Atomistic simulations are carried out for zeolite with ABW framework. The structure is modeled and force field simulations are preformed to investigate its elastic properties, bulk, shear modulus and auxeticity. Bulk moduli (Ks), Shear moduli (G), and Poissons ratios (ν) were found to be Ks=79.71725 GPa, G=16.93265 GPa, νxy = -0.2207, νxz= -0.5730, νyx= -0.71717, νyz=0.87013, νzx= -0.33097 and ...

Mechanical properties of bones are largely determined by their microstructure. The latter comprises a large number of diverse pores. The present paper analyzes a connection between structure of the porous space of the osteonal cortical bone and bone's overall anisotropic elastic moduli. The analysis is based on recent developments in the theory of porous materials that predict the anisotropic e...

We find bounds on the effective elastic moduli of cracked materials in terms of the effective conductivity of such media. These represent the first non-trivial bounds on the effective properties of cracked media which are independent of the shapes and spatial distribution of the cracks. Different approximations for the elastic moduli of cracked media are tested against our bounds. The microgeom...

In this paper we describe a general method of constructing special effective divisors on various moduli spaces using the syzygies of the parametrized objects. The method can be applied to a wide range of moduli problems with the property that the coarse moduli space has canonical singularities hence pluricanonical forms extend over any desingularization of the moduli space. Here we treat the ca...

Non-Abelian vortices in six spacetime dimensions are obtained for a supersymmetric U(N) gauge theory with N hypermultiplets in the fundamental representation. Massless (moduli) fields are identified and classified into Nambu-Goldstone and quasi-Nambu-Goldstone fields. Effective gauge theories for the moduli fields are constructed on the fourdimensional world volume of vortices. A systematic met...

We introduce the moduli stack of pointed curves equipped with effective r-spin structures: these are effective divisors D such that rD is a canonical divisor modified at marked points. We prove that this moduli space is smooth and describe its connected components. We also prove that it always contains a component that projects birationally to the locus S in the moduli space of r-spin curves co...