The Bak-Sneppen model of evolution is a simple model describing the evolution of an ecosystem. It offers a surprising amount of insight given its simplicity. This notebook does not deep dive into the model, but illustrates the basics using the Julia programming language.

magnetism, spin, monte carlo, fortran, f2py, metropolis, equilibrium, autocorrelation, ising

Using the Metropolis algorithm to approximate the magnetization and specific heat for a 2D Ising lattice.

animation, 4th order runge-kutta, system of equations

The 4th order Runge-Kutta method was used to integrate the equations of motion for the system, then the pendulum was stabilised on its inverted equilibrium point using a proportional gain controller and linear quadratic regulator.

specific heat, magnetism, partition function, spin

Computing the internal energy, specific heat and magnetisation in the 1D and 2D Ising model. An analytical solution to the XY model is also provided.