SUMMARYTime-harmonic Green's functions for a triclinic anisotropic full-space are evaluated through the use of symbolic computation system. This procedure allows evaluation of the Green's functions for the most general anisotropic materials. The proposed computational algorithms are programmed in a MATLAB environment by incorporating symbolic calculations performed using Maple Computer Algebra System. Extensive testing of the numerical results has been performed for both displacement and stress ÿleds. The tests demonstrate the accuracy of the proposed algorithm in evaluating the Green's functions.

Clock synchronization is essential for the operation of upper layer applications in Wireless Sensor Networks. When the network hops needed for clock synchronization message transmission is large, synchronization error will accumulate and synchronization accuracy may be reduced significantly. Moreover, in the existing synchronization algorithms, large number of communication resources and node energy will be expended in sending and receiving time messages. To solve the problem, this paper proposes a Bayesian estimation-based time synchronization (BETS) algorithm which uses synchronization error compensation to reduce the amount of time message interaction in clock synchronization. The key idea of BETS is to calibrate the prior information of synchronization error with a small amount of field sampling time information, which will eliminate the impact of environment on clock synchronization accuracy. In addition, the gradient descent method is used to estimate the relative clock drift rate, which provides the reference for setting algorithm execution cycle and ensures clock synchronization during network operation time. In order to evaluate the theoretical lower bound of the performance of BETS, the Bayesian Cramér-Rao bound (BCRB) is derived. Both simulation and hardware experiments show that BETS algorithm makes full use of the prior information of synchronization error, hence fewer time messages are required in synchronization and the resource constraints of WSNs are satisfied.

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SUMMARYBased on the full-space Green's functions, a three-dimensional time-harmonic boundary element method is presented for the scattering of elastic waves in a triclinic full space. The boundary integral equations for incident, scattered and total wave ÿelds are given. An e cient numerical method is proposed to calculate the free terms for any geometry. The discretization of the boundary integral equation is achieved by using a linear triangular element. Applications are discussed for scattering of elastic waves by a spherical cavity in a 3D triclinic medium. The method has been tested by comparing the numerical results with the existing analytical solutions for an isotropic problem. The results show that, in addition to the frequency of the incident waves, the scattered waves strongly depend on the anisotropy of the media.

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