Introduction to Molecular Dynamics¶

In this notebook you will use a Verlet scheme to simulate the dynamics of a 1-D Harmonic Oscillator and 1-D double well potential

Metropolis Monte Carlo for the Ising Model¶

In this notebook you will do Metropolis Monte Carlo to see the properties of the 1-d Ising model, numerically, and compare to the exact results in 1d

Radial distribution function for an ideal gas¶

This week we will compute the radial distribution function for an ideal gas, which will get us ready to do it for a real system next time

First we have to generate a "configuration" of an ideal gas. We'll do it in 2D. Fortunately, this is easy because it just means the x and y for each particle are random between 0 and L.

Radial distribution function for an ideal gas¶

This week we will compute the radial distribution function for an ideal gas, which will get us ready to do it for a real system next time

First we have to generate a "configuration" of an ideal gas. We'll do it in 2D. Fortunately, this is easy because it just means the x and y for each particle are random between 0 and L.

Metropolis Monte Carlo for the Ising Model¶

In this notebook you will do Metropolis Monte Carlo to see the properties of the 1-d Ising model, numerically, and compare to the exact results in 1d

Radial distribution function for an ideal gas¶

This week we will compute the radial distribution function for an ideal gas, which will get us ready to do it for a real system next time

First we have to generate a "configuration" of an ideal gas. We'll do it in 2D. Fortunately, this is easy because it just means the x and y for each particle are random between 0 and L.

In this homework, we're going to test empirically some of the statistical ideas we saw in class¶

Problem 1: Random walk on a 1d lattice¶

In class we looked at how a "random walk" on a 1d lattice leads to diffusion. Let's show that it's true using data

Problem 1a - generating a trajectory for a random walk¶ more ...

Metropolis Monte Carlo for the Ising Model¶

In this notebook you will do Metropolis Monte Carlo to see the properties of the 1-d Ising model, numerically, and compare to the exact results in 1d

Langevin Dynamics¶

In this notebook you will use a Verlet scheme to simulate the dynamics of a 1D- Harmonic Oscillator and 1-D double well potential using Langevin Dynamics

Langevin Dynamics¶

In this notebook you will use a Verlet scheme to simulate the dynamics of a 1D- Harmonic Oscillator and 1-D double well potential using Langevin Dynamics

Introduction to Molecular Dynamics¶

In this notebook you will use a Verlet scheme to simulate the dynamics of a 1-D Harmonic Oscillator and 1-D double well potential

Radial distribution function for an ideal gas¶

This week we will compute the radial distribution function for an ideal gas, which will get us ready to do it for a real system next time

First we have to generate a "configuration" of an ideal gas. We'll do it in 2D. Fortunately, this is easy because it just means the x and y for each particle are random between 0 and L.

In this homework, we're going to test empirically some of the statistical ideas we saw in class¶

Problem 1: Random walk on a 1d lattice¶

In class we looked at how a "random walk" on a 1d lattice leads to diffusion. Let's show that it's true using data

Problem 1a - generating a trajectory for a random walk¶ more ...

Python Tutorial¶

Adapted from this tutorial (https://github.com/kuleshov/cs228-material/blob/master/tutorials/python/cs228-python-tutorial.ipynb) which is by by Volodymyr Kuleshov and Isaac Caswell. That was in turn adapted from the CS231n Python tutorial by Justin Johnson (http://cs231n.github.io/python-numpy-tutorial/).

Introduction¶

Python is a great general-purpose programming language on its own, but with the help of a few popular libraries (numpy, scipy, matplotlib) it becomes a powerful environment for scientific computing.