics , 24, 41-72.
Blackmore, Denis, & Hentosh, Oksana, & Prykarpatski, Anatolij (2017). The novel Lie-algebraic approach to studying integrable heavenly type equations. Journal of Generalized Lie Theory and Applications , 11(3), 19 pages.
Blackmore, Denis, & Rahman, Aminur (2016). Neimark—Sacker bifurcations and evidence of chaos in a discrete dynamical system model of walkers. Chaos, Solitons & Fractals, 91, 339-349.
Rosato, Anthony, & Zuo, Luo, & Blackmore, Denis, & Wu, Hao, & Horntrop, David, & Parker, David, & Windows-Yule, Christopher (2016). Tapped granular column dynamics: simulations, experiments and modeling. Computational Particle Mechanics, 3(3), 333-348.
Blackmore, Denis, & Bogolubov Jr., Nikolai, & Prykarpatsky, Anatoliy (2016). The Lagrangian and Hamiltonian aspects of the electromagnetic vacuum-field theory models. Boson J. Modern Phys. , 2, 92 pages.
Blackmore, Denis, & Rohn, Eli (2015). The augmented unified localizable crisis scale . Technological Forecasting and Social Change , 100, 186-197.
Blackmore, Denis, & Prykarpatsky, Anatoliy, & Özçag, E. , & Soltanov, Kamal (2015). Integrability analysis of a two-component Burgers type hierarchy. Ukr. Math. J., 67, 167- 185.
Blackmore, Denis, & Bogolubov Jr., Nikolai, & Prykarpatsky, Anatoliy (2015). Maxwell--Lorentz electrodynamics models revisited via the Lagrangian formalism and the Feynman proper time paradigm. Mathematics, 3, 190-257.
Blackmore, Denis, & Joshi, Yogesh (2014). Strange attractors for asymptotically zero maps. Chaos, Solitons & Fractals, 68, 123-138.
Blackmore, Denis, & Prykarpatsky, Anatoliy (2014). Dark equations and their light integrability. Journal of Nonlinear Mathematical Physics, 21 , 407-428..
Blackmore, Denis, & Prykarpatsky, Yarema, & Bogolubov (Jr.), Nikolai, & Prykarpatsky, Anatoliy (2014). Integrability of and differential-algebraic structures for spatially 1D hydrodynamics systems of Riemann type. Chaos, Solitons & Fractals, 59, 59-81.
Blackmore, Denis, & Rosato, Anthony, & Tricoche, Xavier, & Urban, Kevin, & Zuo, Luo (2014). Analysis, Simulation, Visualizaiton of 1D Tapping via Reduced Dynamical Systems Models. Physica D, 273-74, 14-27.
Blackmore, Denis, & Prykarpatsky, Yarema, & Golenia, Jolanta, & Prykarpatsky, Anatoliy (2013). Hidden symmetry analysis of Lax integrable nonlinear systems. Applied Mathematics, 4, 96-116.
Blackmore, Denis, & Prykarpatsky, Anatoliy, & Bogolubov (Jr.), Nikolai, & Slawianowski, Jan (2013). Mathematical foundations of the classical Maxwell-Lorentz electrodynamic model via canonical Lagrangian and Hamiltonian. Universal Journal of Physics and Applications, 1(2), 160-178.
Blackmore, Denis, & Prykarpatsky, Anatoliy (2013). New vortex invariants in magneto-hydrodynamics and a related helicity theorem. Chaotic Modeling and Simulation , 2, 239-245.
Blackmore, Denis, & Prykarpatsky, Anatoliy (2013). A new exactly solvable spatially one-dimensional quantum superradiance Fermi-medium model and its quantum solitonic states. Condensed Matter Physics, 16, 1-9.
Blackmore, Denis, & Prykarpatsky, Yarema, & Golenia, Jolanta, & Prykarpatsky, Anatoliy (2013). Invariant measures for discrete dynamical systems and ergodic properties of generalized Boole type transformations. Ukrainian Mathematics Journal, 65(1), 44-57.
Blackmore, Denis, & Prykarpatsky, Yarema, & Golenia, Jolanta, & Prykarpatsky, Anatoliy (2013). A vertex operator representation of solutions to a Gurevich--Zybin hydrodynamical system. Opuscula Mathematica, 33(1), 139-149 .
Blackmore, Denis, & Ratnaswamy, Vish, & Rosato, Anthony, & Tricoche, Xavier, & Ching, Nathaniel, & Zuo, Luo (2012). Evolution of solids fraction surfaces in tapping: Simulation and dynamical systems analysis. Granular Matter, 14, 169-174.
Blackmore, Denis, & Joshi, Yogesh (2012). Exponentially decaying discrete dynamical systems. Recent Patents on Space Tech, 2(1), 37-48.
Ratnaswamy, Vishagan, & Rosato, Anthony, & Blackmore, Denis, & Tricoche, Xavier, & Ching, Nathaniel, & Zuo, Luo (2012). Evolution of Solids Fraction Surfaces in Tapping: Simulation and Dynamic Systems Analysis. Granular Matter, 14, 163-168.
Blackmore, Denis, & Prykarpatsky, Anatoliy (2012). The AKNS hierarchy revisited: A vertex operator approach and its Lie-algebraic structure. J. Nonlinear Math. Phys., 19, 15 pages.
Blackmore, Denis, & Prykarpatsky, Anatoliy, & Prykarpatsky, Yarema (2012). Isospectral integrability analysis of dynamical systems on discrete manifolds. Opuscula Math. , 32(1), 41-66.
Blackmore, Denis, & Prykarpatsky, Yarema, & Golenia, Jolanta, & Prykarpatsky, Anatoliy (2011). The AKNS hierarchy and the Gurevich--Zybin dynamical system integrability revisited. Math. Bull. Shevchenko Scientific Soc, 8, 258-282.
Blackmore, Denis, & Rosato, Anthony, & Tricoche, Xavier, & Urban, Kevin, & Ratnaswamy, Vishagan (2011). Tapping dynamics for a column of particles and beyond. J. Mech. Materials & Structures, 6, 71-86 .
Blackmore, Denis, & Urban, Kevin, & Rosato, Anthony (2010). Integrability analysis of regular and fractional Blackmore-Samulyak-Rosato fields. Condensed Matter Physics, 13, 43403: 1-7.
Blackmore, Denis, & Joshi, Yogesh (2010). Bifurcation and chaos in higher dimensional pioneer-climax systems. Int’l. Electronic J. Pure and Appl. Math., 1(3), 303-337.
Blackmore, Denis, & Zhou, J., & Vas, A. (2010). Fractal geometry surface modeling and measurement for musical cymbal surface texture design and rapid manufacturing. Periodical of Key Engineering Materials, 437, 145-149.
Blackmore, Denis, & Prykarpatsky, Anatoliy (2009). A solution set analysis of a nonlinear operator equation using a. Topology, 48, 182-185.
Blackmore, Denis, & Rohn, Eli (2009). A unified localizable emergency events scale. Int. J. Information Sys. for Crisis Response & Management (IJISCRAM), 1(1), 1-14.
Blackmore, Denis, & Wang, Xiaxia, & Wang, Chengwen (2009). The ω-limit sets of a flow and periodic orbits. Chaos, Solitons and Fractals, 41, 2690-2696.
Blackmore, Denis, & Wang, Chengwen, & Wang, Xiaoxia (2009). Upper and lower solutions method for a superlinear Duffing equation. Communications in Applied Nonlinear Analysis, 16, 19-29.
Blackmore, Denis, & Gafiychuk, V., & Datsko, B., & Meleshko, V. (2009). Analysis of the solutions of coupled nonlinear fractional reaction-diffusion equations. Chaos, Solitons and Fractals/Elsevier, 41, 1095-1104.
Blackmore, Denis, & Rahman, A., & Shah, J. (2009). Discrete dynamical modeling and analysis of the R-S flip-flop circuit. Chaos, Solitons and Fractals/Elsevier, 42, 951-963.
Blackmore, Denis, & Brons, Morten, & Goullet, Arnaud (2008). A coaxial vortex ring model for vortex breakdown. Physica D/Elsevier, 237, 2817-2844.
Rosato, Anthony, & Blackmore, Denis, & Buckley, Liam, & Oshman, Christopher, & Johnson, Mark (2004). Experimental, Simulation and Nonlinear Dynamics Analysis of Galton’s Board. International Journal of Nonlinear Sciences and Numerical Simulation , 5(4), 289-312.
Rosato, Anthony, & Blackmore, Denis, & Zhang, Ninghua, & Lan, Yidan (2002). A Perspective of Vibration-Induced Size Segregation of Granular Materials. Chemical Engineering Science, 57(2), 265-275.
Blackmore, Denis, & Samulyak, Roman, & Rosato, Anthony (2001). Chaos in Vibrating Granular Flows. Dynamic Systems and Applications, 3, 77-84.
Blackmore, Denis, & Samulyak, Roman, & Rosato, Anthony New Mathematical Models for Particle Flow Dynamics. Journal of Nonlinear Mathematical Physics, 6(2), 198-221.
COLLAPSE
Conference Abstract
Direct Numerical Simulations of Electrorheological Fluids
ASME Paper Number AJKFLUIDS2019-5452, July (3rd Quarter/Summer) 2019
Solutocapillary Flow Induced by a Freshwater Source
ASME Paper Number AJKFLUIDS2019-5576, July (3rd Quarter/Summer) 2019
ASME Paper Number AJKFLUIDS2019-5452, July (3rd Quarter/Summer) 2019
Solutocapillary Flow Induced by a Freshwater Source
ASME Paper Number AJKFLUIDS2019-5576, July (3rd Quarter/Summer) 2019
Conference Proceeding
The dispersionless integrable systems and related conformal structure generating equations of mathematical physics
Easy Chair, February 2019
Studies of flow induced on a water surface due to the impingement of a drop or a water source
American Society of Mechanical Engineers, Fluids Engineering Division (Publication) FEDSM, October (4th Quarter/Autumn) 2017
Overview of continuous and discrete Rosato, A., Blackmore, D., Horntrop, D., Zuo, L., Wu, H., Parker, D. and Windows-Yule, C., Overview of continuous and discrete modeling of a tapped column
ASCE 2015 Eng. Mech. Conf. Proceedings, August 2015
Dynamical Systems Model and Discrete Element Simulations of a Tapped Granular Column
Powders and Grains 2013, American Institute of Physics, June 2013
On new invariants in MHD and a related helicity theorem
Proc.Dubrovin Int. Conf. on Geometrical Methods in Math. Phys. in SIGMA (online), December 2011
Easy Chair, February 2019
Studies of flow induced on a water surface due to the impingement of a drop or a water source
American Society of Mechanical Engineers, Fluids Engineering Division (Publication) FEDSM, October (4th Quarter/Autumn) 2017
Overview of continuous and discrete Rosato, A., Blackmore, D., Horntrop, D., Zuo, L., Wu, H., Parker, D. and Windows-Yule, C., Overview of continuous and discrete modeling of a tapped column
ASCE 2015 Eng. Mech. Conf. Proceedings, August 2015
Dynamical Systems Model and Discrete Element Simulations of a Tapped Granular Column
Powders and Grains 2013, American Institute of Physics, June 2013
On new invariants in MHD and a related helicity theorem
Proc.Dubrovin Int. Conf. on Geometrical Methods in Math. Phys. in SIGMA (online), December 2011
SHOW MORE
Dynamical Systems-Simulation-Visualization Approach to Tapping and Other Granular Flow Phenomena: First Steps
Proc. NSF CMMI Grantees Conference, Jan. 4-7, 2011, January (1st Quarter/Winter) 2011
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, October (4th Quarter/Autumn) 2009
Two-vortex models for vortex breakdown
ASME Conference Journal/ASME/DSCC, June 2009
Dynamics of planar vortex clusters with binaries
PAMM/GAMM/ICIAM'07, December 2008
Invariant tori in perturbed three vortex motion
PAMM/GAMM/ICIAM'07, December 2008
Proc. NSF CMMI Grantees Conference, Jan. 4-7, 2011, January (1st Quarter/Winter) 2011
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, October (4th Quarter/Autumn) 2009
Two-vortex models for vortex breakdown
ASME Conference Journal/ASME/DSCC, June 2009
Dynamics of planar vortex clusters with binaries
PAMM/GAMM/ICIAM'07, December 2008
Invariant tori in perturbed three vortex motion
PAMM/GAMM/ICIAM'07, December 2008
COLLAPSE
Chapter
Blackmore, Denis, & Hentosh, Oksana, & Prykarpatsky, Yarema, & Prykarpatski, Anatolij (2018). Pfeifer-Sato solutions of Buhl's problem and a Lagrange--d'Alembert principle for heavenly equations, Norbert Euler (Ed.), CRC Press. (pp. 187 - 222). CRC Press
Blackmore, Denis, & Wang, Chengwen (2011). Recent advances in periodicity in dynamical systems , Advances in Mathematical Research/Nova Science Publ.. (pp. 1-47). Long Island, New York: Advances in Mathematical Research/Nova Science Publ.
Blackmore, Denis, & Wang, Chengwen (2011). Recent advances in periodicity in dynamical systems , Advances in Mathematical Research/Nova Science Publ.. (pp. 1-47). Long Island, New York: Advances in Mathematical Research/Nova Science Publ.
Other
Advances in Systems Dynamics
Mechanics Research Communications-Special Issue/Elsevier, June 2017
A Dynamical Systems-Simulation-Visualization Approach to Tapping and Other Granular Flow Phenomena: Second Steps
CMMI NSF Grantees Conf., June 2012
Tapping Dynamics: Theory and Applications
Gordon Conference, June 2010
Dynamics of Logical Circuits
FACM'10, May 2010
Proceedings of FACM'08 Dedicated to D.S. Ahluwalia on his Seventy-fifth Birthday
World Scientific, December 2008
Mechanics Research Communications-Special Issue/Elsevier, June 2017
A Dynamical Systems-Simulation-Visualization Approach to Tapping and Other Granular Flow Phenomena: Second Steps
CMMI NSF Grantees Conf., June 2012
Tapping Dynamics: Theory and Applications
Gordon Conference, June 2010
Dynamics of Logical Circuits
FACM'10, May 2010
Proceedings of FACM'08 Dedicated to D.S. Ahluwalia on his Seventy-fifth Birthday
World Scientific, December 2008
Magazine/Trade Publication
Interview on Fibonacci Numbers
Pea Green Boat (online magazine), August 2012
Pea Green Boat (online magazine), August 2012
Technical Report
Analysis of the Calogero Projection-Algebraic Scheme for Differential Operators
Abdus Salam International Centre for Theoretical Physics, August 2011
Optimal Strategy Analysis of Competing Portfolio Market with a Polyvariant Profit Function
Abdus Salam International Centre for Theoretical Physics, August 2011
Lagrangian and Hamiltonian Analysis of Infinite-dimensional Dynamical Systems
Abdus Salam International Centre for Theoretical Physics, July (3rd Quarter/Summer) 2011
Abdus Salam International Centre for Theoretical Physics, August 2011
Optimal Strategy Analysis of Competing Portfolio Market with a Polyvariant Profit Function
Abdus Salam International Centre for Theoretical Physics, August 2011
Lagrangian and Hamiltonian Analysis of Infinite-dimensional Dynamical Systems
Abdus Salam International Centre for Theoretical Physics, July (3rd Quarter/Summer) 2011
Book
Blackmore, Denis, & Prykarpatsky, Anatoliy, & Samoylenko, Valeriy (2011). Nonlinear Dynamical Systems of Mathematical Physics: Spectral and Symplectic Integrability Analysis. World Scientific Publ.
Rosato, Anthony, & Blackmore, Denis (2000). IUTAM Symposium on Segregation in Granular Flows. Dordrecht, The Netherlands: Kluwer Academic Publishers
Rosato, Anthony, & Blackmore, Denis (2000). IUTAM Symposium on Segregation in Granular Flows. Dordrecht, The Netherlands: Kluwer Academic Publishers