Fayl:Born series.gif
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Born_series.gif (360 × 382 piksel, fayl hajmi: 678 KB, MIME tipi: image/gif, looped, 11 frames, 11 soniya)
Qisqa izoh
| Taʼrif |
English: In the "first Born approximation", commonly used in Condensed Matter Physics, a wave is assumed to scatter only once from each scattering center. Higher orders of the "Born series" describe the fact that a scattered wave can be scattered again. |
| Sanasi | |
| Manba | https://twitter.com/j_bertolotti/status/1135550283264790532 |
| Muallif | Jacopo Bertolotti |
| Ruxsat (Bu faylning takror foydalanilishi) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 11.0 code
\[Lambda] = 1;
k0 = (2 \[Pi])/\[Lambda];
\[Alpha] = 4/(k0^2 I);
\[Sigma] = (k0^3 Norm[\[Alpha]]^2)/4 // N;
G[r_] := N[I/4 HankelH1[0, k0 Norm[r] ]];
nborn = 10;
source[x_] := E^(I k0 x); (*Plane wave illuminating the scatterers*)
scatterers = RandomReal[{-7, 7}, {15, 2}];
dim = Dimensions[scatterers][[1]];
E0 = Table[
N[source[scatterers[[j, 1]] ]], {j, 1, dim}] ;(*source field on each scatterer*)
Es = E0;
born = Reap[Do[
tmp = Table[\[Alpha] k0^2 Sum[If[i == j, 0, Es[[j]]*G[scatterers[[i]] - scatterers[[j]] ] ], {j, 1, dim}], {i, 1, dim}];
Es = tmp;
Sow[Es];
tmp =.
, {nborn}];][[2, 1]];
Etot = Table[\[Alpha] k0^2 Sum[born[[i, j]]*G[{x, y} - scatterers[[j]]], {j, 1, dim}], {i, 1, nborn}];
intborn =
Table[DensityPlot[Abs[Sum[Etot[[i]], {i, 1, j}] ]^2, {x, -10, 10}, {y, -10, 10}, PlotPoints -> 50, ColorFunction -> "AvocadoColors", PlotRange -> {0, 5}, Epilog -> {White, PointSize[0.02], Point[scatterers]}, Frame -> False, PlotLabel -> "|E\!\(\*SuperscriptBox[\(|\), \(2\)]\)", LabelStyle -> {Black, Bold}], {j, 1, nborn}]
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| Sana/Vaqt | Miniatura | Oʻlchamlari | Foydalanuvchi | Izoh | |
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| joriy | 20:32, 2019-yil 4-iyun | | 360 × 382 (678 KB) | wikimediacommons>Berto | User created page with UploadWizard |
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