David Horntrop
David Horntrop
Associate Professor, Mathematical Sciences
627 Cullimore Hall (CULM)
Education
Ph.D.; Princeton University; Applied And Computational Mathematics; 1995
M.A.; Princeton University; Applied And Computational Mathematics; 1992
B.A.; Washington University in St Louis; Mathematics; 1990
B.S.; Washington University in St Louis; Systems Science And Engineering; 1990
M.A.; Princeton University; Applied And Computational Mathematics; 1992
B.A.; Washington University in St Louis; Mathematics; 1990
B.S.; Washington University in St Louis; Systems Science And Engineering; 1990
Website
2024 Fall Courses
MATH 448 - STOCHASTIC SIMULATION
Past Courses
MATH 111: CALCULUS I
MATH 111: CALCULUS I - HONORS
MATH 112: CALCULUS II
MATH 401: UNDERGRADUATE RESEARCH SEMINAR
MATH 448: STOCHASTIC SIMULATION
MATH 477: STOCHASTIC PROCESSES
MATH 605: STOCHASTIC CALCULUS
MATH 666: SIMULATION FOR FINANCE
MATH 111: CALCULUS I - HONORS
MATH 112: CALCULUS II
MATH 401: UNDERGRADUATE RESEARCH SEMINAR
MATH 448: STOCHASTIC SIMULATION
MATH 477: STOCHASTIC PROCESSES
MATH 605: STOCHASTIC CALCULUS
MATH 666: SIMULATION FOR FINANCE
In Progress
Application of Machine Learning to Discrete Interacting Particle Systems
Application of machine learning models to discrete interacting particle systems using recurrent neural networks, graph neural networks, and physics informed models.
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.
Application of machine learning models to discrete interacting particle systems using recurrent neural networks, graph neural networks, and physics informed models.
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.
Journal Article
Rosato, Anthony D., & Zuo, Luo, & Blackmore, Denis L., & Wu, Hao, & Horntrop, David J., & Parker, David, & Windows-Yule, Christopher (2016). Tapped granular column dynamics: simulations, experiments and modeling. Computational Particle Mechanics, 3(3), 333-348.
Rosato, Anthony D, & Zuo, Luo, & Blackmore, Denis L., & Horntrop, David J., & Parker, David J. , & Windows-Yule, Christopher (2015). Tapped Granular Column Dynamics: Simulations, Experiments and Modeling. Computational Particle Mechanics, 3(ISSN 2196-4378), 333-348.
Rosato, Anthony D., & Dybenko, Oleksandr, & Ratnaswamy, Vishagan, & Horntrop, David J., & Kondic, Lou (2010). Microstructure Development in Tapped Granular Systems. Physical Review E, 81(061301), 1-10.
Horntrop, David J. (2010). Concentration Effects in Mesoscopic Simulation of Coarsening. Math. Comp. Sim., 80(6), 1082-1088.
Rosato, Anthony D, & Zuo, Luo, & Blackmore, Denis L., & Horntrop, David J., & Parker, David J. , & Windows-Yule, Christopher (2015). Tapped Granular Column Dynamics: Simulations, Experiments and Modeling. Computational Particle Mechanics, 3(ISSN 2196-4378), 333-348.
Rosato, Anthony D., & Dybenko, Oleksandr, & Ratnaswamy, Vishagan, & Horntrop, David J., & Kondic, Lou (2010). Microstructure Development in Tapped Granular Systems. Physical Review E, 81(061301), 1-10.
Horntrop, David J. (2010). Concentration Effects in Mesoscopic Simulation of Coarsening. Math. Comp. Sim., 80(6), 1082-1088.
Conference Proceeding
Temporal dynamics in density relaxation
AIP Conference Proceedings, April (2nd Quarter/Spring) 2010
Density Relaxation of Granular Matter Through Monte Carlo Simulations
Springer, July (3rd Quarter/Summer) 2009
AIP Conference Proceedings, April (2nd Quarter/Spring) 2010
Density Relaxation of Granular Matter Through Monte Carlo Simulations
Springer, July (3rd Quarter/Summer) 2009