User:Tom Allen/ta/AddendumX04P08D
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... geodesics start off moving towards the circles ...
uQ0=:,:@(0.05 1 2 8 1 1 1 _0.1 0"_)
vSgDd2=:uQ0([([(0{])@E1cn yRef@hkyX04A),:@(S03yH{]))]
Initx =: (0.55%sin@(0.40p1"_)) , 0.40p1 , 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
pdDP =:vSgD@vS''
pdDP arrayPut 'pdDP'
arrayClose 'pdDP'
Initx =: (1.45%sin@(0.60p1"_)) , 0.60p1 , 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
pdDQ =:vSgD@vS''
pdDQ arrayPut 'pdDQ'
arrayClose 'pdDQ'
NB. ... execute (ijx) ...
arrayOpen 'pdDP'
pdDP=:19201 8 4 arrayGet 'pdDP' NB. ... shape required ...
arrayClose 'pdDP'
arrayOpen 'pdDQ'
pdDQ=:09601 8 4 arrayGet 'pdDQ' NB. ... shape required ...
arrayClose 'pdDQ'
load 'plot'
pd 'reset'
pd <"1@(0|:])@:((cy0,cy1)@(S00yL{])"2) pdDP
pd <"1@(0|:])@:((cy0,cy1)@(S00yL{])"2) pdDQ
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'
... the blue geodesic begins with y2>0 ...
... the red geodesic begins with y2<0 ...
... geodesics are not contained between the green and purple circles ...
... geodesics (support the containment of neutral particles) ...
load 'plot'
pd 'reset'
pd <"1@(0|:])@:((cy3,cy2)@(S00yL{])"2) pdDP
pd <"1@(0|:])@:((cy3,cy2)@(S00yL{])"2) pdDQ
pd 'aspect 1'
pd 'pdf'
... Cartesian coordinate y2 as a function of time (y3) along geodesics ...
... geodesics start off moving away from the circles ...
uQ0=:,:@(0.05 1 2 8 1 1 1 _0.1 0"_)
vSgDd2=:uQ0([([(0{])@E1cn yRef@hkyX04A),:@(S03yH{]))]
Initx =: (0.9675%sin@(0.40p1"_)) , 0.40p1 , 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
pdDR =:vSgD@vS''
pdDR arrayPut 'pdDR'
arrayClose 'pdDR'
Initx =: (1.2832%sin@(0.60p1"_)) , 0.60p1 , 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
pdDS =:vSgD@vS''
pdDS arrayPut 'pdDS'
arrayClose 'pdDS'
NB. ... execute (ijx) ...
arrayOpen 'pdDR'
pdDR=:76801 8 4 arrayGet 'pdDR' NB. ... shape required ...
arrayClose 'pdDR'
arrayOpen 'pdDS'
pdDS=:08961 8 4 arrayGet 'pdDS' NB. ... shape required ...
arrayClose 'pdDS'
load 'plot'
pd 'reset'
pd <"1@(0|:])@:((cy0,cy1)@(S00yL{])"2) pdDR
pd <"1@(0|:])@:((cy0,cy1)@(S00yL{])"2) pdDS
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'
... the blue geodesic begins with y2>0 ...
... the red geodesic begins with y2<0 ...
... geodesics are not contained between the green and purple circles ...
... geodesics (support the containment of neutral particles) ...
load 'plot'
pd 'reset'
pd <"1@(0|:])@:((cy3,cy2)@(S00yL{])"2) pdDR
pd <"1@(0|:])@:((cy3,cy2)@(S00yL{])"2) pdDS
pd 'aspect 1'
pd 'pdf'
... Cartesian coordinate y2 as a function of time (y3) along geodesics ...
... with geodesics not supporting the containment of neutral particles between the brown and light blue lines only an ionized plasma remains ...
load 'plot'
pd 'reset'
uQ0=:,:@(0.05 1 2 8 1 1 1 _0.1 0"_)
xCpts=:_ 0.1 2.5 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:_ 0.00p1 0.00p1 0*10"_
pd (uQ0(cx0"_ 1;[(3{])"1@(-@JEMcn)yRef@([hkyX04A zfyc"_ 1))]) pTtotal xCpts'' NB. ... blue ...
xCpts=:_ 0.1 2.5 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:_ 0.25p1 0.25p1 0*10"_
pd (uQ0(cx0"_ 1;[(3{])"1@(-@JEMcn)yRef@([hkyX04A zfyc"_ 1))]) pTtotal xCpts'' NB. ... red ...
xCpts=:_ 0.1 2.5 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:_ 0.50p1 0.50p1 0*10"_
pd (uQ0(cx0"_ 1;[(3{])"1@(-@JEMcn)yRef@([hkyX04A zfyc"_ 1))]) pTtotal xCpts'' NB. ... green (overwrites blue) ...
xCpts=:_ 0.1 2.5 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:_ 0.75p1 0.75p1 0*10"_
pd (uQ0(cx0"_ 1;[(3{])"1@(-@JEMcn)yRef@([hkyX04A zfyc"_ 1))]) pTtotal xCpts'' NB. ... purple ...
xCpts=:_ 0.1 2.5 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:_ 1.00p1 1.00p1 0*10"_
pd (uQ0(cx0"_ 1;[(3{])"1@(-@JEMcn)yRef@([hkyX04A zfyc"_ 1))]) pTtotal xCpts'' NB. ... pink (overwrites green) ...
pd (((0.9675"_)@]"0);]"0) pTsteps _ _0.00020 0.00020 160
pd (((1.2832"_)@]"0);]"0) pTsteps _ _0.00020 0.00020 160
pd 'pdf'
... the charge density has a maximum value between the lines ...
... cycle of the charge density in 4-dimensional spacetime ...
load 'plot'
pd 'reset'
uQ0=:,:@(0.05 1 2 8 1 1 1 _0.1 0"_)
xCpts=:_ 0.1 2.5 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:_ 0.00p1 0.00p1 0*10"_
pd (uQ0(cx0"_ 1;[((<3 3){])"2@(-@JEMcndn)yRef@([hkyX04A zfyc"_ 1))]) pTtotal xCpts'' NB. ... blue ...
xCpts=:_ 0.1 2.5 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:_ 0.25p1 0.25p1 0*10"_
pd (uQ0(cx0"_ 1;[((<3 3){])"2@(-@JEMcndn)yRef@([hkyX04A zfyc"_ 1))]) pTtotal xCpts'' NB. ... red ...
xCpts=:_ 0.1 2.5 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:_ 0.50p1 0.50p1 0*10"_
pd (uQ0(cx0"_ 1;[((<3 3){])"2@(-@JEMcndn)yRef@([hkyX04A zfyc"_ 1))]) pTtotal xCpts'' NB. ... green ...
xCpts=:_ 0.1 2.5 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:_ 0.75p1 0.75p1 0*10"_
pd (uQ0(cx0"_ 1;[((<3 3){])"2@(-@JEMcndn)yRef@([hkyX04A zfyc"_ 1))]) pTtotal xCpts'' NB. ... purple (overwrites red) ...
xCpts=:_ 0.1 2.5 200,_ 0.5p1 0.5p1 0,_ 0.25p1 0.25p1 0,:_ 1.00p1 1.00p1 0*10"_
pd (uQ0(cx0"_ 1;[((<3 3){])"2@(-@JEMcndn)yRef@([hkyX04A zfyc"_ 1))]) pTtotal xCpts'' NB. ... pink (overwrites blue) ...
pd (((0.9675"_)@]"0);]"0) pTsteps _ _0.00004 0.00004 160
pd (((1.2832"_)@]"0);]"0) pTsteps _ _0.00004 0.00004 160
pd 'pdf'
... the rate of change of the charge density has a maximum value between the lines ...
... cycle of the rate of change of the charge density in 4-dimensional spacetime ...
