User:Tom Allen/TensorExperimentsZ02

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GTEZ0200C.jpg


NB. ... script experimentalZ.ijs ...

qfr2=:(cz0^2:)+(cz1^2:)+cz2^2:


NB. ... script experimentalZ.ijs ...

qfr2UUdz        =:(2*cz0),(2*cz1),(2*cz2),0:
qfr2UUdzdz      =:(2,0,0,0:),(0,2,0,0:),(0,0,2,0:),:0,0,0,0:
qfr2UUdzdzdz    =:(3$4:)$0:
qfr2UUdzdzdzdz  =:(4$4:)$0:
qfr2UUdzdzdzdzdz=:(5$4:)$0:

qfr2XX=:qfr2;qfr2UUdz;qfr2UUdzdz;qfr2UUdzdzdz;qfr2UUdzdzdzdz;qfr2UUdzdzdzdzdz


GTEZ0201C.jpg


NB. ... script experimentalZ.ijs ...

qfr=:qfr2^0.5"_


NB. ... script experimentalZ.ijs ...

qfr2PWR=:0.5"_

qfrU0=:                                                                qfr2^qfr2PWR
qfrU1=:                                                        qfr2PWR*qfr2^qfr2PWR+_1:
qfrU2=:                                          (qfr2PWR+_1:)*qfr2PWR*qfr2^qfr2PWR+_2:
qfrU3=:                            (qfr2PWR+_2:)*(qfr2PWR+_1:)*qfr2PWR*qfr2^qfr2PWR+_3:
qfrU4=:              (qfr2PWR+_3:)*(qfr2PWR+_2:)*(qfr2PWR+_1:)*qfr2PWR*qfr2^qfr2PWR+_4:
qfrU5=:(qfr2PWR+_4:)*(qfr2PWR+_3:)*(qfr2PWR+_2:)*(qfr2PWR+_1:)*qfr2PWR*qfr2^qfr2PWR+_5:

qfrXX=:[cfFN5(qfrU0;qfrU1;qfrU2;qfrU3;qfrU4;qfrU5),:qfr2XX


GTEZ0202C.jpg


NB. ... script experimentalZ.ijs ...

qfrb=:qfr^gXb10


NB. ... script experimentalZ.ijs ...

qfrbU0=:                                                      qfr^gXb10
qfrbU1=:                                                gXb10*qfr^gXb10+_1:
qfrbU2=:                                    (gXb10+_1:)*gXb10*qfr^gXb10+_2:
qfrbU3=:                        (gXb10+_2:)*(gXb10+_1:)*gXb10*qfr^gXb10+_3:
qfrbU4=:            (gXb10+_3:)*(gXb10+_2:)*(gXb10+_1:)*gXb10*qfr^gXb10+_4:
qfrbU5=:(gXb10+_4:)*(gXb10+_3:)*(gXb10+_2:)*(gXb10+_1:)*gXb10*qfr^gXb10+_5:

qfrbXX=:[cfFN5(qfrbU0;qfrbU1;qfrbU2;qfrbU3;qfrbU4;qfrbU5),:qfrXX


GTEZ0203C.jpg


NB. ... script experimentalZ.ijs ...

qfbr=:gXb11*qfr


NB. ... script experimentalZ.ijs ...

qfbrXX=:[cfMP5 gXb11XX,:qfrXX


GTEZ0204C.jpg


NB. ... script experimentalZ.ijs ...

qfsin=:sin@qfbr


NB. ... script experimentalZ.ijs ...

qfsinXX=:[cfFN5(sin@qfbr;cos@qfbr;-@sin@qfbr;-@cos@qfbr;sin@qfbr;cos@qfbr),:qfbrXX


GTEZ0205C.jpg


NB. ... script experimentalZ.ijs ...

qfsinP=:qfsin^gXb12


NB. ... script experimentalZ.ijs ...

qfsinPU0=:                                                      qfsin^gXb12
qfsinPU1=:                                                gXb12*qfsin^gXb12+_1:
qfsinPU2=:                                    (gXb12+_1:)*gXb12*qfsin^gXb12+_2:
qfsinPU3=:                        (gXb12+_2:)*(gXb12+_1:)*gXb12*qfsin^gXb12+_3:
qfsinPU4=:            (gXb12+_3:)*(gXb12+_2:)*(gXb12+_1:)*gXb12*qfsin^gXb12+_4:
qfsinPU5=:(gXb12+_4:)*(gXb12+_3:)*(gXb12+_2:)*(gXb12+_1:)*gXb12*qfsin^gXb12+_5:

qfsinPXX=:[cfFN5(qfsinPU0;qfsinPU1;qfsinPU2;qfsinPU3;qfsinPU4;qfsinPU5),:qfsinXX


GTEZ0206C.jpg


NB. ... script experimentalZ.ijs ...

qfbt=:gXb13*cz3


NB. ... script experimentalZ.ijs ...

qfbtXX=:[cfMP5 gXb13XX,:cz3XX


GTEZ0207C.jpg


NB. ... script experimentalZ.ijs ...

qfsinbt=:sin@qfbt


NB. ... script experimentalZ.ijs ...

qfsinbtXX=:[cfFN5(sin@qfbt;cos@qfbt;-@sin@qfbt;-@cos@qfbt;sin@qfbt;cos@qfbt),:qfbtXX


GTEZ0208C.jpg


NB. ... script experimentalZ.ijs ...

qfcosbt=:cos@qfbt


NB. ... script experimentalZ.ijs ...

qfcosbtXX=:[cfFN5(cos@qfbt;-@sin@qfbt;-@cos@qfbt;sin@qfbt;cos@qfbt;-@sin@qfbt),:qfbtXX


GTEZ0209C.jpg


NB. ... script experimentalZ.ijs ...

qffz0=:gXb14*cz0*qfrb*qfsinP
qffz1=:gXb14*cz1*qfrb*qfsinP
qffz2=:gXb14*cz2*qfrb*qfsinP

qffz0XX=:[cfMP5 gXb14XX,:[cfMP5 cz0XX,:[cfMP5 qfrbXX,:qfsinPXX
qffz1XX=:[cfMP5 gXb14XX,:[cfMP5 cz1XX,:[cfMP5 qfrbXX,:qfsinPXX
qffz2XX=:[cfMP5 gXb14XX,:[cfMP5 cz2XX,:[cfMP5 qfrbXX,:qfsinPXX

OzC0=:qffz0*qfsinbt
OzC1=:qffz1*qfsinbt
OzC2=:qffz2*qfsinbt

OzC0XX  =:[cfMP4 qffz0XX,:qfsinbtXX
OzC1XX  =:[cfMP4 qffz1XX,:qfsinbtXX
OzC2XX  =:[cfMP4 qffz2XX,:qfsinbtXX

gXb13RXX=:%@gXb13;((1$4:)$0:);((2$4:)$0:);((3$4:)$0:);((4$4:)$0:);(5$4:)$0:
OzC3t0XX=:[cfMP4((0{])&.>@}.@qffz0XX,<@(_"_)),:[cfMP4 gXb13RXX,:qfcosbtXX
OzC3t1XX=:[cfMP4((1{])&.>@}.@qffz1XX,<@(_"_)),:[cfMP4 gXb13RXX,:qfcosbtXX
OzC3t2XX=:[cfMP4((2{])&.>@}.@qffz2XX,<@(_"_)),:[cfMP4 gXb13RXX,:qfcosbtXX
OzC3XX  =:OzC3t2XX+&.>OzC3t1XX+&.>OzC3t0XX

OzCXXS=:<@:>"1@(0|:])@(OzC0XX,OzC1XX,OzC2XX,:OzC3XX)


load 'plot'

gXcw  =:  _  _  _  _  _  _"_
gXbAll=: _1  1  7  1  1  _"_

zCpts=:_ 0 2p1 300,_ 0 0 0,_ 0 0 0,:_ 0.00p1 0.00p1 0"_

pd (gXZ(cz0"_ 1;OzC0"_ 1)]) pTtotal zCpts''

zCpts=:_ 0 2p1 300,_ 0 0 0,_ 0 0 0,:_ 0.07p1 0.07p1 0"_

pd (gXZ(cz0"_ 1;OzC0"_ 1)]) pTtotal zCpts''

zCpts=:_ 0 2p1 300,_ 0 0 0,_ 0 0 0,:_ 0.15p1 0.15p1 0"_

pd (gXZ(cz0"_ 1;OzC0"_ 1)]) pTtotal zCpts''

zCpts=:_ 0 2p1 300,_ 0 0 0,_ 0 0 0,:_ 0.25p1 0.25p1 0"_

pd (gXZ(cz0"_ 1;OzC0"_ 1)]) pTtotal zCpts''

zCpts=:_ 0 2p1 300,_ 0 0 0,_ 0 0 0,:_ 0.50p1 0.50p1 0"_

pd (gXZ(cz0"_ 1;OzC0"_ 1)]) pTtotal zCpts''

zCpts=:_ 0 2p1 300,_ 0 0 0,_ 0 0 0,:_ 0.75p1 0.75p1 0"_

pd (gXZ(cz0"_ 1;OzC0"_ 1)]) pTtotal zCpts''

zCpts=:_ 0 2p1 300,_ 0 0 0,_ 0 0 0,:_ 1.00p1 1.00p1 0"_

pd (gXZ(cz0"_ 1;OzC0"_ 1)]) pTtotal zCpts''

zCpts=:_ 0 2p1 300,_ 0 0 0,_ 0 0 0,:_ 1.07p1 1.07p1 0"_

pd (gXZ(cz0"_ 1;OzC0"_ 1)]) pTtotal zCpts''

zCpts=:_ 0 2p1 300,_ 0 0 0,_ 0 0 0,:_ 1.15p1 1.15p1 0"_

pd (gXZ(cz0"_ 1;OzC0"_ 1)]) pTtotal zCpts''

zCpts=:_ 0 2p1 300,_ 0 0 0,_ 0 0 0,:_ 1.25p1 1.25p1 0"_

pd (gXZ(cz0"_ 1;OzC0"_ 1)]) pTtotal zCpts''

zCpts=:_ 0 2p1 300,_ 0 0 0,_ 0 0 0,:_ 1.50p1 1.50p1 0"_

pd (gXZ(cz0"_ 1;OzC0"_ 1)]) pTtotal zCpts''

zCpts=:_ 0 2p1 300,_ 0 0 0,_ 0 0 0,:_ 1.75p1 1.75p1 0"_

pd (gXZ(cz0"_ 1;OzC0"_ 1)]) pTtotal zCpts''

pd 'pdf'
pd 'show'


Zgraphic0200.jpg
... a standing wave ...


GTEZ0210C.jpg


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

   gXcw  =:  _    _    _  _    _    _"_
   gXbAll=: _0.6  3.5  3  1.3  1.2  _"_

   zCpts=:_ 0.1p1 0.5p1 27,_ 0.1p1 0.5p1 27,_ 0.1p1 0.5p1 27,:_ 0.1p1 0.9p1 27"_

NB. ... derivatives ...

   (gXZ(cfXX1@OzCXXS"_ 1(((2^_44);2^_14)qteq[;])"2(0|:[:(gXZ cfXX0@OzCXXS])D.1])"_ 1)]) ((0;50"_)pTRandom zCpts)''
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

   (gXZ(cfXX2@OzCXXS"_ 1(((2^_44);2^_10)qteq[;])"3(0|:[:(gXZ cfXX1@OzCXXS])D.1])"_ 1)]) ((0;50"_)pTRandom zCpts)''
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

   (gXZ(cfXX3@OzCXXS"_ 1(((2^_44);2^_06)qteq[;])"4(0|:[:(gXZ cfXX2@OzCXXS])D.1])"_ 1)]) ((0;50"_)pTRandom zCpts)''
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

   (gXZ(cfXX4@OzCXXS"_ 1(((2^_44);2^_06)qteq[;])"5(0|:[:(gXZ cfXX3@OzCXXS])D.1])"_ 1)]) ((0;50"_)pTRandom zCpts)''
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                          ...
NB. ... (compare Derek F. Lawden equation 28.18) ...

   (0=]) ((2^_44)qtsz]) +/@((<0 1)|:])"2 (gXZ cfXX1@OzCXXS"_ 1]) ((0;50"_)pTRandom zCpts)''
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. ... script experimentalZ.ijs ...

OzCD4        =:>@((<4 0){])
OzCD4dz      =:>@((<4 1){])
OzCD4dzdz    =:>@((<4 2){])
OzCD4dzdzdz  =:>@((<4 3){])
OzCD4dzdzdzdz=:>@((<4 4){])

OzCXX=:<@:>"1@(0|:])@:(OzCXXS"_ 1)

hkxL=:[(],[OzCXX zpts)hkxK
hkyL=:[(],[OzCXX zpts)hkyK



Download: File:LTEZ0200C.txt
Download: File:LTEZ0201C.txt
Download: File:LTEZ0202C.txt
Download: File:LTEZ0203C.txt
Download: File:LTEZ0204C.txt
Download: File:LTEZ0205C.txt
Download: File:LTEZ0206C.txt
Download: File:LTEZ0207C.txt
Download: File:LTEZ0208C.txt
Download: File:LTEZ0209C.txt
Download: File:LTEZ0210C.txt




Download MoinMoin source: File:TensorExperimentsZ02.ijs