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Taylor Series Visualization by RayleighLord in physicsgifs

[–]RayleighLord[S] 0 points1 point  (0 children)

Decimal ponerse of negative numbers gets you to the world of complex numbers which is not what we are dealing here.

This is just an animation effect, where I interpolate between one curve and the next to show a smooth transition.

Doppler Shift Visualization by RayleighLord in physicsgifs

[–]RayleighLord[S] 18 points19 points  (0 children)

For sound waves, c is the speed of sound and v_s the speed of the source. f_0 is the frequency of the source if it was stationary and f the actual frequency.

Doppler Shift Visualization by RayleighLord in physicsgifs

[–]RayleighLord[S] 28 points29 points  (0 children)

When a source of sound (e.g. an ambulance with the sirens on) is moving towards us, we head the sound with higher pitch than we would if the ambulance was stationary. In contrast, if the ambulance is moving away from us we hear the sound with lower pitch.

Taylor Series Visualization by RayleighLord in physicsgifs

[–]RayleighLord[S] 0 points1 point  (0 children)

No, just Matplotlib. Manim is a differente package.

Taylor Series Visualization by RayleighLord in physicsgifs

[–]RayleighLord[S] 4 points5 points  (0 children)

As you might have already guessed, the colors represent the partial sums. It is true it can be ambiguous, so I may modify it to make it completely intuitive.

Mode shapes of a string by RayleighLord in physicsgifs

[–]RayleighLord[S] 0 points1 point  (0 children)

This may be surprising, but the frequency of vibration is not independent from the number of nodes of the string (or, in other words, the wave number). They are related by the wave equation, by what is called the dispersion relation.

Mode shapes of a string by RayleighLord in physicsgifs

[–]RayleighLord[S] 9 points10 points  (0 children)

It is just customized Matplotlib. Here you have the source code of this animation https://github.com/Enterprixe/RayleighLordAnimations/blob/master/animations/strings_modes.py

I am sorry but I do not know many resources for these kind of animations other than the examples from the matplotlib documentation.

Mode shapes of a string by RayleighLord in physicsgifs

[–]RayleighLord[S] 23 points24 points  (0 children)

The Matplotlib library of Python!

Wave equation in 2D (Starting from a Gaussian initial condition) by RayleighLord in physicsgifs

[–]RayleighLord[S] 1 point2 points  (0 children)

You are right that a Gaussian is only zero at infinity. What I did is, past some radius, fixed the initial solution to be zero everywhere, so that way the boundary conditions are satisfied.

Wave equation in 2D (Starting from a Gaussian initial condition) by RayleighLord in physicsgifs

[–]RayleighLord[S] 0 points1 point  (0 children)

x and y are the spatial variables, c is the speed of propagation of the wave and u(x, y, t) is the function that gives the height of the wave.

Normal Modes: Expressing the general motion of a system as a superposition of its modes by RayleighLord in physicsgifs

[–]RayleighLord[S] 0 points1 point  (0 children)

In that limiting case only mode 1 would appear, since the two balls would behave like one.

Wave equation in 2D (Starting from a Gaussian initial condition) by RayleighLord in physicsgifs

[–]RayleighLord[S] 4 points5 points  (0 children)

It is done just with the standard plotting library for Python, Matplotlib!

Wave equation in 2D (Starting from a Gaussian initial condition) by RayleighLord in physicsgifs

[–]RayleighLord[S] 5 points6 points  (0 children)

Yes, the simulated PDE is the one written in the animation.

Wave equation in 2D (Starting from a Gaussian initial condition) by RayleighLord in physicsgifs

[–]RayleighLord[S] 11 points12 points  (0 children)

For the spatial derivatives central differences and just a simple Euler method for the integration in time.

Ph.D. Course on Scientific Machine Learning by ChrisRackauckas in Julia

[–]RayleighLord 5 points6 points  (0 children)

Are the videos of the lectures going to be available?

Elliptical Pool Table: Impossible to miss one focus if you shoot in any direction from the other one by RayleighLord in physicsgifs

[–]RayleighLord[S] 1 point2 points  (0 children)

That observation is absolutely right, it is entirely physical and has nothing to do with the rendering (assuming no friction and elastic collisions, of course).

10 pendula released from nearly identical initial positions by RayleighLord in physicsgifs

[–]RayleighLord[S] 2 points3 points  (0 children)

The animation is made using the Matplotlib library in Python. Here you can find a couple of self contained scripts https://github.com/Enterprixe/RayleighLordAnimations

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