Some of my tools

When a real system is too fast, too slow, too expensive, too dangerous, too large or too small to adequately explore in reality, we often resort to computer simulation methods to better understand it. Of course, the best reason to simulate any system is the consuming curiosity that drives all scientists to attempt a better understanding of how the world works. Although I like to model many different systems in a wide variety of lenghscales and timescales, I am mainly a condensed matter theorist who uses deterministic and probabilistic computer simulation tools to model atomic and molecular systems adsorbed (attached with no electron sharing allowed!) onto surfaces.

Almost no computer simulation technique used to model atomic and molecular systems is so intuitive for undergraduate students as is molecular dynamics(MD). The central theme of the algorithm is that forces are calculated on each atom in the simulation and then the positions are updated based on the corresponding kinematic parameters (initial position, initial velocity and acceleration). Students get excellent practice in differential calculus because the program requires forces but almost exclusively the interactions are in the form of pair potential interactions. In addition, each step in the simulation corresponds to a particular time interval thus providing the researcher(s) with a direct dynamical interpretation of the system’s phase space trajectory and various thermodynamic averages are calculated as averages over time and particles.

Another computer simulation technique, Monte Carlo (MC) entails an algorithm which moves the system around in the most likely configurations based on the system's potential energy and using, subsequently averaging over the sequence of configurations. Although it doesn't provide direct dynamical information, MC has dynamical interpretations and can be very useful in studying phase transitions in atomic and molecular systems. 

Yet another very useful technique is the Marerial Point Method, or MPM. MPM can be used to model the elastic defirmation of various bodies by mapping the system's mass and momentum onto a grid, doing the physics (solving governing equations) on the grid and then mapping the new mass and mementum back onto the system, which is comprised of a set of material points. Its algorithm makes it very efficient because the contact between material points does not have to be taken into account explcitly.

Using the tools described above (as well as others), I have been fortunate enough to work with talented students on problems such as alkanes on graphite,  confined alkanes, noble gases inside and escaping from  C₆₀ fullerenes, noble gases trapped inside C₆₀ fullerenes, gradient driven diffusion of hydrocarbons through zeolites, the spectral behavior of Mg⁺ trapped inside C₆₀ fullerenes, gradient - driven diffusion of noble gases through carbon nanotubes,  noble gases and nitrogen adsorbed onto graphite, fullerenes on graphite, groundwater contaminant transport,  volleyball simulations, chaotic behavior in pool games, planet collisions and noble gases adsorbed in spherical and confined geometries.

Last updated: August 19, 2007

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