User:Tom Allen/ta/AddendumX04P08A

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FOR THIS MODEL




... 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 ...



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'


JX04P08A00D.jpg
... 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'


JX04P08A01D.jpg
... 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'


JX04P08A02C.jpg
... (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'


JX04P08A03E.jpg
... 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'


JX04P08A04C.jpg
... (velocity along geodesics)<1 ...