%0 Journal Article %A Guzina, Bojan B. %A Meng, Shixu %A Oudghiri-Idrissi, Othman %D 2019 %T ESM: (A) auxiliary proofs; (B) application to polyatomic chains; (C) comparison with previously published results, and (D) effective description of nearby dispersion branches from A rational framework for dynamic homogenization at finite wavelengths and frequencies. 13 August 2018 12 February 2019 %U https://rs.figshare.com/articles/journal_contribution/ESM_A_auxiliary_proofs_B_application_to_polyatomic_chains_C_comparison_with_previously_published_results_and_D_effective_description_of_nearby_dispersion_branches_from_A_rational_framework_for_dynamic_homogenization_at_finite_wavelengths_and_frequencies_1/7765088 %R 10.6084/m9.figshare.7765088.v1 %2 https://rs.figshare.com/ndownloader/files/14457773 %K waves in periodic media %K dynamic homogenization %K finite wavenumber %K finite frequency %K repeated and nearby eigenvalues %K Dirac points %K Green's function %X Appendix A - proofs of the featured lemmas and theorems; Appendix B - specialization of the mathematical framework to polyatomic chains; Appendix C - comparison of the numerical results with previously published data, and Appendix D - Detailed numerical analysis of nearby dispersion branches. %I The Royal Society