TAILIEUCHUNG - Waves in fluids and solids Part 12

Tham khảo tài liệu 'waves in fluids and solids part 12', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 264 Waves in Fluids and Solids Fig. . Geometry for spatial correlation function of wave fields at r r 2 and r - r 2 . Consider the interaction between the two spatial points r r 2 and r - r 2 as shown in Fig. . The spatial correlation is defined as the average over the sphere s that is located at r and of radius 2 . Here r is the distance between r r 2 and r - r 2 . Note that the normalized wave field T r is axially symmetric about r and depends only on 0 . The average can thus be accomplished by performing the integration with respect to 0 . Then the spatial correlation function is expressed as follows r 2n T r r 2 T r - rỴ2 2 2sin d g r r 12 r - r 12 ------------------------------------------------ 4n ệ 2 2 1 f n 2J0 T r r l2 T r - r l21 sin0d0 where r r 21 yjr2 4 cos0 and refers to the ensemble average carried over random configuration of bubble clouds. It is apparent that the preceding definition of the spatial correlation function refers to the average interaction between the wave fields at every pair of spatial points for which the distance is and the center of symmetry locates at r . By using Eq. and taking the ensemble average over the whole bubble cloud then we define the total correlation function that is a function of the distance so as to describe the overall correlation characteristics of the wave field. In respect that the normalized wave field T r is symmetric about the origin the total correlation function can be obtained by merely performing the integration with respect to r given as below i 04nr2g r r 2 r-r l2 dr 10 2-15 Acoustic localization in bubbly elastic soft media A set of numerical experiments has been carried out for various bubble radii numbers and volume fractions. Figure presents the typical results of the total transmission and the total backscattering versus frequency kr0 for bubbly gelatin with the parameters N 200 r0 1 mm and p 10-3 respectively. The total transmission is defined as I d T 2 and Acoustic .

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