“Choices of gauge”
“Choices of gauge”
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Table[{x,0},{x,10}]
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{{1,0},{2,0},{3,0},{4,0},{5,0},{6,0},{7,0},{8,0},{9,0},{10,0}}
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UpdatesPicture[cfun_,len_Integer,t_Integer,pitch_:0.1]:=Graphics[{Line/@#,Point/@#}&@MapIndexed[If[#2[[3]]1,#,-#-pitch#2[[1]]]&,NestList[MapAt[{First[#],Last[#]+1}&,#,List/@cfun[#]]&,Table[{x,0},{x,len}],t],{3}]]
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UpdatesPicture[{1}&,10,5]
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RandomSample[Range[10],3]
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{7,9,3}
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UpdatesPicture[RandomSample[Range[10],3]&,10,5,.2]
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UpdatesPicture[RandomSample[Range[20],6]&,20,15,.2]
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UpdatesPicture[Range[10]&,10,5,.2]
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UpdatesPicture[{1,5}&,10,5,.2]
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“strong hyperbolicity” : the succession of hypersurfaces don’t intersect
I.e. in each update, every point occurs at least once....
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UpdatesPicture[Flatten[Table[Table[i,1+RandomInteger[3]],{i,20}]]&,20,5,.2]
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UpdatesPicture[Flatten[Table[Table[i,RandomInteger[3]],{i,20}]]&,20,5,.2]
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A known case in GR where there is strong hyperbolicity is the Z4 gauge, with a vector (“BSSN formalism”)
z
μ
cfun picks which points to update
cfun picks which points to update
E.g. light cone gauge is ______