#PhysicsFactlet
In its simplest form Monte-Carlo integration allows to estimate a area/volume with complicated boundaries by taking a number of samples and looking at which fraction fall inside the object of interest.
🎢🧪⚛️ #ComputationalPhysics

#PhysicsFactlet
A geodesics on a surface is the shortest* curve connecting two points.

*if you know/care what goes in this footnote, you don't need me to explain 😉

This non-randomness has a number of consequences, among them the fact that the you get predictable patterns in the apparently random output. We show that a focused input will always result in a ring of excess intensity at the same radius of the input (and suggest how this might be useful).
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#PhysicsFactlet
The most naïve way to integrate (ordinary) differential equations, is to use the instantaneous velocity to update the position, and the instantaneous force to update the velocity (Euler method). While this is simple and intuitive, it accumulates errors very quickly.
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#PhysicsFactlet
Thanks to some humidity in the air the air flow around the plane wing is clearly visible. Instead of just being deflected by the wing, the air flow tend to stick to the wing (and vice versa), which pulls the wing up and allow the plane to fly.
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#PhysicsFactlet
If evaluating the derivative of your function is not too computationally expensive, one can use the crossing point of the tangent line with the axis as your next best guess ("Newton-Raphson).
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#PhysicsFactlet
The "false position" method works great if the function is roughly linear in the bracketed region, so why don't we multiply by a function (of constant sign, so we don't add spurious zeros) that makes it more linear before applying it?
This is the "Ridders' method"
⚛️🎢

#PhysicsFactlet
An improvement over the bisection method is the so-called "false position" method, where instead of dividing the bracket region in two, you cut at the point where the line through the two bracket extremes crosses zero.
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#PhysicsFactlet
The bisection method is a simple and effective way to find the root(s) of a function
The idea is that you start by "bracketing" your root . You then take the midpoint between them, check if your function there is positive or negative and update the bracket.

⚛️🎢 #Computing #Algorithm

#PhysicsFactlet
Wavefront Shaping is a family of techniques used to control light (or, more generally, a wave) propagating through a scattering medium.

A 🧵
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🧪⚛️🎢💡

#PhysicsFactlet
A Shack-Hartmann sensor is a simple and widely used device to measure the phase profile of a wavefront (aka "where the light is coming from").

A mini 🧵
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#Optics #Physics

#PhysicsFactlet
A Stone-Wales defect is a 90 degrees rotation of a chemical bond between two carbon atoms that commonly happens in graphene and fullerene.

#Crystallography #Chemistry #Physics

#PhysicsFactlet
Remake of an old animation about quantum tunnelling in the time domain.
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A few details:
* The incident and reflected wavefunctions interfere, creating fringes when it hits the barrier.
* Even when far away from the barrier, the wavefunction is slowly broadening.