Wave Propagation 2011 Part 2 pot

... (57) 12 21 RR0 = = (58) 22 22 jk dcos 12 23 11 j2k dcos 12 23 TTe TT 1R R e θ θ == +    22 22 jk dcos 12 23 22 j2k d cos 12 23 TTe TT 1R R e θ ⊥⊥ ⊥ θ ⊥⊥ == + (59) 12 21 TT0 = = ... (Gennarelli & Riccio, 20 09a), the elements of R and T are: 22 22 j2k dcos 12 23 11 j2k dcos 12 23 RRe RR 1R R e θ θ + == +    22 22 j2k d cos 12 23 2...

Ngày tải lên: 21/06/2014, 23:20

... carbon nanotubes are using as examples. Equation (60) becomes 22 22 4 23 2 1 22 2 2 23 22 12 12 22 11 22 22 4 23 2 1 2 22 2 23 22 12 12 22 11 i( ) 0 0 11 (1) i( ) (1 ) 0 00 i() (1 ) 1 1 0i()(1) p p p p kc krk ... the wave dispersion relation as following υ ω − ++− =−   ∓  22 22 2 22 2 22 11(1) ()()4 (1 ) 2 p k kk RRR crk. (41) Then, the group ve...

Ngày tải lên: 21/06/2014, 23:20

... to define 0 cos , 1, 2 jj j nk j  , to rewrite Eg. (22 ) as    12 12 2 2 12 1 2 22 2 2 12 12 TE r ii i                     (24 ) The same calculation ...    2 , 2 k zkz z Rz      ( 32) where, the beam propagates to z-direction, 22 2 x y  . On the beam center, 0 , the Eq.( 32) represents a plan wave.  ...

Ngày tải lên: 19/06/2014, 21:20

... # 0 20 1 .2 0.1 -3.48 10 .24 0 2# 8 0 1 .2 0.1 -7.83 18.00 0 3# 12 0 1 .2 0.1 -9.35 18.00 0 4 # 20 0 1 .2 0.1 -8.48 17.78 0 5 # 8 12 1 .2 0.1 -11 .21 16.16 1.5 6 # 12 8 1 .2 0.1 -13.36 14 .24 2. 8 ... 12 8 1.5±0.1 -23 .07 12. 16 5 8 # 12 8 2. 2±0.1 -23 .23 12. 8 4.4 9 # 12 8 2. 7±0.1 -19.95 8.16 2. 56 Table 3. Microwave absorption properties of prepared CNTs/T-ZnO/EP compo...

Ngày tải lên: 21/06/2014, 23:20

... H Aly 11. Wave Propagation in Elastic Media with Micro/Nano-Structures 20 1 G. L. Huang, C.T. Sun and F. Song 12. Wave Propagation in Carbon Nanotubes 22 5 Lifeng Wang, ... (21 ) In Eq. (21 ), ν 0 is the Poisson ratio obtained from the back ground Lamé constants λ 0 and μ 0 , k L , and k T are the wavenumber of the P and S waves obtained from...

Ngày tải lên: 21/06/2014, 23:20

... wave equation. Thus we get form (55): () 1 22 21 2 1 22 2 2 2 2 2 1) 2 = 12 , nn nn n ccc ccc tD xxx c tD y ηηη − − −+ ⎛⎞ ∂∂∂ ⎟ ⎜ ⎟ ⎜ Δ+−+ ⎟ ⎜ ⎟ ⎟ ⎜ ∂∂∂ ⎝⎠ ∂ +Δ ∂   (57) () () 11 22 21 2 1 22 2 21 ... KNOutKeτττ τ − −≤ +  Part 1.) The differential equations are given by: 22 2 1 12 222 =() () , (, ) mm anal anal anal uuu Dt Dt t t t txy + ∂∂∂ +∈ ∂∂∂ ( 52)...

Ngày tải lên: 21/06/2014, 23:20

... ⎦ FU K FU pp h p h p , (23 ) where () () () () 11 01 01 12 01 01 01 12 01 12 11 12 11 22 21 12 11 22 12 02 11 12 12 01 01 12 12 12 01 12 21 11 22 21 22 21 11 22 12 −− −− ⎡ ⎤ +− −− ⎢ ⎥ = ⎢ ⎥ −−− ⎢ ⎥ ⎣ ⎦ KKKK ... following scheme for the two dimensional wave equation: 22 22 1 ,11,,1, 22 22 ,1 1,,1, 22 2, 1,,1 22 1 22 1 1 ,11,, 1) ( ) ( 2 ) = 2 ( )(1...

Ngày tải lên: 21/06/2014, 23:20

... 1 21 E mm mc m aJaJa aa ξξ ξ + − ⎡ ⎤ =− ⎢ ⎥ ⎣ ⎦ , () () () () 2 266 66 12 1 2 2 13 2 13 2 13 2 2 22 1 EE EE m m cc aJaikcecmmJa aa ξ ξ ημ ξ ξ + ⎡⎤ =++−+− ⎢⎥ ⎣⎦ , () () () 22 2 44 2 15 2 1 2 2 E mm m aikceJaJa a ημξξξ + ⎡⎤ ⎡⎤ =− ... ξ + − ⎡ ⎤ =− + ⎢ ⎥ ⎣ ⎦ , () () () () 2 266 66 12 1 2 2 13 2 13 2 13 2 2 2 2 1 E E EE m m c c aIaikcecmmIa aa ξ ξημξ ξ + ⎡...

Ngày tải lên: 21/06/2014, 23:20

... relation (23 ) provides then for the electromagnetic modes 2 22 2 2 , FI 00 22 22 ==1 2 12 . pe x yy th th x th x th kc v v Z v v kv kv ω ωω ωω ⎡ ⎤ ⎛⎞⎛⎞ +++ ⎢ ⎥ ⎜⎟⎜⎟ ⎢ ⎥ ⎝⎠⎝⎠ ⎣ ⎦ ε (24 ) The ... as (16) The wave is approximated to be ω~u n λ /2 κλ D 2 ~10 5 s -1 with k r =2 /λ, u n ~10 2 , κ~10 -2 . Then, we have the wave length λ~10 (2 λ D 2 )~0.1 mm. T...

Ngày tải lên: 21/06/2014, 23:20

... % % % SK1 SPT 1 1.00-1.45 0 98 42 22 20 CI 32 98 46 SPT2 2. 00 -2. 45 0 87 27 20 7 CL 32 87 18 UD1 2. 50-3.00 0 85 26 20 6 CL 32 85 16 SPT 3 3.00-3.45 50 21 NPNPNP GM 9 SPT 4 4.50-4.95 59 ... element should be replaced by (using β 2 = εμ − − 2 0 c sin 2 θ and − 2 0 c= ε 0 μ 0 ) ωμ θ ωμ θ μμ −− ⎡ ⎤ ⎡⎤ +− − +− ⎢ ⎥ ⎢⎥ ⎣⎦ ⎣ ⎦ εε 22 22 00 0 22 2 2 00 cc j(...

Ngày tải lên: 21/06/2014, 23:20