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'
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
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... 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'
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 ...
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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 , 0.0583095"_)*%@(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'
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