User:Tom Allen/ta/AddendumX00P04
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gX0=:,:@(1.5 1 2 8 1 1 1 _1 0 0"_)
vSgDd2=:''([-@([(0{])@E1cn yRef@([hkxX00B zfxc"_ 1)),:@(S03yH{]))]
Initx =: 1.03 , 0.5p1 , 0.25p1 , 0p1 "_
Initdx=: (0 , 0 , 0.000625 , 0.00066248"_)*%@InitInt=:1"_
Inity =:zfyc@Initx
Initdy=:zfyc@(Initx+Initdx)+-@zfyc@Initx
NB. ... 'ds' is defined by the first interval of the integration as in flat spacetime ...
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=:(0,9268"_)*InitInt
pdDQ =:vSgD@vS''
pdDQ arrayPut 'pdDQ'
arrayClose 'pdDQ'
Initx =: 1.03 , 0.5p1 , 0.25p1 , 0p1 "_
Initdx=: (0 , 0 , 0.000625 , 0.00066248"_)*%@InitInt=:2"_
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=:(0,9268"_)*InitInt
pdDR =:vSgD@vS''
pdDR arrayPut 'pdDR'
arrayClose 'pdDR'
Initx =: 1.03 , 0.5p1 , 0.25p1 , 0p1 "_
Initdx=: (0 , 0 , 0.000625 , 0.00066248"_)*%@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=:(0,9268"_)*InitInt
pdDS =:vSgD@vS''
pdDS arrayPut 'pdDS'
arrayClose 'pdDS'
Initx =: 1.03 , 0.5p1 , 0.25p1 , 0p1 "_
Initdx=: (0 , 0 , 0.000625 , 0.00066248"_)*%@InitInt=:8"_
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=:(0,9268"_)*InitInt
pdDT =:vSgD@vS''
pdDT arrayPut 'pdDT'
arrayClose 'pdDT'
Initx =: 1.03 , 0.5p1 , 0.25p1 , 0p1 "_
Initdx=: (0 , 0 , 0.000625 , 0.00066248"_)*%@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=:(0,9268"_)*InitInt
pdDU =:vSgD@vS''
pdDU arrayPut 'pdDU'
arrayClose 'pdDU'
NB. ... execute (ijx) ...
arrayOpen 'pdDQ'
pdDQ=:009269 8 4 arrayGet 'pdDQ' NB. ... shape required ...
arrayClose 'pdDQ'
arrayOpen 'pdDR'
pdDR=:018537 8 4 arrayGet 'pdDR' NB. ... shape required ...
arrayClose 'pdDR'
arrayOpen 'pdDS'
pdDS=:037073 8 4 arrayGet 'pdDS' NB. ... shape required ...
arrayClose 'pdDS'
arrayOpen 'pdDT'
pdDT=:074145 8 4 arrayGet 'pdDT' NB. ... shape required ...
arrayClose 'pdDT'
arrayOpen 'pdDU'
pdDU=:148289 8 4 arrayGet 'pdDU' NB. ... shape required ...
arrayClose 'pdDU'
load 'plot'
pd 'reset'
pd ((1.03*cos@]"0);1.03*sin@]"0) pTsteps _ 0p1 2p1 160
pd <"1@(0|:])@:((cy0,cy1)@(S00yL{])"2) pdDQ
pd <"1@(0|:])@:((cy0,cy1)@(S00yL{])"2) pdDR
pd <"1@(0|:])@:((cy0,cy1)@(S00yL{])"2) pdDS
pd <"1@(0|:])@:((cy0,cy1)@(S00yL{])"2) pdDT
pd <"1@(0|:])@:((cy0,cy1)@(S00yL{])"2) pdDU
pd 'aspect 1'
pd 'pdf'
... path of the electromagnetic wave (blue) ...
... a geodesic once around (converges) ...
NB. ... execute (ijx) ...
NB. ... spacetime coordinates start/end geodesic ...
((cos@(0.25p1"_)*1.03"_),(sin@(0.25p1"_)*1.03"_),0,0:)''
0.72832 0.72832 0 0
(10j6":]) ((2^_44)qtsz]) (S00yL{])@{:@> pdDQ;pdDR;pdDS;pdDT;pdDU
0.728533 0.728212 0.000000 6.373235
0.728592 0.728174 0.000000 6.373159
0.728622 0.728155 0.000000 6.373120
0.728637 0.728145 0.000000 6.373101
0.728644 0.728140 0.000000 6.373092
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)) pdDQ
pd (((S06ds{])*i.@(S0700nmbr{]))@{:;incy2@:((S00yL{])"2)) pdDQ
pd (((S06ds{])*i.@(S0700nmbr{]))@{:;veloc@:((S00yL{])"2)) pdDR
pd (((S06ds{])*i.@(S0700nmbr{]))@{:;incy2@:((S00yL{])"2)) pdDR
pd (((S06ds{])*i.@(S0700nmbr{]))@{:;veloc@:((S00yL{])"2)) pdDS
pd (((S06ds{])*i.@(S0700nmbr{]))@{:;incy2@:((S00yL{])"2)) pdDS
pd (((S06ds{])*i.@(S0700nmbr{]))@{:;veloc@:((S00yL{])"2)) pdDT
pd (((S06ds{])*i.@(S0700nmbr{]))@{:;incy2@:((S00yL{])"2)) pdDT
pd (((S06ds{])*i.@(S0700nmbr{]))@{:;veloc@:((S00yL{])"2)) pdDU
pd (((S06ds{])*i.@(S0700nmbr{]))@{:;incy2@:((S00yL{])"2)) pdDU
pd 'pdf'
... velocity of geodesic plotted against 4D length (converges) ...
NB. ... execute (ijx) ...
incy0=:(2-~/\])@:(cy0"1)
incy1=:(2-~/\])@:(cy1"1)
incy2=:(2-~/\])@:(cy2"1)
incy3=:(2-~/\])@:(cy3"1)
NB. ... the length of the path of an electromagnetic wave is the elapsed time ...
NB. ... the time for the electromagnetic wave to go once around ...
1.03*2p1 NB. ... from start point of geodesic ...
6.47168
((((cy0^2:)+(cy1^2:)+cy2^2:)^0.5"_)@(S00yL{])@{:*2p1"_) pdDU NB. ... from end point of geodesic ...
6.47232
NB. ... the distance travelled by the geodesic (once around) ...
+/@(((incy0^2:)+(incy1^2:)+incy2^2:)^0.5"_)@:((S00yL{])"2) pdDU
6.37024
NB. ... the time for the geodesic (once around) ...
+/@incy3@:((S00yL{])"2) pdDU
6.37309
NB. ... the average velocity of the geodesic (once around) is less than 1 ...
6.37024%6.37309
0.999553
...
...
...
gX0=:,:@(1.5 1 2 8 1 1 1 _1 0 0"_)
vSgDd2=:''([-@([(0{])@E1cn yRef@([hkxX00B zfxc"_ 1)),:@(S03yH{]))]
Initx =: 1.03 , 0.5p1 , 0.25p1 , 0p1 "_
Initdx=: (0 , 0 , 0.000625 , 0.00066248"_)*%@InitInt=:1"_
Inity =:zfyc@Initx
Initdy=:zfyc@(Initx+Initdx)+-@zfyc@Initx
NB. ... 'ds' is defined by the first interval of the integration as in flat spacetime ...
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=:(0,48000"_)*InitInt
pdDV =:vSgD@vS''
pdDV arrayPut 'pdDV'
arrayClose 'pdDV'
Initx =: 1.03 , 0.5p1 , 0.25p1 , 0p1 "_
Initdx=: (0 , 0 , 0.000625 , 0.00066248"_)*%@InitInt=:2"_
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=:(0,48000"_)*InitInt
pdDW =:vSgD@vS''
pdDW arrayPut 'pdDW'
arrayClose 'pdDW'
NB. ... execute (ijx) ...
arrayOpen 'pdDV'
pdDV=:48001 8 4 arrayGet 'pdDV' NB. ... shape required ...
arrayClose 'pdDV'
arrayOpen 'pdDW'
pdDW=:96001 8 4 arrayGet 'pdDW' NB. ... shape required ...
arrayClose 'pdDW'
load 'plot'
pd 'reset'
pd ((1.03*cos@]"0);1.03*sin@]"0) pTsteps _ 0p1 2p1 160
pd <"1@(0|:])@:((cy0,cy1)@(S00yL{])"2) (i.@(20500"_){]) pdDV
pd <"1@(0|:])@:((cy0,cy1)@(S00yL{])"2) (i.@(41000"_){]) pdDW
pd 'aspect 1'
pd 'pdf'
... path of the electromagnetic wave (blue) ...
... a geodesic (converges) ...
... the geodesic is not contained like it is contained in the standing wave ...
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.@(25000"_){]) pdDV
pd (((S06ds{])*i.@(S0700nmbr{]))@{:;incy2@:((S00yL{])"2)) (i.@(25000"_){]) pdDV
pd (((S06ds{])*i.@(S0700nmbr{]))@{:;veloc@:((S00yL{])"2)) (i.@(50000"_){]) pdDW
pd (((S06ds{])*i.@(S0700nmbr{]))@{:;incy2@:((S00yL{])"2)) (i.@(50000"_){]) pdDW
pd 'pdf'
... velocity of geodesic plotted against 4D length (converges) ...
load 'plot'
pd 'reset'
gX0=:,:@(1.5 1 2 8 1 1 1 _1 0 0"_)
pdDVE1cn=:(''([E1cn xRef@([hkxX00B zfxc"_ 1))(S00yL{])"2) ((5*i.@(5000"_)){]) (i.@(25000"_){]) pdDV
pd (i.@{.@$;-@(0{])"1) pdDVE1cn NB. ... divergence x0 ...
pd 'pdf'
... divergence of x0 along geodesic ...
... divergence of x0 (y0/y1 plane) ...
load 'plot'
pd 'reset'
gX0=:,:@(1.5 1 2 8 1 1 1 _1 0 0"_)
pdDVE1cn=:(''([E1cn xRef@([hkxX00B zfxc"_ 1))(S00yL{])"2) ((5*i.@(5000"_)){]) (i.@(25000"_){]) pdDV
pd (i.@{.@$;-@(2{])"1) pdDVE1cn NB. ... divergence x2 (blue) ...
pd (i.@{.@$;-@(3{])"1) pdDVE1cn NB. ... divergence x3 (red) ...
pd (i.@{.@$;-@(1{])"1) pdDVE1cn NB. ... divergence x1 (green) ...
pd 'pdf'
... divergence of x2 x3 x1 along geodesic...
... divergence of x2 x3 x1 (y0/y1 plane) ...
load 'plot'
pd 'reset'
gX0=:,:@(1.5 1 2 8 1 1 1 _1 0 0"_)
pdDVEEMcn=:(''([(}:"1@}:"2@xdy smx"2 1 EEMcn)yRef@([hkxX00B zfxc"_ 1))(S00yL{])"2) ((5*i.@(5000"_)){]) (i.@(25000"_){]) pdDV
pdDVHEMcn=:(''([(}:"1@}:"2@xdy smx"2 1 HEMcn)yRef@([hkxX00B zfxc"_ 1))(S00yL{])"2) ((5*i.@(5000"_)){]) (i.@(25000"_){]) pdDV
pd (i.@{.@$;-@(0{])"1) pdDVEEMcn NB. ... electric field x0 (blue) ...
pd (i.@{.@$;-@(1{])"1) pdDVHEMcn NB. ... magnetic field x1 (red) ...
pd (i.@{.@$;-@(1{])"1) pdDVEEMcn NB. ... electric field x1 (zero) ...
pd (i.@{.@$;-@(2{])"1) pdDVEEMcn NB. ... electric field x2 (zero) ...
pd (i.@{.@$;-@(0{])"1) pdDVHEMcn NB. ... magnetic field x0 (zero) ...
pd (i.@{.@$;-@(2{])"1) pdDVHEMcn NB. ... magnetic field x2 (zero) ...
pd 'pdf'
... the electric field and magnetic field are othogonal ...
... the electric field and magnetic field on geodesic ...
NB. ... execute (ijx) ...
gX0=:,:@(1.5 1 2 8 1 1 1 _1 0 0"_)
xCpts=:_ 0.7 1.3 26,_ 0.4p1 0.6p1 26,_ 0 2p1 26,:_ 0 2p1 26"_
(0=]) ((2^_44)qtsz]) (''([+/@((<0 1)|:])"2@(}:"1@}:"2@mcv smx"2 2 EEMcn*/"1 HEMcn)yRef@hkxX00B)]) ((0;50"_)pTRandom xCpts)''
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
load 'plot'
pd 'reset'
gX0=:,:@(1.5 1 2 8 1 1 1 _1 0 0"_)
pdDVJEMcn=:(''([(xdy smx"2 1 JEMcn)yRef@([hkxX00B zfxc"_ 1))(S00yL{])"2) ((5*i.@(5000"_)){]) (i.@(25000"_){]) pdDV
pd (i.@{.@$;-@(0{])"1) pdDVJEMcn NB. ... charge flow x0 (blue) ...
pd (i.@{.@$;-@(1{])"1) pdDVJEMcn NB. ... charge flow x1 (red) ...
pd (i.@{.@$;-@(2{])"1) pdDVJEMcn NB. ... charge flow x2 (green) ...
pd (i.@{.@$;-@(3{])"1) pdDVJEMcn NB. ... charge density x3 (purple) ...
pd 'pdf'
... charge flow and charge density along geodesic ...
... charge flow and charge density along geodesic ...
