We review recent progresses in the study of flat band systems, especially focusing on fundamental physics related to singularity band’s Bloch wave functions. first explain that bands can be classified into two classes: singular and non-singular bands, based presence or absence The is generated by crossing with another dispersive band. In band, one find a special kind eigenmodes, called non-cont...

Abstract Bootstrap methods, initially developed for solving statistical and quantum field theories, have recently been shown to capture the discrete spectrum of mechanical problems, such as single particle Schrödinger equation with an anharmonic potential. The core bootstrap methods builds on exact recursion relations arbitrary moments some operator use adequate set positivity criteria. We exte...

In the current paper, finite element method is employed for numerical simulations and the study of influential parameters on elastic modulus of polymer-matrix nano-composites. Effects of different key parameters including particle elastic modulus, interphase elastic modulus, matrix elastic modulus, interphase thickness and particle volume fraction on total elastic modulus of nano-composite mate...