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A Monte Carlo N-Body Simulation of Self-Assembly


It is remarkable that the slight adjustment of atomic number or rearrangement of atoms in a molecule can significantly change the bulk properties of a material. More fundamentally, how does the local configuration of atoms or molecules affect the global behavior of a material? This project sought to gain insight to this question by examining self-assembly which is the process by which several constituents interact to form local structures. The applications of self-assembly are realized in many areas of science. For example, biologists are interested in how certain proteins are crystallized. Nanotechnologists aim to form minute structures from a small number of particles. A major theoretical question in physics and material science is how these structures give rise to properties found in bulk materials. Research in self-assembly is essential in each of these fields.  


This presentation focuses on an N-body simulation which is designed to model current self-assembly experiments. Six spheres are necessary to produce multiple, unique structures, so this established a natural starting point for the study. A Monte Carlo method is implemented by initializing the spheres with random positions and velocities, as well as accounting for random fluctuations due to Brownian motion. The dynamics of the simulation are driven by the attractive depletion force given by Asakura-Oosawa theory, until stable structures are formed. These structures can be closely examined and classified. A vast number of simulations were performed, and the frequency of each structure was tallied. The total count of each structure was compared to experimental results for accuracy. These simulations were run in parallel, tens of thousands at a time, creating a very efficient and detailed study.


Travis Salzillo

Justin Eiland

Eli Symm


Student Presentations

94th Texas Section Meeting of the Mathematical Association of America

Texas A&M International University April 3-5 2014

  • A Monte Carlo N-Body Simulation of Self-Assembly – Travis Salzillo

Sigma Xi SW Research Conference

University of Texas at Dallas 1/11-13/2013

  • A Monte Carlo N-Body Simulation of Self-Assembly – Travis Salzillo

16th Annual North Texas Area Student Conference

Midwestern State University 3/31/2012

  • Specific Local Structure Formation Between Hard Spheres Using Particle Modeling – Eli Symm

Closing Remarks

There could be a lot more work done on this project.

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