Essays/Tensor Experiments/TensorExperiments23

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GTE2300C.jpg


NB. ... script experimental.ijs ...

vSgDd2M=:[([(0{])@(mcn smx"2 1 B2kCEr1+SBkCEr1)xRef@hkxF),:@(S03xH{])
vSgDd2 =:gXT(-@(([([(0{])@ch2k xRef@hkxF),:@(S03xH{]))+/"1@((<0 2)|:])@((0|:[)smx])(]*/])@(S02d1L{]))+vSgDd2M)]    NB. ... (+) divergence ...


NB. ... script experimental.ijs ...

S00xL       =:00 00;00 01;00 02;00 03"_
S01dxL      =:01 00;01 01;01 02;01 03"_
S02d1L      =:02 00;02 01;02 02;02 03"_
S03xH       =:03 00;03 01;03 02;03 03"_
S04dxH      =:04 00;04 01;04 02;04 03"_
S05d1H      =:05 00;05 01;05 02;05 03"_
S06ds       =:(<06 00)"_
S07count    =:07 00;07 01"_
   S0700nmbr=:(<07 00)"_
   S0701max =:(<07 01)"_

vS00=:''vS00xL   `S00xL   `]}]
vS01=:''vS01dxL  `S01dxL  `]}]
vS02=:''vS02d1L  `S02d1L  `]}]
vS06=:''vS06ds   `S06ds   `]}]
vS07=:''vS07count`S07count`]}]
vS  =:vS07@vS06@vS02@vS01@vS00@(8 4$_"_)

vSgDxH    =:''((S00xL{])+(S02d1L{])*S06ds{])`S03xH`]}]
vSgDdxH   =:''((S02d1L{])*S06ds{])`S04dxH`]}]
vSgDd1H   =:''((S02d1L{])+vSgDd2*S06ds{])`S05d1H`]}]
vSgDxHtoL =:''(S03xH{]) `S00xL `]}]
vSgDdxHtoL=:''(S04dxH{])`S01dxL`]}]
vSgDd1HtoL=:''(S05d1H{])`S02d1L`]}]
vSgDnmbr  =:''(1+S0700nmbr{])`S0700nmbr`]}]
vSgD      =:(vSgDnmbr@vSgDd1HtoL@vSgDdxHtoL@vSgDxHtoL@vSgDd1H@vSgDdxH@vSgDxH)`]@.((S0700nmbr{])=S0701max{])^:a:

vSgDplot=:<"1@(0|:])@:((((cx0*sin@cx1)*cos@cx2),(cx0*sin@cx1)*sin@cx2)@(S00xL{])"2)


GTE2301C.jpg


NB. ... script experimental.ijs ...

Initds2=:(gXT([(0{])@mcv xRef@hkxF),:@Initx)+/^:2@:*(]*/])@Initdx
Initds =:%:@|@Initds2


GTE2302C.jpg


NB. ... script experimental.ijs ...

Initd1=:Initdx%Initds


load 'plot'


NB. ... x coordinates ...


gXcw  =: 1  0  _  _   _  "_
gXpAll=: 1  1  1  2  _0.6"_

Initx =:  5 , 0.5p1 ,  1p1  , 0    "_
Initdx=: (0 , 0     , _0.01 , 0.220"_)*%@(128"_)

vS00xL    =:Initx
vS01dxL   =:0,0,0,0:
vS02d1L   =:Initd1
vS06ds    =:Initds
vS07count =:(0,160"_)*128"_
pd vSgDplot pdDA=:vSgD@vS''


gXcw  =: 1  0  _  _   _  "_
gXpAll=: 1  1  1  2  _0.6"_

Initx =:  5 , 0.5p1 ,  1p1  , 0    "_
Initdx=: (0 , 0     , _0.01 , 0.220"_)*%@(256"_)

vS00xL    =:Initx
vS01dxL   =:0,0,0,0:
vS02d1L   =:Initd1
vS06ds    =:Initds
vS07count =:(0,160"_)*256"_
pd vSgDplot pdDB=:vSgD@vS''    NB. ... convergence ...


NB. ... y coordinates ...


E3  =.+/"1@((<0 3)|:])"5@R
E1cv=.+/"1@((<0 1)|:])"3@(mcn([smx 0|:])"2 3 E3)
E1cn=.mcn smx"2 1 E1cv

hkyGmetric=.<@:>"1@(0|:])@:(((1 0 0 0,0 1 0 0,0 0 1 0,:0 0 0 _1"_);((3$4:)$0:);((4$4:)$0:);((5$4:)$0:);((6$4:)$0:);1$_"_)"_ 1)
hkyG      =.(6$a:"_),(6$a:"_),hkyGmetric,(6$a:"_),<@:>"1@(0|:])@:(OyAXXS"_ 1),:6$a:"_


gXcw  =: 1  0  _  _   _  "_
gXpAll=: 1  1  1  2  _0.6"_

Inity =:  _5 , 0    , 0 , 0     "_
Initdy=: ( 0 , 0.16 , 0 , 0.7042"_)*%@(256"_)

Initds=.%:@|@((gXT([(0{])@mcv yRef@hkyG),:@Inity)+/^:2@:*(]*/])@Initdy)

vSgDd2=.gXT([([(0{])@E1cn yRef@hkyG),:@(S03xH{]))]

vS00xL   =:Inity
vS01dxL  =:0,0,0,0:
vS02d1L  =:Initdy%Initds
vS06ds   =:Initds
vS07count=:(0,50"_)*256"_
pd <"1@(0|:])@:((cy0,cy1)@(S00xL{])"2) pdDC=:vSgD@vS''


gXcw  =: 1  0  _  _   _  "_
gXpAll=: 1  1  1  2  _0.6"_

Inity =:  _5 , 0    , 0 , 0     "_
Initdy=: ( 0 , 0.16 , 0 , 0.7042"_)*%@(512"_)

Initds=.%:@|@((gXT([(0{])@mcv yRef@hkyG),:@Inity)+/^:2@:*(]*/])@Initdy)

vSgDd2=.gXT([([(0{])@E1cn yRef@hkyG),:@(S03xH{]))]

vS00xL   =:Inity
vS01dxL  =:0,0,0,0:
vS02d1L  =:Initdy%Initds
vS06ds   =:Initds
vS07count=:(0,50"_)*512"_
pd <"1@(0|:])@:((cy0,cy1)@(S00xL{])"2) pdDD=:vSgD@vS''    NB. ... convergence ...


pd 'pdf'
pd 'show'


TEgraphic2300.jpg
... geodesics ...


GTE2303C.jpg


load 'plot'

gXcw  =. 1  0  _  _   _  "_
gXpAll=. 1  1  1  2  _0.6"_

pd (cy3"1@:((S00xL{])"2);(gXT([mcv xRef@hkxF)(S00xL{])"2)%:@|@:(+/^:2"2)@:*(]*/])"1@:((S01dxL{])"2)) }. pdDB

hkyGmetric=.<@:>"1@(0|:])@:(((1 0 0 0,0 1 0 0,0 0 1 0,:0 0 0 _1"_);((3$4:)$0:);((4$4:)$0:);((5$4:)$0:);((6$4:)$0:);1$_"_)"_ 1)
hkyG      =.(6$a:"_),(6$a:"_),hkyGmetric,(6$a:"_),<@:>"1@(0|:])@:(OyAXXS"_ 1),:6$a:"_

pd (cy3"1@:((S00xL{])"2);(gXT([mcv yRef@hkyG)(S00xL{])"2)%:@|@:(+/^:2"2)@:*(]*/])"1@:((S01dxL{])"2)) }. pdDD

pd 'pdf'
pd 'show'


TEgraphic2301.jpg
... 'curvature' resulting from Riemann-Christoffel tensor ...


GTE2304C.jpg


NB. ... execute (ijx) ...

   *./@(0<])@(2-~/\])@:(cx3@(S00xL{])"2) pdDA
1
   *./@(0<])@(2-~/\])@:(cx3@(S00xL{])"2) pdDB
1
   *./@(0<])@(2-~/\])@:(cy3@(S00xL{])"2) pdDC
1
   *./@(0<])@(2-~/\])@:(cy3@(S00xL{])"2) pdDD
1


GTE2305C.jpg


NB. ... execute (ijx) ...

   *./ (0=]) ((2^_11)qtsz]) (]-0.5p1"_)@:(cx1@(S00xL{])"2) pdDA
1
   *./ (0=]) ((2^_14)qtsz]) (]-0.5p1"_)@:(cx1@(S00xL{])"2) pdDB
1
   *./ (0=])                             (cy2@(S00xL{])"2) pdDC
1
   *./ (0=])                             (cy2@(S00xL{])"2) pdDD
1



Download: File:LTE2300C.txt
Download: File:LTE2301C.txt
Download: File:LTE2302C.txt
Download: File:LTE2303C.txt
Download: File:LTE2304C.txt
Download: File:LTE2305C.txt




Download MoinMoin source: File:TensorExperiments23.ijs




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