User:Tom Allen/TensorExperimentsR17
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load 'plot'
gXRAll=:,:@(0.15 1.0 2 8 1 1 8 _8 0 0"_)
gXSAll=:,:@(0.15 0.9 2 8 1 1 8 8 0 0"_)
xCpts=:_ 0.3 2.0 200,_ 0.5p1 0.5p1 0,(_ 0.25p1 0.25p1 0"_*0.125"_),:_ 0.00p1 0.00p1 0"_*0.125"_
pd (gXR(cx0"_ 1;[(0{])"1@rfE1cn xRef@hkxR03S)]) pTtotal xCpts''
xCpts=:_ 0.3 2.0 200,_ 0.5p1 0.5p1 0,(_ 0.25p1 0.25p1 0"_*0.125"_),:_ 0.25p1 0.25p1 0"_*0.125"_
pd (gXR(cx0"_ 1;[(0{])"1@rfE1cn xRef@hkxR03S)]) pTtotal xCpts''
xCpts=:_ 0.3 2.0 200,_ 0.5p1 0.5p1 0,(_ 0.25p1 0.25p1 0"_*0.125"_),:_ 0.40p1 0.40p1 0"_*0.125"_
pd (gXR(cx0"_ 1;[(0{])"1@rfE1cn xRef@hkxR03S)]) pTtotal xCpts''
xCpts=:_ 0.3 2.0 200,_ 0.5p1 0.5p1 0,(_ 0.25p1 0.25p1 0"_*0.125"_),:_ 0.50p1 0.50p1 0"_*0.125"_
pd (gXR(cx0"_ 1;[(0{])"1@rfE1cn xRef@hkxR03S)]) pTtotal xCpts''
xCpts=:_ 0.3 2.0 200,_ 0.5p1 0.5p1 0,(_ 0.25p1 0.25p1 0"_*0.125"_),:_ 0.60p1 0.60p1 0"_*0.125"_
pd (gXR(cx0"_ 1;[(0{])"1@rfE1cn xRef@hkxR03S)]) pTtotal xCpts''
xCpts=:_ 0.3 2.0 200,_ 0.5p1 0.5p1 0,(_ 0.25p1 0.25p1 0"_*0.125"_),:_ 0.75p1 0.75p1 0"_*0.125"_
pd (gXR(cx0"_ 1;[(0{])"1@rfE1cn xRef@hkxR03S)]) pTtotal xCpts''
xCpts=:_ 0.3 2.0 200,_ 0.5p1 0.5p1 0,(_ 0.25p1 0.25p1 0"_*0.125"_),:_ 1.00p1 1.00p1 0"_*0.125"_
pd (gXR(cx0"_ 1;[(0{])"1@rfE1cn xRef@hkxR03S)]) pTtotal xCpts''
pd (((0.8800"_)@]"0);]"0) pTsteps _ _1.5 2 160
pd (((0.9400"_)@]"0);]"0) pTsteps _ _1.5 2 160
pd (((0.9900"_)@]"0);]"0) pTsteps _ _1.5 2 160
pd 'pdf'
pd 'show'
vSgDd2M=.[([(0{])@rfE1cn xRef@hkxR03S),:@(S03xH{])
vSgDd2 =.gXR(-@(([([(0{])@ch2k xRef@hkxR03S),:@(S03xH{]))+/"1@((<0 2)|:])@((0|:[)smx])(]*/])@(S02d1L{]))+vSgDd2M)]
Initds2=.(gXR([(0{])@mcv xRef@hkxR03S),:@Initx)+/^:2@:*(]*/])@Initdx
Initds =.%:@|@Initds2
gXRAll=:,:@(0.15 1.0 2 8 1 1 8 _8 0 0"_)
gXSAll=:,:@(0.15 0.9 2 8 1 1 8 8 0 0"_)
Initx =: 0.88 , 0.5p1 , 0.03125p1 , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,60000"_)*1"_
pdDU =:vSgD@vS''
pdDU arrayPut 'pdDU'
arrayClose 'pdDU'
Initx =: 0.94 , 0.5p1 , 0.03125p1 , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,1000"_)*1"_
pdDV =:vSgD@vS''
pdDV arrayPut 'pdDV'
arrayClose 'pdDV'
Initx =: 0.99 , 0.5p1 , 0.03125p1 , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,1000"_)*1"_
pdDW =:vSgD@vS''
pdDW arrayPut 'pdDW'
arrayClose 'pdDW'
NB. ... execute (ijx) ...
arrayOpen 'pdDU'
pdDU=:60001 8 4 arrayGet 'pdDU' NB. ... shape required ...
arrayClose 'pdDU'
arrayOpen 'pdDV'
pdDV=:01001 8 4 arrayGet 'pdDV' NB. ... shape required ...
arrayClose 'pdDV'
arrayOpen 'pdDW'
pdDW=:01001 8 4 arrayGet 'pdDW' NB. ... shape required ...
arrayClose 'pdDW'
load 'plot' pd vSgDplot pdDU pd vSgDplot pdDV pd vSgDplot pdDW pd ((0.88*cos@]"0);0.88*sin@]"0) pTsteps _ 0p1 0.0625p1 160 pd ((0.94*cos@]"0);0.94*sin@]"0) pTsteps _ 0p1 0.0625p1 160 pd ((0.99*cos@]"0);0.99*sin@]"0) pTsteps _ 0p1 0.0625p1 160 pd 'aspect 1' pd 'pdf' pd 'show'
... geodesics in a standing wave ...
load 'plot'
gXRAll=:,:@(0.15 1.0 2 8 1 1 8 _8 0 0"_)
gXSAll=:,:@(0.15 0.9 2 8 1 1 8 8 0 0"_)
xCpts=:_ 0.3 2.0 200,_ 0.5p1 0.5p1 0,(_ 0.25p1 0.25p1 0"_*0.125"_),:_ 0.00p1 0.00p1 0"_*0.125"_
pd (gXR(cx0"_ 1;[(0{])"1@E1cn xRef@hkxR03S)]) pTtotal xCpts''
xCpts=:_ 0.3 2.0 200,_ 0.5p1 0.5p1 0,(_ 0.25p1 0.25p1 0"_*0.125"_),:_ 0.25p1 0.25p1 0"_*0.125"_
pd (gXR(cx0"_ 1;[(0{])"1@E1cn xRef@hkxR03S)]) pTtotal xCpts''
xCpts=:_ 0.3 2.0 200,_ 0.5p1 0.5p1 0,(_ 0.25p1 0.25p1 0"_*0.125"_),:_ 0.40p1 0.40p1 0"_*0.125"_
pd (gXR(cx0"_ 1;[(0{])"1@E1cn xRef@hkxR03S)]) pTtotal xCpts''
xCpts=:_ 0.3 2.0 200,_ 0.5p1 0.5p1 0,(_ 0.25p1 0.25p1 0"_*0.125"_),:_ 0.50p1 0.50p1 0"_*0.125"_
pd (gXR(cx0"_ 1;[(0{])"1@E1cn xRef@hkxR03S)]) pTtotal xCpts''
xCpts=:_ 0.3 2.0 200,_ 0.5p1 0.5p1 0,(_ 0.25p1 0.25p1 0"_*0.125"_),:_ 0.60p1 0.60p1 0"_*0.125"_
pd (gXR(cx0"_ 1;[(0{])"1@E1cn xRef@hkxR03S)]) pTtotal xCpts''
xCpts=:_ 0.3 2.0 200,_ 0.5p1 0.5p1 0,(_ 0.25p1 0.25p1 0"_*0.125"_),:_ 0.75p1 0.75p1 0"_*0.125"_
pd (gXR(cx0"_ 1;[(0{])"1@E1cn xRef@hkxR03S)]) pTtotal xCpts''
xCpts=:_ 0.3 2.0 200,_ 0.5p1 0.5p1 0,(_ 0.25p1 0.25p1 0"_*0.125"_),:_ 1.00p1 1.00p1 0"_*0.125"_
pd (gXR(cx0"_ 1;[(0{])"1@E1cn xRef@hkxR03S)]) pTtotal xCpts''
pd (((1.1500"_)@]"0);]"0) pTsteps _ _2 1.5 160
pd (((1.1700"_)@]"0);]"0) pTsteps _ _2 1.5 160
pd (((1.1600"_)@]"0);]"0) pTsteps _ _2 1.5 160
pd 'pdf'
pd 'show'
vSgDd2M=.[([(0{])@E1cn xRef@hkxR03S),:@(S03xH{])
vSgDd2 =.gXR(-@(([([(0{])@ch2k xRef@hkxR03S),:@(S03xH{]))+/"1@((<0 2)|:])@((0|:[)smx])(]*/])@(S02d1L{]))+vSgDd2M)]
Initds2=.(gXR([(0{])@mcv xRef@hkxR03S),:@Initx)+/^:2@:*(]*/])@Initdx
Initds =.%:@|@Initds2
gXRAll=:,:@(0.15 1.0 2 8 1 1 8 _8 0 0"_)
gXSAll=:,:@(0.15 0.9 2 8 1 1 8 8 0 0"_)
Initx =: 1.15 , 0.5p1 , 0.03125p1 , 0p1 "_
Initdx=: (0 , 0 , 0.0001 , 0.02"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,80000"_)*1"_
pdDX =:vSgD@vS''
pdDX arrayPut 'pdDX'
arrayClose 'pdDX'
Initx =: 1.17 , 0.5p1 , 0.03125p1 , 0p1 "_
Initdx=: (0 , 0 , 0.0001 , 0.02"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,5000"_)*1"_
pdDY =:vSgD@vS''
pdDY arrayPut 'pdDY'
arrayClose 'pdDY'
Initx =: 1.16 , 0.5p1 , 0.03125p1 , 0p1 "_
Initdx=: (0 , 0 , 0.0001 , 0.02"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,5000"_)*1"_
pdDZ =:vSgD@vS''
pdDZ arrayPut 'pdDZ'
arrayClose 'pdDZ'
NB. ... execute (ijx) ...
arrayOpen 'pdDX'
pdDX=:80001 8 4 arrayGet 'pdDX' NB. ... shape required ...
arrayClose 'pdDX'
arrayOpen 'pdDY'
pdDY=:05001 8 4 arrayGet 'pdDY' NB. ... shape required ...
arrayClose 'pdDY'
arrayOpen 'pdDZ'
pdDZ=:05001 8 4 arrayGet 'pdDZ' NB. ... shape required ...
arrayClose 'pdDZ'
load 'plot' pd vSgDplot pdDX pd vSgDplot pdDY pd vSgDplot pdDZ pd ((1.15*cos@]"0);1.15*sin@]"0) pTsteps _ 0p1 0.0625p1 160 pd ((1.17*cos@]"0);1.17*sin@]"0) pTsteps _ 0p1 0.0625p1 160 pd ((1.16*cos@]"0);1.16*sin@]"0) pTsteps _ 0p1 0.0625p1 160 pd 'aspect 1' pd 'pdf' pd 'show'
... geodesics in a standing wave ...
vSgDd2M=.[([(0{])@rfE1cn xRef@hkxR03S),:@(S03xH{])
vSgDd2 =.gXR(-@(([([(0{])@ch2k xRef@hkxR03S),:@(S03xH{]))+/"1@((<0 2)|:])@((0|:[)smx])(]*/])@(S02d1L{]))+vSgDd2M)]
Initds2=.(gXR([(0{])@mcv xRef@hkxR03S),:@Initx)+/^:2@:*(]*/])@Initdx
Initds =.%:@|@Initds2
gXRAll=:,:@(0.15 1.0 2 8 1 1 8 _8 0 0"_)
gXSAll=:,:@(0.15 0.9 2 8 1 1 8 8 0 0"_)
Initx =: 0.94 , 0.5p1 , ((0.25p1*0.125)+(0*2p1*0.125)+(2p1*0.125)*0.00) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,1000"_)*1"_
pdEA =:vSgD@vS''
pdEA arrayPut 'pdEA'
arrayClose 'pdEA'
Initx =: 0.94 , 0.5p1 , ((0.25p1*0.125)+(1*2p1*0.125)+(2p1*0.125)*0.00) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,1000"_)*1"_
pdEB =:vSgD@vS''
pdEB arrayPut 'pdEB'
arrayClose 'pdEB'
Initx =: 0.94 , 0.5p1 , ((0.25p1*0.125)+(2*2p1*0.125)+(2p1*0.125)*0.00) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,1000"_)*1"_
pdEC =:vSgD@vS''
pdEC arrayPut 'pdEC'
arrayClose 'pdEC'
Initx =: 0.94 , 0.5p1 , ((0.25p1*0.125)+(3*2p1*0.125)+(2p1*0.125)*0.00) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,1000"_)*1"_
pdED =:vSgD@vS''
pdED arrayPut 'pdED'
arrayClose 'pdED'
Initx =: 0.94 , 0.5p1 , ((0.25p1*0.125)+(4*2p1*0.125)+(2p1*0.125)*0.00) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,1000"_)*1"_
pdEE =:vSgD@vS''
pdEE arrayPut 'pdEE'
arrayClose 'pdEE'
Initx =: 0.94 , 0.5p1 , ((0.25p1*0.125)+(5*2p1*0.125)+(2p1*0.125)*0.00) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,1000"_)*1"_
pdEF =:vSgD@vS''
pdEF arrayPut 'pdEF'
arrayClose 'pdEF'
Initx =: 0.94 , 0.5p1 , ((0.25p1*0.125)+(6*2p1*0.125)+(2p1*0.125)*0.00) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,1000"_)*1"_
pdEG =:vSgD@vS''
pdEG arrayPut 'pdEG'
arrayClose 'pdEG'
Initx =: 0.94 , 0.5p1 , ((0.25p1*0.125)+(7*2p1*0.125)+(2p1*0.125)*0.00) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,1000"_)*1"_
pdEH =:vSgD@vS''
pdEH arrayPut 'pdEH'
arrayClose 'pdEH'
NB. ... execute (ijx) ...
arrayOpen 'pdEA'
pdEA=:1001 8 4 arrayGet 'pdEA' NB. ... shape required ...
arrayClose 'pdEA'
arrayOpen 'pdEB'
pdEB=:1001 8 4 arrayGet 'pdEB' NB. ... shape required ...
arrayClose 'pdEB'
arrayOpen 'pdEC'
pdEC=:1001 8 4 arrayGet 'pdEC' NB. ... shape required ...
arrayClose 'pdEC'
arrayOpen 'pdED'
pdED=:1001 8 4 arrayGet 'pdED' NB. ... shape required ...
arrayClose 'pdED'
arrayOpen 'pdEE'
pdEE=:1001 8 4 arrayGet 'pdEE' NB. ... shape required ...
arrayClose 'pdEE'
arrayOpen 'pdEF'
pdEF=:1001 8 4 arrayGet 'pdEF' NB. ... shape required ...
arrayClose 'pdEF'
arrayOpen 'pdEG'
pdEG=:1001 8 4 arrayGet 'pdEG' NB. ... shape required ...
arrayClose 'pdEG'
arrayOpen 'pdEH'
pdEH=:1001 8 4 arrayGet 'pdEH' NB. ... shape required ...
arrayClose 'pdEH'
vSgDd2M=.[([(0{])@rfE1cn xRef@hkxR03S),:@(S03xH{])
vSgDd2 =.gXR(-@(([([(0{])@ch2k xRef@hkxR03S),:@(S03xH{]))+/"1@((<0 2)|:])@((0|:[)smx])(]*/])@(S02d1L{]))+vSgDd2M)]
Initds2=.(gXR([(0{])@mcv xRef@hkxR03S),:@Initx)+/^:2@:*(]*/])@Initdx
Initds =.%:@|@Initds2
gXRAll=:,:@(0.15 1.0 2 8 1 1 8 _8 0 0"_)
gXSAll=:,:@(0.15 0.9 2 8 1 1 8 8 0 0"_)
Initx =: 0.94 , 0.5p1 , ((0.25p1*0.125)+(0*2p1*0.125)+(2p1*0.125)*0.50) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,1000"_)*1"_
pdFA =:vSgD@vS''
pdFA arrayPut 'pdFA'
arrayClose 'pdFA'
Initx =: 0.94 , 0.5p1 , ((0.25p1*0.125)+(1*2p1*0.125)+(2p1*0.125)*0.50) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,1000"_)*1"_
pdFB =:vSgD@vS''
pdFB arrayPut 'pdFB'
arrayClose 'pdFB'
Initx =: 0.94 , 0.5p1 , ((0.25p1*0.125)+(2*2p1*0.125)+(2p1*0.125)*0.50) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,1000"_)*1"_
pdFC =:vSgD@vS''
pdFC arrayPut 'pdFC'
arrayClose 'pdFC'
Initx =: 0.94 , 0.5p1 , ((0.25p1*0.125)+(3*2p1*0.125)+(2p1*0.125)*0.50) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,1000"_)*1"_
pdFD =:vSgD@vS''
pdFD arrayPut 'pdFD'
arrayClose 'pdFD'
Initx =: 0.94 , 0.5p1 , ((0.25p1*0.125)+(4*2p1*0.125)+(2p1*0.125)*0.50) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,1000"_)*1"_
pdFE =:vSgD@vS''
pdFE arrayPut 'pdFE'
arrayClose 'pdFE'
Initx =: 0.94 , 0.5p1 , ((0.25p1*0.125)+(5*2p1*0.125)+(2p1*0.125)*0.50) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,1000"_)*1"_
pdFF =:vSgD@vS''
pdFF arrayPut 'pdFF'
arrayClose 'pdFF'
Initx =: 0.94 , 0.5p1 , ((0.25p1*0.125)+(6*2p1*0.125)+(2p1*0.125)*0.50) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,1000"_)*1"_
pdFG =:vSgD@vS''
pdFG arrayPut 'pdFG'
arrayClose 'pdFG'
Initx =: 0.94 , 0.5p1 , ((0.25p1*0.125)+(7*2p1*0.125)+(2p1*0.125)*0.50) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,1000"_)*1"_
pdFH =:vSgD@vS''
pdFH arrayPut 'pdFH'
arrayClose 'pdFH'
NB. ... execute (ijx) ...
arrayOpen 'pdFA'
pdFA=:1001 8 4 arrayGet 'pdFA' NB. ... shape required ...
arrayClose 'pdFA'
arrayOpen 'pdFB'
pdFB=:1001 8 4 arrayGet 'pdFB' NB. ... shape required ...
arrayClose 'pdFB'
arrayOpen 'pdFC'
pdFC=:1001 8 4 arrayGet 'pdFC' NB. ... shape required ...
arrayClose 'pdFC'
arrayOpen 'pdFD'
pdFD=:1001 8 4 arrayGet 'pdFD' NB. ... shape required ...
arrayClose 'pdFD'
arrayOpen 'pdFE'
pdFE=:1001 8 4 arrayGet 'pdFE' NB. ... shape required ...
arrayClose 'pdFE'
arrayOpen 'pdFF'
pdFF=:1001 8 4 arrayGet 'pdFF' NB. ... shape required ...
arrayClose 'pdFF'
arrayOpen 'pdFG'
pdFG=:1001 8 4 arrayGet 'pdFG' NB. ... shape required ...
arrayClose 'pdFG'
arrayOpen 'pdFH'
pdFH=:1001 8 4 arrayGet 'pdFH' NB. ... shape required ...
arrayClose 'pdFH'
vSgDd2M=.[([(0{])@E1cn xRef@hkxR03S),:@(S03xH{])
vSgDd2 =.gXR(-@(([([(0{])@ch2k xRef@hkxR03S),:@(S03xH{]))+/"1@((<0 2)|:])@((0|:[)smx])(]*/])@(S02d1L{]))+vSgDd2M)]
Initds2=.(gXR([(0{])@mcv xRef@hkxR03S),:@Initx)+/^:2@:*(]*/])@Initdx
Initds =.%:@|@Initds2
gXRAll=:,:@(0.15 1.0 2 8 1 1 8 _8 0 0"_)
gXSAll=:,:@(0.15 0.9 2 8 1 1 8 8 0 0"_)
Initx =: 0.94 , 0.5p1 , ((0.25p1*0.125)+(0*2p1*0.125)+(2p1*0.125)*0.25) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,1000"_)*1"_
pdGA =:vSgD@vS''
pdGA arrayPut 'pdGA'
arrayClose 'pdGA'
Initx =: 0.94 , 0.5p1 , ((0.25p1*0.125)+(1*2p1*0.125)+(2p1*0.125)*0.25) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,1000"_)*1"_
pdGB =:vSgD@vS''
pdGB arrayPut 'pdGB'
arrayClose 'pdGB'
Initx =: 0.94 , 0.5p1 , ((0.25p1*0.125)+(2*2p1*0.125)+(2p1*0.125)*0.25) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,1000"_)*1"_
pdGC =:vSgD@vS''
pdGC arrayPut 'pdGC'
arrayClose 'pdGC'
Initx =: 0.94 , 0.5p1 , ((0.25p1*0.125)+(3*2p1*0.125)+(2p1*0.125)*0.25) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,1000"_)*1"_
pdGD =:vSgD@vS''
pdGD arrayPut 'pdGD'
arrayClose 'pdGD'
Initx =: 0.94 , 0.5p1 , ((0.25p1*0.125)+(4*2p1*0.125)+(2p1*0.125)*0.25) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,1000"_)*1"_
pdGE =:vSgD@vS''
pdGE arrayPut 'pdGE'
arrayClose 'pdGE'
Initx =: 0.94 , 0.5p1 , ((0.25p1*0.125)+(5*2p1*0.125)+(2p1*0.125)*0.25) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,1000"_)*1"_
pdGF =:vSgD@vS''
pdGF arrayPut 'pdGF'
arrayClose 'pdGF'
Initx =: 0.94 , 0.5p1 , ((0.25p1*0.125)+(6*2p1*0.125)+(2p1*0.125)*0.25) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,1000"_)*1"_
pdGG =:vSgD@vS''
pdGG arrayPut 'pdGG'
arrayClose 'pdGG'
Initx =: 0.94 , 0.5p1 , ((0.25p1*0.125)+(7*2p1*0.125)+(2p1*0.125)*0.25) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,1000"_)*1"_
pdGH =:vSgD@vS''
pdGH arrayPut 'pdGH'
arrayClose 'pdGH'
NB. ... execute (ijx) ...
arrayOpen 'pdGA'
pdGA=:1001 8 4 arrayGet 'pdGA' NB. ... shape required ...
arrayClose 'pdGA'
arrayOpen 'pdGB'
pdGB=:1001 8 4 arrayGet 'pdGB' NB. ... shape required ...
arrayClose 'pdGB'
arrayOpen 'pdGC'
pdGC=:1001 8 4 arrayGet 'pdGC' NB. ... shape required ...
arrayClose 'pdGC'
arrayOpen 'pdGD'
pdGD=:1001 8 4 arrayGet 'pdGD' NB. ... shape required ...
arrayClose 'pdGD'
arrayOpen 'pdGE'
pdGE=:1001 8 4 arrayGet 'pdGE' NB. ... shape required ...
arrayClose 'pdGE'
arrayOpen 'pdGF'
pdGF=:1001 8 4 arrayGet 'pdGF' NB. ... shape required ...
arrayClose 'pdGF'
arrayOpen 'pdGG'
pdGG=:1001 8 4 arrayGet 'pdGG' NB. ... shape required ...
arrayClose 'pdGG'
arrayOpen 'pdGH'
pdGH=:1001 8 4 arrayGet 'pdGH' NB. ... shape required ...
arrayClose 'pdGH'
vSgDd2M=.[([(0{])@E1cn xRef@hkxR03S),:@(S03xH{])
vSgDd2 =.gXR(-@(([([(0{])@ch2k xRef@hkxR03S),:@(S03xH{]))+/"1@((<0 2)|:])@((0|:[)smx])(]*/])@(S02d1L{]))+vSgDd2M)]
Initds2=.(gXR([(0{])@mcv xRef@hkxR03S),:@Initx)+/^:2@:*(]*/])@Initdx
Initds =.%:@|@Initds2
gXRAll=:,:@(0.15 1.0 2 8 1 1 8 _8 0 0"_)
gXSAll=:,:@(0.15 0.9 2 8 1 1 8 8 0 0"_)
Initx =: 0.94 , 0.5p1 , ((0.25p1*0.125)+(0*2p1*0.125)+(2p1*0.125)*0.75) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,1000"_)*1"_
pdHA =:vSgD@vS''
pdHA arrayPut 'pdHA'
arrayClose 'pdHA'
Initx =: 0.94 , 0.5p1 , ((0.25p1*0.125)+(1*2p1*0.125)+(2p1*0.125)*0.75) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,1000"_)*1"_
pdHB =:vSgD@vS''
pdHB arrayPut 'pdHB'
arrayClose 'pdHB'
Initx =: 0.94 , 0.5p1 , ((0.25p1*0.125)+(2*2p1*0.125)+(2p1*0.125)*0.75) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,1000"_)*1"_
pdHC =:vSgD@vS''
pdHC arrayPut 'pdHC'
arrayClose 'pdHC'
Initx =: 0.94 , 0.5p1 , ((0.25p1*0.125)+(3*2p1*0.125)+(2p1*0.125)*0.75) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,1000"_)*1"_
pdHD =:vSgD@vS''
pdHD arrayPut 'pdHD'
arrayClose 'pdHD'
Initx =: 0.94 , 0.5p1 , ((0.25p1*0.125)+(4*2p1*0.125)+(2p1*0.125)*0.75) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,1000"_)*1"_
pdHE =:vSgD@vS''
pdHE arrayPut 'pdHE'
arrayClose 'pdHE'
Initx =: 0.94 , 0.5p1 , ((0.25p1*0.125)+(5*2p1*0.125)+(2p1*0.125)*0.75) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,1000"_)*1"_
pdHF =:vSgD@vS''
pdHF arrayPut 'pdHF'
arrayClose 'pdHF'
Initx =: 0.94 , 0.5p1 , ((0.25p1*0.125)+(6*2p1*0.125)+(2p1*0.125)*0.75) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,1000"_)*1"_
pdHG =:vSgD@vS''
pdHG arrayPut 'pdHG'
arrayClose 'pdHG'
Initx =: 0.94 , 0.5p1 , ((0.25p1*0.125)+(7*2p1*0.125)+(2p1*0.125)*0.75) , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,1000"_)*1"_
pdHH =:vSgD@vS''
pdHH arrayPut 'pdHH'
arrayClose 'pdHH'
NB. ... execute (ijx) ...
arrayOpen 'pdHA'
pdHA=:1001 8 4 arrayGet 'pdHA' NB. ... shape required ...
arrayClose 'pdHA'
arrayOpen 'pdHB'
pdHB=:1001 8 4 arrayGet 'pdHB' NB. ... shape required ...
arrayClose 'pdHB'
arrayOpen 'pdHC'
pdHC=:1001 8 4 arrayGet 'pdHC' NB. ... shape required ...
arrayClose 'pdHC'
arrayOpen 'pdHD'
pdHD=:1001 8 4 arrayGet 'pdHD' NB. ... shape required ...
arrayClose 'pdHD'
arrayOpen 'pdHE'
pdHE=:1001 8 4 arrayGet 'pdHE' NB. ... shape required ...
arrayClose 'pdHE'
arrayOpen 'pdHF'
pdHF=:1001 8 4 arrayGet 'pdHF' NB. ... shape required ...
arrayClose 'pdHF'
arrayOpen 'pdHG'
pdHG=:1001 8 4 arrayGet 'pdHG' NB. ... shape required ...
arrayClose 'pdHG'
arrayOpen 'pdHH'
pdHH=:1001 8 4 arrayGet 'pdHH' NB. ... shape required ...
arrayClose 'pdHH'
load 'plot' pd vSgDplot pdEA pd vSgDplot pdEB pd vSgDplot pdEC pd vSgDplot pdED pd vSgDplot pdEE pd vSgDplot pdEF pd vSgDplot pdEG pd vSgDplot pdEH pd vSgDplot pdFA pd vSgDplot pdFB pd vSgDplot pdFC pd vSgDplot pdFD pd vSgDplot pdFE pd vSgDplot pdFF pd vSgDplot pdFG pd vSgDplot pdFH pd vSgDplot pdGA pd vSgDplot pdGB pd vSgDplot pdGC pd vSgDplot pdGD pd vSgDplot pdGE pd vSgDplot pdGF pd vSgDplot pdGG pd vSgDplot pdGH pd vSgDplot pdHA pd vSgDplot pdHB pd vSgDplot pdHC pd vSgDplot pdHD pd vSgDplot pdHE pd vSgDplot pdHF pd vSgDplot pdHG pd vSgDplot pdHH pd ((0.94*cos@]"0);0.94*sin@]"0) pTsteps _ 0 2p1 160 pd 'aspect 1' pd 'pdf' pd 'show'
... geodesics in a standing wave ...
vSgDd2M=.[([(0{])@rfE1cn xRef@hkxR03S),:@(S03xH{])
vSgDd2 =.gXR(-@(([([(0{])@ch2k xRef@hkxR03S),:@(S03xH{]))+/"1@((<0 2)|:])@((0|:[)smx])(]*/])@(S02d1L{]))+vSgDd2M)]
Initds2=.(gXR([(0{])@mcv xRef@hkxR03S),:@Initx)+/^:2@:*(]*/])@Initdx
Initds =.%:@|@Initds2
gXRAll=:,:@(0.15 1.0 2 8 1 1 8 _8 0 0"_)
gXSAll=:,:@(0.15 0.9 2 8 1 1 8 8 0 0"_)
Initx =: 0.99 , 0.5p1 , 0.03125p1 , 0p1 "_
Initdx=: (0 , 0 , 0.001 , 0.04"_)*%@(1"_)
vS00xL =:Initx
vS01dxL =:0,0,0,0:
vS02d1L =:Initd1
vS06ds =:Initds
vS07count =:(0,72000"_)*1"_
pdIA =:vSgD@vS''
pdIA arrayPut 'pdIA'
arrayClose 'pdIA'
NB. ... execute (ijx) ...
arrayOpen 'pdIA'
pdIA=:72001 8 4 arrayGet 'pdIA' NB. ... shape required ...
arrayClose 'pdIA'
load 'plot' pd vSgDplot pdIA pd ((0.99*cos@]"0);0.99*sin@]"0) pTsteps _ 0p1 0.0625p1 160 pd 'aspect 1' pd 'pdf' pd 'show'
... geodesic localized in standing wave ...
load 'plot'
pd (cx3"1;cx0"1)@:((S00xL{])"2) (i.@(72001"_){]) pdIA
pd 'pdf'
pd 'show'
... x0 increases with elapsed time along geodesic ...
load 'plot'
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)@:(rfyc"1)@:((S00xL{])"2) (i.@(72001"_){]) pdIA
pd (}:@:(cy3"1);incy2)@:(rfyc"1)@:((S00xL{])"2) (i.@(72001"_){]) pdIA NB. ... incy2 is zero ...
pd 'pdf'
pd 'show'
... velocity with elapsed time along geodesic ...
