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Summary
| Description |
English: Relaxation of the nuclear magnetization in the presence of an external magnetic field, as described by the Bloch equations.
The chosen values for the relaxation times are not realistic and were selected to result in a simple visualization more than Physical realism. |
| Date | |
| Source | https://twitter.com/j_bertolotti/status/1369962983074455552 |
| Author | Jacopo Bertolotti |
| Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 12.0 code
\[Gamma] = 1; (*gyromagnetic ratio*)
m0 = {1, 0, 0}; (*initial magnetization*)
b = {0, 0, 1}; (*external magnetic field*)
T1 = 1; T2 = 1; (*relaxation times*)
meq = {0, 0, 0.1}; (*equilibrium magnetization*)
matrix[B_] := {{-1/T2, \[Gamma] B[[3]], -\[Gamma] B[[2]]}, {-\[Gamma] B[[3]], -1/T2, \[Gamma] B[[1]]}, {\[Gamma] B[[2]], -\[Gamma] B[[1]], -1/T1}}; (*evolution matrix*)
dt = 0.05; (*time step*)
m = m0;
evo = Reap[Do[
m = m/Norm[m]; (*make sure the vector is normalized*)
m = m + dt*(matrix[b] . m + meq/T1);
Sow[m]
, 1000]][[2, 1]];
frames = Table[
Graphics3D[{
Black, Sphere[{0, 0, 0}, 0.05], Sphere[evo[[j]], 0.02], Thick, Line[{{0, 0, 0}, evo[[j]]}],
Orange, Line[evo[[1 ;; j]] ],
Black, Arrow[{{-1, -1, 0}, {-1, -1, 0.8}}],
Text[Style["\!\(\*SubscriptBox[OverscriptBox[\(B\), \(\[Rule]\)], \\(ext\)]\)", Black, Bold], {-1, -1, 1}],
Thin, Gray,
Line[{{-1, -1, 0}, {-1, 1, 0}, {1, 1, 0}, {1, -1, 0}, {-1, -1, 0}}],
Black, Thick,
Arrow[{{-1, 1, 0}, {-1, 1, 0.5}}],
Arrow[{{-1, 1, 0}, {-0.5, 1, 0}}],
Arrow[{{-1, 1, 0}, {-1, 0.5, 0}}],
Text[Style["y", Black, Bold], {-0.4, 1, 0}],
Text[Style["x", Black, Bold], {-1, 0.4, 0}],
Text[Style["z", Black, Bold], {-1, 1, 0.6}]
}, PlotRange -> {{-1.2, 1.2}, {-1.2, 1.2}, {0, 1.2}},
Boxed -> False, ImageSize -> 400]
, {j, 2, 1000, 5}];
ListAnimate[frames]
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
 
|
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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File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 14:14, 12 March 2021 | | 534 × 497 (2.43 MB) | Berto | Uploaded own work with UploadWizard |
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