File:Born series.gif
Born_series.gif (360 × 382 pixels, file size: 678 KB, MIME type: image/gif, looped, 11 frames, 11 s)
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Summary[edit]
DescriptionBorn series.gif |
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. |
Date | |
Source | https://twitter.com/j_bertolotti/status/1135550283264790532 |
Author | Jacopo Bertolotti |
Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 11.0 code[edit]
\[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}]
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 | 15:32, 4 June 2019 | 360 × 382 (678 KB) | Berto (talk | contribs) | User created page with UploadWizard |
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- Usage on en.wikipedia.org
- Forward scatter
- Wide-angle X-ray scattering
- Inverse scattering problem
- Dalitz plot
- Scattering amplitude
- Incoherent scatter
- Core-excited shape resonance
- Scattering channel
- Multi-configuration time-dependent Hartree
- High-frequency approximation
- Forward scattering alignment
- Wolf effect
- Raman amplification
- Secular resonance
- Neutron time-of-flight scattering
- Marchenko equation
- Soft photon
- Spectral energy distribution
- Kramers–Heisenberg formula
- Dynamic scattering mode
- Single-scattering albedo
- Hapke parameters
- Schwinger variational principle
- Gans theory
- Scattering-matrix method
- Low-angle laser light scattering
- R (cross section ratio)
- Deflection (physics)
- Engineering diffraction
- Transport length
- Lamb–Mössbauer factor
- Dynamic structure factor
- Electron wake
- Free streaming
- Cloud drop effective radius
- McStas
- Codes for electromagnetic scattering by cylinders
- Diffraction tomography
- Ionized impurity scattering
- Lattice scattering
- Goniophotometry
- Spin-polarized electron energy loss spectroscopy
- Neutron-acceptance diagram shading
- Lindblad resonance
- Kramers' opacity law
- Gaunt factor
- Plane-wave expansion
- Partial-wave analysis
- Turbidimetry
- Hagen–Rubens relation
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