David Horntrop

Associate Professor, Mathematical Sciences

627 Cullimore Hall

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

2022 Fall Courses

MATH 790B - DOCT DISSERTATION & RES

MATH 448 - STOCHASTIC SIMULATION

MATH 790E - DOCTORAL DISSERTATION

MATH 448 - STOCHASTIC SIMULATION

MATH 790E - DOCTORAL DISSERTATION

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

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

Rosato, Anthony, & Dybenko, Oleksandr, & Ratnaswamy, Vishagan, & Horntrop, David, & Kondic, Lou (2010). Microstructure Development in Tapped Granular Systems.

Horntrop, David (2010). Concentration Effects in Mesoscopic Simulation of Coarsening.

*Computational Particle Mechanics*,*3*(3), 333-348.Rosato, Anthony, & Dybenko, Oleksandr, & Ratnaswamy, Vishagan, & Horntrop, David, & Kondic, Lou (2010). Microstructure Development in Tapped Granular Systems.

*Physical Review E*,*81*(061301), 1-10.Horntrop, David (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