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

Average fractional polarization of extragalactic sources at Planck frequencies

Recent detailed simulations have shown that an insufficiently accurate characterization of the contamination of unresolved polarized extragalactic sources can seriously bias measurements of the primordial cosmic microwave background (CMB) power spectrum if the tensor-to-scalar ratio $r\sim 0.001,$ as predicted by models currently of special interest (e.g., Starobinsky's $R^2$ and Higgs inflation). This has motivated a reanalysis of the median polarization fraction of extragalactic sources (radio-loud AGNs and dusty galaxies) using data from the \textit{Planck} polarization maps. Our approach, exploiting the intensity distribution analysis, mitigates or overcomes the most delicate aspects of earlier analyses based on stacking techniques. By means of simulations, we have shown that the residual noise bias on the median polarization fraction, $\Pi_{\rm median}$, of extragalactic sources is generally \simlt 0.1\%. For radio sources, we have found $\Pi_{\rm median} \simeq 2.83\%$, with no significant dependence on either frequency or flux density, in good agreement with the earlier estimate and with high-sensitivity measurements in the frequency range 5--40\,GHz. No polarization signal is detected in the case of dusty galaxies, implying 90\% confidence upper limits of \Pi_{\rm dusty}\simlt 2.2\% at 353\,GHz and of \simlt 3.9\% at 217\,GHz. The contamination of CMB polarization maps by unresolved point sources is discussed.Comment: 10 pages, 3 figures, 7 tables; revised version. In press on Astronomy and Astrophysic

Material-informed topology optimization for Wire-and-Arc Additive Manufacturing

Wire-and-Arc Additive Manufacturing (WAAM) is a metal 3d printing technique that allows fabricating elements ranging from simple geometry to extremely complex shapes. “Layer-by-layer” manufacturing produces a printed material with significant elastic anisotropy, whereas “dot-by-dot” printing may be used to fabricate funicular geometries in which the mechanical properties of the single bars are affected by the printing process. The design of WAAM components is addressed by formulating problems of structural optimizations that account for the peculiar features of the printed alloy. Topology optimization by distribution of anisotropic material is exploited to find optimal shapes in layer-by-layer manufacturing. Two-dimensional specimens are addressed along with I-beams. In the latter case it is assumed that a web plate and two flanges are printed and subsequently welded to assemble the structural component. A constrained force density method is proposed for the design of grid shells in dot-by-dot printing, formulating local enforcements to govern the magnitude of the axial force in each branch of the network. In both formulations, the arising multi-constrained problem is efficiently tackled through methods of sequential convex programming. Lightweight solutions for layer-by-layer and dot-by-dot manufacturing are found for given printing directions. Extensions of the proposed numerical tools are highlighted to endow the optimization problems with additional set of materialrelated constraints

A numerical approach to the design of gridshells for WAAM

A novel approach based on funicular analysis is investigated to cope with the design of spatial truss networks fabricated by Wire-and-Arc Additive Manufacturing (WAAM). The minimization of the horizontal thrusts of networks with fixed plan geometry is stated both in terms of any independent subset of the force densities and in terms of the height of the restrained nodes. Local enforcements are formulated to prescribe lower and upper bounds for the vertical coordinates of the nodes, and to control the stress regime in the branches. This allows also for a straightforward control of the length and maximum force magnitude in each branch. Constraints are such that sequential convex programming can be conveniently exploited to handle grids with general topology and boundary conditions. Optimal networks for WAAM are preliminary investigated, accounting for different sets of the above prescriptions

Seismic-proof buildings in developing countries

The use of \u201cductile seismic frames,\u201d whose proper seismic behavior largely depends upon construction details and specific design rules, may do not always lead to effective seismic resistant structures, as dramatically denounced by the famous Chinese artist Ai Weiwei in his artwork Straight. The artwork (96 t of undulating metal bars that were salvaged from schools destroyed by the 2008 Sichuan, China earthquake, where over 5,000 students were killed) is a clear denounce against the corruption yielding to shoddy construction methods. The issue of safe constructions against natural hazards appears even more important in developing countries where, in most cases, building structures are realized by non-expert workers, or even by simple \u201cpeople from the street,\u201d who does not have any technical knowledge on construction techniques and seismic engineering. In this paper, a brief history from the first frame structures to the more efficient wall-based structures is provided within Earthquake Engineering perspectives. The superior structural properties of box-type wall structures with respect to conventional frame structures envisage a change of paradigm from actual \u201cductility-based\u201d Earthquake Engineering (centered on frame structures) toward 100% safe buildings through a \u201cstrength-based\u201d design exploiting the use of box-type wall-based structures

Blended structural optimization for wire-and-arc additively manufactured beams

Current manufacturing techniques in the construction sector are slow, expensive and constrained in terms of architectural shapes. In other manufacturing sectors (such as automotive and aerospace) the use of automated construction systems significantly improved the safety, speed, quality and complexity of products. To realize real-scale structural elements for construction applications without ideally any geometrical constraints either in size or shape, the most suitable manufacturing solution for metallic elements is a directed energy deposition (DED) process referred to as wire-and-arc additive manufacturing (WAAM). The main advantage of WAAM relies on the possibility to create new shapes and forms following the breakthrough design tools for modern architecture as algorithm-aided design. At the same time, the printed part ensures high structural performances with reduced material use with respect to the conventional solution. The study presents a new approach called “blended” structural optimization, which blends topology optimization with basic principles of structural design and manufacturing constraints proper of WAAM technology, towards the realization of new efficient structural elements. The approach is applied to the case study of a I-type stainless steel beam on a multi-storey frame building. The approach could pave the way towards an efficient use of WAAM process to produce a new generation of structurally optimized elements for construction, with a more conscious use of the optimization tools and an efficient application of metal 3D printing

Long-term seismometric monitoring of the two towers of Bologna (Italy): Modal frequencies identification and effects due to traffic induced vibrations

The rise of human activities and the constant increase of vehicles traffic in the cities, and in particular of heavy vehicles such as buses and trucks, causes continues ambient vibrations that can detrimentally affect the conservation of built artifacts, especially historical constructions. The effects of urban vibrations on buildings and monuments are far from being fully investigated. In general, peak levels of traffic-induced vibrations are rarely high enough to be the main cause of heavy structural damages. On the other hand, they contribute to the process of deterioration by adding extra stresses\u2014through fatigue damage accumulation occurring as a result of long periods of exposure to low levels of vibration\u2014or by contributing to soil densification\u2014which can lead to the settlement of building foundations. As such, the estimation of threshold levels above which traffic-induced vibrations may cause damages to monumental buildings requires specific studies including long-time monitoring campaigns. Data from experimental campaign can, indeed, be used to extract information on the variation of dynamic properties of buildings, thus providing valuable pieces of information for a complete knowledge to plan effective preservation interventions. The present work aims to identify the effects of traffic induced urban vibrations on the two Towers of Bologna, particularly prone to fatigue-related damages and close to a high transit of vehicles, through a preliminary analysis of data from several dynamic monitoring campaigns conducted during the last years

Effect of a multifactorial fall-and-fracture risk assessment and management program on gait and balance performances and disability in hospitalized older adults: a controlled study

Summary: This controlled intervention study in hospitalized oldest old adults showed that a multifactorial fall-and-fracture risk assessment and management program, applied in a dedicated geriatric hospital unit, was effective in improving fall-related physical and functional performances and the level of independence in activities of daily living in high-risk patients. Introduction: Hospitalization affords a major opportunity for interdisciplinary cooperation to manage fall-and-fracture risk factors in older adults. This study aimed at assessing the effects on physical performances and the level of independence in activities of daily living (ADL) of a multifactorial fall-and-fracture risk assessment and management program applied in a geriatric hospital setting. Methods: A controlled intervention study was conducted among 122 geriatric inpatients (mean ± SD age, 84 ± 7years) admitted with a fall-related diagnosis. Among them, 92 were admitted to a dedicated unit and enrolled into a multifactorial intervention program, including intensive targeted exercise. Thirty patients who received standard usual care in a general geriatric unit formed the control group. Primary outcomes included gait and balance performances and the level of independence in ADL measured 12 ± 6days apart. Secondary outcomes included length of stay, incidence of in-hospital falls, hospital readmission, and mortality rates. Results: Compared to the usual care group, the intervention group had significant improvements in Timed Up and Go (adjusted mean difference [AMD] = −3.7s; 95% CI = −6.8 to −0.7; P = 0.017), Tinetti (AMD = −1.4; 95% CI = −2.1 to −0.8; P < 0.001), and Functional Independence Measure (AMD = 6.5; 95%CI = 0.7-12.3; P = 0.027) test performances, as well as in several gait parameters (P < 0.05). Furthermore, this program favorably impacted adverse outcomes including hospital readmission (hazard ratio = 0.3; 95% CI = 0.1-0.9; P = 0.02). Conclusions: A multifactorial fall-and-fracture risk-based intervention program, applied in a dedicated geriatric hospital unit, was effective and more beneficial than usual care in improving physical parameters related to the risk of fall and disability among high-risk oldest old patient