Extending Ornstein-Uhlenbeck process with added memory (2007-2011)
Applying Brownian motion to modeling bioturbation phenomena (2011 - 2013)
Recent publications:
"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.
NSF Grants:
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
Distance-To-Empty: Better Prediction, Supervision of Mingyu Chen, Anh Duong, and Xue Gan's senior project, Spring 2016
Elastic Balls Collisions Within a 3D Container, Natalie Khalil, Summer 2016
Differential Equations: Beyond the Basics, Kendal Karch, Summer-Fall 2016
Center-of-Mass Considerations in Hierarchical Elastic Collisions, Stefano Monzon, Fall 2016 - Spring 2017
Energy Transfer in Hierarchical Elastic Collisions, Stefano Monzon, Isabelle Gehrs (PURE), and Omar Khan (PURE) June - August 2017 (See pictures)
Creative Collaborations Conference April 19, 2018 (See pictures)