File:Green Function of Wave Equation - 2D vs 3D.gif
Green_Function_of_Wave_Equation_-_2D_vs_3D.gif (556 × 354 pixels, file size: 798 KB, MIME type: image/gif, looped, 50 frames, 5.0 s)
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Summary
[edit]DescriptionGreen Function of Wave Equation - 2D vs 3D.gif |
English: A 2D world would be a weird one for many reasons. One of them is that a point perturbation would not expand as a thin spherical shell (as it does in 3D), but would leave a long tail behind.
(Notice that in order to plot the 3D Green's function I had to cheat and convolve it with a narrow Gaussian. Hence the finite width etc) |
Date | |
Source | https://twitter.com/j_bertolotti/status/1540287379797319683 |
Author | Jacopo Bertolotti |
Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 13.0 code
[edit]c = 1;
g3[x_, y_, t_] := DiracDelta[c t - Sqrt[x^2 + y^2]]/(4 \[Pi] Sqrt[x^2 + y^2])
g3bis[x_, y_, t_] := PDF[NormalDistribution[0, 5*10^-2], c t - Sqrt[x^2 + y^2]]/(4 \[Pi] Sqrt[x^2 + y^2])
g2[x_, y_, t_] := 1/(2 \[Pi]) HeavisideTheta[c t - Sqrt[x^2 + y^2]]/Sqrt[c^2 t^2 - (x^2 + y^2)]
frames = Table[
Grid[{
{"",
Style["3D Green's function", Bold, White]
,
Style["2D Green's function", Bold, White]
}, {
Style["1D cut", Bold, White],
Plot[g3bis[x, 0, t], {x, -5, 5}, PlotRange -> {-0.05, 1}, Exclusions -> None, Axes -> False, PlotStyle -> {Thick, White}, Background -> Black, AspectRatio -> 1/3]
,
Plot[g2[x, 0, t], {x, -5, 5}, PlotRange -> {-0.05, 1}, Exclusions -> None, Axes -> False, PlotStyle -> {Thick, White}, Background -> Black, AspectRatio -> 1/3]
}, {
Style["2D cut", Bold, White],
DensityPlot[g3bis[x, y, t], {x, -5, 5}, {y, -5, 5}, ColorFunction -> "AvocadoColors", PlotRange -> {0, 1}, Frame -> False, PlotPoints -> 100, Exclusions -> None, Background -> White, PlotRangePadding -> None]
,
DensityPlot[g2[x, y, t], {x, -5, 5}, {y, -5, 5}, ColorFunction -> "AvocadoColors", PlotRange -> {0, 1}, Frame -> False, PlotPoints -> 50, PlotRangePadding -> None]
}
}, Background -> Black]
, {t, 0.075, 5, 0.1}];
ListAnimate[frames]
Licensing
[edit]This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. | |
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
http://creativecommons.org/publicdomain/zero/1.0/deed.enCC0Creative Commons Zero, Public Domain Dedicationfalsefalse |
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current | 09:01, 27 June 2022 | 556 × 354 (798 KB) | Berto (talk | contribs) | Uploaded own work with UploadWizard |
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