User:Tom Allen/ta/AddendumX04P08D
... 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 ...
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'
... 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 ...
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'
... 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 ...
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 ...