Viewing posts for the category Featured on frontpage
Least-squares fitting to an exponential function
Posted by: christian in Featured on frontpage on 13 Jan 2022
Many phenomena can be described in terms of a measured variable varying exponentially with a quantity. For example, a processes such as radioactive decay and first-order reaction rates are described by an ordinary differential equation of the form
COVID deaths and vaccination rates
Posted by: christian in Featured on frontpage on 3 Jan 2022
The Python script below generates the following visualization of COVID deaths per 100,000 people for two classes of European country: those with less than 75% of the population vaccinated and those with at least this percentage vaccinated. The ongoing (as of January 2022) third wave of infections is causing fewer deaths in the countries with a higher vaccination rate.
The Klein–Nishina formula
Posted by: christian in Featured on frontpage on 18 Dec 2021
The Klein–Nishina formula gives the differential cross section for the scattering of photons off an electron. At low energies, light scatters elastically (Thomson scattering); at higher energies (for example, gamma radiation), inelastic Compton scattering occurs. In terms of the incoming and outgoing photon wavelengths, $\lambda$ and $\lambda'$:
Floyd-Steinberg Dithering
Posted by: christian in Featured on frontpage on 13 Oct 2021
Floyd-Steinberg dithering is a technique for reducing the colour palette of an image (for example, to reduce its file size) whilst keeping as much of the perceived detail as possible. For each pixel in the original image, the nearest colour to that pixel is chosen from a restricted palette and any "error" (difference in pixel colour value, original - new) is distributed across the neighbouring pixels as follows:
Mass Parabolas
Posted by: christian in Featured on frontpage on 7 Sep 2021
An atomic nucleus consists of protons and neutrons (collectively referred to as nucleons) bound together through the strong nuclear force. Models for the nuclear binding energy were introduced in a couple of previous posts on this blog.