From the Brunn-Minkowski inequality to a class of generalized Poincar\'{e}-type inequality for torsional rigidity

In this paper, we put forward an argument which leads from the Brunn-Minkowski inequality to a class of Poincar\'{e}-type inequality for torsional rigidity on the boundary of a convex body of class $C^{2}_{+}$ in \rnnn

Monitoring of the 2008 Chaitén Eruption Cloud Using MODIS Data and its Impacts

This chapter presents the monitoring of the 2008 Chaitén eruption cloud using Moderate Resolution Imaging Spectroradiometer (MODIS) data and its impacts. The 8-day MODIS data from 3 to 10 May 2008 were used to track the movement and dispersion of the eruption cloud of the Chaitén volcano in Chile following the eruption on 2 May 2008. For detecting volcanic particulates, the procedure is adopted based on the brightness temperature difference (BTD) algorithm, by which the thermal infrared channels were centered on 11–12 μm of multispectral satellite sensors. The BTD is generally negative for volcanic ash but positive for ice and water vapor. The eruption cloud was found to drift northeastward, eastward, and southeastward crossing the central and northern part of Argentina and over the Atlantic Ocean. The timing of heavy rainfall in South Africa during May–June, in central Australia during June 2008 and in Hong Kong during June (the wettest since record began in 1884), was considered to have been connected to the dispersion of the particulates from this Chaitén eruption to further impact downstream

Intrinsic Piezoelectric Anisotropy of Tetragonal ABO3 Perovskites: A High-Throughput Study

A comprehensive understand of the intrinsic piezoelectric anisotropy stemming from diverse chemical and physical factors is a key step for the rational design of highly anisotropic materials. We performed high-throughput calculations on tetragonal ABO3 perovskites to investigate the piezoelectricity and the interplay between lattice, displacement, polarization and elasticity. Among the 123 types of perovskites, the structural tetragonality is naturally divided into two categories: normal tetragonal (c/a ratio < 1.1) and super-tetragonal (c/a ratio > 1.17), exhibiting distinct ferroelectric, elastic, and piezoelectric properties. Charge analysis revealed the mechanisms underlying polarization saturation and piezoelectricity suppression in the super-tetragonal region, which also produces an inherent contradiction between high d33 and large piezoelectric anisotropy ratio |d33/d31|. The polarization axis and elastic softness direction jointly determine the maximum longitudinal piezoelectric response d33 direction. The validity and deficiencies of the widely utilized |d33/d31| ratio for representing piezoelectric anisotropy were reevaluated