User:Tom Allen/ta/AddendumX04P08A

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FOR THIS MODEL

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... the mathematics displays a symmetry (+/-) ...

... geodesics can be calculated using E1cn or -@E1cn ...
... in the real world this symmetry must be broken to support the containment of neutral particles ...

... E1cn must be used to calculate real geodesics ...

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load 'plot'

pd 'reset'

uQ0=:,:@(0.05 1 2 8 1 1 1 _0.1 0"_)

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

pd (uQ0(cx0"_ 1;[(0{])"1@E1cn xRef@([hkyX04A zfyc"_ 1))]) pTtotal xCpts''
pd (uQ0(cx0"_ 1;[(1{])"1@E1cn xRef@([hkyX04A zfyc"_ 1))]) pTtotal xCpts''
pd (uQ0(cx0"_ 1;[(2{])"1@E1cn xRef@([hkyX04A zfyc"_ 1))]) pTtotal xCpts''
pd (uQ0(cx0"_ 1;[(3{])"1@E1cn xRef@([hkyX04A zfyc"_ 1))]) pTtotal xCpts''

pd (((0.9675"_)@]"0);]"0) pTsteps _ _9 7 160
pd (((1.2832"_)@]"0);]"0) pTsteps _ _9 7 160

pd 'pdf'

... divergence of spacetime in x-coordinates (synchronized in 3D space at initial condition time=0) ...

uQ0=:,:@(0.05 1 2 8 1 1 1 _0.1 0"_)

vSgDd2=:uQ0([([(0{])@E1cn yRef@hkyX04A),:@(S03yH{]))]

Initx =:  0.5500 , 0.5p1 , 0.25p1 , 0p1"_
Initdx=: (0      , 0     , 0      , 0.1"_)*%@InitInt=:32"_

Inity =:zfyc@Initx
Initdy=:zfyc@(Initx+Initdx)+-@zfyc@Initx

Initds=:|@((((0{])^2:)+((1{])^2:)+((2{])^2:)+-@((3{])^2:))^0.5"_)@Initdy

vS00yL   =:Inity
vS01dyL  =:0,0,0,0:
vS02d1L  =:Initdy%Initds
vS06ds   =:Initds
vS07count=:(0,600"_)*InitInt
pdDH     =:vSgD@vS''

pdDH arrayPut   'pdDH'
     arrayClose 'pdDH'

Initx =:  1.4500 , 0.5p1 , 0.25p1 , 0p1"_
Initdx=: (0      , 0     , 0      , 0.1"_)*%@InitInt=:16"_

Inity =:zfyc@Initx
Initdy=:zfyc@(Initx+Initdx)+-@zfyc@Initx

Initds=:|@((((0{])^2:)+((1{])^2:)+((2{])^2:)+-@((3{])^2:))^0.5"_)@Initdy

vS00yL   =:Inity
vS01dyL  =:0,0,0,0:
vS02d1L  =:Initdy%Initds
vS06ds   =:Initds
vS07count=:(0,600"_)*InitInt
pdDI     =:vSgD@vS''

pdDI arrayPut   'pdDI'
     arrayClose 'pdDI'

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

                arrayOpen  'pdDH'
pdDH=:19201 8 4 arrayGet   'pdDH'   NB. ... shape required ...
                arrayClose 'pdDH'

                arrayOpen  'pdDI'
pdDI=:09601 8 4 arrayGet   'pdDI'   NB. ... shape required ...
                arrayClose 'pdDI'

load 'plot'

pd 'reset'

pd <"1@(0|:])@:((cy0,cy1)@(S00yL{])"2) pdDH
pd <"1@(0|:])@:((cy0,cy1)@(S00yL{])"2) pdDI

pd ((0.9675*cos@]"0);0.9675*sin@]"0) pTsteps _ 0p1 2p1 160
pd ((1.2832*cos@]"0);1.2832*sin@]"0) pTsteps _ 0p1 2p1 160

pd 'aspect 1'
pd 'pdf'

... geodesics (support the containment of neutral particles) ...

load 'plot'

pd 'reset'

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)@:((S00yL{])"2) pdDH
pd (}:@:(cy3"1);veloc)@:((S00yL{])"2) pdDI

pd 'pdf'

... (velocity along geodesics)<1 ...

uQ0=:,:@(0.05 1 2 8 1 1 1 _0.1 0"_)

vSgDd2=:uQ0([([(0{])@E1cn yRef@hkyX04A),:@(S03yH{]))]

Initx =:  0.9675 , 0.5p1 , 0.25p1 , 0p1"_
Initdx=: (0      , 0     , 0      , 0.1"_)*%@InitInt=:128"_

Inity =:zfyc@Initx
Initdy=:zfyc@(Initx+Initdx)+-@zfyc@Initx

Initds=:|@((((0{])^2:)+((1{])^2:)+((2{])^2:)+-@((3{])^2:))^0.5"_)@Initdy

vS00yL   =:Inity
vS01dyL  =:0,0,0,0:
vS02d1L  =:Initdy%Initds
vS06ds   =:Initds
vS07count=:(0,600"_)*InitInt
pdDJ     =:vSgD@vS''

pdDJ arrayPut   'pdDJ'
     arrayClose 'pdDJ'

Initx =:  1.2832 , 0.5p1 , 0.25p1 , 0p1"_
Initdx=: (0      , 0     , 0      , 0.1"_)*%@InitInt=:16"_

Inity =:zfyc@Initx
Initdy=:zfyc@(Initx+Initdx)+-@zfyc@Initx

Initds=:|@((((0{])^2:)+((1{])^2:)+((2{])^2:)+-@((3{])^2:))^0.5"_)@Initdy

vS00yL   =:Inity
vS01dyL  =:0,0,0,0:
vS02d1L  =:Initdy%Initds
vS06ds   =:Initds
vS07count=:(0,560"_)*InitInt
pdDK     =:vSgD@vS''

pdDK arrayPut   'pdDK'
     arrayClose 'pdDK'

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

                arrayOpen  'pdDJ'
pdDJ=:76801 8 4 arrayGet   'pdDJ'   NB. ... shape required ...
                arrayClose 'pdDJ'

                arrayOpen  'pdDK'
pdDK=:08961 8 4 arrayGet   'pdDK'   NB. ... shape required ...
                arrayClose 'pdDK'

load 'plot'

pd 'reset'

pd <"1@(0|:])@:((cy0,cy1)@(S00yL{])"2) pdDJ
pd <"1@(0|:])@:((cy0,cy1)@(S00yL{])"2) pdDK

pd ((0.9675*cos@]"0);0.9675*sin@]"0) pTsteps _ 0p1 2p1 160
pd ((1.2832*cos@]"0);1.2832*sin@]"0) pTsteps _ 0p1 2p1 160

pd 'aspect 1'
pd 'pdf'

... geodesics (support the containment of neutral particles) ...

load 'plot'

pd 'reset'

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)@:((S00yL{])"2) pdDJ
pd (}:@:(cy3"1);veloc)@:((S00yL{])"2) pdDK

pd 'pdf'

... (velocity along geodesics)<1 ...