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..
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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
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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