Viewing posts for the category Featured on frontpage
The Möbius function and the Mertens conjecture
Posted by: christian in Featured on frontpage on 25 Jan 2020
This blog post was inspired by Holly Krieger's video for Numberphile.
Processing UK Ordnance Survey terrain data
Posted by: christian in Featured on frontpage on 10 Oct 2019
The UK's Ordnance Survey mapping agency now makes its 50 m resolution elevation data freely-available through its online OpenData download service. This article uses Python, NumPy and Matplotlib to process and visualize these data without using a specialized GIS library.
Visualizing the Earth's dipolar magnetic field
Posted by: christian in Featured on frontpage on 28 Aug 2019
The magnetic field due to a magnetic dipole moment, $\boldsymbol{m}$ at a point $\boldsymbol{r}$ relative to it may be written $$ \boldsymbol{B}(\boldsymbol{r}) = \frac{\mu_0}{4\pi r^3}[3\boldsymbol{\hat{r}(\boldsymbol{\hat{r}} \cdot \boldsymbol{m}) - \boldsymbol{m}}], $$ where $\mu_0$ is the vacuum permeability. In geomagnetism, it is usual to write the radial and angular components of $\boldsymbol{B}$ as: $$ \begin{align*} B_r & = -2B_0\left(\frac{R_\mathrm{E}}{r}\right)^3\cos\theta, \\ B_\theta & = -B_0\left(\frac{R_\mathrm{E}}{r}\right)^3\sin\theta, \\ B_\phi &= 0, \end{align*} $$ where $\theta$ is polar (colatitude) angle (relative to the magnetic North pole), $\phi$ is the azimuthal angle (longitude), and $R_\mathrm{E}$ is the Earth's radius, about 6370 km. See below for a derivation of these formulae.
Impact craters on Earth
Posted by: christian in Featured on frontpage on 28 Jul 2019
The Earth Impact Database is a collection of images, publications and abstracts that provides information about confirmed impact structures for the scientific community. It is hosted at the Planetary and Space Science Centre (PASSC) of the University of New Brunswick.
Two-dimensional collisions
Posted by: christian in Featured on frontpage on 24 Jun 2019
This small Python project is a physical simulation of two-dimensional physics. The animation is carried out using Matplotlib's FuncAnimation method and is implemented by the class Simulation. Each "particle" of the simulation is represented by an instance of the Particle class and depicted as a circle with a fixed radius which undergoes elastic collisions with other particles.