• Math 111H, Honors Calculus I
  • Syllabus
• Math 448, Stochastic Simulation
  • Syllabus

• Scientific computing
• Monte Carlo methods
• Numerical solution of stochastic equations
• Statistical mechanics
• Turbulent transport
• Fluid dynamics

The research of David J. Horntrop has focused on the development and numerical simulation of stochastic models of physical phenomena for problems ranging from materials science to fluid dynamics.  His studies of turbulent diffusion were based on random field models for the advection of passive scalars and involved asymptotics, stochastic analysis, and the creation of novel wavelet-based Monte Carlo numerical schemes for the simulation of random fields. 

His current studies of materials involve the development and use of mesoscopic models to describe surface processes in order to gain insight on the importance of small scale phenomena on the creation of large scale patterns.  He is presently developing and validating new spectral methods for the numerical solution of stochastic partial differential equations for these studies.

• Horntrop, D. and Majda, A., Subtle statistical behavior in simple models for random advection-diffusion, J. Math. Sci. Univ. Tokyo 1, 23-70, 1994.
• Horntrop, D., Monte Carlo Simulation for Turbulent Transport, Ph.D. Thesis, Program in Applied and Computational Mathematics, Princeton University, advisor: Andrew J. Majda, 1995.
• Elliott, F., Majda, A., Horntrop, D., and McLaughlin, R., Hierarchical Monte Carlo methods for fractal random fields, J. Stat. Phys. 81, 717-736, 1995.
• Elliott, F., Horntrop, D., and Majda, A., Monte Carlo methods for turbulent tracers with long range and fractal random velocity fields, Chaos 7, 39-48, 1997.
• Elliott, F., Horntrop, D., and Majda, A., A Fourier-wavelet Monte Carlo method for fractal random fields, J. Comp. Phys. 132, 384-408, 1997.
• Horntrop, D., and Majda, A., An overview of Monte Carlo simulation techniques for the generation of random fields, in Monte Carlo Simulations in Oceanography, Proceedings of the Ninth `Aha Huliko´a Hawaiian Winter Workshop. P. Muller and D. Henderson, editors, 67-79, 1997.
• Horntrop, D., Katsoulakis, M., and Vlachos, D., Spectral methods for mesoscopic models of pattern formations, J. Comp. Phys. 173, 364-390, 2001.
• Horntrop, D., Monte Carlo simulation of a random field model for transport, Monte Carlo Meth. App. 8, 31-49, 2002.
• Horntrop, D., Spectral schemes for stochastic partial differential equations, (under review).
• Horntrop, D., Mesoscopic simulation for self-organization in surface processes, in Computational Science--ICCS 2005, edited by V. Sunderam, et al, Springer Lecture Notes in Computer Science 3514, 851-859, 2005.
• Horntrop, D., Mesoscopic simulation of Ostwald ripening, J. Comp. Phys., 218, 429-441, 2006.
• Bailon, M., and Horntrop, D., On the calculation of convolutions with Gaussian kernels, Applied Math. Comp., 176, 383-387, 2006.
• Horntrop, D., Concentration effects in mesoscopic simulation of coarsening, (under review).
• Horntrop, D., A spectral method study of domain coarsening, Phys. Rev. E, 75, 046703, 2007.
• Dybenko, O., Rosato, A., and Horntrop, D., Three-dimensional Monte Carlo simulations of density relaxation, KONA Powder and Particle, 25, 133-144, 2007.