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'
... 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'
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'
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'
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'