We describe the localized folding of thick layers embedded in a viscoelastic framework. Higher-order partial differential equations such as Swift-Hohenberg equation are standard for modelling process. Using high-order shear theory, we modify to buckling and consider folded layer's behavior. The use enables us strains parallel during folding. Our model naturally captures softening-stiffening beh...

We introduce a connection between Newhouse thickness and patterns through variant of Schmidt’s game introduced by Broderick, Fishman Simmons. This yields an explicit, robust checkable condition that ensures Cantor set in the real line contains long arithmetic progressions and, more generally, homothetic copies large finite sets.