User:Tom Allen/TensorExperimentsR22

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NB. ... time provides the measure of length (ds) where space and time do not diverge ...

vSgDd2M=.[([(0{])@rfE1cn xRef@hkxR03S),:@(S03xH{])
vSgDd2 =.gXR(-@(([([(0{])@ch2k xRef@hkxR03S),:@(S03xH{]))+/"1@((<0 2)|:])@((0|:[)smx])(]*/])@(S02d1L{]))+vSgDd2M)]

Initds2=.(gXR([(0{])@mcv xRef@hkxR03S),:@Initx)+/^:2@:*(]*/])@Initdx
Initds =.%:@|@Initds2

gXRAll=:,:@(0.15 1 2 8 1 1 8 _8 0 0"_)
gXSAll=:,:@(0.15 1 2 8 1 1 8  8 0 0"_)

Initx =:  0.94 , 0.5p1 , 0.03125p1 , 0p1 "_
Initdx=: (0    , 0     , 0         , 0.04"_)*%@(1"_)

vS00xL    =:Initx
vS01dxL   =:0,0,0,0:
vS02d1L   =:Initd1
vS06ds    =:Initds
vS07count =:(0,30000"_)*1"_
pdDA      =:vSgD@vS''

pdDA arrayPut   'pdDA'
     arrayClose 'pdDA'

Initx =:  0.94 , 0.5p1 , 0.03125p1 , 0p1 "_
Initdx=: (0    , 0     , 0         , 0.04"_)*%@(2"_)

vS00xL    =:Initx
vS01dxL   =:0,0,0,0:
vS02d1L   =:Initd1
vS06ds    =:Initds
vS07count =:(0,15000"_)*2"_
pdDB      =:vSgD@vS''

pdDB arrayPut   'pdDB'
     arrayClose 'pdDB'


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

                arrayOpen  'pdDA'
pdDA=:30001 8 4 arrayGet   'pdDA'   NB. ... shape required ...
                arrayClose 'pdDA'

                arrayOpen  'pdDB'
pdDB=:30001 8 4 arrayGet   'pdDB'   NB. ... shape required ...
                arrayClose 'pdDB'


load 'plot'

pd vSgDplot pdDA
pd vSgDplot pdDB
pd ((0.94*cos@]"0);0.94*sin@]"0) pTsteps _ 0p1 0.0625p1 160

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


JTER2200C.jpg
... a geodesic ...


load 'plot'

pd (cx3"1;cx0"1)@:((S00xL{])"2) (i.@(30001"_){]) pdDA

pd (]"0;((0.94034"_)@]"0)) pTsteps _ 0 1302 160

pd (cx3"1;cx0"1)@:((S00xL{])"2) (i.@(30001"_){]) pdDB

pd (]"0;((0.92078"_)@]"0)) pTsteps _ 0 1302 160

pd 'pdf'
pd 'show'


JTER2201D.jpg
... X0 with elapsed time along geodesic ...


load 'plot'

incy0=.(2-~/\])@:(cy0"1)
incy1=.(2-~/\])@:(cy1"1)
incy2=.(2-~/\])@:(cy2"1)
incy3=.(2-~/\])@:(cy3"1)
veloc=.(((incy0^2:)+incy1^2:)^0.5"_)%incy3

pd (}:@:(cy3"1);veloc)@:(rfyc"1)@:((S00xL{])"2) pdDA
pd (}:@:(cy3"1);incy2)@:(rfyc"1)@:((S00xL{])"2) pdDA    NB. ... incy2 is zero ...

pd (}:@:(cy3"1);veloc)@:(rfyc"1)@:((S00xL{])"2) pdDB
pd (}:@:(cy3"1);incy2)@:(rfyc"1)@:((S00xL{])"2) pdDB    NB. ... incy2 is zero ...

pd (]"0;((0.04417"_)@]"0)) pTsteps _ 0 1302 160

pd 'pdf'
pd 'show'


JTER2202D.jpg
... velocity with elapsed time along geodesic ...


...
...
...


NB. ...
NB. ... the array pdDX can be generated in about 10 days ...
NB. ... on ...
NB. ... an Intel Core i5-6600k processor ...
NB. ...

vSgDd2M=.[([(0{])@rfE1cn xRef@hkxR03S),:@(S03xH{])
vSgDd2 =.gXR(-@(([([(0{])@ch2k xRef@hkxR03S),:@(S03xH{]))+/"1@((<0 2)|:])@((0|:[)smx])(]*/])@(S02d1L{]))+vSgDd2M)]

Initds2=.(gXR([(0{])@mcv xRef@hkxR03S),:@Initx)+/^:2@:*(]*/])@Initdx
Initds =.%:@|@Initds2

gXRAll=:,:@(0.15 1 2 8 1 1 8 _8 0 0"_)
gXSAll=:,:@(0.15 1 2 8 1 1 8  8 0 0"_)

Initx =:  0.94 , 0.5p1 , 0.03125p1 , 0p1 "_
Initdx=: (0    , 0     , 0.001     , 0.04"_)*%@(128"_)

vS00xL    =:Initx
vS01dxL   =:0,0,0,0:
vS02d1L   =:Initd1
vS06ds    =:Initds
vS07count =:(0,11250"_)*128"_
pdDX      =:vSgD@vS''

pdDX arrayPut   'pdDX'
     arrayClose 'pdDX'


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

                  arrayOpen  'pdDX'
pdDX=:1440001 8 4 arrayGet   'pdDX'   NB. ... shape required ...
                  arrayClose 'pdDX'


load 'plot'

pd ((0.94*cos@]"0);0.94*sin@]"0) pTsteps _ 0p1 0.0625p1 160

pd vSgDplot pdDX

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


JTER2203C.jpg
... a geodesic ...


... the motion of energy (+/-) in space ...
... generates ...
... geodesics which are generally not straight lines ...
... and ...
... this gives rise to some interesting patterns ...


load 'plot'

pd (cx3"1;cx0"1)@:((S00xL{])"2) pdDX

pd (]"0;((0.94"_)@]"0)) pTsteps _ 0 490 160

pd 'pdf'
pd 'show'


JTER2204C.jpg
... x0 with elapsed time along geodesic ...


load 'plot'

incy0=.(2-~/\])@:(cy0"1)
incy1=.(2-~/\])@:(cy1"1)
incy2=.(2-~/\])@:(cy2"1)
incy3=.(2-~/\])@:(cy3"1)
veloc=.(((incy0^2:)+incy1^2:)^0.5"_)%incy3

pd (}:@:(cy3"1);veloc)@:(rfyc"1)@:((S00xL{])"2) pdDX
pd (}:@:(cy3"1);incy2)@:(rfyc"1)@:((S00xL{])"2) pdDX    NB. ... incy2 is zero ...

pd (]"0;((0.04837"_)@]"0)) pTsteps _ 0 490 160

pd 'pdf'
pd 'show'


JTER2205C.jpg
... velocity with elapsed time along geodesic ...