In this paper we describe recent developments in the application of mathematical and computational techniques to problems in di ractive optics, particularly to problems involving spatially periodic structures (gratings). Many of the techniques are also applicable to other scattering problems involving periodic structures. We focus on variational techniques, nite element approximations, inverse ...

It is now established that the 3D structure of homogeneous nanocrystals can be recovered from in-line hologram of single projections. The method builds on a quantitative contrast interpretation of electron exit wave functions. Since simulated exit wave functions of single and bilayers of graphene reveal the atomic structure of carbon-based materials with sufficient resolution, we explore theore...

In this paper, we develop the second-order two-scale (SOTS) analysis method and numerical algorithm for dynamic thermo-mechanical problems of composite materials with 3-D periodic configuration. In the problem considered, there exists a mutual interaction between the displacement and temperature fields. By the asymptotic expansion of temperature and displacement fields, the cell problems, effec...

Self-assembly is an effective strategy for the creation of periodic structures at the nanoscale. However, because microelectronic devices use free-form design principles, the insertion point of self-assembling materials into existing nanomanufacturing processes is unclear. We directed ternary blends of diblock copolymers and homopolymers that naturally form periodic arrays to assemble into nonr...

Nonlinear photonic crystals can be used to provide phase matching for frequency conversion in optically isotropic materials. The phase-matching mechanism proposed here is a combination of form birefringence and phase velocity dispersion in a periodic structure. Since the phase matching relies on the geometry of the photonic crystal, it becomes possible to use highly nonlinear materials. This is...

The aim of this paper is to evaluate the effective properties of composite materials with periodic random packing of ellipsoids of different volume fractions and aspect ratios. Therefore, we employ computational homogenization. A very efficient MD-based method is applied to generate the periodic random packing of the ellipsoids. The method is applicable even for extremely high volume fractions ...

Network phase aqueous lyotropic liquid crystals (LLCs) are technologically useful materials with myriad applications in chemistry, biology, and materials science, which stem from their structurally periodic aqueous and hydrophobic nanodomains (∼0.7-5.0 nm in diameter) that are lined with well-defined chemical functionalities. The exclusive observation of bicontinuous cubic network phase LLCs (e...

Magnetoelectric coupling is of interest for a variety of applications, but is weak in natural materials. Strain-coupled fibrous composites of piezoelectric and piezomagnetic materials are an attractive way of obtaining enhanced effective magnetoelectricity. This paper studies the effective magnetoelectric behaviors of two-phase multiferroic composites with periodic array of inhomogeneities. For...

Following to the recent development of the organic-templated growth of materials, new types of photonic hybrid composite materials have emerged whose structure and function are organized hierarchically. Ordered, periodic mesoscopic materials allow the construction of composites with many types of guest, such as organic molecules or polymers. These host–guest materials combine the high stability...

In this paper, the Two-Scale computation Method (TSM) is presented for the mechanics parameters of composite materials with small periodic configuration, including stiffness parameters and strength parameters. First the major formulation of the Two-Scale Asymptotic expressions (TSA) for composite materials with periodic configuration is briefly given. And then the two-scale computation (TSM) fo...