Recent Thoughts

I haven't had any. But I am trying hard, I promise.:-)
Meanwhile, here are the most recent (on-going) research activities.
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1. mathematical modeling of the spread of infectious diseases,
2. collective phenomena in animal motion: flocking and home ranges,
3. evolution of bacterial populations and the Fisher equation,
4. NMR microscopy for medical imaging and the Torrey-Bloch equation,
5. microscopic origin of friction,
6. tunneling of Bose-Einstein condensates in traps,
7. mobility of injected carriers in organic crystals and related transport issues.
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The first uses simple nonlinear models of mice-mice interaction and stability analysis as well as numerical procedures to understand key features of the spread of the Hanta virus. Collaborators are Luca Giuggioli (UNM), Guillermo Abramson and Marcelo Kuperman (Centro Atomico Bariloche, Argentina), and Terry Yates and Bob Parmenter (UNM).

The second and third attempt to analyze movement of animate beings of different sizes and types as a cooperative phenomenon, both dynamic and static aspects being of interest. Collaborators are Maximino Aldana (UNAM), Luca Giuggioli and Victor Dossetti (UNM).

The fourth, addresses the theory of NMR probes to study connectivity and other aspects of confined spaces as in pores of rock or blood vessels. This is in collaboration with Francisco Sevilla (UNM) and Miguel Fuentes (Centro Atomico Bariloche, Argentina).

The fifth is in collaboration with Sebastian Gonçalves (Porto Alegre) and Alan Bishop (Los Alamos).

The sixth utilizes similarities of the Gross-Pitaevskii and the nonlinear Schroedinger equations to study condensate tunneling. Collaborators are George Kalosakas and Alan Bishop (Los Alamos National Laboratory) as also Vladimir Konotop (Lisbon), Jayanthi Santhanam (UNM) and Srikanth Raghavan (Corning).

The seventh deals with dynamic and static disorder, is of fundamental as well as practical interest and is done in collaboration with Paul Parris (Missouri) and Luca Giuggioli (UNM).