A gap in the spectrum of the Neumann-Laplacian on a periodic waveguide

We will study the spectral problem related to the Laplace operator in a singularly perturbed periodic waveguide. The waveguide is a quasi-cylinder with contains periodic arrangement of inclusions. On the boundary of the waveguide we consider both Neumann and Dirichlet conditions. We will prove that provided the diameter of the inclusion is small enough in the spectrum of Laplacian opens spectral gaps, i.e. frequencies that does not propagate through the waveguide. The existence of the band gaps will verified using the asymptotic analysis of elliptic operators.Comment: 26 pages, 6 figure

Asymptotic analysis of an elastic rod with rounded ends

We derive a one-dimensional model for an elastic shuttle, that is, a thin rod with rounded ends and small fixed terminals, by means of an asymptotic procedure of dimension reduction. In the model, deformation of the shuttle is described by a system of ordinary differential equations with variable degenerating coefficients, and the number of the required boundary conditions at the end points of the one-dimensional image of the rod depends on the roundness exponent m is an element of(0,1). Error estimates are obtained in the case m is an element of(0,1/4) by using an anisotropic weighted Korn inequality, which was derived in an earlier paper by the authors. We also briefly discuss boundary layer effects, which can be neglected in the case m is an element of(0,1/4) but play a crucial role in the formulation of the limit problem for m >= 1/4.Peer reviewe

Synthetic Geopolymers for Controlled Delivery of Oxycodone: Adjustable and Nanostructured Porosity Enables Tunable and Sustained Drug Release

In this article we for the first time present a fully synthetic mesoporous geopolymer drug carrier for controlled release of opioids. Nanoparticulate precursor powders with different Al/Si-ratios were synthesized by a sol-gel route and used in the preparation of different geopolymers, which could be structurally tailored by adjusting the Al/Si-ratio and the curing temperatures. In particular, it was shown that the pore sizes of the geopolymers decreased with increasing Al/Si ratio and that completely mesoporous geopolymers could be produced from precursor particles with the Al/Si ratio 2∶1. The mesoporosity was shown to be associated with a sustained and linear in vitro release profile of the opioid oxycodone. A clinically relevant release period of about 12 h was obtained by adjusting the size of the pellets. The easily fabricated and tunable geopolymers presented in this study constitute a novel approach in the development of controlled release formulations, not only for opioids, but whenever the clinical indication is best treated with a constant supply of drugs and when the mechanical stability of the delivery vehicle is crucial

Examination of alkali-activated material nanostructure during thermal treatment

The key nanostructural changes occurring in a series of alkali-activated materials (AAM) based on blends of slag and fly ash precursors during exposure to temperatures up to 1000 °C are investigated. The main reaction product in each AAM is a crosslinked sodium- and aluminium-substituted calcium silicate hydrate (C-(N)-A-S-H)-type gel. Increased alkali content promotes the formation of an additional sodium aluminosilicate hydrate (N-A-S-(H)) gel reaction product due to the structural limitations on Al substitution within the C-(N)-A-S-H gel. Heating each AAM to 1000 °C results in the crystallisation of the disordered gels and formation of sodalite, nepheline and wollastonite. Increased formation of N-A-S-(H) reduces binder structural water content after thermal treatment and correlates closely with previous observations of improved strength retention and reduced microcracking in these AAM after heating to 1000 °C. This provides new insight into thermally induced changes to gel atomic structure and thermal durability of C-(N)-A-S-H/N-A-S-H gel blends which are fundamental for the development of new fire-resistant construction materials