In today’s recreational coding exercise, we learn how to fit model parameters to data (with error bars) and obtain the most likely distribution of modeling parameters that best explain the data, called the posterior distribution. We will do so in a Bayesian framework, which is a very powerful approach because…

In today’s recreational coding exercise, we will simulate the Orszag-Tang vortex — a demonstration of supersonic 2D magnetohydrodynamics (MHD) turbulence — using a constrained transport finite volume algorithm. This tutorial builds on our Finite Volume tutorial for the compressible Euler equations. Here, we will add a magnetic field coupled to…

For today’s recreational coding exercise, we will expand on the Finite Volume method for simulating the compressible fluid equations. We will add boundary conditions and source terms. For Part 1, please see the Python tutorial on the Kelvin-Helmholtz Instability, which we build on. Here in Part 2, we will simulate…

For today’s recreational coding exercise, we will simulate a spring network: an array of nodes connected by springs that obey Hooke’s Law. The spring system will fall down due to gravity and bounce off the floor. We use a particle algorithm similar to our N-body simulation. You may find the…

For today’s recreational coding exercise, we learn how to simulate dilute gas with the Direct Simulation Monte Carlo (DSMC) method. This approach is useful when gas is weakly collisional. We will look at the Rayleigh Problem: the response of rarified gas between two plates after one suddenly starts moving. You…

For today’s recreational coding exercise, we simulate active matter, i.e., swarming. Such a system may describe a flock of birds or a school of fish. We will look at how very simple rules may lead to the emergence of self-ordered motions. You may find the accompanying Python code on github. …

For today’s recreational coding exercise, we simulate fluid flow past a cylinder using the Lattice Boltzmann method. This is a really cool and simple technique to simulate fluid flow: instead of evolving the fluid (Navier-Stokes) equations directly, microscopic particles on a lattice are simulated with streaming and collision processes. The…

For today’s recreational coding exercise, we look at a simple way to create volume renderings to visualize 3D simulation datacubes. This technique is incredibly useful when you have space-filling data you would like to visualize. Such data shows up often in astrophysical datasets but also in other areas of computer…

For today’s recreational coding exercise, we will look at quantum mechanical systems, in particular, the Schrodinger-Poisson equations. We will create a simulation for the evolution of a wavefunction under its self-potential. Such a system may describe certain superfluids/Bose-Einstein condensate or exotic dark matter. You may find the accompanying Python code…