User:Tom Allen/TensorExperimentsR15

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NB. ... script experimentalR.ijs ...

rfE3=:+/"1@((<0 2)|:])"5@R

rfE1cv=:+/"1@((<0 1)|:])"3@(mcn([smx 0|:])"2 3 rfE3)

rfE1cn=:mcn smx"2 1 rfE1cv


load 'plot'

gXRAll=:,:@(0.05 1 2 8 1 1 1 _0.1 0 0"_)

xCpts=:_ 0.4 1.7 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.00p1 0.00p1 0"_)*10"_

pd (gXR(cx0"_ 1;[(0{])"1@rfE1cn xRef@hkxR03)]) pTtotal xCpts''

xCpts=:_ 0.4 1.7 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.25p1 0.25p1 0"_)*10"_

pd (gXR(cx0"_ 1;[(0{])"1@rfE1cn xRef@hkxR03)]) pTtotal xCpts''

xCpts=:_ 0.4 1.7 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.40p1 0.40p1 0"_)*10"_

pd (gXR(cx0"_ 1;[(0{])"1@rfE1cn xRef@hkxR03)]) pTtotal xCpts''

xCpts=:_ 0.4 1.7 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.50p1 0.50p1 0"_)*10"_

pd (gXR(cx0"_ 1;[(0{])"1@rfE1cn xRef@hkxR03)]) pTtotal xCpts''

xCpts=:_ 0.4 1.7 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.60p1 0.60p1 0"_)*10"_

pd (gXR(cx0"_ 1;[(0{])"1@rfE1cn xRef@hkxR03)]) pTtotal xCpts''

xCpts=:_ 0.4 1.7 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.75p1 0.75p1 0"_)*10"_

pd (gXR(cx0"_ 1;[(0{])"1@rfE1cn xRef@hkxR03)]) pTtotal xCpts''

xCpts=:_ 0.4 1.7 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 1.00p1 1.00p1 0"_)*10"_

pd (gXR(cx0"_ 1;[(0{])"1@rfE1cn xRef@hkxR03)]) pTtotal xCpts''

pd (((0.8723"_)@]"0);]"0) pTsteps _ _6 8 160

pd (((1.0912"_)@]"0);]"0) pTsteps _ _6 8 160

pd (((1.3202"_)@]"0);]"0) pTsteps _ _6 8 160

pd 'pdf'
pd 'show'


JTER1500G.jpg
... divergence of x0 (E1cn = -rfE1cn) ...


vSgDd2M=.[([(0{])@E1cn xRef@hkxR03),:@(S03xH{])
vSgDd2 =.gXR(-@(([([(0{])@ch2k xRef@hkxR03),:@(S03xH{]))+/"1@((<0 2)|:])@((0|:[)smx])(]*/])@(S02d1L{]))+vSgDd2M)]

Initds2=.(gXR([(0{])@mcv xRef@hkxR03),:@Initx)+/^:2@:*(]*/])@Initdx
Initds =.%:@|@Initds2

gXRAll=:,:@(0.05 1 2 8 1 1 1 _0.1 0 0"_)

Initx =:  0.8723 , 0.5p1 , 0.25p1 , 0p1 "_
Initdx=: (0      , 0     , 0.001  , 0.01"_)*%@(1"_)

vS00xL    =:Initx
vS01dxL   =:0,0,0,0:
vS02d1L   =:Initd1
vS06ds    =:Initds
vS07count =:(0,6283"_)*1"_
pdDE      =:vSgD@vS''

pdDE arrayPut   'pdDE'
     arrayClose 'pdDE'

vSgDd2M=.[([(0{])@rfE1cn xRef@hkxR03),:@(S03xH{])
vSgDd2 =.gXR(-@(([([(0{])@ch2k xRef@hkxR03),:@(S03xH{]))+/"1@((<0 2)|:])@((0|:[)smx])(]*/])@(S02d1L{]))+vSgDd2M)]

Initds2=.(gXR([(0{])@mcv xRef@hkxR03),:@Initx)+/^:2@:*(]*/])@Initdx
Initds =.%:@|@Initds2

gXRAll=:,:@(0.05 1 2 8 1 1 1 _0.1 0 0"_)

Initx =:  1.0912 , 0.5p1 , 0.25p1 , 0p1 "_
Initdx=: (0      , 0     , 0.001  , 0.01"_)*%@(1"_)

vS00xL    =:Initx
vS01dxL   =:0,0,0,0:
vS02d1L   =:Initd1
vS06ds    =:Initds
vS07count =:(0,6283"_)*1"_
pdDF      =:vSgD@vS''

pdDF arrayPut   'pdDF'
     arrayClose 'pdDF'

vSgDd2M=.[([(0{])@E1cn xRef@hkxR03),:@(S03xH{])
vSgDd2 =.gXR(-@(([([(0{])@ch2k xRef@hkxR03),:@(S03xH{]))+/"1@((<0 2)|:])@((0|:[)smx])(]*/])@(S02d1L{]))+vSgDd2M)]

Initds2=.(gXR([(0{])@mcv xRef@hkxR03),:@Initx)+/^:2@:*(]*/])@Initdx
Initds =.%:@|@Initds2

gXRAll=:,:@(0.05 1 2 8 1 1 1 _0.1 0 0"_)

Initx =:  1.3202 , 0.5p1 , 0.25p1 , 0p1 "_
Initdx=: (0      , 0     , 0.001  , 0.01"_)*%@(1"_)

vS00xL    =:Initx
vS01dxL   =:0,0,0,0:
vS02d1L   =:Initd1
vS06ds    =:Initds
vS07count =:(0,6283"_)*1"_
pdDG      =:vSgD@vS''

pdDG arrayPut   'pdDG'
     arrayClose 'pdDG'


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

               arrayOpen  'pdDE'
pdDE=:6284 8 4 arrayGet   'pdDE'   NB. ... shape required ...
               arrayClose 'pdDE'

               arrayOpen  'pdDF'
pdDF=:6284 8 4 arrayGet   'pdDF'   NB. ... shape required ...
               arrayClose 'pdDF'

               arrayOpen  'pdDG'
pdDG=:6284 8 4 arrayGet   'pdDG'   NB. ... shape required ...
               arrayClose 'pdDG'


load 'plot'

pd ((0.8723*cos@]"0);0.8723*sin@]"0) pTsteps _ 0p1 2p1 160

pd vSgDplot pdDE

pd ((1.0912*cos@]"0);1.0912*sin@]"0) pTsteps _ 0p1 2p1 160

pd vSgDplot pdDF

pd ((1.3202*cos@]"0);1.3202*sin@]"0) pTsteps _ 0p1 2p1 160

pd vSgDplot pdDG

pd 'aspect 1'
pd 'pdf'
pd 'show'


JTER1501E.jpg
... geodesics synchronized with EM wave ...


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

   (S00xL{])@{: pdDE
0.872299 1.5708 7.06839 62.83

   (S00xL{])@{: pdDF
1.09118 1.5708 7.06839 62.8299

   (S00xL{])@{: pdDG
1.3202 1.5708 7.0684 62.83


load 'plot'

gXRAll=:,:@(0.05 1 2 8 1 1 1 _0.1 0 0"_)

xCpts=:_ 0.4 1.7 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.00p1 0.00p1 0"_)*10"_

pd (gXR(cx0"_ 1;[(2{])"1@rfE1cn xRef@hkxR03)]) pTtotal xCpts''

xCpts=:_ 0.4 1.7 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.25p1 0.25p1 0"_)*10"_

pd (gXR(cx0"_ 1;[(2{])"1@rfE1cn xRef@hkxR03)]) pTtotal xCpts''

xCpts=:_ 0.4 1.7 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.40p1 0.40p1 0"_)*10"_

pd (gXR(cx0"_ 1;[(2{])"1@rfE1cn xRef@hkxR03)]) pTtotal xCpts''

xCpts=:_ 0.4 1.7 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.50p1 0.50p1 0"_)*10"_

pd (gXR(cx0"_ 1;[(2{])"1@rfE1cn xRef@hkxR03)]) pTtotal xCpts''

xCpts=:_ 0.4 1.7 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.60p1 0.60p1 0"_)*10"_

pd (gXR(cx0"_ 1;[(2{])"1@rfE1cn xRef@hkxR03)]) pTtotal xCpts''

xCpts=:_ 0.4 1.7 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.75p1 0.75p1 0"_)*10"_

pd (gXR(cx0"_ 1;[(2{])"1@rfE1cn xRef@hkxR03)]) pTtotal xCpts''

xCpts=:_ 0.4 1.7 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 1.00p1 1.00p1 0"_)*10"_

pd (gXR(cx0"_ 1;[(2{])"1@rfE1cn xRef@hkxR03)]) pTtotal xCpts''

pd (((0.8723"_)@]"0);]"0) pTsteps _ _0.7 0.7 160

pd (((1.0912"_)@]"0);]"0) pTsteps _ _0.7 0.7 160

pd (((1.3202"_)@]"0);]"0) pTsteps _ _0.7 0.7 160

pd 'pdf'
pd 'show'


JTER1502G.jpg
... divergence of x2 ...


load 'plot'

gXRAll=:,:@(0.05 1 2 8 1 1 1 _0.1 0 0"_)

xCpts=:_ 0.4 1.7 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.00p1 0.00p1 0"_)*10"_

pd (gXR(cx0"_ 1;[(3{])"1@rfE1cn xRef@hkxR03)]) pTtotal xCpts''

xCpts=:_ 0.4 1.7 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.25p1 0.25p1 0"_)*10"_

pd (gXR(cx0"_ 1;[(3{])"1@rfE1cn xRef@hkxR03)]) pTtotal xCpts''

xCpts=:_ 0.4 1.7 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.40p1 0.40p1 0"_)*10"_

pd (gXR(cx0"_ 1;[(3{])"1@rfE1cn xRef@hkxR03)]) pTtotal xCpts''

xCpts=:_ 0.4 1.7 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.50p1 0.50p1 0"_)*10"_

pd (gXR(cx0"_ 1;[(3{])"1@rfE1cn xRef@hkxR03)]) pTtotal xCpts''

xCpts=:_ 0.4 1.7 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.60p1 0.60p1 0"_)*10"_

pd (gXR(cx0"_ 1;[(3{])"1@rfE1cn xRef@hkxR03)]) pTtotal xCpts''

xCpts=:_ 0.4 1.7 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.75p1 0.75p1 0"_)*10"_

pd (gXR(cx0"_ 1;[(3{])"1@rfE1cn xRef@hkxR03)]) pTtotal xCpts''

xCpts=:_ 0.4 1.7 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 1.00p1 1.00p1 0"_)*10"_

pd (gXR(cx0"_ 1;[(3{])"1@rfE1cn xRef@hkxR03)]) pTtotal xCpts''

pd (((0.8723"_)@]"0);]"0) pTsteps _ _0.09 0.09 160

pd (((1.0912"_)@]"0);]"0) pTsteps _ _0.09 0.09 160

pd (((1.3202"_)@]"0);]"0) pTsteps _ _0.09 0.09 160

pd 'pdf'
pd 'show'


JTER1503F.jpg
... divergence of x3 ...


load 'plot'

gXRAll=:,:@(0.05 1 2 8 1 1 1 _0.1 0 0"_)

xCpts=:_ 1 1 0,_ 0.5p1 0.5p1 0,_ 0.25p1 2.25p1 100,:_ 0p1 0p1 0"_

pd (gXR(cx2"_ 1;[(0{])"1@rfE1cn xRef@hkxR03)]) pTtotal xCpts''

xCpts=:_ 1 1 0,_ 0.5p1 0.5p1 0,_ 0.25p1 2.25p1 100,:_ 0p1 0p1 0"_

pd (gXR(cx2"_ 1;[(1{])"1@rfE1cn xRef@hkxR03)]) pTtotal xCpts''

xCpts=:_ 1 1 0,_ 0.5p1 0.5p1 0,_ 0.25p1 2.25p1 100,:_ 0p1 0p1 0"_

pd (gXR(cx2"_ 1;[(2{])"1@rfE1cn xRef@hkxR03)]) pTtotal xCpts''

xCpts=:_ 1 1 0,_ 0.5p1 0.5p1 0,_ 0.25p1 2.25p1 100,:_ 0p1 0p1 0"_

pd (gXR(cx2"_ 1;[(3{])"1@rfE1cn xRef@hkxR03)]) pTtotal xCpts''

pd 'pdf'
pd 'show'


JTER1504F.jpg
... divergence of x0 x1 x2 x3 ...


vSgDd2M=.[([(0{])@rfE1cn xRef@hkxR03),:@(S03xH{])
vSgDd2 =.gXR(-@(([([(0{])@ch2k xRef@hkxR03),:@(S03xH{]))+/"1@((<0 2)|:])@((0|:[)smx])(]*/])@(S02d1L{]))+vSgDd2M)]

Initds2=.(gXR([(0{])@mcv xRef@hkxR03),:@Initx)+/^:2@:*(]*/])@Initdx
Initds =.%:@|@Initds2

gXRAll=:,:@(0.05 1 2 8 1 1 1 _0.1 0 0"_)

Initx =:  1 , 0.5p1 , 0.25p1 , 0p1"_
Initdx=: (0 , 0     , 0.01   , 0.1"_)*%@(512"_)

vS00xL    =:Initx
vS01dxL   =:0,0,0,0:
vS02d1L   =:Initd1
vS06ds    =:Initds
vS07count =:(0,628"_)*512"_
pdDH      =:vSgD@vS''

pdDH arrayPut   'pdDH'
     arrayClose 'pdDH'


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

                 arrayOpen  'pdDH'
pdDH=:321537 8 4 arrayGet   'pdDH'   NB. ... shape required ...
                 arrayClose 'pdDH'


load 'plot'

pd ((1*cos@]"0);1*sin@]"0) pTsteps _ 0p1 2p1 160

pd vSgDplot pdDH

pd 'aspect 1'
pd 'pdf'
pd 'show'


JTER1505D.jpg
... a geodesic synchronized with EM wave ...


load 'plot'

gXRAll=:,:@(0.05 1 2 8 1 1 1 _0.1 0 0"_)

xCpts=:_ 1.1955 1.1955 0,_ 0.5p1 0.5p1 0,_ 0.25p1 2.25p1 100,:_ 0p1 0p1 0"_

pd (gXR(cx2"_ 1;[(0{])"1@rfE1cn xRef@hkxR03)]) pTtotal xCpts''

xCpts=:_ 1.1955 1.1955 0,_ 0.5p1 0.5p1 0,_ 0.25p1 2.25p1 100,:_ 0p1 0p1 0"_

pd (gXR(cx2"_ 1;[(1{])"1@rfE1cn xRef@hkxR03)]) pTtotal xCpts''

xCpts=:_ 1.1955 1.1955 0,_ 0.5p1 0.5p1 0,_ 0.25p1 2.25p1 100,:_ 0p1 0p1 0"_

pd (gXR(cx2"_ 1;[(2{])"1@rfE1cn xRef@hkxR03)]) pTtotal xCpts''

xCpts=:_ 1.1955 1.1955 0,_ 0.5p1 0.5p1 0,_ 0.25p1 2.25p1 100,:_ 0p1 0p1 0"_

pd (gXR(cx2"_ 1;[(3{])"1@rfE1cn xRef@hkxR03)]) pTtotal xCpts''

pd 'pdf'
pd 'show'


JTER1506C.jpg
... divergence of x0 x1 x2 x3 ...


vSgDd2M=.[([(0{])@rfE1cn xRef@hkxR03),:@(S03xH{])
vSgDd2 =.gXR(-@(([([(0{])@ch2k xRef@hkxR03),:@(S03xH{]))+/"1@((<0 2)|:])@((0|:[)smx])(]*/])@(S02d1L{]))+vSgDd2M)]

Initds2=.(gXR([(0{])@mcv xRef@hkxR03),:@Initx)+/^:2@:*(]*/])@Initdx
Initds =.%:@|@Initds2

gXRAll=:,:@(0.05 1 2 8 1 1 1 _0.1 0 0"_)

Initx =:  1.1955 , 0.5p1 , 0.25p1 , 0p1"_
Initdx=: (0      , 0     , 0.01   , 0.1"_)*%@(512"_)

vS00xL    =:Initx
vS01dxL   =:0,0,0,0:
vS02d1L   =:Initd1
vS06ds    =:Initds
vS07count =:(0,628"_)*512"_
pdDI      =:vSgD@vS''

pdDI arrayPut   'pdDI'
     arrayClose 'pdDI'


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

                 arrayOpen  'pdDI'
pdDI=:321537 8 4 arrayGet   'pdDI'   NB. ... shape required ...
                 arrayClose 'pdDI'


load 'plot'

pd ((1.1955*cos@]"0);1.1955*sin@]"0) pTsteps _ 0p1 2p1 160

pd vSgDplot pdDI

pd 'aspect 1'
pd 'pdf'
pd 'show'


JTER1507F.jpg
... a geodesic synchronized with EM wave ...


vSgDd2M=.[([(0{])@rfE1cn xRef@hkxR03),:@(S03xH{])
vSgDd2 =.gXR(-@(([([(0{])@ch2k xRef@hkxR03),:@(S03xH{]))+/"1@((<0 2)|:])@((0|:[)smx])(]*/])@(S02d1L{]))+vSgDd2M)]

Initds2=.(gXR([(0{])@mcv xRef@hkxR03),:@Initx)+/^:2@:*(]*/])@Initdx
Initds =.%:@|@Initds2

gXRAll=:,:@(0.05 1 2 8 1 1 1 _0.1 0 0"_)

Initx =:  1.3170 , 0.5p1 , 0.25p1 , 0p1"_
Initdx=: (0      , 0     , 0.01   , 0.1"_)*%@(128"_)

vS00xL    =:Initx
vS01dxL   =:0,0,0,0:
vS02d1L   =:Initd1
vS06ds    =:Initds
vS07count =:(0,60"_)*128"_
pdDQ      =:vSgD@vS''

pdDQ arrayPut   'pdDQ'
     arrayClose 'pdDQ'

vSgDd2M=.[([(0{])@rfE1cn xRef@hkxR03),:@(S03xH{])
vSgDd2 =.gXR(-@(([([(0{])@ch2k xRef@hkxR03),:@(S03xH{]))+/"1@((<0 2)|:])@((0|:[)smx])(]*/])@(S02d1L{]))+vSgDd2M)]

Initds2=.(gXR([(0{])@mcv xRef@hkxR03),:@Initx)+/^:2@:*(]*/])@Initdx
Initds =.%:@|@Initds2

gXRAll=:,:@(0.05 1 2 8 1 1 1 _0.1 0 0"_)

Initx =:  1.0912 , 0.5p1 , 0.25p1 , 0p1 "_
Initdx=: (0      , 0     , 0.001  , 0.01"_)*%@(1"_)

vS00xL    =:Initx
vS01dxL   =:0,0,0,0:
vS02d1L   =:Initd1
vS06ds    =:Initds
vS07count =:(0,6283"_)*1"_
pdDR      =:vSgD@vS''

pdDR arrayPut   'pdDR'
     arrayClose 'pdDR'

vSgDd2M=.[([(0{])@rfE1cn xRef@hkxR03),:@(S03xH{])
vSgDd2 =.gXR(-@(([([(0{])@ch2k xRef@hkxR03),:@(S03xH{]))+/"1@((<0 2)|:])@((0|:[)smx])(]*/])@(S02d1L{]))+vSgDd2M)]

Initds2=.(gXR([(0{])@mcv xRef@hkxR03),:@Initx)+/^:2@:*(]*/])@Initdx
Initds =.%:@|@Initds2

gXRAll=:,:@(0.05 1 2 8 1 1 1 _0.1 0 0"_)

Initx =:  0.9645 , 0.5p1 , 0.25p1 , 0p1"_
Initdx=: (0      , 0     , 0.01   , 0.1"_)*%@(128"_)

vS00xL    =:Initx
vS01dxL   =:0,0,0,0:
vS02d1L   =:Initd1
vS06ds    =:Initds
vS07count =:(0,60"_)*128"_
pdDS      =:vSgD@vS''

pdDS arrayPut   'pdDS'
     arrayClose 'pdDS'


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

               arrayOpen  'pdDQ'
pdDQ=:7681 8 4 arrayGet   'pdDQ'   NB. ... shape required ...
               arrayClose 'pdDQ'

               arrayOpen  'pdDR'
pdDR=:6284 8 4 arrayGet   'pdDR'   NB. ... shape required ...
               arrayClose 'pdDR'

               arrayOpen  'pdDS'
pdDS=:7681 8 4 arrayGet   'pdDS'   NB. ... shape required ...
               arrayClose 'pdDS'


load 'plot'

pd ((1.3170*cos@]"0);1.3170*sin@]"0) pTsteps _ 0p1 2p1 160

pd vSgDplot (i.@(5801"_){]) pdDQ

pd ((1.0912*cos@]"0);1.0912*sin@]"0) pTsteps _ 0p1 2p1 160

pd vSgDplot (i.@(6284"_){]) pdDR     NB. ... balanced ...

pd ((0.9645*cos@]"0);0.9645*sin@]"0) pTsteps _ 0p1 2p1 160

pd vSgDplot (i.@(5801"_){]) pdDS

pd 'aspect 1'
pd 'pdf'
pd 'show'


JTER1508C.jpg
... moves out ...