User:Tom Allen/TensorExperimentsB00

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NOTE: TensorExperimentsB is stand-alone using verbs from Essays/TensorExperiments.



NB. ... script experimentalB.ijs ...

load jpath '~temp\experimental.ijs'

gXq20=:(<2 0){[
gXq21=:(<2 1){[
gXq22=:(<2 2){[
gXq23=:(<2 3){[
gXq30=:(<3 0){[
gXq31=:(<3 1){[
gXq32=:(<3 2){[
gXq33=:(<3 3){[
gXq34=:(<3 4){[
gXq40=:(<4 0){[
gXq41=:(<4 1){[
gXq42=:(<4 2){[
gXq43=:(<4 3){[
gXq50=:(<5 0){[
gXq51=:(<5 1){[
gXq52=:(<5 2){[
gXq53=:(<5 3){[
gXq54=:(<5 4){[
gXq60=:(<6 0){[
gXq61=:(<6 1){[
gXq62=:(<6 2){[
gXq63=:(<6 3){[
gXq70=:(<7 0){[
gXq71=:(<7 1){[
gXq72=:(<7 2){[
gXq73=:(<7 3){[
gXq74=:(<7 4){[

gXB=:gXcw,gXpAll,gXq2All,gXq3All,gXq4All,gXq5All,gXq6All,:gXq7All


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

NB. ... check ...

   gXcw   =: 0.0  0.1  _    _    _  "_
   gXpAll =: 1.0  1.1  1.2  1.3  1.4"_
   gXq2All=: 2.0  2.1  2.2  2.3  _  "_
   gXq3All=: 3.0  3.1  3.2  3.3  3.4"_
   gXq4All=: 4.0  4.1  4.2  4.3  _  "_
   gXq5All=: 5.0  5.1  5.2  5.3  5.4"_
   gXq6All=: 6.0  6.1  6.2  6.3  _  "_
   gXq7All=: 7.0  7.1  7.2  7.3  7.4"_

   yCpts=:__ 0.5 5 8,__ 0.5 5 8,__ 0.5 5 8,:_ 0 20 8"_

   (gXB(gXc,gXw                      )]) ((0;50"_)pTRandom yCpts)''
0 0.1
   (gXB(gXp0,gXp1,gXp2,gXp3,gXp4     )]) ((0;50"_)pTRandom yCpts)''
1 1.1 1.2 1.3 1.4
   (gXB(gXq20,gXq21,gXq22,gXq23      )]) ((0;50"_)pTRandom yCpts)''
2 2.1 2.2 2.3
   (gXB(gXq30,gXq31,gXq32,gXq33,gXq34)]) ((0;50"_)pTRandom yCpts)''
3 3.1 3.2 3.3 3.4
   (gXB(gXq40,gXq41,gXq42,gXq43      )]) ((0;50"_)pTRandom yCpts)''
4 4.1 4.2 4.3
   (gXB(gXq50,gXq51,gXq52,gXq53,gXq54)]) ((0;50"_)pTRandom yCpts)''
5 5.1 5.2 5.3 5.4
   (gXB(gXq60,gXq61,gXq62,gXq63      )]) ((0;50"_)pTRandom yCpts)''
6 6.1 6.2 6.3
   (gXB(gXq70,gXq71,gXq72,gXq73,gXq74)]) ((0;50"_)pTRandom yCpts)''
7 7.1 7.2 7.3 7.4


GTEB0000C.jpg


load 'plot'

r=. ({.+(1&{-{.)*(i.&>:%])@{:) 0.00001 4 160

pd r; (1-^@-@(]^3:)       )"0 r
pd r;((1-^@-@(]^3:))*]^_2:)"0 r
pd r;((1-^@-@(]^3:))*]^_3:)"0 r

pd 'pdf'
pd 'show'


Egraphic0000.jpg


GTEB0001C.jpg


NB. ... script experimentalB.ijs ...

fbrS=:((gXq20*cy0)^2:)+((gXq21*cy1)^2:)+(gXq22*cy2)^2:

fbrSy0=:2*(gXq20^2:)*cy0
fbrSy1=:2*(gXq21^2:)*cy1
fbrSy2=:2*(gXq22^2:)*cy2

fbrSdy=:fbrSy0,fbrSy1,fbrSy2,0:

fbrSy0y0=:2*gXq20^2:
fbrSy1y1=:2*gXq21^2:
fbrSy2y2=:2*gXq22^2:

fbrSdydyt0=:fbrSy0y0,0,0,0:
fbrSdydyt1=:0,fbrSy1y1,0,0:
fbrSdydyt2=:0,0,fbrSy2y2,0:
fbrSdydyt3=:0,0,0,0:
fbrSdydy  =:fbrSdydyt0,fbrSdydyt1,fbrSdydyt2,:fbrSdydyt3


GTEB0002C.jpg


NB. ... script experimentalB.ijs ...

fbrB=:fbrS^0.5"_

fbrBdy=:0.5*(fbrS^_0.5"_)*fbrSdy

fbrBdydyt0=: 0.5 *(fbrS^_0.5"_)*fbrSdydy
fbrBdydyt1=:_0.25*(fbrS^_1.5"_)*fbrSdy*/fbrSdy
fbrBdydy  =:fbrBdydyt0+fbrBdydyt1


GTEB0003C.jpg


NB. ... script experimentalB.ijs ...

fbC00  =:gXq30
fbC00dy=:0,0,0,0:

fbC10  =:^@(gXq31*cy3)
fbC10dy=:(0,0,0,gXq31)*^@(gXq31*cy3)

fbC11  =:(gXq33*cos@((gXq32*fbrB)+gXq33*cy3))+gXq31*sin@((gXq32*fbrB)+gXq33*cy3)+gXq34
fbC11dy=:((gXq32*fbrBdy)+0,0,0,gXq33)*(-@gXq33*sin@((gXq32*fbrB)+gXq33*cy3))+gXq31*cos@((gXq32*fbrB)+gXq33*cy3)

fbC=:gXq23*fbC00+fbC10*fbC11

fbCdyt0=:gXq23*fbC10  *fbC11dy
fbCdyt1=:gXq23*fbC10dy*fbC11
fbCdy  =:fbCdyt0+fbCdyt1


GTEB0004C.jpg


NB. ... script experimentalB.ijs ...

fbDc=:gXq23*gXq32*fbrBdy*^@(gXq31*cy3)*cos@((gXq32*fbrB)+gXq33*cy3)

fbDcdyt0=:-@gXq23*gXq32*fbrBdy*/((gXq32*fbrBdy)+0,0,0,gXq33)*^@(gXq31*cy3)*sin@((gXq32*fbrB)+gXq33*cy3)
fbDcdyt1=:gXq23*gXq32*fbrBdy*/(0,0,0,gXq31)*^@(gXq31*cy3)*cos@((gXq32*fbrB)+gXq33*cy3)
fbDcdyt2=:gXq23*gXq32*fbrBdydy*^@(gXq31*cy3)*cos@((gXq32*fbrB)+gXq33*cy3)
fbDcdy  =:fbDcdyt0+fbDcdyt1+fbDcdyt2


GTEB0005C.jpg


NB. ... script experimentalB.ijs ...

fbEt0=:gXq23*gXq30*cy3
fbEt1=:gXq23*^@(gXq31*cy3)*sin@((gXq32*fbrB)+gXq33*cy3)+gXq34
fbE  =:fbEt0+fbEt1

fbEdyt00=:0,0,0,gXq23*gXq30
fbEdyt10=:gXq23*((gXq32*fbrBdy)+0,0,0,gXq33)*^@(gXq31*cy3)*cos@((gXq32*fbrB)+gXq33*cy3)
fbEdyt11=:gXq23*(0,0,0,gXq31)*^@(gXq31*cy3)*sin@((gXq32*fbrB)+gXq33*cy3)+gXq34
fbEdy   =:fbEdyt00+fbEdyt10+fbEdyt11


GTEB0006C.jpg


NB. ... script experimentalB.ijs ...

fbrT=:((gXq40*cy0)^2:)+((gXq41*cy1)^2:)+(gXq42*cy2)^2:

fbrTy0=:2*(gXq40^2:)*cy0
fbrTy1=:2*(gXq41^2:)*cy1
fbrTy2=:2*(gXq42^2:)*cy2

fbrTdy=:fbrTy0,fbrTy1,fbrTy2,0:

fbrTy0y0=:2*gXq40^2:
fbrTy1y1=:2*gXq41^2:
fbrTy2y2=:2*gXq42^2:

fbrTdydyt0=:fbrTy0y0,0,0,0:
fbrTdydyt1=:0,fbrTy1y1,0,0:
fbrTdydyt2=:0,0,fbrTy2y2,0:
fbrTdydyt3=:0,0,0,0:
fbrTdydy  =:fbrTdydyt0,fbrTdydyt1,fbrTdydyt2,:fbrTdydyt3


fbrA=:fbrT^0.5"_

fbrAdy=:0.5*(fbrT^_0.5"_)*fbrTdy

fbrAdydyt0=: 0.5 *(fbrT^_0.5"_)*fbrTdydy
fbrAdydyt1=:_0.25*(fbrT^_1.5"_)*fbrTdy*/fbrTdy
fbrAdydy  =:fbrAdydyt0+fbrAdydyt1


GTEB0007C.jpg


NB. ... script experimentalB.ijs ...

fbAp0=:gXq50-^@-@((gXq51*fbrA)^gXq52)

fbAp0T0  =:gXq51*fbrAdy
fbAp0T0dy=:gXq51*fbrAdydy
fbAp0T1  =:gXq52*(gXq51*fbrA)^gXq52-1:
fbAp0T1dy=:gXq52*(gXq51*fbrAdy)*(gXq52-1:)*(gXq51*fbrA)^gXq52-2:
fbAp0T2  =:^@-@((gXq51*fbrA)^gXq52)
fbAp0T2dy=:(gXq51*fbrAdy)*-@(gXq52*(gXq51*fbrA)^gXq52-1:)*^@-@((gXq51*fbrA)^gXq52)

fbAp0dy  =:fbAp0T0*fbAp0T1*fbAp0T2

fbAp0dydyt0=:fbAp0T0  */fbAp0T1  */fbAp0T2dy
fbAp0dydyt1=:fbAp0T0  */fbAp0T1dy*/fbAp0T2
fbAp0dydyt2=:fbAp0T0dy*/fbAp0T1  */fbAp0T2
fbAp0dydy  =:fbAp0dydyt0+fbAp0dydyt1+fbAp0dydyt2


fbAp1=:(gXq53*fbrA)^gXq54

fbAp1dy=:(gXq53*fbrAdy)*gXq54*(gXq53*fbrA)^gXq54-1:

fbAp1dydyt0=:(gXq53*fbrAdy)*/gXq54*(gXq53*fbrAdy)*(gXq54-1:)*(gXq53*fbrA)^gXq54-2:
fbAp1dydyt1=:(gXq53*fbrAdydy)*gXq54*(gXq53*fbrA)^gXq54-1:
fbAp1dydy  =:fbAp1dydyt0+fbAp1dydyt1


fbA=:gXq43*fbAp0*fbAp1

fbAdyt0=:gXq43*fbAp0  *fbAp1dy
fbAdyt1=:gXq43*fbAp0dy*fbAp1
fbAdy  =:fbAdyt0+fbAdyt1

fbAdydyt0=:gXq43*fbAp0    */fbAp1dydy
fbAdydyt1=:gXq43*fbAp0dy  */fbAp1dy
fbAdydyt2=:gXq43*fbAp0dy  */fbAp1dy
fbAdydyt3=:gXq43*fbAp0dydy*/fbAp1
fbAdydy  =:fbAdydyt0+fbAdydyt1+fbAdydyt2+fbAdydyt3


GTEB0008C.jpg


NB. ... script experimentalB.ijs ...

fbrU=:((gXq60*cy0)^2:)+((gXq61*cy1)^2:)+(gXq62*cy2)^2:

fbrUy0=:2*(gXq60^2:)*cy0
fbrUy1=:2*(gXq61^2:)*cy1
fbrUy2=:2*(gXq62^2:)*cy2

fbrUdy=:fbrUy0,fbrUy1,fbrUy2,0:


fbrF=:fbrU^0.5"_

fbrFdy=:0.5*(fbrU^_0.5"_)*fbrUdy


GTEB0009C.jpg


NB. ... script experimentalB.ijs ...

fbFp0=:gXq70-^@-@((gXq71*fbrF)^gXq72)

fbFp0T0=:gXq71*fbrFdy
fbFp0T1=:gXq72*(gXq71*fbrF)^gXq72-1:
fbFp0T2=:^@-@((gXq71*fbrF)^gXq72)
fbFp0dy=:fbFp0T0*fbFp0T1*fbFp0T2


fbFp1=:(gXq73*fbrF)^gXq74

fbFp1dy=:(gXq73*fbrFdy)*gXq74*(gXq73*fbrF)^gXq74-1:


fbF=:gXq63*fbFp0*fbFp1

fbFdyt0=:gXq63*fbFp0  *fbFp1dy
fbFdyt1=:gXq63*fbFp0dy*fbFp1
fbFdy  =:fbFdyt0+fbFdyt1


GTEB0010C.jpg


NB. ... script experimentalB.ijs ...

OyBcK0=:gXq20*cy0*fbA*fbC
OyBcK1=:gXq21*cy1*fbA*fbC
OyBcK2=:gXq22*cy2*fbA*fbC

OyBcK3t0=:(gXq20*cy0*(fbA*(0{])@fbDc)+(0{])@fbAdy*fbE)+gXq20*fbA*fbE
OyBcK3t1=:(gXq21*cy1*(fbA*(1{])@fbDc)+(1{])@fbAdy*fbE)+gXq21*fbA*fbE
OyBcK3t2=:(gXq22*cy2*(fbA*(2{])@fbDc)+(2{])@fbAdy*fbE)+gXq22*fbA*fbE
OyBcK3t3=:fbF
OyBcK3  =:-@(OyBcK3t0+OyBcK3t1+OyBcK3t2+OyBcK3t3)

OyBcK=:OyBcK0,OyBcK1,OyBcK2,OyBcK3


OyBcK0dy=:(gXq20*cy0*(fbA*fbCdy)+fbAdy*fbC)+(gXq20,0,0,0:)*fbA*fbC
OyBcK1dy=:(gXq21*cy1*(fbA*fbCdy)+fbAdy*fbC)+(0,gXq21,0,0:)*fbA*fbC
OyBcK2dy=:(gXq22*cy2*(fbA*fbCdy)+fbAdy*fbC)+(0,0,gXq22,0:)*fbA*fbC

OyBcK3dyt00=:gXq20*cy0*(fbA*/(0{])@fbDcdy)+(fbAdy*/(0{])@fbDc)+((0{])@fbAdy*/fbEdy)+(0{])@fbAdydy*/fbE
OyBcK3dyt01=:(gXq20,0,0,0:)*(fbA*(0{])@fbDc)+(0{])@fbAdy*fbE
OyBcK3dyt02=:gXq20*(fbA*fbEdy)+fbAdy*fbE

OyBcK3dyt10=:gXq21*cy1*(fbA*/(1{])@fbDcdy)+(fbAdy*/(1{])@fbDc)+((1{])@fbAdy*/fbEdy)+(1{])@fbAdydy*/fbE
OyBcK3dyt11=:(0,gXq21,0,0:)*(fbA*(1{])@fbDc)+(1{])@fbAdy*fbE
OyBcK3dyt12=:gXq21*(fbA*fbEdy)+fbAdy*fbE

OyBcK3dyt20=:gXq22*cy2*(fbA*/(2{])@fbDcdy)+(fbAdy*/(2{])@fbDc)+((2{])@fbAdy*/fbEdy)+(2{])@fbAdydy*/fbE
OyBcK3dyt21=:(0,0,gXq22,0:)*(fbA*(2{])@fbDc)+(2{])@fbAdy*fbE
OyBcK3dyt22=:gXq22*(fbA*fbEdy)+fbAdy*fbE

OyBcK3dyt30=:fbFdy

OyBcK3dyt0=:OyBcK3dyt00+OyBcK3dyt01+OyBcK3dyt02
OyBcK3dyt1=:OyBcK3dyt10+OyBcK3dyt11+OyBcK3dyt12
OyBcK3dyt2=:OyBcK3dyt20+OyBcK3dyt21+OyBcK3dyt22
OyBcK3dyt3=:OyBcK3dyt30

OyBcK3dy=:-@(OyBcK3dyt0+OyBcK3dyt1+OyBcK3dyt2+OyBcK3dyt3)


OyBcKdy=:OyBcK0dy,OyBcK1dy,OyBcK2dy,:OyBcK3dy


load 'plot'

gXcw   =:  1     0     _     _   _"_
gXpAll =:  0     0     0     0   0"_
gXq2All=:  0.06  0.06  0.06  3   _"_
gXq3All=:  1     0     0     0   0"_
gXq4All=:  0.06  0.06  0.06  1   _"_
gXq5All=:  1     1     3     1  _3"_
gXq6All=:  0.06  0.06  0.06  0   _"_
gXq7All=:  1     1     3     1  _3"_

yCpts=:_ 0 83 300,_ 0 0 0,_ 0 0 0,:_ 0 0 0"_

pd (gXB(cy0"_ 1;OyBcK0"_ 1)]) pTtotal yCpts''

pd 'pdf'
pd 'show'


Egraphic0001.jpg
... steady state (no wave) ...


load 'plot'

gXcw   =:   1     0     _      _     _"_
gXpAll =:   0     0     0      0     0"_
gXq2All=:   0.06  0.06  0.06  _1.5   _"_
gXq3All=:  _1     0     4     _1     0"_
gXq4All=:   0.06  0.06  0.06   1     _"_
gXq5All=:   1     1     3      1    _3"_
gXq6All=:   0.06  0.06  0.06   0     _"_
gXq7All=:   1     1     3      1    _3"_

yCpts=:_ 0 83 300,_ 0 0 0,_ 0 0 0,:_ 0 0 0"_

pd (gXB(cy0"_ 1;OyBcK0"_ 1)]) pTtotal yCpts''

yCpts=:_ 0 83 300,_ 0 0 0,_ 0 0 0,:_ 1 1 0"_

pd (gXB(cy0"_ 1;OyBcK0"_ 1)]) pTtotal yCpts''

yCpts=:_ 0 83 300,_ 0 0 0,_ 0 0 0,:_ 2 2 0"_

pd (gXB(cy0"_ 1;OyBcK0"_ 1)]) pTtotal yCpts''

yCpts=:_ 0 83 300,_ 0 0 0,_ 0 0 0,:_ 3 3 0"_

pd (gXB(cy0"_ 1;OyBcK0"_ 1)]) pTtotal yCpts''

pd 'pdf'
pd 'show'


Egraphic0002.jpg
... steady state wave ...


load 'plot'

gXcw   =:  1      0     _      _     _"_
gXpAll =:  0      0     0      0     0"_
gXq2All=:  0.06   0.06  0.06  _1.5   _"_
gXq3All=:  0     _0.7   4     _1     0"_
gXq4All=:  0.06   0.06  0.06   1     _"_
gXq5All=:  1      1     3      1    _3"_
gXq6All=:  0.06   0.06  0.06   0     _"_
gXq7All=:  1      1     3      1    _3"_

yCpts=:_ 0 83 300,_ 0 0 0,_ 0 0 0,:_ 0.0 0.0 0"_

pd (gXB(cy0"_ 1;OyBcK0"_ 1)]) pTtotal yCpts''

yCpts=:_ 0 83 300,_ 0 0 0,_ 0 0 0,:_ 1.5 1.5 0"_

pd (gXB(cy0"_ 1;OyBcK0"_ 1)]) pTtotal yCpts''

yCpts=:_ 0 83 300,_ 0 0 0,_ 0 0 0,:_ 3.0 3.0 0"_

pd (gXB(cy0"_ 1;OyBcK0"_ 1)]) pTtotal yCpts''

yCpts=:_ 0 83 300,_ 0 0 0,_ 0 0 0,:_ 4.0 4.0 0"_

pd (gXB(cy0"_ 1;OyBcK0"_ 1)]) pTtotal yCpts''

pd 'pdf'
pd 'show'


Egraphic0003.jpg
... attenuated wave ...


load 'plot'

gXcw   =:  1    0    _    _     _"_
gXpAll =:  0    0    0    0     0"_
gXq2All=:  0.1  0.1  0.1  0     _"_
gXq3All=:  1    0    0    0     0"_
gXq4All=:  0.1  0.1  0.1  0     _"_
gXq5All=:  1    1    3    1    _3"_
gXq6All=:  0.1  0.1  0.1  2     _"_
gXq7All=:  1    0.5  3    0.5  _2"_

yCpts=:_ 0 83 300,_ 0 0 0,_ 0 0 0,:_ 0 0 0"_

pd (gXB(cy0"_ 1;OyBcK3"_ 1)]) pTtotal yCpts''

pd 'pdf'
pd 'show'


Egraphic0004.jpg
... time-independent component of OyB3 ...


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

NB. ... check for valid energy distribution ...

   gXcw   =:  1     0     _     _     _  "_
   gXpAll =:  0     0     0     0     0  "_
   gXq2All=:  0.1   0.1   0.1  _4     _  "_
   gXq3All=:  0.6  _0.05  4    _0.5  _0.3"_
   gXq4All=:  0.1   0.1   0.1   1     _  "_
   gXq5All=:  1     1     3     1    _3  "_
   gXq6All=:  0.1   0.1   0.1   2     _  "_
   gXq7All=:  1     0.5   3     0.5  _2  "_

   yCpts=:__ 0.1 48 20,__ 0.1 48 20,__ 0.1 48 20,:_ 0 80 20"_

NB. ... a tensor ...

   (gXB(OyBcKdy"_ 1(((2^_44);2^_09)qteq[;])"2(0|:[:(gXB OyBcK])D.1])"_ 1)]) ((0;50"_)pTRandom yCpts)''
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

NB. ... divergence is 0 ...

   (0=]) ((2^_44)qtsz]) (gXB+/@((<0 1)|:])"2@:(OyBcKdy"_ 1)]) ((0;50"_)pTRandom yCpts)''
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



Download: File:LTEB0000C.txt
Download: File:LTEB0001C.txt
Download: File:LTEB0002C.txt
Download: File:LTEB0003C.txt
Download: File:LTEB0004C.txt
Download: File:LTEB0005C.txt
Download: File:LTEB0006C.txt
Download: File:LTEB0007C.txt
Download: File:LTEB0008C.txt
Download: File:LTEB0009C.txt
Download: File:LTEB0010C.txt




Download MoinMoin source: File:TensorExperimentsB00.ijs