2018 - Present
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These are some of the tools I've developed are for research, and some are for personal and/or casual use. They range from adaptive integration and Runge-Kutta ODE solvers to Bayesian modelling and MCMC simulations. Here are a few of my favourites:
Solving the Ising model with Monte Carlo methods
Solving the Ising model with Monte Carlo methods
A staple of statistical mechanics, the Ising model is a simplistic yet beautiful description of a ferromagnet. Here, I solve the nearest + next-nearest neighbour model (8 surrounding spins) numerically in Python. Have a look:
Magnetization over MC time for T<Tc with a random (hot) initial state.
Final states as a function of temperature. Can you spot the critical temperature?
Magnetization (bordeaux) and heat capacity (cadet blue) as a function of temperature. The yellow line demarks Tc. All spins are initially at m=+1. Taken in units of kb = |coupling constant| = 1.
Using supernovae to determine cosmological parameters
Using supernovae to determine cosmological parameters
How do we calculate the age of our universe? One way is to
use observations to pin down the cosmological parameters;
put the data into the Friedman equation;
integrate the Friedman equation to give us the scale factor and thus, age of the universe.
As part of a coding lab for an observational astrophysics course, that's precisely what I did. Here are some results:
How different matter densities affect the size and age of our universe.
Angular diameter distance and luminosity distance as a function of redshift.
Supernova distance modulus as a function of redshift fitted to various matter densities. A more rigorous fit is done using MCMC algorithms in a subsequent coding lab.
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