On a P\'olya functional for rhombi, isosceles triangles, and thinning convex sets

Let $\Omega$ be an open convex set in ${\mathbb R}^m$ with finite width, and let $v_{\Omega}$ be the torsion function for $\Omega$, i.e. the solution of $-\Delta v=1, v\in H_0^1(\Omega)$. An upper bound is obtained for the product of $\Vert v_{\Omega}\Vert_{L^{\infty}(\Omega)}\lambda(\Omega)$, where $\lambda(\Omega)$ is the bottom of the spectrum of the Dirichlet Laplacian acting in $L^2(\Omega)$. The upper bound is sharp in the limit of a thinning sequence of convex sets. For planar rhombi and isosceles triangles with area $1$, it is shown that $\Vert v_{\Omega}\Vert_{L^{1}(\Omega)}\lambda(\Omega)\ge \frac{\pi^2}{24}$, and that this bound is sharp.Comment: 12 pages, 4 figure

Fibre-reinforced geopolymer concretes for sensible heat thermal energy storage: Simulations and environmental impact

Power plants based on solar energy are spreading to accomplish the incoming green energy transition. Besides, affordable high-temperature sensible heat thermal energy storage (SHTES) is required. In this work, the temperature distribution and thermal performance of novel solid media for SHTES are investigated by finite element method (FEM) modelling. A geopolymer, with/without fibre reinforcement, is simulated during a transient charging/discharging cycle. A life cycle assessment (LCA) analysis is also carried out to investigate the environmental impact and sustainability of the proposed materials, analysing the embodied energy, the transport, and the production process. A Multi-Criteria Decision Making (MCDM) with the Analytical Hierarchy Process (AHP) approach, taking into account thermal/environmental performance, is used to select the most suitable material. The results show that the localized reinforcement with fibres increases thermal storage performance, depending on the type of fibre, creating curvatures in the temperature profile and accelerating the charge/discharge. High-strength, high-conductivity carbon fibres performed well, and the simulation approach can be applied to any fibre arrangement/material. On the con-trary, the benefit of the fibres is not straightforward according to the three different scenarios developed for the LCA and MCDM analyses, due to the high impact of the fibre production processes. More investigations are needed to balance and optimize the coupling of the fibre material and the solid medium to obtain high thermal performance and low impacts

Alkali-Activated Red Mud and Construction and Demolition Waste-Based Components: Characterization and Environmental Assessment

The aluminum Bayer production process is the most diffused process in the world, but it creates a high amount of basic waste material known as red mud (RM). The use of RM as a precursor of alkali-activated materials is one of the best opportunities for both the ecosystem and the economy. In the present work, mortar samples were obtained by alkali activation of RM with various percentages of blast-furnace slag (BFS) and inert construction and demolition sands. This process creates samples that have a low environmental impact and that can be used as an alternative in the construction industry to cement materials or ceramic ones. The development of these new materials could also represent a way to reduce the CO2 emissions linked to cement and ceramic brick production. In the present study, cubic 40 mm samples reported very interesting values in compressive strength, with a maximum of about 70 MPa for low environmental impact mortars. With such a material, it is possible to create solid bricks for structural use and concrete tiles for road paving or use it for other purposes. Mortar specimens were prepared and characterized, and an LCA analysis with a “cradle-to-gate” approach was carried out for a comparison of the environmental impact of the studied mortars with other materials currently marketed

Existence and multiplicity for elliptic problems with quadratic growth in the gradient

We show that a class of divergence-form elliptic problems with quadratic growth in the gradient and non-coercive zero order terms are solvable, under essentially optimal hypotheses on the coefficients in the equation. In addition, we prove that the solutions are in general not unique. The case where the zero order term has the opposite sign was already intensively studied and the uniqueness is the rule.Comment: To appear in Comm. PD

Zeolite-based monoliths for water softening by ion exchange/precipitation process

In this work, the design of a monolithic softener obtained by geopolymer gel conversion is proposed. The softener used consists in a geopolymeric macroporous matrix functionalized by the co-crystallization of zeolite A and X in mixture. The dual nature of the proposed material promotes a softening process based on the synergistic effect of cation exchange and alkaline precipitation. A softening capacity of 90% and 54% for Ca2+ and Mg2+ respectively was attained in 24 h. In fact, the softener reported a Cation Exchange Capacity (CEC) value of 4.43 meq g−1. Technical features such as density, porosity and mechanical resistance were also measured. The use of this monolithic softener can improve performance and sustainability of hardness removal from tap water, reducing the production of sludge and adding the possibility to partially regenerate or reuse it