User:Tom Allen/ta/AddendumX04P01

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load 'plot'

pd 'reset'

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

xCpts=:_ 0.2 1.4 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.00p1 0.00p1 0"_)*10"_

pd (uQ0(cx0"_ 1;[-@(0{])"1@E1cn xRef@([hkyX04B zfyc"_ 1))]) pTtotal xCpts''

xCpts=:_ 0.2 1.4 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.25p1 0.25p1 0"_)*10"_

pd (uQ0(cx0"_ 1;[-@(0{])"1@E1cn xRef@([hkyX04B zfyc"_ 1))]) pTtotal xCpts''

xCpts=:_ 0.2 1.4 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.40p1 0.40p1 0"_)*10"_

pd (uQ0(cx0"_ 1;[-@(0{])"1@E1cn xRef@([hkyX04B zfyc"_ 1))]) pTtotal xCpts''

xCpts=:_ 0.2 1.4 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.50p1 0.50p1 0"_)*10"_

pd (uQ0(cx0"_ 1;[-@(0{])"1@E1cn xRef@([hkyX04B zfyc"_ 1))]) pTtotal xCpts''

xCpts=:_ 0.2 1.4 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.60p1 0.60p1 0"_)*10"_

pd (uQ0(cx0"_ 1;[-@(0{])"1@E1cn xRef@([hkyX04B zfyc"_ 1))]) pTtotal xCpts''

xCpts=:_ 0.2 1.4 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.75p1 0.75p1 0"_)*10"_

pd (uQ0(cx0"_ 1;[-@(0{])"1@E1cn xRef@([hkyX04B zfyc"_ 1))]) pTtotal xCpts''

xCpts=:_ 0.2 1.4 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 1.00p1 1.00p1 0"_)*10"_

pd (uQ0(cx0"_ 1;[-@(0{])"1@E1cn xRef@([hkyX04B zfyc"_ 1))]) pTtotal xCpts''

pd 'pdf'


... an appropriate scale (or gauge) must be assigned ...


JX04P0100D.jpg
... cycle divergence of space (x0/y2=0) ...


load 'plot'

pd 'reset'

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

xCpts=:_ 0.7 2.8 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.00p1 0.00p1 0"_)*10"_

pd (uQ0(cx0"_ 1;[-@(0{])"1@E1cn xRef@([hkyX04B zfyc"_ 1))]) pTtotal xCpts''

xCpts=:_ 0.7 2.8 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.25p1 0.25p1 0"_)*10"_

pd (uQ0(cx0"_ 1;[-@(0{])"1@E1cn xRef@([hkyX04B zfyc"_ 1))]) pTtotal xCpts''

xCpts=:_ 0.7 2.8 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.40p1 0.40p1 0"_)*10"_

pd (uQ0(cx0"_ 1;[-@(0{])"1@E1cn xRef@([hkyX04B zfyc"_ 1))]) pTtotal xCpts''

xCpts=:_ 0.7 2.8 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.50p1 0.50p1 0"_)*10"_

pd (uQ0(cx0"_ 1;[-@(0{])"1@E1cn xRef@([hkyX04B zfyc"_ 1))]) pTtotal xCpts''

xCpts=:_ 0.7 2.8 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.60p1 0.60p1 0"_)*10"_

pd (uQ0(cx0"_ 1;[-@(0{])"1@E1cn xRef@([hkyX04B zfyc"_ 1))]) pTtotal xCpts''

xCpts=:_ 0.7 2.8 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 0.75p1 0.75p1 0"_)*10"_

pd (uQ0(cx0"_ 1;[-@(0{])"1@E1cn xRef@([hkyX04B zfyc"_ 1))]) pTtotal xCpts''

xCpts=:_ 0.7 2.8 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:(_ 1.00p1 1.00p1 0"_)*10"_

pd (uQ0(cx0"_ 1;[-@(0{])"1@E1cn xRef@([hkyX04B zfyc"_ 1))]) pTtotal xCpts''

pd 'pdf'


... an appropriate scale (or gauge) must be assigned ...


JX04P0101E.jpg
... cycle divergence of space (x0/y2=0) ...


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

vSgDd2=:uQ0([-@([(0{])@E1cn yRef@hkyX04B),:@(S03yH{]))]

Initx =:  1.01 , 0.5p1 , 0.25p1 , 0p1"_
Initdx=: (0    , 0     , 0.01   , 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=:(0,6280"_)*InitInt
pdDK     =:vSgD@vS''

pdDK arrayPut   'pdDK'
     arrayClose 'pdDK'

Initx =:  0.53 , 0.5p1 , 0.25p1 , 0p1"_
Initdx=: (0    , 0     , 0.01   , 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=:(0,6280"_)*InitInt
pdDL     =:vSgD@vS''

pdDL arrayPut   'pdDL'
     arrayClose 'pdDL'

Initx =:  2.400 , 0.5p1 , 0.25p1 , 0p1"_
Initdx=: (0     , 0     , 0.01   , 0.1"_)*%@InitInt=:4"_

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=:(0,72000"_)*InitInt
pdDM     =:vSgD@vS''

pdDM arrayPut   'pdDM'
     arrayClose 'pdDM'


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

                 arrayOpen  'pdDK'
pdDK=:200961 8 4 arrayGet   'pdDK'   NB. ... shape required ...
                 arrayClose 'pdDK'

                 arrayOpen  'pdDL'
pdDL=:200961 8 4 arrayGet   'pdDL'   NB. ... shape required ...
                 arrayClose 'pdDL'

                 arrayOpen  'pdDM'
pdDM=:288001 8 4 arrayGet   'pdDM'   NB. ... shape required ...
                 arrayClose 'pdDM'


load 'plot'

pd 'reset'

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

pd 'aspect 1'
pd 'pdf'


... three geodesics (blue red and green) in a single rotating energy distribution (y2=0) ...


JX04P0102H.jpg
... geodesics (F) blue(up) red(up) green(down) ...


load 'plot'

pd 'reset'

pd (cy3"1;(((cy0^2:)+(cy1^2:)+cy2^2:)^0.5"_)"1)@:((S00yL{])"2) ((0+i.@(20000"_)){]) pdDK    NB. ... colour blue ...

pd 'show'


... a pattern (based on the geodesic) ...


JX04P0103G.png
... a pattern (based on the geodesic) ...


load 'plot'

pd 'reset'

pd (cy3"1;(((cy0^2:)+(cy1^2:)+cy2^2:)^0.5"_)"1)@:((S00yL{])"2) ((0+i.@(00001"_)){]) pdDL    NB. ... change colour ...
pd (cy3"1;(((cy0^2:)+(cy1^2:)+cy2^2:)^0.5"_)"1)@:((S00yL{])"2) ((0+i.@(05000"_)){]) pdDL    NB. ... colour red    ...

pd 'show'


... a pattern (based on the geodesic) ...


JX04P0104G.png
... a pattern (based on the geodesic) ...


load 'plot'

pd 'reset'

pd (cy3"1;(((cy0^2:)+(cy1^2:)+cy2^2:)^0.5"_)"1)@:((S00yL{])"2) ((0+i.@(00001"_)){]) pdDM    NB. ... change colour ...
pd (cy3"1;(((cy0^2:)+(cy1^2:)+cy2^2:)^0.5"_)"1)@:((S00yL{])"2) ((0+i.@(00001"_)){]) pdDM    NB. ... change colour ...
pd (cy3"1;(((cy0^2:)+(cy1^2:)+cy2^2:)^0.5"_)"1)@:((S00yL{])"2) ((0+i.@(14000"_)){]) pdDM    NB. ... colour green  ...

pd 'show'


... a pattern (based on the geodesic) ...


JX04P0105F.png
... a pattern (based on the geodesic) ...


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 (((S06ds{])*i.@(S0700nmbr{]))@{:;veloc@:((S00yL{])"2)) (i.@(6280*32"_){]) pdDK    NB. ... velocity along geodesic (blue)  ...
pd (((S06ds{])*i.@(S0700nmbr{]))@{:;veloc@:((S00yL{])"2)) (i.@(6000*32"_){]) pdDL    NB. ... velocity along geodesic (red)   ...
pd (((S06ds{])*i.@(S0700nmbr{]))@{:;veloc@:((S00yL{])"2)) (i.@(6000*04"_){]) pdDM    NB. ... velocity along geodesic (green) ...

pd (((S06ds{])*i.@(S0700nmbr{]))@{:;incy2@:((S00yL{])"2)) (i.@(6280*32"_){]) pdDK    NB. ... y2=0 ...
pd (((S06ds{])*i.@(S0700nmbr{]))@{:;incy2@:((S00yL{])"2)) (i.@(6000*32"_){]) pdDL    NB. ... y2=0 ...
pd (((S06ds{])*i.@(S0700nmbr{]))@{:;incy2@:((S00yL{])"2)) (i.@(6000*04"_){]) pdDM    NB. ... y2=0 ...

pd 'pdf'


... velocity along geodesics as a fraction of the velocity of electromagnetic waves (temperature) ...


JX04P0106C.jpg
... velocity along geodesics blue red and green ...