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.

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.

Blackmore, Denis, & Benouaguef, Islam, & Musunuri, Naga, & Amah, Edison, & Fischer, Ian, & Singh, Pushpendra (2021). Solutocapillary Marangoni flow induced in a waterbody by a solute source.

Blackmore, Denis, & Murthy, Karthik, & Jordan, Ian, & Sojitra, Parth, & Rahman, Aminur (2020). Generalized attracting horseshoe in the Rössler attractor.

Blackmore, Denis, & Rahman, Aminur (2020). Interesting bifurcations in walking droplet dynamics.

Blackmore, Denis, & Rahman, Aminur (2020). Walking droplets through the lens of dynamical systems.

*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.. SHOW MORE

Blackmore, Denis, & Balinsky, Alexander, & Kycia, Radoslaw, & Prykarpatski, Anatolij (2020). Geometric aspects of isentropic liquid dynamics and vorticity invariants.

Blackmore, Denis, & Byszewski, Ludwik, & Balinsky, Alexander, & Prykarpatski, Anatolij, & Lustyk, M. (2020). Solvability, completeness and computational analysis of a perturbed control system with delays.

Blackmore, Denis, & Artemovych, Orest, & Prykarpatski, Anatolij (2020). Non-associative structure of commutative algebras related with quadratic Poisson brackets.

Blackmore, Denis, & Samoilenko, Anatoliy, & Prykarpatsky, Yarema, & Prkarpatski, Anatolij (2019). Theory of multidimensional Delsarte--Lions transmutation operators. II.

Blackmore, Denis, & Hentosh, Oksana, & Prykarpatsky, Yarema, & Prykarpatski, Anatolij (2019). Dispersionless multi-dimensional integrable systems and related conformal structure generating equations of mathematical physics.

Blackmore, Denis, & Addabbo, Raymond (2019). A Dynamical Systems-Based Hierarchy for Shannon, Metric and Topological Entropy.

Blackmore, Denis, & Samoilenko, Anatoliy, & Prykarpatsky, Yarema, & Prykarpatski, Anatolij (2019). Theory of multidimensional Delsarte--Lions transmutation operators. I.

Blackmore, Denis, & Hentosh, Oksana, & Kyshakevych, Bohdan, & Prykarpatski, Anatolij (2019). New Fractional Nonlinear Integrable Hamiltonian Systems.

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.

Blackmore, Denis, & Samoilenko, Anatoliy, & Prykarpatsky, Yarema, & Prykarpatski, Anatolij (2018). A novel integrability analysis of a generalized Riemann type hydrodynamic hierarchy.

Blackmore, Denis, & Hentosh, Oksana, & Prykarpatsky, Yarema, & Prykarpatski, Anatolij (2018). Generalized Lie-algebraic structures related to integrable dispersionless dynamical systems and their application.

Blackmore, Denis, & Artemovych, Orest, & Prykarpatski, Anatolij (2018). Examples of Lie and Balinsky--Novikov algebras related to Hamiltonian operators.

Blackmore, Denis, & Rahman, Aminur, & Jordan, Ian (2018). Qualitative models and experimental investigation of chaotic NOR gates and set/reset flip-flops.

Blackmore, Denis, & Rahman, Aminur, & Joshi, Yogesh (2017). Sigma Map Dynamics and Bifurcations.

Blackmore, Denis, & Prykarpatski, Anatolij, & Vovk, M., & Pukach, P., & Prykarpatsky, Yarema (2017). The Pfeiffer-Lax-Sato vector field equations and related integrable versal deformations.

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.

Blackmore, Denis, & Rahman, Aminur (2017). Threshold voltage dynamics of chaotic RS flip-flops.

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?.

Blackmore, Denis, & Hentosh, Oksana, & Prykarpatsky, Yarema, & Prykarpatski, Anatolij (2017). Lie-algebraic structure of Lax—Sato integrable heavenly equations and the Lagrange—d’Alembert principle.

Blackmore, Denis, & Soltanov, Kamal, & Prykarpatski, Anatolij (2017). Long-time behavior of solutions and chaos in reaction-diffusion equations .

Blackmore, Denis, & Artemovych, Orest, & Prykarpatski, Anatolij (2017). Hamiltonian operators and related integrable differential-algebraic Novikov—Leibniz type structures .

Blackmore, Denis, & Rosato, Anthony, & Sen, Surajit, & Wu, Hao (2017). Simulation, modeling and dynamical analysis of multibody flows.

Blackmore, Denis, & Artemovych, Orest, & Prykarpatski, Anatolij (2017). Poisson brackets, Novikov—Leibniz structures and integrable Riemann hydrodynamic systems.

Blackmore, Denis, & Hentosh, Oksana, & Prykarpatski, Anatolij (2017). The novel Lie-algebraic approach to studying integrable heavenly type equations.

Blackmore, Denis, & Rahman, Aminur (2016). Neimark—Sacker bifurcations and evidence of chaos in a discrete dynamical system model of walkers.

Rosato, Anthony, & Zuo, Luo, & Blackmore, Denis, & Wu, Hao, & Horntrop, David, & Parker, David, & Windows-Yule, Christopher (2016). Tapped granular column dynamics: simulations, experiments and modeling.

Blackmore, Denis, & Bogolubov Jr., Nikolai, & Prykarpatsky, Anatoliy (2016). The Lagrangian and Hamiltonian aspects of the electromagnetic vacuum-field theory models.

Blackmore, Denis, & Rohn, Eli (2015). The augmented unified localizable crisis scale .

Blackmore, Denis, & Prykarpatsky, Anatoliy, & Özçag, E. , & Soltanov, Kamal (2015). Integrability analysis of a two-component Burgers type hierarchy.

Blackmore, Denis, & Bogolubov Jr., Nikolai, & Prykarpatsky, Anatoliy (2015). Maxwell--Lorentz electrodynamics models revisited via the Lagrangian formalism and the Feynman proper time paradigm.

Blackmore, Denis, & Joshi, Yogesh (2014). Strange attractors for asymptotically zero maps.

Blackmore, Denis, & Prykarpatsky, Anatoliy (2014). Dark equations and their light integrability.

Blackmore, Denis, & Prykarpatsky, Yarema, & Bogolubov (Jr.), Nikolai, & Prykarpatsky, Anatoliy (2014). Integrability of and differential-algebraic structures for spatially 1D hydrodynamics systems of Riemann type.

Blackmore, Denis, & Rosato, Anthony, & Tricoche, Xavier, & Urban, Kevin, & Zuo, Luo (2014). Analysis, Simulation, Visualizaiton of 1D Tapping via Reduced Dynamical Systems Models.

Blackmore, Denis, & Prykarpatsky, Yarema, & Golenia, Jolanta, & Prykarpatsky, Anatoliy (2013). Hidden symmetry analysis of Lax integrable nonlinear systems.

Blackmore, Denis, & Prykarpatsky, Anatoliy, & Bogolubov (Jr.), Nikolai, & Slawianowski, Jan (2013). Mathematical foundations of the classical Maxwell-Lorentz electrodynamic model via canonical Lagrangian and Hamiltonian.

Blackmore, Denis, & Prykarpatsky, Anatoliy (2013). New vortex invariants in magneto-hydrodynamics and a related helicity theorem.

Blackmore, Denis, & Prykarpatsky, Anatoliy (2013). A new exactly solvable spatially one-dimensional quantum superradiance Fermi-medium model and its quantum solitonic states.

Blackmore, Denis, & Prykarpatsky, Yarema, & Golenia, Jolanta, & Prykarpatsky, Anatoliy (2013). Invariant measures for discrete dynamical systems and ergodic properties of generalized Boole type transformations.

Blackmore, Denis, & Prykarpatsky, Yarema, & Golenia, Jolanta, & Prykarpatsky, Anatoliy (2013). A vertex operator representation of solutions to a Gurevich--Zybin hydrodynamical system.

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.

Blackmore, Denis, & Joshi, Yogesh (2012). Exponentially decaying discrete dynamical systems.

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.

Blackmore, Denis, & Prykarpatsky, Anatoliy (2012). The AKNS hierarchy revisited: A vertex operator approach and its Lie-algebraic structure.

Blackmore, Denis, & Prykarpatsky, Anatoliy, & Prykarpatsky, Yarema (2012). Isospectral integrability analysis of dynamical systems on discrete manifolds.

Blackmore, Denis, & Prykarpatsky, Yarema, & Golenia, Jolanta, & Prykarpatsky, Anatoliy (2011). The AKNS hierarchy and the Gurevich--Zybin dynamical system integrability revisited.

Blackmore, Denis, & Rosato, Anthony, & Tricoche, Xavier, & Urban, Kevin, & Ratnaswamy, Vishagan (2011). Tapping dynamics for a column of particles and beyond.

Blackmore, Denis, & Urban, Kevin, & Rosato, Anthony (2010). Integrability analysis of regular and fractional Blackmore-Samulyak-Rosato fields.

Blackmore, Denis, & Joshi, Yogesh (2010). Bifurcation and chaos in higher dimensional pioneer-climax systems.

Blackmore, Denis, & Zhou, J., & Vas, A. (2010). Fractal geometry surface modeling and measurement for musical cymbal surface texture design and rapid manufacturing.

Blackmore, Denis, & Prykarpatsky, Anatoliy (2009). A solution set analysis of a nonlinear operator equation using a.

Blackmore, Denis, & Rohn, Eli (2009). A unified localizable emergency events scale.

Blackmore, Denis, & Wang, Xiaxia, & Wang, Chengwen (2009). The ω-limit sets of a flow and periodic orbits.

Blackmore, Denis, & Wang, Chengwen, & Wang, Xiaoxia (2009). Upper and lower solutions method for a superlinear Duffing equation.

Blackmore, Denis, & Gafiychuk, V., & Datsko, B., & Meleshko, V. (2009). Analysis of the solutions of coupled nonlinear fractional reaction-diffusion equations.

Blackmore, Denis, & Rahman, A., & Shah, J. (2009). Discrete dynamical modeling and analysis of the R-S flip-flop circuit.

Blackmore, Denis, & Brons, Morten, & Goullet, Arnaud (2008). A coaxial vortex ring model for vortex breakdown.

Rosato, Anthony, & Blackmore, Denis, & Buckley, Liam, & Oshman, Christopher, & Johnson, Mark (2004). Experimental, Simulation and Nonlinear Dynamics Analysis of Galton’s Board.

Rosato, Anthony, & Blackmore, Denis, & Zhang, Ninghua, & Lan, Yidan (2002). A Perspective of Vibration-Induced Size Segregation of Granular Materials.

Blackmore, Denis, & Samulyak, Roman, & Rosato, Anthony (2001). Chaos in Vibrating Granular Flows.

Blackmore, Denis, & Samulyak, Roman, & Rosato, Anthony New Mathematical Models for Particle Flow Dynamics.

*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.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.),

Blackmore, Denis, & Wang, Chengwen (2011). Recent advances in periodicity in dynamical systems ,

*CRC Press*. (pp. 187 - 222). CRC PressBlackmore, 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).

Rosato, Anthony, & Blackmore, Denis (2000).

*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