#physicsfactlet — Public Fediverse posts

#PhysicsFactlet
The "stretch and fold" dynamics of the phase-space representation of a chaotic system (in this case a periodically driven simple pendulum) is always fun to see.

(Made for a lecture, so I am quickly putting it here. Maybe will write a thread about it in the near future.)

#Chaos

#PhysicsFactlet
The "stretch and fold" dynamics of the phase-space representation of a chaotic system (in this case a periodically driven simple pendulum) is always fun to see.

(Made for a lecture, so I am quickly putting it here. Maybe will write a thread about it in the near future.)

#Chaos

#PhysicsFactlet
The "stretch and fold" dynamics of the phase-space representation of a chaotic system (in this case a periodically driven simple pendulum) is always fun to see.

(Made for a lecture, so I am quickly putting it here. Maybe will write a thread about it in the near future.)

#Chaos

#PhysicsFactlet
The "stretch and fold" dynamics of the phase-space representation of a chaotic system (in this case a periodically driven simple pendulum) is always fun to see.

(Made for a lecture, so I am quickly putting it here. Maybe will write a thread about it in the near future.)

#Chaos

#PhysicsFactlet
The "stretch and fold" dynamics of the phase-space representation of a chaotic system (in this case a periodically driven simple pendulum) is always fun to see.

(Made for a lecture, so I am quickly putting it here. Maybe will write a thread about it in the near future.)

#Chaos

#PhysicsFactlet
Scattering VS Extinction
In #Optics, the concepts of scattering and extinction are closely related. So closely related that many people tend to confuse them.
Imagine to illuminate a small object with a beam of light. If the object is small the scattered field will be essentially a spherical wave, and the total field will be the incident one plus the scattered field.
If we were able to measure directly the field (as we can do in the microwave regime) we could happily stop here, but in optics we can only measure intensities, and the intensity is defined as the time average of the modulus of the Pointing vector. In most cases of interest, the modulus of the Poynting vector is proportional to the modulus squared of the electric field (which explains why we often that a shortcut and just talk about |E|²).
So the quantity we measure is proportional to |Eᵢₙ +Eₛ|², which is the sum of the Poynting vector of the incident field, the Poynting vector of the scattered field, plus the cross terms. These cross terms are what we usually call "extinction" and are the result of the interference between the incident and scattering fields(and the reason why you get a "shadow" behind the scatterer).

#Scattering #Electrodynamics

#PhysicsFactlet
Scattering VS Extinction
In #Optics, the concepts of scattering and extinction are closely related. So closely related that many people tend to confuse them.
Imagine to illuminate a small object with a beam of light. If the object is small the scattered field will be essentially a spherical wave, and the total field will be the incident one plus the scattered field.
If we were able to measure directly the field (as we can do in the microwave regime) we could happily stop here, but in optics we can only measure intensities, and the intensity is defined as the time average of the modulus of the Pointing vector. In most cases of interest, the modulus of the Poynting vector is proportional to the modulus squared of the electric field (which explains why we often that a shortcut and just talk about |E|²).
So the quantity we measure is proportional to |Eᵢₙ +Eₛ|², which is the sum of the Poynting vector of the incident field, the Poynting vector of the scattered field, plus the cross terms. These cross terms are what we usually call "extinction" and are the result of the interference between the incident and scattering fields(and the reason why you get a "shadow" behind the scatterer).

#Scattering #Electrodynamics

#PhysicsFactlet
Scattering VS Extinction
In #Optics, the concepts of scattering and extinction are closely related. So closely related that many people tend to confuse them.
Imagine to illuminate a small object with a beam of light. If the object is small the scattered field will be essentially a spherical wave, and the total field will be the incident one plus the scattered field.
If we were able to measure directly the field (as we can do in the microwave regime) we could happily stop here, but in optics we can only measure intensities, and the intensity is defined as the time average of the modulus of the Pointing vector. In most cases of interest, the modulus of the Poynting vector is proportional to the modulus squared of the electric field (which explains why we often that a shortcut and just talk about |E|²).
So the quantity we measure is proportional to |Eᵢₙ +Eₛ|², which is the sum of the Poynting vector of the incident field, the Poynting vector of the scattered field, plus the cross terms. These cross terms are what we usually call "extinction" and are the result of the interference between the incident and scattering fields(and the reason why you get a "shadow" behind the scatterer).

#Scattering #Electrodynamics

#PhysicsFactlet
Scattering VS Extinction
In #Optics, the concepts of scattering and extinction are closely related. So closely related that many people tend to confuse them.
Imagine to illuminate a small object with a beam of light. If the object is small the scattered field will be essentially a spherical wave, and the total field will be the incident one plus the scattered field.
If we were able to measure directly the field (as we can do in the microwave regime) we could happily stop here, but in optics we can only measure intensities, and the intensity is defined as the time average of the modulus of the Pointing vector. In most cases of interest, the modulus of the Poynting vector is proportional to the modulus squared of the electric field (which explains why we often that a shortcut and just talk about |E|²).
So the quantity we measure is proportional to |Eᵢₙ +Eₛ|², which is the sum of the Poynting vector of the incident field, the Poynting vector of the scattered field, plus the cross terms. These cross terms are what we usually call "extinction" and are the result of the interference between the incident and scattering fields(and the reason why you get a "shadow" behind the scatterer).

#Scattering #Electrodynamics

#PhysicsFactlet
Scattering VS Extinction
In #Optics, the concepts of scattering and extinction are closely related. So closely related that many people tend to confuse them.
Imagine to illuminate a small object with a beam of light. If the object is small the scattered field will be essentially a spherical wave, and the total field will be the incident one plus the scattered field.
If we were able to measure directly the field (as we can do in the microwave regime) we could happily stop here, but in optics we can only measure intensities, and the intensity is defined as the time average of the modulus of the Pointing vector. In most cases of interest, the modulus of the Poynting vector is proportional to the modulus squared of the electric field (which explains why we often that a shortcut and just talk about |E|²).
So the quantity we measure is proportional to |Eᵢₙ +Eₛ|², which is the sum of the Poynting vector of the incident field, the Poynting vector of the scattered field, plus the cross terms. These cross terms are what we usually call "extinction" and are the result of the interference between the incident and scattering fields(and the reason why you get a "shadow" behind the scatterer).

#Scattering #Electrodynamics

#PhysicsFactlet
While electrodynamics is well understood, there aren't many scattering problems we can actually solve. A plane wave scattering from a uniform dielectric sphere is one of those few, and the solution was originally found by Gustav Mie in 1908. The solution is extremely elegant (albeit cumbersome), but not very practical for larger spheres, as it takes the form of a summation, and the number of terms we need to take into account grows fast with the radius.
Nevertheless it has become the prototype for all scattering solutions, and it has been extended to coated spheres, metallic spheres, birefringent spheres, ellipsoids etc etc.

In the animation: the scattered field from a uniform, dielectric disk (the 2D equivalent of the Mie solution). The source is from the bottom, and the (linear) polarization is assumed to be out of the plane.
The numerical solution has been obtained using a hand-coded finite-difference method to solve the Helmholtz equation.

#Optics #Physics #MieScattering

#PhysicsFactlet
I haven't made a single scientific animation in months. I just don't have the mental space right now.
But I am preparing a series of lectures on scattering for the Plasmonica 2026 School (https://www.plasmonica.it/2026school/), and it feels like a good excuse to make a few new ones.

This one shows a simple finite element simulation of a pulse scattering on a small dielectric obstacle.

#Physics #Optics #Scattering #Diffraction

#PhysicsFactlet
I haven't made a single scientific animation in months. I just don't have the mental space right now.
But I am preparing a series of lectures on scattering for the Plasmonica 2026 School (https://www.plasmonica.it/2026school/), and it feels like a good excuse to make a few new ones.

This one shows a simple finite element simulation of a pulse scattering on a small dielectric obstacle.

#Physics #Optics #Scattering #Diffraction

#PhysicsFactlet
I haven't made a single scientific animation in months. I just don't have the mental space right now.
But I am preparing a series of lectures on scattering for the Plasmonica 2026 School (https://www.plasmonica.it/2026school/), and it feels like a good excuse to make a few new ones.

This one shows a simple finite element simulation of a pulse scattering on a small dielectric obstacle.

#Physics #Optics #Scattering #Diffraction

#PhysicsFactlet
I haven't made a single scientific animation in months. I just don't have the mental space right now.
But I am preparing a series of lectures on scattering for the Plasmonica 2026 School (https://www.plasmonica.it/2026school/), and it feels like a good excuse to make a few new ones.

This one shows a simple finite element simulation of a pulse scattering on a small dielectric obstacle.

#Physics #Optics #Scattering #Diffraction

#PhysicsFactlet
I haven't made a single scientific animation in months. I just don't have the mental space right now.
But I am preparing a series of lectures on scattering for the Plasmonica 2026 School (https://www.plasmonica.it/2026school/), and it feels like a good excuse to make a few new ones.

This one shows a simple finite element simulation of a pulse scattering on a small dielectric obstacle.

#Physics #Optics #Scattering #Diffraction

#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 #Integration

#PhysicsFactlet
Sometimes you need to forgo the intuitive way to define stuff for the sake of actually being able to do anything useful with those definitions.
An example of this I always found funny is in knot theory, where a simple loop is considered to be a knot, while anything where the two extremes are dangling are not, including the common overhand knot.
This looks weird the first time you see it, but there is a very good reason to go with such a definition: you want to study what you can and can't do by manipulating the knot, and if you have the two extremes dangling, you can always untie any knot, making them all equivalent to a piece of string. In order to be able to say anything interesting about them you need to remove this trivial option, and thus accept the simple loop as a knot.
#knots

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

*or longest, if you want to be pedantic 😉

#PhysicsFactlet
The most naïve way to integrate (ordinary) differential equations, like the equation of motion of a simple pendulum, is to use the instantaneous velocity to update the position, and the instantaneous force to update the velocity (known as the Euler method). While this is simple and intuitive, it accumulates errors very quickly and (importantly) doesn't conserve energy.

#Physics #ComputationalPhysics

#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, 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.
#Physics #FluidDynamics #CoandaEffect #Aerodynamics #Airplanes

#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).
#Physics #Computing #Algorithm

#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"
#Physics #Computing #Algorithm

#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.

#Physics #Computing #Algorithm

#PhysicsFactlet
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.
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.

#Physics #Computing #Algorithm

#PhysicsFactlet
Optical fibre modes are weird but oddly mesmerizing.
#Optics #OpticalFibers

#PhysicsFactlet
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.
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.
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.

#Optics #Physics

#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 🧵 1/ #Optics #Physics

#PhysicsFactlet
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.
#Optics #Physics

#PhysicsFactlet
Inspired by a short thread by @johncarlosbaez (https://mathstodon.xyz/@johncarlosbaez/114459727454034873) I made a visualization of a Stone-Wales defect in fullerene, released it into the #PublicDomain, and uploaded it on Wikimedia Commons.
https://commons.wikimedia.org/wiki/File:Stone-Wales_defect_in_Fullerene.gif

#PhysicsFactlet
I had to redo an old animation about quantum tunnelling in the time domain, so why not post it here?
#QuantumMechanics #ITeachPhysics

A few details:
* The incident and reflected waves interfere, creating fringes in the wavefunction modulus when it hits the barrier.
* Even when far away from the barrier, the wavefunction of the "free" particle is slowly broadening.

#PhysicsFactlet
It's a foggy day here in Albion, so let's talk about light (multiple) scattering!
Fog is composed of micrometre sized water droplet that can scatter light. This has two main effects: some of the light that was supposed to reach your eyes don't (because it is scattered away), and some of the light that was not supposed to reach you gets scattered into your eyes.
The denser is the fog and the further an object is from you, the more likely light is to be scattered away before it reaches your eyes. The amount of unscattered light (i.e. the one your eyes can use to form a sharp image) goes down exponentially (Lambert-Beer law), so an object in the fog gets dimmer pretty quickly. On the other hand there is a chance that light that was never meant to reach you is now scattered into your eyes, but since it arrives from a largely random direction, mixed up with a lot of other scattered light, your brain perceived it as a white blur on top of everything else. And since far away object were already dim, this white halo can easily overpower them, so you can't see them anymore.

#Physics #Optics #ITeachPhysics #EverydayPhysics

#PhysicsFactlet
It's a foggy day here in Albion, so let's talk about light (multiple) scattering!
Fog is composed of micrometre sized water droplet that can scatter light. This has two main effects: some of the light that was supposed to reach your eyes don't (because it is scattered away), and some of the light that was not supposed to reach you gets scattered into your eyes.
The denser is the fog and the further an object is from you, the more likely light is to be scattered away before it reaches your eyes. The amount of unscattered light (i.e. the one your eyes can use to form a sharp image) goes down exponentially (Lambert-Beer law), so an object in the fog gets dimmer pretty quickly. On the other hand there is a chance that light that was never meant to reach you is now scattered into your eyes, but since it arrives from a largely random direction, mixed up with a lot of other scattered light, your brain perceived it as a white blur on top of everything else. And since far away object were already dim, this white halo can easily overpower them, so you can't see them anymore.

#Physics #Optics #ITeachPhysics #EverydayPhysics

#PhysicsFactlet
It's a foggy day here in Albion, so let's talk about light (multiple) scattering!
Fog is composed of micrometre sized water droplet that can scatter light. This has two main effects: some of the light that was supposed to reach your eyes don't (because it is scattered away), and some of the light that was not supposed to reach you gets scattered into your eyes.
The denser is the fog and the further an object is from you, the more likely light is to be scattered away before it reaches your eyes. The amount of unscattered light (i.e. the one your eyes can use to form a sharp image) goes down exponentially (Lambert-Beer law), so an object in the fog gets dimmer pretty quickly. On the other hand there is a chance that light that was never meant to reach you is now scattered into your eyes, but since it arrives from a largely random direction, mixed up with a lot of other scattered light, your brain perceived it as a white blur on top of everything else. And since far away object were already dim, this white halo can easily overpower them, so you can't see them anymore.

#Physics #Optics #ITeachPhysics #EverydayPhysics

#PhysicsFactlet
It's a foggy day here in Albion, so let's talk about light (multiple) scattering!
Fog is composed of micrometre sized water droplet that can scatter light. This has two main effects: some of the light that was supposed to reach your eyes don't (because it is scattered away), and some of the light that was not supposed to reach you gets scattered into your eyes.
The denser is the fog and the further an object is from you, the more likely light is to be scattered away before it reaches your eyes. The amount of unscattered light (i.e. the one your eyes can use to form a sharp image) goes down exponentially (Lambert-Beer law), so an object in the fog gets dimmer pretty quickly. On the other hand there is a chance that light that was never meant to reach you is now scattered into your eyes, but since it arrives from a largely random direction, mixed up with a lot of other scattered light, your brain perceived it as a white blur on top of everything else. And since far away object were already dim, this white halo can easily overpower them, so you can't see them anymore.

#Physics #Optics #ITeachPhysics #EverydayPhysics

#PhysicsFactlet
It's a foggy day here in Albion, so let's talk about light (multiple) scattering!
Fog is composed of micrometre sized water droplet that can scatter light. This has two main effects: some of the light that was supposed to reach your eyes don't (because it is scattered away), and some of the light that was not supposed to reach you gets scattered into your eyes.
The denser is the fog and the further an object is from you, the more likely light is to be scattered away before it reaches your eyes. The amount of unscattered light (i.e. the one your eyes can use to form a sharp image) goes down exponentially (Lambert-Beer law), so an object in the fog gets dimmer pretty quickly. On the other hand there is a chance that light that was never meant to reach you is now scattered into your eyes, but since it arrives from a largely random direction, mixed up with a lot of other scattered light, your brain perceived it as a white blur on top of everything else. And since far away object were already dim, this white halo can easily overpower them, so you can't see them anymore.

#Physics #Optics #ITeachPhysics #EverydayPhysics

#PhysicsFactlet
Light propagates in a straight line (actually it is more complicated than that, but this is good enough for us here) and we see only the light that comes to our eyes. As a result you usually don't see the light going from its source to the objects it illuminates.
Unless it is misty, in which case light can scatter on the water droplets and you can "see" the light's path ("Tyndall effect").

#Physics #Optics #EverydayPhysics

#PhysicsFactlet
Light propagates in a straight line (actually it is more complicated than that, but this is good enough for us here) and we see only the light that comes to our eyes. As a result you usually don't see the light going from its source to the objects it illuminates.
Unless it is misty, in which case light can scatter on the water droplets and you can "see" the light's path ("Tyndall effect").

#Physics #Optics #EverydayPhysics

#PhysicsFactlet
Light propagates in a straight line (actually it is more complicated than that, but this is good enough for us here) and we see only the light that comes to our eyes. As a result you usually don't see the light going from its source to the objects it illuminates.
Unless it is misty, in which case light can scatter on the water droplets and you can "see" the light's path ("Tyndall effect").

#Physics #Optics #EverydayPhysics

#PhysicsFactlet
Light propagates in a straight line (actually it is more complicated than that, but this is good enough for us here) and we see only the light that comes to our eyes. As a result you usually don't see the light going from its source to the objects it illuminates.
Unless it is misty, in which case light can scatter on the water droplets and you can "see" the light's path ("Tyndall effect").

#Physics #Optics #EverydayPhysics

#PhysicsFactlet
Light propagates in a straight line (actually it is more complicated than that, but this is good enough for us here) and we see only the light that comes to our eyes. As a result you usually don't see the light going from its source to the objects it illuminates.
Unless it is misty, in which case light can scatter on the water droplets and you can "see" the light's path ("Tyndall effect").

#Physics #Optics #EverydayPhysics

#PhysicsFactlet
Do you want an interpretation of quantum mechanics that doesn't really work that well in practice, but that would look fantastic for your Sci-Fi novel? I have for you "Many interacting words" (not to be confused with the similarly named "Many worlds interpretation").
In this interpretation the universe is 100% classical, but instead of being one universe there is a VERY large number of them, all classical and weakly interacting with each other. In particular each particle is classical, but is repelled by its "copies" in the other universes. This is able to replicate a lot of the most weird effects of quantum mechanics. For instance, classically a particle is not able to overcome a potential barrier if it doesn't have enough energy to do so, but in this interpretation the particle would be repelled by its copies, so it has a non-zero chance of getting enough of a kick to jump on the other side of the barrier, producing the phenomenon we usually call "quantum tunnelling".
Another effect replicated by this model is the "zero point energy" i.e. the fact that the lowest energy a particle can have is not zero, but a bit higher than that. In this interpretation this comes to be because the particle (which is classic) would like to sit at zero energy, but so do all of its "copies", and they repel, so none of them can really sit at zero energy.
If you want, in this interpretation the very fact we see quantum effects is evidence of parallel universes!
https://journals.aps.org/prx/abstract/10.1103/PhysRevX.4.041013

#Physics #QuantumMechanics

#PhysicsFactlet
Schematic of the epicycle model, as requested by @johncarlosbaez (see https://mathstodon.xyz/@johncarlosbaez/113652794327730499 for his thread on the topic).
Apart from having (hopefully) more colorblind-friendly colors, this one is in the #PublicDomain instead of being copyrighted.
#Physics #Astronomy

#PhysicsFactlet: The "Ashcroft/Mermin Project" Chapter 7: Crystal systems
As a Bravais lattice must be invariant under discrete translations, there are only a small number of possible types of Bravais lattices (5 in 2D and 14 in 3D).
#Physics #ITeachPhysics

#PhysicsFactlet: The "Ashcroft/Mermin Project" Chapter 6: Diffraction from a crystal
A wave with a wavelength comparable with the interatomic spacing of a crystal will diffract, resulting in intensity peaks at different angles, that act as a "fingerprint" of the crystal structure.

#PhysicsFactlet
A work in progress (trying to show diffraction by a crystal, but right now the whole thing is way too messy).

#PhysicsFactlet
Not a great animation, but I made it for a lecture, so I am sharing it 😃
Electric (red line) and magnetic (black lines) fields of the TE₁,₁ mode propagating in a rectangular waveguide.

Not a #PhysicsFactlet, but a full beginner-friendly tutorial on how to use speckle correlations for imaging through a scattering medium, complete with a step-by-step guide on how to set up your first experiment and analyse the data (including a full code in Mathematica and one in Matlab to analyse the data, and all the raw data used to generate the plots to make your tests):
#Physics #Optics #Photonics #ITeachPhysics
https://iopscience.iop.org/article/10.1088/2515-7647/ad7cb1

#PhysicsFactlet
Game of life, played on a Klein bottle (still very much a work in progress)
#ITeachMath #ITeachPhysics

#PhysicsFactlet
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.
#ITeachPhysics #Optics #Physics