File:Array of magnetic dipoles.gif
Array_of_magnetic_dipoles.gif (360 × 360 pixels, file size: 3.96 MB, MIME type: image/gif, looped, 600 frames)
Captions
Summary edit
DescriptionArray of magnetic dipoles.gif |
English: The lowest energy configuration for two magnetic dipoles is to align head-to-tail. But if we put the magnetic dipoles in a square array the ground state is composed of cross-like structures known as "microvortices". |
Date | |
Source | https://twitter.com/j_bertolotti/status/1091360729914064897 |
Author | Jacopo Bertolotti |
Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 11.0 code edit
ClearAll["Global`*"] \[Mu]0 = 1.; dt = 0.1; (*time interval*) B[pos_, m_] := \[Mu]0/(4 \[Pi]) (3 ( pos (m.pos))/Norm[pos]^5 - m/Norm[pos]^3); mm = 1.; (*magnitue of the magnetic dipoles. Same for all of them*) mI = 1; (*moment of inertia of each magnetic dipole. Same for all of them*) ndip = 36; (*number of dipoles. As they are arranged on a square it MUST be a perfect square*) ell = 1; (*distance between a dipole and its nearest neighbour*) dipoles = RandomReal[{0, 2 \[Pi]}, {ndip}] ;(*angle with respect to the vertical of each dipole*) vd = Table[0, {ndip}]; positions = Flatten[Table[ell {i, j, 0}, {i, 1, Sqrt[ndip]}, {j, 1, Sqrt[ndip]}], 1]; nsteps = 3000; evo = Reap[Do[ torques = Table[If[i == j, {0, 0, 0}, Cross[mm {Cos[dipoles[[j]]], Sin[dipoles[[j]]], 0}, B[positions[[j]] - positions[[i]], mm {Cos[dipoles[[i]]], Sin[dipoles[[i]]], 0}] ] ], {i, 1, ndip}, {j, 1, ndip}]; (*torque generated by the ith dipole on the jth dipole (assuming I=1)*) ttorques = Table[Sum[torques[[i, j]], {i, 1, ndip}], {j, 1, ndip}][[All, 3]]; vdold = vd; vd = vdold + (ttorques - 0.03 vdold)/mI dt; dold = dipoles; dipoles = dipoles + vd dt; Sow[dipoles]; , nsteps];][[2, 1]]; p1 = Table[Graphics[{Thick, Table[Disk[positions[[i]][[1 ;; 2]], 0.05], {i, 1, ndip}], Table[Arrow[{positions[[i]][[1 ;; 2]] - ell/3 {Cos[evo[[k, i]]], Sin[evo[[k, i]]]}, positions[[i]][[1 ;; 2]] + ell/3 {Cos[evo[[k, i]]], Sin[evo[[k, i]]]}}], {i, 1, ndip}] }, PlotRange -> {{0, ell (Sqrt[ndip] + 1)}, {0, ell (Sqrt[ndip] + 1)}}, AspectRatio -> Automatic], {k, 1, nsteps, 5}]; ListAnimate[p1]
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 |
This file, which was originally posted to
https://twitter.com/j_bertolotti/status/1030470604418428929, was reviewed on 5 February 2019 by reviewer Ronhjones, who confirmed that it was available there under the stated license on that date.
|
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 12:40, 5 February 2019 | 360 × 360 (3.96 MB) | Berto (talk | contribs) | User created page with UploadWizard |
You cannot overwrite this file.
File usage on Commons
There are no pages that use this file.
Metadata
This file contains additional information such as Exif metadata which may have been added by the digital camera, scanner, or software program used to create or digitize it. If the file has been modified from its original state, some details such as the timestamp may not fully reflect those of the original file. The timestamp is only as accurate as the clock in the camera, and it may be completely wrong.
GIF file comment | Created with the Wolfram Language : www.wolfram.com |
---|