#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
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
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
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
Field lines are a convenient way to visualize vector fields, and are defined to be tangent to them at each point.
Due to inertia, field lines do not represent the trajectory that a test mass would follow in a force field.
#VectorFields #DifferentialGeometry #Visualization

#PhysicsFactlet
A large number of double pendula starting with very similar initial conditions and four 2D projections of their (4-dimensional) phase space.
#Visualization #Physics #PhaseSpace #ClassicalMechanics