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#physicsfactlet

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j_bertolotti<p><a href="https://mathstodon.xyz/tags/PhysicsFactlet" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PhysicsFactlet</span></a> <br>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, the wing tends to stick to the air flow, a phenomenon known as the Coanda effect), which pulls the wing up and allow the plane to fly.<br><a href="https://mathstodon.xyz/tags/Physics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Physics</span></a> <a href="https://mathstodon.xyz/tags/FluidDynamics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>FluidDynamics</span></a> <a href="https://mathstodon.xyz/tags/CoandaEffect" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>CoandaEffect</span></a> <a href="https://mathstodon.xyz/tags/Aerodynamics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Aerodynamics</span></a> <a href="https://mathstodon.xyz/tags/Airplanes" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Airplanes</span></a></p>
j_bertolotti<p><a href="https://mathstodon.xyz/tags/PhysicsFactlet" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PhysicsFactlet</span></a> <br>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).<br><a href="https://mathstodon.xyz/tags/Physics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Physics</span></a> <a href="https://mathstodon.xyz/tags/Computing" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Computing</span></a> <a href="https://mathstodon.xyz/tags/Algorithm" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Algorithm</span></a></p>
j_bertolotti<p><a href="https://mathstodon.xyz/tags/PhysicsFactlet" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PhysicsFactlet</span></a> <br>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?<br>This is the "Ridders' method"<br><a href="https://mathstodon.xyz/tags/Physics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Physics</span></a> <a href="https://mathstodon.xyz/tags/Computing" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Computing</span></a> <a href="https://mathstodon.xyz/tags/Algorithm" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Algorithm</span></a></p>
j_bertolotti<p><a href="https://mathstodon.xyz/tags/PhysicsFactlet" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PhysicsFactlet</span></a> <br>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.</p><p><a href="https://mathstodon.xyz/tags/Physics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Physics</span></a> <a href="https://mathstodon.xyz/tags/Computing" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Computing</span></a> <a href="https://mathstodon.xyz/tags/Algorithm" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Algorithm</span></a></p>
j_bertolotti<p><a href="https://mathstodon.xyz/tags/PhysicsFactlet" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PhysicsFactlet</span></a> <br>Finding the roots of a function is a very common problem in computational Physics, and the bisection method is a simple and effective (albeit far from optimal) way to do that.<br>The idea is that you start by "bracketing" your root between a value of x where the function is negative and one where it is positive. You then take the midpoint between them, check if your function there is positive or negative and update the bracket.</p><p><a href="https://mathstodon.xyz/tags/Physics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Physics</span></a> <a href="https://mathstodon.xyz/tags/Computing" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Computing</span></a> <a href="https://mathstodon.xyz/tags/Algorithm" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Algorithm</span></a></p>
j_bertolotti<p><a href="https://mathstodon.xyz/tags/PhysicsFactlet" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PhysicsFactlet</span></a> <br>Optical fibre modes are weird but oddly mesmerizing.<br><a href="https://mathstodon.xyz/tags/Optics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Optics</span></a> <a href="https://mathstodon.xyz/tags/OpticalFibers" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>OpticalFibers</span></a></p>
j_bertolotti<p><a href="https://mathstodon.xyz/tags/PhysicsFactlet" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PhysicsFactlet</span></a> <br>Scattering scrambles coherent light into a speckle pattern, where the field at each point can be seen as the superposition of a large number of random phasors. At some point the result is brighter, and at some points the result is dimmer, creating the "speckly" pattern.<br>By changing the phase of the incident light one can change the phase of the phasors making up the resulting field, and since elastic scattering is linear, changing the phase of different input modes is going to rotate different phasors without cross-talk.<br>As a result it is possible to find an incident wavefront such that all the phasors making up the field at one point are in a straight line (constructive interference), resulting in a single bright dot (a focus) through a completely scattering material.</p><p><a href="https://mathstodon.xyz/tags/Optics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Optics</span></a> <a href="https://mathstodon.xyz/tags/Physics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Physics</span></a></p>
j_bertolotti<p><a href="https://mathstodon.xyz/tags/PhysicsFactlet" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PhysicsFactlet</span></a> <br>A Shack-Hartmann sensor is made my an array of small lenses and a camera. If the light hitting the lenses is collimated, we will get a number of equispaced foci on the camera. But if the light is not collimated, the position of the foci will change in a predictable way, so we can reconstruct where the ray were coming from.<br><a href="https://mathstodon.xyz/tags/Optics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Optics</span></a> <a href="https://mathstodon.xyz/tags/Physics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Physics</span></a></p>
j_bertolotti<p><a href="https://mathstodon.xyz/tags/PhysicsFactlet" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PhysicsFactlet</span></a><br>Temporal coherence can be a bit confusing the first time you encounter it, so I made a small animation that might help teachers to explain it to students.<br><a href="https://mathstodon.xyz/tags/ITeachPhysics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>ITeachPhysics</span></a> <a href="https://mathstodon.xyz/tags/Optics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Optics</span></a> <a href="https://mathstodon.xyz/tags/Physics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Physics</span></a></p>
j_bertolotti<p><a href="https://mathstodon.xyz/tags/PhysicsFactlet" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PhysicsFactlet</span></a>: The "Ashcroft/Mermin Project" Chapter 4: Crystal Lattices<br>The "Wigner-Seitz" primitive cell is the region of space that is closer to a given point in the lattice. It has the advantage of being a primitive cell with the same symmetries as the Bravais lattice.</p>
j_bertolotti<p><a href="https://mathstodon.xyz/tags/PhysicsFactlet" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PhysicsFactlet</span></a>: The "Ashcroft/Mermin Project" Chapter 4: Crystal Lattices<br>A Bravais lattice is an infinite array of points generated by discrete translations, so that every point can be written as a (integral) linear combination of the basis vectors.</p>
j_bertolotti<p><a href="https://mathstodon.xyz/tags/PhysicsFactlet" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PhysicsFactlet</span></a>: The "Ashcroft/Mermin Project"<br>Chapter 2: Sommerfeld model<br>Electrons in a metal can be approximated as a Fermi gas, where only one electron can occupy a given state. At low temperature most of them are difficult to excite, because there is no free state available.</p>
j_bertolotti<p><a href="https://mathstodon.xyz/tags/PhysicsFactlet" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PhysicsFactlet</span></a>: The "Ashcroft/Mermin Project"<br>Chapter 1: The Drude Theory of metals<br>Electrons in a metal are accelerated by an electric field, but they keep bouncing on the metal defects/impurities. The resulting diffusion-like motion produces a roughly steady current.</p>
j_bertolotti<p><a href="https://mathstodon.xyz/tags/PhysicsFactlet" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PhysicsFactlet</span></a>: The "Ashcroft/Mermin Project"<br>I will try to (likely very slowly) go through the classic textbook "Solid State Physics" by Ashcroft and Mermin and make one or more animation/visualization per chapter.<br>This will (hopefully) help people digest the topic and/or be useful to lecturers who are teaching about it. As with all my animations, feel free to use them.<br>The idea is that the animations are a companion to the book, so I will give only very brief explanations here.</p>
j_bertolotti<p><a href="https://mathstodon.xyz/tags/PhysicsFactlet" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PhysicsFactlet</span></a> <br>Common misunderstanding about <a href="https://mathstodon.xyz/tags/Entropy" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Entropy</span></a>: the two configurations below have exactly the same entropy, and in both cases the entropy is zero (as you know exactly where each dot is, so there is only one possible microstate they can be in).</p>
j_bertolotti<p><a href="https://mathstodon.xyz/tags/PhysicsFactlet" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PhysicsFactlet</span></a> <br>A quantum simple pendulum.<br>The pendulum position is spread out, with opacity here being proportional to the probability that the pendulum is at that position at a given time. The average position of the quantum dynamics is the same as the classical pendulum dynamics (Ehrenfest theorem).</p><p>Technicalities: I used the Crank-Nicholson method to evolve the system in time. This is a 1D problem, and the only variable I considered was the angle, with the initial state being a Gaussian.</p><p><a href="https://mathstodon.xyz/tags/QuantumMechanics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>QuantumMechanics</span></a> <a href="https://mathstodon.xyz/tags/Physics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Physics</span></a> <a href="https://mathstodon.xyz/tags/ITeachPhysics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>ITeachPhysics</span></a> <a href="https://mathstodon.xyz/tags/Visualization" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Visualization</span></a></p>
j_bertolotti<p><a href="https://mathstodon.xyz/tags/PhysicsFactlet" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PhysicsFactlet</span></a><br>Magnetic hysteresis: In a ferromagnet the equilibrium configuration is with all magnetic moments aligned with each other. If we want to flip them, we need to flip all of them at the same time, which requires a stronger field than if the moments were independent, resulting in the characteristic hysteresis loop.</p><p>(Simulation done by numerically solve the Landau–Lifshitz equation with a tiny bit of noise added to speed the process up on a square grid of magnetic moment with periodic boundary conditions.)</p><p><a href="https://mathstodon.xyz/tags/Physics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Physics</span></a> <a href="https://mathstodon.xyz/tags/Visualization" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Visualization</span></a> <a href="https://mathstodon.xyz/tags/ITeachPhysics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>ITeachPhysics</span></a> <a href="https://mathstodon.xyz/tags/Magnetism" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Magnetism</span></a></p>
j_bertolotti<p><a href="https://mathstodon.xyz/tags/PhysicsFactlet" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PhysicsFactlet</span></a><br>In a dielectric medium, the charges are not free to move around, so electromagnetic waves are slowed down a bit, but otherwise can freely propagate.<br>In a metal, some of the electrons can move around, and thus tend to absorb and/or reflect electromagnetic waves.<br>But at the interface between a dielectric and a metal it is possible to have a mode that is part electron oscillation and part electromagnetic field, travelling along the interface, known as a "surface plasma polariton" (sometimes abbreviated as "plasmon").</p><p>Shown in the animation is the electric field (which is a vector quantity, hence the arrows).</p><p><a href="https://mathstodon.xyz/tags/Physics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Physics</span></a> <a href="https://mathstodon.xyz/tags/Optics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Optics</span></a> <a href="https://mathstodon.xyz/tags/Plasmonics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Plasmonics</span></a> <a href="https://mathstodon.xyz/tags/Visualization" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Visualization</span></a> <a href="https://mathstodon.xyz/tags/SciComm" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>SciComm</span></a></p>
j_bertolotti<p><a href="https://mathstodon.xyz/tags/PhysicsFactlet" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PhysicsFactlet</span></a><br>The dynamics of a rigid sphere can be surprisingly complicated. In fact, beside rotating around an axis, the sphere can also precess (i.e. the axis of rotation is itself rotating) and nutate (i.e. the axis of rotation oscillates back and forth).</p><p>Euler's angles are particularly useful to describe such motion, as:<br>* Rotation is a change in the third Euler angle.<br>* Precession is a change in the first Euler angle.<br>* Nutation is a change in the second Euler angle.</p><p><a href="https://mathstodon.xyz/tags/Physics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Physics</span></a> <a href="https://mathstodon.xyz/tags/ClassicalMechanics" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>ClassicalMechanics</span></a> <a href="https://mathstodon.xyz/tags/EulerAngles" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>EulerAngles</span></a> <a href="https://mathstodon.xyz/tags/Visualization" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>Visualization</span></a></p>
j_bertolotti<p>* You have my blessing to use my animations (<a href="https://mathstodon.xyz/tags/PhysicsFactlet" class="mention hashtag" rel="nofollow noopener" target="_blank">#<span>PhysicsFactlet</span></a>) for your lectures etc. Just let me know when you do 🙂<br>* I tried to explain how I make them here: <a href="https://www.youtube.com/watch?v=2zOUZlHKKbs" rel="nofollow noopener" target="_blank"><span class="invisible">https://www.</span><span class="ellipsis">youtube.com/watch?v=2zOUZlHKKb</span><span class="invisible">s</span></a><br>* I release almost all of my scientific visualizations in the public domain, and upload them (with the code used to generate them) on Wikimedia Commons. The only exceptions are those that I consider not interesting enough. You can find them here: <a href="https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Berto&amp;ilshowall=1" rel="nofollow noopener" target="_blank"><span class="invisible">https://</span><span class="ellipsis">commons.wikimedia.org/w/index.</span><span class="invisible">php?title=Special:ListFiles/Berto&amp;ilshowall=1</span></a></p>
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