Nonaxisymmetric Particles

In Fig. 3.19, we compare the results obtained with the TNONAXSYM routine to the discrete dipole approximation solutions. Calculations are performed for 

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The null-field method is a general technique and is applicable for arbitrarily shaped particles. However, for nonaxisymmetric particles, a semi-convergent... 

The use of distributed vector spherical wave functions improves the numerical stability of the null-field method for highly elongated and flattened layered particles. Although the above formalism is valid for nonaxisymmetric particles, the method is most effective for axisymmetric particles, in which case the 2 -axis of the particle coordinate system is the axis of rotation. Applications of the null-field method with distributed sources to axisymmetric layered spheroids with large aspect ratios have been given by Doicu and Wriedt [50]. 

The contributions of Zheng [276,277], Zheng and Strom [279], and Zheng and Shao [278] demonstrated the applicability of the null-field method to particles with complex geometries and optical properties. The above formalism can be extended to nonaxisymmetric particles in which case, the domain of analysis can be discretized into many volume elements with different shapes and optical constants. 

Homogeneous, dielectric (isotropic, uniaxial anisotropic, chiral) and perfectly conducting, nonaxisymmetric particles (TNONAXSYM.fQO)... 

The scattering characteristics depend on the type of the orientation distribution function. By convention, the uniform distribution function is called complete if the Euler angles Op, / p and 7p are uniformly distributed in the intervals (0,360°), (0,180°) and (0,360°), respectively. The normalization constant is 47t for axisymmetric particles and for nonaxisymmetric particles. The uniform distribution function is called incomplete if the Euler angles Op, /3p and 7p are uniformly distributed in the intervals (apmin, pmax), (/ pmin,/ pmax), and (7pmin, 7pmax)> respectively. For axisymmetric particles, the orientational average is performed over Op and / p, and the normalization constant is... 

Some nonaxisymmetric particle shapes such as ellipsoids, quadratic prisms and regular polyhedral prisms are directly included in the Fortran program... 

Eshelby s method, to predict the coefficients of thermal expansion of composites containing either aligned axisymmetric or nonaxisymmetric ellipsoidal particles. 

For composites consisting of axisymmetric particles (e.g., spheres, fibers, and disks) and epoxy resin, they predicted that (i) the coefficients of thermal expansion for spherical inclusions are the same in all directions and decrease modestly as the volume fraction of particles increases and (ii) with the increase in aspect ratio, the thermal expansion becomes anisotropic. For composites consisting of three-dimensional nonaxisymmetric ellipsoidal particles (i.e., day platelets) and nylon 6, they predicted that (i) the coefficient of thermal expansion in the longitudinal direction decreases as the primary and secondary aspect ratios increase and (ii) the value in the transverse direction decreases as the primary aspect ratio increases but decrease with the secondary aspect ratio. 

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