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...

Ngày tải lên: 19/06/2014, 12:20

... 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...

Ngày tải lên: 19/06/2014, 12:20

... 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...

Ngày tải lên: 19/06/2014, 12:20

... 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   ...

Ngày tải lên: 19/06/2014, 12:20

... [ ] 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...

Ngày tải lên: 19/06/2014, 12:20

... 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...

Ngày tải lên: 19/06/2014, 12:20

... 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 __...

Ngày tải lên: 19/06/2014, 12:20

... 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...

Ngày tải lên: 19/06/2014, 12:20

... 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...

Ngày tải lên: 19/06/2014, 12:20

... 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))...

Ngày tải lên: 19/06/2014, 12:20