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| Title: | Computation of Defects in Materials |
| Authors: | Veit, Max |
| Keywords: | College of Science & Engineering
School of Mathematics |
| Issue Date: | 11-Aug-2011 |
| Abstract: | Abstract
The purpose of this project is to investigate and assess, using the MATLAB com-
puter language, some numerical methods used in several elds of computational molec-
ular dynamics. First a theoretical model of a one-dimensional chain of atoms was
studied. The atoms in this chain would interact based on the Lennard-Jones potential
energy function. Several algorithms were investigated that found con gurations of the
chain where the total potential energy was lowest. Aspects of the one-dimensional
chain were then carried over into a model of a two-dimensional system of atoms. For
this model a full simulation of the movement of the atoms in the system was used to
study the system. It was found that one of the simplest atom con gurations, a square
lattice pattern, was unstable. In the simulation, this structure evolved over time into
several disconnected regions, called \grains," of a more stable triangular-hexagonal lat-
tice pattern. These structures are similar to crystal grains in real-world polycrystalline
materials. Some basic computational thermodynamics (more speci cally, Langevin
dynamics) was also used in the simulation. It was found that by regulating the \tem-
perature," or average kinetic energy, of the system, the formation of grains could be
controlled to some degree. |
| Description: | Additional contributors: Brian Vankoten; Mitchell Luskin (faculty mentor) |
| Permanent URL: | http://purl.umn.edu/115367 |
| Appears in Collections: | Undergraduate Research Presentations
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Files in This Item:
| File |
Description |
Size | Format |
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| Veit_Max.pdf | | 459Kb | PDF | View/Open |
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