We analyze the integrand spectrum in the plane wave expansion of spherical functions,and present a standard of(2L,4L) point quadrature for spatial angles satisfying the sampling theorem.Numerical results with the method of moments(MOM) and fast multipole method(FMM) in different quadrature schemes are compared to show the validation of our quadrature scheme.

Correlated scattering of very dense(fractional volume more than 0.4) randomly distributed spherical particles is studied. A Monte Carlo method and a random shuffling process are employed to generate the very dense and randomly distributed particles. With solution of the volumetric integral equation of the electric fields, the scattering, absorption and extinction coefficients, as well as effective permittivity of the very dense and randomly distributed spherical particles are numerically calculated. For a validation purpose, they are compared with other approaches such as QCA, QCA-CP and Maxwell-Garnett mixing formula at lower fractions. It shows that very dense particles demonstrate particles clustering and enhance the scattering of bigger or clustered particles.

Employing the first-order Mueller matrix solution of vector radiative transfer equation for one layer of small random spheroids, simulated measurements of high-order co-polarized and cross-polarized backscattering are obtained. Iterative inversion of the dielectric constant of small spheroids and the number of particles per unit area is developed. The inversion from simulated and real AirSAR data and its dependencies upon the parameters and the random noise are discussed.

By using the turbulence model proposed by Dubois & Samain and Lichtenberg, a transport code is presented to simulate a particular sawtooth discharge in T-10 tokamak under Ohmic heating situation. A trigger condition is also coupled into the transport code. The numerical results show that in many respects those with turbulent model agree with the experiment results. In contrast, it was impossible to obtain satisfactory simulations with the reconnection model.

A numerical approach of the iterative conjugate gradient method is developed to solve the volume integral equation of EM scattering. This method is effectively applied to calculate scattering from multi scatterers with large electric scales.