In this paper, super-resolution imaging and negative refraction by a two-dimensional (2D) triangular lattices graded photonic crystal (GPC) were studied. The graded photonic crystal (GPC) was obtained by varying the radius in each row so that its effective refractive index changes along the transverse direction. By using Plane Wave Expansion (PWE) method and Finite-Difference Time-Domain (FDTD)...

Stability of functionally graded beams with piezoelectric layers subjected to axial compressive load that is simply supported at both ends is studied in this paper. The displacement field of beam is assumed based on first order shear deformation beam theory. Applying the Hamilton's principle, the governing equation is established. The influences of applied voltage, dimensionless geometrical par...

We define an integer graded symplectic Floer cohomology and a Fintushel–Stern type spectral sequence which are new invariants for monotone Lagrangian sub–manifolds and exact isotopes. The Z–graded symplectic Floer cohomology is an integral lifting of the usual ZΣ(L) –graded Floer–Oh cohomology. We prove the Künneth formula for the spectral sequence and an ring structure on it. The ring structur...

This paper studies mechanical buckling of functionally graded beams subjected to axial compressive load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on EngesserTimoshenko beam theory. Applying the Hamilton's principle, the equilibrium equation is established. The influences of dimensionless geometrical parameter, ...

In this paper dynamic analysis of multi-directional functionally graded panel is studied using a semi-analytical numerical method entitled the state-space based differential method (SSDQM) and comparative behavior modeling by artificial neural network (ANN) for different parameters. A semi-analytical approach which makes use the three-dimensional elastic theory and assuming the material propert...

We define a noncommutative algebra of flag-enumeration functionals on graded posets and show it to be isomorphic to the free associative algebra on countably many generators. Restricted to Eulerian posets, this ring has a particularly appealing presentation with kernel generated by Euler relations. A consequence is that even on Eulerian posets, the algebra is free, with generators corresponding...

We generalize chain enumeration in graded partially ordered sets by relaxing the graded, poset and Eulerian requirements. The resulting balanced digraphs, which include the classical Eulerian posets having an R-labeling, implies the existence of the (non-homogeneous) cd-index, a key invariant for studying inequalities for the flag vector of polytopes. Mirroring Alexander duality for Eulerian po...

The ommatidium of the butterfly's afocal apposition eye exhibits angular performance that can only be achieved by transforming the diffraction pattern of its corneal lens into the fundamental mode of its rhabdom waveguide. A graded index model of the ommatidium has been proposed and verified but the efforts to extract the transformation's underlying physics from it have been hindered by its ext...

this work reports the effect of nanotube aspect ratio and waviness index on stress and displacement distributions of functionally graded nanocomposite cylinders reinforced by wavy single walled carbon nanotubes based on a mesh-free method. the mechanical properties of these composites are assumed to be graded along radial direction and estimate by a micro mechanical model. in the mesh-free anal...