Waves in fluids and solids Part 1 pot
Waves in fluids and solids Part 1 pot
... second-order approximations
22 2
11 12 12 11 22 11 12 12 11 22
2 2
22 2
12 11 22 12 22 12 11 22 22 12
11 1
1
22 2
,
11 1
1
22 2
D D
gg f f ggg ggf g fgg
fggg ggf g fgg ggf
... are given by
11 22 21 12
12 21 22 11
2
222 2
11 12 21 22 11 21 12 22
2
22 2 2
11 21 12 22 11 12 21 22
det det
2
det det
det( )det
det...
Waves in fluids and solids Part 2 pot
... 700
-1
0
1
Frequency [Hz]
-1
0
1
-1
0
1
-1
0
1
-1
0
1
-1
0
1
-1
0
1
M1
M2
M4
M8
M16
M32
M64
r=0.48
0 10 0 200 300 400 500 600 700
-1
0
1
Frequency [Hz]
-1
0
1
-1
0
1
-1
0
1
-1
0
1
-1
0
1
-1
0
1
M1
M2
M4
M8
M16
M32
M64
r=0.87
... domain 1 and 2) is also
Waves in Fluids and Solids
30
0 10 0 200 300 400 500 600 700
-2
-1
0...
Waves in fluids and solids Part 6 pot
... field defined by the 13 -component vector
Ψ
f
(r, t) ≡
⎛
⎜
⎝
0
−
1
√
ρ(r)
f(r, t)
(
0)
T
9
⎞
⎟
⎠
, (18 )
13 8
Waves in Fluids and Solids
Waves in Fluids and Solids
11 8
(Tarasov, 19 50) of the flexure ... propagates
from one grain to its neighbors only through their mutual contacts and not via air, we have
13 0
Waves in Fluids and Solids
Waves in F...
Waves in fluids and solids Part 7 potx
... zz
xz
p
xz
,
(27a)
(27b)
in the water, and
22 22
11 1 1
11 1 1
22 2
22 2
11 1
11
22
22 22
11 1 1
11 1 1
22 2
22
2
22
xx
xz
zz
xz
xz z
xz
xz
xz
xz x
...
(49b)
in the water, and
11
11
ˆ
(,)sin , ( 0)
ˆ
(,)cos , ( 0)
xx
zz
uukz kxtz
uukz kxtz
,
(50a)
(50b)
where
...
Waves in fluids and solids Part 12 potx
...
[
]
22
11 22 21 12 1 2
()()()CMNMNiMNMN NN=++− +
,
where
24 2 2 2 2
11 111 111 2
(3 )( )2MNeGHABAB
ρ
ωω ωδ
=−−+
,
24 2 2 2 2
211 1 211 11
()2(3)MNeAB ABGH
ρω ωδ ω
=−−−
,
11 12 12 1
(4 ... as follows:
22
11 1 1 11 1
(1 ) 0
g
CVC
ρω
∇Φ + + Φ =
, (4.28a)
()
()
2
2
(1)
22 2
11 2 2 11 2 11 11 1
4 (1 )
g
CVCCVC
ρω
Γ
∇Φ + + Φ = ∇Φ
, (4...
Waves in fluids and solids Part 3 doc
... to
r
) of the exponential mappings in (3.2), yields
41 342
4 1 342
11 1 1
2
41 3 21 3 41 2 3 21 2
11 1 1
41 3 21 3 41 2 3 21 2
11 1
11
41 21 3 31 3
41 3 4 1
2
1
21 3
3
1!
()
2!
()
3!
irh
irh
irh
... AAAAAA
AA AA A AA A AA A
YA A A A
11
12 3 212
3
22
11 11 1
41 3 4 1 2 31 2 21 3 21 2
2
11
14 2 412 3 212
3
22
11...
Waves in fluids and solids Part 4 docx
... metal layer and the transfer matrix of the metal
layer has the simplest form:
11 12 13 11 12 13
21 22 23 21 22 23
31 32 33 31 32 33
11 12 13 11 12 13
21 22 23 21 22 23
31 32 33 31 32 33
00
00
00
00
00
00
00
uu ... have a
nontrivial solution only if the determinant of its coefficients is equal to zero:
___ _
11 11 112 1 11 31
____
12 11 12 21 12 31
__...
Waves in fluids and solids Part 5 docx
... the transfer matrix
M
FE1QE2G
by the following expression:
(2)
11 12 13 11 12 13 1 1
1
(2)
21 22 23 21 22 23 2 2
2
(2)
31 32 33 31 32 33 3 3
3
11 12 13 11 12 13 1
(2)
0
0
0
0
uu uu uu uT ...
M
FE1QE2G
does
not have generally the special form with 0 and 1 in the 7
th
column and the 8
th
row (as in
(57)), but it is of the most general form:
11 12...
Waves in fluids and solids Part 8 pptx
...
1
1
.
nn
nn
aABa
bCDb
−
−
=
(11 )
The matrix elements in this equation are:
() ()
() ()
21 21
12 2 1 2
12 12
21 21
1 212
12 12
11
exp cos sin , exp sin ,
22
11
exp sin , exp cos
22
zz zz
zz z z ... zl
−
==+ΛEE E (17 )
Waves in Fluids and Solids
18 4
0246 810 1 214 1 618
0
2
4
6
8
10
12
K, 10
6
1/ m
ω,
10
15
rad/s
3...
Waves in fluids and solids Part 9 doc
...
Waves in Fluids and Solids
200
vibrating molecules. The standing waves are induced in each globule of the crystal. The
pulsating modes arising in the PNC globules are ... obtained from the synthetic opals under different technological
conditions.
Waves in Fluids and Solids
19 2
(a)
(b)
Fig. 10 . The images of (11 1) surfaces for two ((a) and (b))...
Từ khóa:
- dreamweaver cs5 tutorial how to make a website using photoshop and dreamweaver part 1
- lord of the rings war in the north gameplay part 1
- giáo trình sản lượng rừng part 1 potx
- stress waves in non elastic solids
- developing web page using html and css part 1
- the lord of the rings war in the north gameplay part 1