User:Tom Allen/ta/AddendumX00P01

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load 'plot'

pd 'reset'

gX0=:,:@(0.15 1 2 8 1 1 8 _8 0 0"_)
gX1=:,:@(0.15 1 2 8 1 1 8  8 0 0"_)

xCpts=:_ 0.94 0.94 0,_ 0.5p1 0.5p1 0,(_,(0.25p1%8"_),((0.25p1%8"_)+0.25p1"_),400"_),:_ 0.00p1 0.00p1 0*0.125"_

pd (''(cx2"_ 1;[(2{])"1@Ocn xRef@hkxX00C)]) pTtotal xCpts''

xCpts=:_ 0.94 0.94 0,_ 0.5p1 0.5p1 0,(_,(0.25p1%8"_),((0.25p1%8"_)+0.25p1"_),400"_),:_ 0.25p1 0.25p1 0*0.125"_

pd (''(cx2"_ 1;[(2{])"1@Ocn xRef@hkxX00C)]) pTtotal xCpts''

xCpts=:_ 0.94 0.94 0,_ 0.5p1 0.5p1 0,(_,(0.25p1%8"_),((0.25p1%8"_)+0.25p1"_),400"_),:_ 0.40p1 0.40p1 0*0.125"_

pd (''(cx2"_ 1;[(2{])"1@Ocn xRef@hkxX00C)]) pTtotal xCpts''

xCpts=:_ 0.94 0.94 0,_ 0.5p1 0.5p1 0,(_,(0.25p1%8"_),((0.25p1%8"_)+0.25p1"_),400"_),:_ 0.50p1 0.50p1 0*0.125"_

pd (''(cx2"_ 1;[(2{])"1@Ocn xRef@hkxX00C)]) pTtotal xCpts''

xCpts=:_ 0.94 0.94 0,_ 0.5p1 0.5p1 0,(_,(0.25p1%8"_),((0.25p1%8"_)+0.25p1"_),400"_),:_ 0.60p1 0.60p1 0*0.125"_

pd (''(cx2"_ 1;[(2{])"1@Ocn xRef@hkxX00C)]) pTtotal xCpts''

xCpts=:_ 0.94 0.94 0,_ 0.5p1 0.5p1 0,(_,(0.25p1%8"_),((0.25p1%8"_)+0.25p1"_),400"_),:_ 0.75p1 0.75p1 0*0.125"_

pd (''(cx2"_ 1;[(2{])"1@Ocn xRef@hkxX00C)]) pTtotal xCpts''

xCpts=:_ 0.94 0.94 0,_ 0.5p1 0.5p1 0,(_,(0.25p1%8"_),((0.25p1%8"_)+0.25p1"_),400"_),:_ 1.00p1 1.00p1 0*0.125"_

pd (''(cx2"_ 1;[(2{])"1@Ocn xRef@hkxX00C)]) pTtotal xCpts''

pd 'pdf'
pd 'show'


JX00P0100D.jpg
... a standing wave ...


load 'plot'

pd 'reset'

gX0=:,:@(0.15 1 2 8 1 1 8 _8 0 0"_)
gX1=:,:@(0.15 1 2 8 1 1 8  8 0 0"_)

xCpts=:_ 0.94 0.94 0,_ 0.5p1 0.5p1 0,(_,(0.25p1%8"_),((0.25p1%8"_)+0.25p1"_),400"_),:_ 0.00p1 0.00p1 0*0.125"_

pd (''(cx2"_ 1;[-@(0{])"1@E1cn xRef@hkxX00C)]) pTtotal xCpts''

xCpts=:_ 0.94 0.94 0,_ 0.5p1 0.5p1 0,(_,(0.25p1%8"_),((0.25p1%8"_)+0.25p1"_),400"_),:_ 0.25p1 0.25p1 0*0.125"_

pd (''(cx2"_ 1;[-@(0{])"1@E1cn xRef@hkxX00C)]) pTtotal xCpts''

xCpts=:_ 0.94 0.94 0,_ 0.5p1 0.5p1 0,(_,(0.25p1%8"_),((0.25p1%8"_)+0.25p1"_),400"_),:_ 0.40p1 0.40p1 0*0.125"_

pd (''(cx2"_ 1;[-@(0{])"1@E1cn xRef@hkxX00C)]) pTtotal xCpts''

xCpts=:_ 0.94 0.94 0,_ 0.5p1 0.5p1 0,(_,(0.25p1%8"_),((0.25p1%8"_)+0.25p1"_),400"_),:_ 0.50p1 0.50p1 0*0.125"_

pd (''(cx2"_ 1;[-@(0{])"1@E1cn xRef@hkxX00C)]) pTtotal xCpts''

xCpts=:_ 0.94 0.94 0,_ 0.5p1 0.5p1 0,(_,(0.25p1%8"_),((0.25p1%8"_)+0.25p1"_),400"_),:_ 0.60p1 0.60p1 0*0.125"_

pd (''(cx2"_ 1;[-@(0{])"1@E1cn xRef@hkxX00C)]) pTtotal xCpts''

xCpts=:_ 0.94 0.94 0,_ 0.5p1 0.5p1 0,(_,(0.25p1%8"_),((0.25p1%8"_)+0.25p1"_),400"_),:_ 0.75p1 0.75p1 0*0.125"_

pd (''(cx2"_ 1;[-@(0{])"1@E1cn xRef@hkxX00C)]) pTtotal xCpts''

xCpts=:_ 0.94 0.94 0,_ 0.5p1 0.5p1 0,(_,(0.25p1%8"_),((0.25p1%8"_)+0.25p1"_),400"_),:_ 1.00p1 1.00p1 0*0.125"_

pd (''(cx2"_ 1;[-@(0{])"1@E1cn xRef@hkxX00C)]) pTtotal xCpts''

pd 'pdf'
pd 'show'


JX00P0101C.jpg
... divergence of x0 ...


NB. ... execute (ijx) ...

   gX0=:,:@(0.15 1 2 8 1 1 8 _8 0 0"_)
   gX1=:,:@(0.15 1 2 8 1 1 8  8 0 0"_)

   xCpts=:_ 0.4 1.7 26,_ 0.5p1 0.5p1 0,(_,(0.25p1%8"_),((0.25p1%8"_)+0.25p1"_),26"_),:_ 0 0.25p1 26"_

NB. ... divergence of x1 ...

   (0=]) ((2^_44)qtsz]) (''([-@(1{])"1@E1cn xRef@hkxX00C)]) ((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=:,:@(0.15 1 2 8 1 1 8 _8 0 0"_)
gX1=:,:@(0.15 1 2 8 1 1 8  8 0 0"_)

xCpts=:_ 0.94 0.94 0,_ 0.5p1 0.5p1 0,(_,(0.25p1%8"_),((0.25p1%8"_)+0.25p1"_),400"_),:_ 0.00p1 0.00p1 0*0.125"_

pd (''(cx2"_ 1;[-@(2{])"1@E1cn xRef@hkxX00C)]) pTtotal xCpts''

xCpts=:_ 0.94 0.94 0,_ 0.5p1 0.5p1 0,(_,(0.25p1%8"_),((0.25p1%8"_)+0.25p1"_),400"_),:_ 0.25p1 0.25p1 0*0.125"_

pd (''(cx2"_ 1;[-@(2{])"1@E1cn xRef@hkxX00C)]) pTtotal xCpts''

xCpts=:_ 0.94 0.94 0,_ 0.5p1 0.5p1 0,(_,(0.25p1%8"_),((0.25p1%8"_)+0.25p1"_),400"_),:_ 0.40p1 0.40p1 0*0.125"_

pd (''(cx2"_ 1;[-@(2{])"1@E1cn xRef@hkxX00C)]) pTtotal xCpts''

xCpts=:_ 0.94 0.94 0,_ 0.5p1 0.5p1 0,(_,(0.25p1%8"_),((0.25p1%8"_)+0.25p1"_),400"_),:_ 0.50p1 0.50p1 0*0.125"_

pd (''(cx2"_ 1;[-@(2{])"1@E1cn xRef@hkxX00C)]) pTtotal xCpts''

xCpts=:_ 0.94 0.94 0,_ 0.5p1 0.5p1 0,(_,(0.25p1%8"_),((0.25p1%8"_)+0.25p1"_),400"_),:_ 0.60p1 0.60p1 0*0.125"_

pd (''(cx2"_ 1;[-@(2{])"1@E1cn xRef@hkxX00C)]) pTtotal xCpts''

xCpts=:_ 0.94 0.94 0,_ 0.5p1 0.5p1 0,(_,(0.25p1%8"_),((0.25p1%8"_)+0.25p1"_),400"_),:_ 0.75p1 0.75p1 0*0.125"_

pd (''(cx2"_ 1;[-@(2{])"1@E1cn xRef@hkxX00C)]) pTtotal xCpts''

xCpts=:_ 0.94 0.94 0,_ 0.5p1 0.5p1 0,(_,(0.25p1%8"_),((0.25p1%8"_)+0.25p1"_),400"_),:_ 1.00p1 1.00p1 0*0.125"_

pd (''(cx2"_ 1;[-@(2{])"1@E1cn xRef@hkxX00C)]) pTtotal xCpts''

pd 'pdf'
pd 'show'


JX00P0102C.jpg
... divergence of x2 ...


load 'plot'

pd 'reset'

gX0=:,:@(0.15 1 2 8 1 1 8 _8 0 0"_)
gX1=:,:@(0.15 1 2 8 1 1 8  8 0 0"_)

xCpts=:_ 0.94 0.94 0,_ 0.5p1 0.5p1 0,(_,(0.25p1%8"_),((0.25p1%8"_)+0.25p1"_),400"_),:_ 0.00p1 0.00p1 0*0.125"_

pd (''(cx2"_ 1;[-@(3{])"1@E1cn xRef@hkxX00C)]) pTtotal xCpts''

xCpts=:_ 0.94 0.94 0,_ 0.5p1 0.5p1 0,(_,(0.25p1%8"_),((0.25p1%8"_)+0.25p1"_),400"_),:_ 0.25p1 0.25p1 0*0.125"_

pd (''(cx2"_ 1;[-@(3{])"1@E1cn xRef@hkxX00C)]) pTtotal xCpts''

xCpts=:_ 0.94 0.94 0,_ 0.5p1 0.5p1 0,(_,(0.25p1%8"_),((0.25p1%8"_)+0.25p1"_),400"_),:_ 0.40p1 0.40p1 0*0.125"_

pd (''(cx2"_ 1;[-@(3{])"1@E1cn xRef@hkxX00C)]) pTtotal xCpts''

xCpts=:_ 0.94 0.94 0,_ 0.5p1 0.5p1 0,(_,(0.25p1%8"_),((0.25p1%8"_)+0.25p1"_),400"_),:_ 0.50p1 0.50p1 0*0.125"_

pd (''(cx2"_ 1;[-@(3{])"1@E1cn xRef@hkxX00C)]) pTtotal xCpts''

xCpts=:_ 0.94 0.94 0,_ 0.5p1 0.5p1 0,(_,(0.25p1%8"_),((0.25p1%8"_)+0.25p1"_),400"_),:_ 0.60p1 0.60p1 0*0.125"_

pd (''(cx2"_ 1;[-@(3{])"1@E1cn xRef@hkxX00C)]) pTtotal xCpts''

xCpts=:_ 0.94 0.94 0,_ 0.5p1 0.5p1 0,(_,(0.25p1%8"_),((0.25p1%8"_)+0.25p1"_),400"_),:_ 0.75p1 0.75p1 0*0.125"_

pd (''(cx2"_ 1;[-@(3{])"1@E1cn xRef@hkxX00C)]) pTtotal xCpts''

xCpts=:_ 0.94 0.94 0,_ 0.5p1 0.5p1 0,(_,(0.25p1%8"_),((0.25p1%8"_)+0.25p1"_),400"_),:_ 1.00p1 1.00p1 0*0.125"_

pd (''(cx2"_ 1;[-@(3{])"1@E1cn xRef@hkxX00C)]) pTtotal xCpts''

pd 'pdf'
pd 'show'


JX00P0103C.jpg
... divergence of x3 ...


gX0=:,:@(0.15 1 2 8 1 1 8 _8 0 0"_)
gX1=:,:@(0.15 1 2 8 1 1 8  8 0 0"_)

vSgDd2=:''([-@([(0{])@E1cn yRef@([hkxX00C zfxc"_ 1)),:@(S03yH{]))]


Initx =:  0.94 , 0.5p1 , (0.25p1%8:) , 0p1 "_
Initdx=: (0    , 0     ,  0.001      , 0.04"_)*%@InitInt=:1"_

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=:(0,1000"_)*InitInt
pdDT     =:vSgD@vS''

pdDT arrayPut   'pdDT'
     arrayClose 'pdDT'


Initx =:  0.94 , 0.5p1 , (0.25p1%8:) , 0p1 "_
Initdx=: (0    , 0     ,  0.001      , 0.04"_)*%@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=:(0,1000"_)*InitInt
pdDU     =:vSgD@vS''

pdDU arrayPut   'pdDU'
     arrayClose 'pdDU'


Initx =:  0.94 , 0.5p1 , (0.25p1%8:) , 0p1 "_
Initdx=: (0    , 0     ,  0.001      , 0.04"_)*%@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=:(0,1000"_)*InitInt
pdDV     =:vSgD@vS''

pdDV arrayPut   'pdDV'
     arrayClose 'pdDV'


Initx =:  0.94 , 0.5p1 , (0.25p1%8:) , 0p1 "_
Initdx=: (0    , 0     ,  0.001      , 0.04"_)*%@InitInt=:80"_

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=:(0,1000"_)*InitInt
pdDW     =:vSgD@vS''

pdDW arrayPut   'pdDW'
     arrayClose 'pdDW'


NB. ... execute (ijx) ...

                arrayOpen  'pdDT'
pdDT=:01001 8 4 arrayGet   'pdDT'   NB. ... shape required ...
                arrayClose 'pdDT'

                arrayOpen  'pdDU'
pdDU=:02001 8 4 arrayGet   'pdDU'   NB. ... shape required ...
                arrayClose 'pdDU'

                arrayOpen  'pdDV'
pdDV=:04001 8 4 arrayGet   'pdDV'   NB. ... shape required ...
                arrayClose 'pdDV'

                arrayOpen  'pdDW'
pdDW=:80001 8 4 arrayGet   'pdDW'   NB. ... shape required ...
                arrayClose 'pdDW'


load 'plot'

pd 'reset'

pd ((0.94*cos@]"0);0.94*sin@]"0) pTsteps (_,0p1,((0.25p1%8"_)*2"_),160"_)''

pd <"1@(0|:])@:((cy0,cy1)@(S00yL{])"2) pdDT
pd <"1@(0|:])@:((cy0,cy1)@(S00yL{])"2) pdDU
pd <"1@(0|:])@:((cy0,cy1)@(S00yL{])"2) pdDV
pd <"1@(0|:])@:((cy0,cy1)@(S00yL{])"2) pdDW

pd 'aspect 1'
pd 'pdf'
pd 'show'


JX00P0104C.jpg
... a geodesic ...


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 (}:@:(cy3"1);veloc)@:((S00yL{])"2) pdDT
pd (}:@:(cy3"1);incy2)@:((S00yL{])"2) pdDT    NB. ... incy2 is zero ...

pd (}:@:(cy3"1);veloc)@:((S00yL{])"2) pdDU
pd (}:@:(cy3"1);incy2)@:((S00yL{])"2) pdDU    NB. ... incy2 is zero ...

pd (}:@:(cy3"1);veloc)@:((S00yL{])"2) pdDV
pd (}:@:(cy3"1);incy2)@:((S00yL{])"2) pdDV    NB. ... incy2 is zero ...

pd (}:@:(cy3"1);veloc)@:((S00yL{])"2) pdDW
pd (}:@:(cy3"1);incy2)@:((S00yL{])"2) pdDW    NB. ... incy2 is zero ...

pd 'pdf'
pd 'show'


... compare TensorExperimentsR21 (JTER2117C.jpg) ...


JX00P0105C.jpg
... velocity (maximum temperature) with 8 cycles ...