- •Modeling Brownian motion (2005-2007)
- •Extending Ornstein-Uhlenbeck process with added memory (2007-2011)
- •Applying Brownian motion to modeling bioturbation phenomena (2011 - 2013)
- •"Brownian Motion with Inert Drift, but Without a Flux: a Model" (with K. Burdzy. R. Holyst), Physica A 384(2007) 278-284
- •"Fractal Trace of Earthworm" (with K. Burdzy, R. Holyst), Phys. Rev. E 87, 052120 (2013)
- •"An Integrative Approach to Teaching Mathematics, Computer Science and Physics with MATLAB" (with J. Friedman). Mathematics and Computer Science Education, , Vol. 48, No. 1, p. 6-18, 2014.
- •Co-PI on a NSF-funded S-STEM grant ($598,000), Attracting students to Computer Science, Mathematics and Physics at USD (2010 - 2015)
- •Co-PI on a NSF-funded S-STEM grant, Supporting Students for Success in Mathematics, Computer Science and Physics at the University of San Diego (2015 - )
Recent Research Projects Conducted with Students
- •Neural Networks Learn Algebra and Calculus, Sara Salerno, USD SURE, 2002
- •Finding Initial Bounding Functions for the Chaplygin Method of Solving First-Order Differential Equations, Brian Sullivan, USD SURE, 2003
- •Extending the Ornstein-Uhlenbeck Process: From Randomness to Order, James Gill, USD SURE, 2009
- •3D Brownian Motion in an Incompressible Medium, Nicholas Nobles, McNair, 2012
- •Interpolation Search, Standard and Improved, vs. Other Searching Methods, Michael Habana, Mater Dei High School Internship, 2012
- •Modeling Motor Coordination with an Android Device, Independent study with Theresa Chadwick, Spring 2014
- •Using Android to Aid Athletes, Supervision of Luis Retana's senior thesis, Spring 2014
- •Using Difference Equations and MATLAB to Model Biological and Economics Processes, Luis Foglio, Mater Dei High School Internship, Summer 2014
- •A Voxel-Based Game Engine, Supervision of James Ruther's senior project, Spring 2015
- •Biomechanics of sports and optimization of sports strategies
- •Mathematical modeling and digital simulation
- •Heuristics in mathematical problem solving
- •Misconceptions and errors in novice computer programming
- •Neural networks and machine learning
