Wolfram Computation Meets Knowledge

Wolfram Summer School

Alumni

Colin Nancarrow

Science and Technology

Class of 2018

Bio

Colin Nancarrow is a first-year graduate student of theoretical physics at Boston University. He holds a degree in physics and a degree in applied mathematics from the University of Chicago. Broadly, he is interested in quantum field theories with conformal symmetry and in leveraging results from conformal theories to learn about nonconformal theories.

Computational Essay

Introduction to Stochastic Processes »

Project: Lattice Plot

Goal

To code a preliminary framework for visualizing computation on 3D lattices. Problems formulated in three dimensions and on nontrivial lattice structures often prove difficult to approach with analytical methods; this is a big problem in condensed matter physics.

Main Results in Detail

We can plot new cellular automata in three dimensions on the body-centered cubic lattice. We can plot new cellular automata in three dimensions on the body-centered cubic lattice. Shown is the evolution of a simple cellular automaton whose rule is basically “grow outward” starting from a single point. Then we show the neighborhood structure of an atom on the corner of a lattice cell and an atom in the center of a lattice cell. Finally, the infinite-time evolution of a 3D game of life, which has left five “still lifes” of three different types.

Future Work

  • 1. Code can be made vastly more efficient and modular.
  • 2. Two other Bravais lattices of interest, as well as the pyrochlore lattice.
  • 3. The Ising model should be implemented; the code is too slow to accommodate this currently.
  • 4. TomographyPlot for Bravais lattices, which would produce animations of cross-sections of the lattice along planes specified by the Miller indices. This would probably be necessary for seeing deep inside any complicated structures on a large lattice.

Wolfram Summer School | Champaign, IL, USA | July 3 29–July 22, 2022

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