User:Tom Allen/ta/AddendumX00P04
< User:Tom Allen | ta
Jump to navigation
Jump to search
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) ...
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.@{.@$;-@(0{])"1) pdDVE1cn NB. ... divergence x0 ... pd 'pdf'
... divergence of x0 along geodesic ...
load 'plot' pd 'reset' gX0=:,:@(1.5 1 2 8 1 1 1 _1 0 0"_) pdDVE1cn=:(''([E1cn xRef@([hkxX00B zfxc"_ 1))(S00yL{])"2) ((5*i.@(5000"_)){]) (i.@(25000"_){]) pdDV pd (i.@{.@$;-@(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...
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 ...
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 ...