User:Tom Allen/TensorExperimentsZ33
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... ADDENDUM ...
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... the scheme for this model ...
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... NOTE 1 ...
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... NOTE 2 ...
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... NOTE 3 ...
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... plot a geodesic with increasing accuracy ...
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NB. ... compare with TensorExperimentsZ31 ...
gXm0All=. 1 _0.02 _ 0"_
gXm1All=. 1 _0.02 1 1"_
Initn =. 1 , 0 , 0 , 0 "_
Initdn=. (0 , 0.01 , 0 , 0.06"_)*%@(2"_)
Initds=.|@((((0{])^2:)+((1{])^2:)+((2{])^2:)+-@((3{])^2:))^0.5"_)@Initdn
vS00xL =.Initn
vS01dxL =.0,0,0,0:
vS02d1L =.Initdn%Initds
vS06ds =.Initds
vS07count=.(0,9000"_)*2"_
vSgDd2=.gXM([([(0{])@E1cn nRef@hknQ),:@(S03xH{]))]
pdDA=:vSgD@vS''
Initn =. 1 , 0 , 0 , 0 "_
Initdn=. (0 , 0.01 , 0 , 0.06"_)*%@(4"_)
Initds=.|@((((0{])^2:)+((1{])^2:)+((2{])^2:)+-@((3{])^2:))^0.5"_)@Initdn
vS00xL =.Initn
vS01dxL =.0,0,0,0:
vS02d1L =.Initdn%Initds
vS06ds =.Initds
vS07count=.(0,9000"_)*4"_
vSgDd2=.gXM([([(0{])@E1cn nRef@hknQ),:@(S03xH{]))]
pdDB=:vSgD@vS''
Initn =. 1 , 0 , 0 , 0 "_
Initdn=. (0 , 0.01 , 0 , 0.06"_)*%@(8"_)
Initds=.|@((((0{])^2:)+((1{])^2:)+((2{])^2:)+-@((3{])^2:))^0.5"_)@Initdn
vS00xL =.Initn
vS01dxL =.0,0,0,0:
vS02d1L =.Initdn%Initds
vS06ds =.Initds
vS07count=.(0,9000"_)*8"_
vSgDd2=.gXM([([(0{])@E1cn nRef@hknQ),:@(S03xH{]))]
pdDC=:vSgD@vS''
Initn =. 1 , 0 , 0 , 0 "_
Initdn=. (0 , 0.01 , 0 , 0.06"_)*%@(16"_)
Initds=.|@((((0{])^2:)+((1{])^2:)+((2{])^2:)+-@((3{])^2:))^0.5"_)@Initdn
vS00xL =.Initn
vS01dxL =.0,0,0,0:
vS02d1L =.Initdn%Initds
vS06ds =.Initds
vS07count=.(0,9000"_)*16"_
vSgDd2=.gXM([([(0{])@E1cn nRef@hknQ),:@(S03xH{]))]
pdDD=:vSgD@vS''
Initn =. 1 , 0 , 0 , 0 "_
Initdn=. (0 , 0.01 , 0 , 0.06"_)*%@(32"_)
Initds=.|@((((0{])^2:)+((1{])^2:)+((2{])^2:)+-@((3{])^2:))^0.5"_)@Initdn
vS00xL =.Initn
vS01dxL =.0,0,0,0:
vS02d1L =.Initdn%Initds
vS06ds =.Initds
vS07count=.(0,9000"_)*32"_
vSgDd2=.gXM([([(0{])@E1cn nRef@hknQ),:@(S03xH{]))]
pdDE=:vSgD@vS''
pdDA arrayPut 'pdDA'
arrayClose 'pdDA'
pdDB arrayPut 'pdDB'
arrayClose 'pdDB'
pdDC arrayPut 'pdDC'
arrayClose 'pdDC'
pdDD arrayPut 'pdDD'
arrayClose 'pdDD'
pdDE arrayPut 'pdDE'
arrayClose 'pdDE'
NB. ... establish arrays if necessary ...
arrayOpen 'pdDA'
pdDA=: 18001 8 4 arrayGet 'pdDA' NB. ... shape required ...
arrayClose 'pdDA'
arrayOpen 'pdDB'
pdDB=: 36001 8 4 arrayGet 'pdDB' NB. ... shape required ...
arrayClose 'pdDB'
arrayOpen 'pdDC'
pdDC=: 72001 8 4 arrayGet 'pdDC' NB. ... shape required ...
arrayClose 'pdDC'
arrayOpen 'pdDD'
pdDD=:144001 8 4 arrayGet 'pdDD' NB. ... shape required ...
arrayClose 'pdDD'
arrayOpen 'pdDE'
pdDE=:288001 8 4 arrayGet 'pdDE' NB. ... shape required ...
arrayClose 'pdDE'
load 'plot'
pd <"1@(0|:])@:((cn0,cn1)@(S00xL{])"2) pdDA
pd <"1@(0|:])@:((cn0,cn1)@(S00xL{])"2) pdDB
pd <"1@(0|:])@:((cn0,cn1)@(S00xL{])"2) pdDC
pd <"1@(0|:])@:((cn0,cn1)@(S00xL{])"2) pdDD
pd <"1@(0|:])@:((cn0,cn1)@(S00xL{])"2) pdDE
pd 'pdf'
pd 'show'
... geodesic ...
NB. ... execute (ijx) ...
NB. ... path in n0/n1 plane ...
*./ (0=]) cn2"1@:((S00xL{])"2) pdDE
1
NB. ... time increases continually (a real path in spacetime) ...
*./@(0<])@(2-~/\])@:(cn3@(S00xL{])"2) pdDE
1
...
... additional precision ...
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NB. ... compare with TensorExperimentsZ31 ...
gXm0All=. 1 _0.02 _ 0"_
gXm1All=. 1 _0.02 1 1"_
Initn =. 1 , 0 , 0 , 0 "_
Initdn=. (0 , 0.01 , 0 , 0.06"_)*%@(32"_)
Initds=.|@((((0{])^2:)+((1{])^2:)+((2{])^2:)+-@((3{])^2:))^0.5"_)@Initdn
vS00xL =.Initn
vS01dxL =.0,0,0,0:
vS02d1L =.Initdn%Initds
vS06ds =.Initds
vS07count=.(0,9000"_)*32"_
vSgDd2=.gXM([([(0{])@E1cn nRef@hknQ),:@(S03xH{]))]
pdDF=:vSgD@vS''
Initn =. 1 , 0 , 0 , 0 "_
Initdn=. (0 , 0.01 , 0 , 0.06"_)*%@(64"_)
Initds=.|@((((0{])^2:)+((1{])^2:)+((2{])^2:)+-@((3{])^2:))^0.5"_)@Initdn
vS00xL =.Initn
vS01dxL =.0,0,0,0:
vS02d1L =.Initdn%Initds
vS06ds =.Initds
vS07count=.(0,9000"_)*64"_
vSgDd2=.gXM([([(0{])@E1cn nRef@hknQ),:@(S03xH{]))]
pdDG=:vSgD@vS''
Initn =. 1 , 0 , 0 , 0 "_
Initdn=. (0 , 0.01 , 0 , 0.06"_)*%@(128"_)
Initds=.|@((((0{])^2:)+((1{])^2:)+((2{])^2:)+-@((3{])^2:))^0.5"_)@Initdn
vS00xL =.Initn
vS01dxL =.0,0,0,0:
vS02d1L =.Initdn%Initds
vS06ds =.Initds
vS07count=.(0,9000"_)*128"_
vSgDd2=.gXM([([(0{])@E1cn nRef@hknQ),:@(S03xH{]))]
pdDH=:vSgD@vS''
pdDF arrayPut 'pdDF'
arrayClose 'pdDF'
pdDG arrayPut 'pdDG'
arrayClose 'pdDG'
pdDH arrayPut 'pdDH'
arrayClose 'pdDH'
NB. ... establish arrays if necessary ...
arrayOpen 'pdDF'
pdDF=: 288001 8 4 arrayGet 'pdDF' NB. ... shape required ...
arrayClose 'pdDF'
arrayOpen 'pdDG'
pdDG=: 576001 8 4 arrayGet 'pdDG' NB. ... shape required ...
arrayClose 'pdDG'
arrayOpen 'pdDH'
pdDH=:1152001 8 4 arrayGet 'pdDH' NB. ... shape required ...
arrayClose 'pdDH'
load 'plot'
pd <"1@(0|:])@:((cn0,cn1)@(S00xL{])"2) pdDF
pd <"1@(0|:])@:((cn0,cn1)@(S00xL{])"2) pdDG
pd <"1@(0|:])@:((cn0,cn1)@(S00xL{])"2) pdDH
pd 'pdf'
pd 'show'
... geodesic ...
NB. ... execute (ijx) ...
NB. ... path in n0/n1 plane ...
*./ (0=]) cn2"1@:((S00xL{])"2) pdDH
1
NB. ... time increases continually (a real path in spacetime) ...
*./@(0<])@(2-~/\])@:(cn3@(S00xL{])"2) pdDH
1
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... plot paths in spacetime ...
...
NB. ... compare with TensorExperimentsZ31 ...
gXm0All=. 1 _0.02 _ 0"_
gXm1All=. 1 _0.02 1 1"_
Initn =. 1 , 0 , 0 , 0 "_
Initdn=. (0 , 0.01 , 0 , 0.0583095"_)*%@(2"_)
Initds=.((((0{])^2:)+((1{])^2:)+((2{])^2:)+((3{])^2:))^0.5"_)@Initdn
vS00xL =.Initn
vS01dxL =.0,0,0,0:
vS02d1L =.Initdn%Initds
vS06ds =.Initds
vS07count=.(0,9000"_)*2"_
vSgDd2=.gXM([([(0{])@E1cn nRef@hknQ),:@(S03xH{]))]
pdDJ=:vSgD@vS''
Initn =. 1 , 0 , 0 , 0 "_
Initdn=. (0 , 0.01 , 0 , 0.0583095"_)*%@(4"_)
Initds=.((((0{])^2:)+((1{])^2:)+((2{])^2:)+((3{])^2:))^0.5"_)@Initdn
vS00xL =.Initn
vS01dxL =.0,0,0,0:
vS02d1L =.Initdn%Initds
vS06ds =.Initds
vS07count=.(0,9000"_)*4"_
vSgDd2=.gXM([([(0{])@E1cn nRef@hknQ),:@(S03xH{]))]
pdDK=:vSgD@vS''
Initn =. 1 , 0 , 0 , 0 "_
Initdn=. (0 , 0.01 , 0 , 0.0583095"_)*%@(8"_)
Initds=.((((0{])^2:)+((1{])^2:)+((2{])^2:)+((3{])^2:))^0.5"_)@Initdn
vS00xL =.Initn
vS01dxL =.0,0,0,0:
vS02d1L =.Initdn%Initds
vS06ds =.Initds
vS07count=.(0,9000"_)*8"_
vSgDd2=.gXM([([(0{])@E1cn nRef@hknQ),:@(S03xH{]))]
pdDL=:vSgD@vS''
Initn =. 1 , 0 , 0 , 0 "_
Initdn=. (0 , 0.01 , 0 , 0.0583095"_)*%@(16"_)
Initds=.((((0{])^2:)+((1{])^2:)+((2{])^2:)+((3{])^2:))^0.5"_)@Initdn
vS00xL =.Initn
vS01dxL =.0,0,0,0:
vS02d1L =.Initdn%Initds
vS06ds =.Initds
vS07count=.(0,9000"_)*16"_
vSgDd2=.gXM([([(0{])@E1cn nRef@hknQ),:@(S03xH{]))]
pdDM=:vSgD@vS''
Initn =. 1 , 0 , 0 , 0 "_
Initdn=. (0 , 0.01 , 0 , 0.0583095"_)*%@(32"_)
Initds=.((((0{])^2:)+((1{])^2:)+((2{])^2:)+((3{])^2:))^0.5"_)@Initdn
vS00xL =.Initn
vS01dxL =.0,0,0,0:
vS02d1L =.Initdn%Initds
vS06ds =.Initds
vS07count=.(0,9000"_)*32"_
vSgDd2=.gXM([([(0{])@E1cn nRef@hknQ),:@(S03xH{]))]
pdDN=:vSgD@vS''
pdDJ arrayPut 'pdDJ'
arrayClose 'pdDJ'
pdDK arrayPut 'pdDK'
arrayClose 'pdDK'
pdDL arrayPut 'pdDL'
arrayClose 'pdDL'
pdDM arrayPut 'pdDM'
arrayClose 'pdDM'
pdDN arrayPut 'pdDN'
arrayClose 'pdDN'
NB. ... establish arrays if necessary ...
arrayOpen 'pdDJ'
pdDJ=: 18001 8 4 arrayGet 'pdDJ' NB. ... shape required ...
arrayClose 'pdDJ'
arrayOpen 'pdDK'
pdDK=: 36001 8 4 arrayGet 'pdDK' NB. ... shape required ...
arrayClose 'pdDK'
arrayOpen 'pdDL'
pdDL=: 72001 8 4 arrayGet 'pdDL' NB. ... shape required ...
arrayClose 'pdDL'
arrayOpen 'pdDM'
pdDM=:144001 8 4 arrayGet 'pdDM' NB. ... shape required ...
arrayClose 'pdDM'
arrayOpen 'pdDN'
pdDN=:288001 8 4 arrayGet 'pdDN' NB. ... shape required ...
arrayClose 'pdDN'
load 'plot'
pd <"1@(0|:])@:((cn0,cn1)@(S00xL{])"2) pdDJ
pd <"1@(0|:])@:((cn0,cn1)@(S00xL{])"2) pdDK
pd <"1@(0|:])@:((cn0,cn1)@(S00xL{])"2) pdDL
pd <"1@(0|:])@:((cn0,cn1)@(S00xL{])"2) pdDM
pd <"1@(0|:])@:((cn0,cn1)@(S00xL{])"2) pdDN
pd 'pdf'
pd 'show'
... paths in spacetime ...
NB. ... execute (ijx) ...
NB. ... path in n0/n1 plane ...
*./ (0=]) cn2"1@:((S00xL{])"2) pdDN
1
NB. ... time increases continually (a real path in spacetime) ...
*./@(0<])@(2-~/\])@:(cn3@(S00xL{])"2) pdDN
1
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... NOTE 4 ...
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... energy is manifested in the divergence of space and time ...
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Download: File:LTEZ3300C.txt
Download: File:LTEZ3301C.txt
Download: File:LTEZ3302D.txt
Download: File:LTEZ3303C.txt
Download: File:LTEZ3305D.txt
Download MoinMoin source: File:TensorExperimentsZ33.ijs