Numerical analysis of dissolution processes in cementitious materials using discontinuous and continuous Galerkin time integration schemes

The present paper is concerned with the numerical integration of non‐linear reaction–diffusion problems by means of discontinuous and continuous Galerkin methods. The first‐order semidiscrete initial value problem of calcium leaching of cementitious materials, based on a phenomenological dissolution model, an electrolyte diffusion model and the spatial p‐finite element discretization, is used as a highly non‐linear model problem. A p‐finite element method is used for the spatial discretization. In the context of discontinuous Galerkin methods the semidiscrete mass balance and the continuity of the primary variables are weakly formulated within time steps and between time steps, respectively. Continuous Galerkin methods are obtained by the strong enforcement of the continuity condition as special cases. The introduction of a natural time co‐ordinate allows for the application of standard higher order temporal shape functions of the p‐Lagrange type and the well‐known Gauss–Legendre quadrature of associated time integrals. It is shown, that arbitrary order accurate integration schemes can be developed within the framework of the proposed temporal p‐Galerkin methods. Selected benchmark analyses of calcium dissolution demonstrate the robustness of these methods with respect to pronounced changes of the reaction term and non‐smooth changes of Dirichlet boundary conditions. Copyright © 2006 John Wiley & Sons, Ltd.     

2D Freestanding Janus Gold Nanocrystal Superlattices

2D freestanding nanocrystal superlattices represent a new class of advanced metamaterials in that they can integrate mechanical flexibility with novel optical, electrical, plasmonic, and magnetic properties into one multifunctional system. The freestanding 2D superlattices reported to date are typically constructed from symmetrical constituent building blocks, which have identical structural and functional properties on both sides. Here, a general ligand symmetry‐breaking strategy is reported to grow 2D Janus gold nanocrystal superlattice sheets with nanocube morphology on one side yet with nanostar on the opposite side. Such asymmetric metallic structures lead to distinct wetting and optical properties as well as surface‐enhanced Raman scattering (SERS) effects. In particular, the SERS enhancement of the nanocube side is about 20‐fold of that of the nanostar side, likely due to the combined “hot spot + lightening‐rod” effects. This is nearly 700‐fold of SERS enhancement as compared with the symmetric nanocube superlattices without Janus structures.     

Modulated On-axis Circular Zone Plates for a Generation of Three-dimensional Focal Curves

Abstract

This paper presents a new kind of computer-generated zone plate, which we call a modulated circular zone plate. These plates reconstruct a special class of focal curves. The curves are three-dimensional and lie on the lateral surface of a cylinder. As a particular case, we propose zone plates which are able to focus light on to a line segment along the optical axis. The experimental results illustrate the focusing properties of the zone plates.     

Results of Measuring the Influence of Casimir Energy on Superconducting Phase Transitions

The ALADIN experiment aims at observing how the critical magnetic field of a superconducting aluminum film is modified, when it constitutes one of the reflecting surfaces of a Casimir cavity. If successful, such an observation would reveal the influence of vacuum energy on the superconducting phase transition. In this paper, a rigorous analysis of experimental data is reported, the results are discussed and compared with theoretical predictions based on Lifshitz theory of dispersion forces, and the BCS formula for the optical conductivity of superconductors. Thanks to this rigorous analysis, it can now be asserted that in the region of energy where it is expected that Casimir energy is comparable with condensation energy and the deviations of critical field from BCS formula to be not negligible, an anomalous behavior is found.