We present an analytic formulation for elastic medium under uniform stress and in plane strain, with a very large number of cracks that are allowed to intersect. The singularities at the tips represented exactly; solution is written terms series expansions negative powers complex variable defined outside unit circle reference plane. modeled assembly 10,000 show trajectories both whole model ind...

Abstract Climate models and observations robustly agree that Earth’s clear-sky longwave feedback has a value of about −2 W m K −1 , suggesting this can be estimated from first principles. In study, we derive an analytic model for feedback. Our approach uses novel spectral decomposition splits the into four components: surface Planck three atmospheric feedbacks CO 2 H O, O continuum. We obtain e...