Spectral measure computations for composite materials

摘要: The analytic continuation method of homogenization theory provides Stieltjes integral representations for the eective parameters composite media. These involve spectral measures self-adjoint random operators which depend only on geometry. On nite bond lattices, these are represented by matrices and given explicitly in terms their eigenvalues eigenvectors. Here we provide mathematical foundation rigorous computation such media, develop a numerically ecient projection to enable computations. This is accomplished providing unied formulation equivalent original holds innite as well continuum settings. We also introduce family lattices directly compute associated parameters. computed excellent agreement with known theoretical results. behavior consistent symmetries predictions models, values fall within bounds. Some previous calculations have relied nding boundary imaginary part parameter complex plane. Our instead relies direct eigenvectors enables, example, statistical analysis data.