File:Green Function of Wave Equation - 2D vs 3D.gif

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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)

Captions

Captions

Comparison of the Green's function of the wave equation for the 3D and the 2D case.

Summary

[edit]
Description
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]
I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero 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.

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Date/TimeThumbnailDimensionsUserComment
current09:01, 27 June 2022Thumbnail for version as of 09:01, 27 June 2022556 × 354 (798 KB)Berto (talk | contribs)Uploaded own work with UploadWizard

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