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
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'
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
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
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
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
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
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
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
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
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
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'
... 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'
... 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'
... 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'
... 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