User:Tom Allen/ta/AddendumX00P04

From J Wiki
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) ...


JX00P0400J.jpg


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) ...


JX00P0401K.jpg


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) ...


JX00P0402H.jpg
... 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) ...


JX00P0403G.jpg


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 ...


JX00P0404C.jpg
... 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...


JX00P0405C.jpg
... 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 ...


JX00P0406C.jpg
... 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 ...


JX00P0407C.jpg
... charge flow and charge density along geodesic ...