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Least-squares fitting to an exponential function

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

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

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

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

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.