We finish the first half of the semester by studying how molecular dynamics models based on classical mechanics give rise to macroscopic phenomena. Students turn in their mid-term projects at the end of the week.
The Lennard Jones Molecular Dynamics Model uses the Lennard-Jones potential to approximate the motion of molecules using Newtonian dynamics.
Lennard-Jones potential
This potential is a reasonably accurate model of interactions between polarizable atoms such as noble gases. The motion of the molecules is computed using the Verlet algorithm with the indicated time step. For sufficiently small time steps dt, the system's total energy should be approximately conserved. Reduce the time step if the energy drifts or if the system becomes unstable.
The statistics displayed at the top of the simulation are temperature, pressure, total energy, kinetic energy, potential energy (from interactions between molecules and interactions with the walls), and gravitational energy. Note that the temperature and pressure are computed from the average values and may not be accurate for short times or when there's organized motion on a large scale.
Note: The potential is truncated at a distance of 3 molecular diameters to reduce computation.
The following models use the Lennard-Jones potential to model molecular dynamics.
Additional models may be be posted for self-study.
The Lennard-Jones Molecular Dynamics Dynamics Model was created for teaching computer modeling by Wolfgang Christian using the Easy Java Simulations (EJS) version 4.1 authoring and modeling tool. It is based on a Java applet written by Dan Schroeder, Physics Department, Weber State University. See: <http://physics.weber.edu/schroeder/software/>
You can examine and modify a compiled EJS model if you run the model (double click on the model's jar file), right-click within a plot, and select "Open Ejs Model" from the pop-up menu. You must, of course, have EJS installed on your computer. Information about Ejs is available at: <http://www.um.es/fem/Ejs/> and in the OSP comPADRE collection <http://www.compadre.org/OSP/>.