Elastic anisotropy measures for heterogeneous materials

Heterogeneous materials exhibit anisotropy to varying extent that is influenced by factors such as individual phase properties and microstructural configuration. A review of the existing anisotropy measures proposed in the context of single crystals reveal that they do not account for the material and microstructural descriptors influencing the extent of anisotropy in heterogeneous materials. To overcome this limitation, existing anisotropy indices have been re-interpreted by considering the effective elastic properties of heterogeneous materials obtained by appropriate effective property estimates. Anisotropy quantification has been demonstrated considering two phase composite materials highlighting the role of constituent volume fractions, secondary phase shape and elastic contrast in influencing the extent of anisotropy. The proposed approach can be generalized to consider other physical fields, multiphysics and non-linearity

CONVEXITY AND CONCAVITY OF MEANS

In this paper, convexity and concavity among Greek means are discussed and the results are interpreted with Vander monde's determinant

Highly sensitive N-(1-naphthyl)ethylene diamine method for the spectrophotometric determination of trace amounts of nitrite in various water samples

A rapid, simple, sensitive and selective spectrophotometric determination of trace nitrite is described. The method is based on a diazotization-coupling reaction between dapsone and N-(1-naphthyl)ethylenediamine dihydrochloride (NEDA) in a hydrochloric acid medium. The molar absorptivity and Sandell's sensitivity were found to be 7.2x10(4) 1 mol(-1) cm(-1) and 0.00063 mug ml(-1), respectively. The calibration graph is linear for 0.002-0.6 mug ml(-1) of nitrite. The interference effects of various cations and anions were also studied and reported. This method has been found to be applicable to the determination of nitrite in various water samples

Roto-translated Local Coordinate Frames For Interacting Dynamical Systems

Modelling interactions is critical in learning complex dynamical systems, namely systems of interacting objects with highly non-linear and time-dependent behaviour. A large class of such systems can be formalized as $\textit{geometric graphs}$, $\textit{i.e.}$, graphs with nodes positioned in the Euclidean space given an $\textit{arbitrarily}$ chosen global coordinate system, for instance vehicles in a traffic scene. Notwithstanding the arbitrary global coordinate system, the governing dynamics of the respective dynamical systems are invariant to rotations and translations, also known as $\textit{Galilean invariance}$. As ignoring these invariances leads to worse generalization, in this work we propose local coordinate frames per node-object to induce roto-translation invariance to the geometric graph of the interacting dynamical system. Further, the local coordinate frames allow for a natural definition of anisotropic filtering in graph neural networks. Experiments in traffic scenes, 3D motion capture, and colliding particles demonstrate that the proposed approach comfortably outperforms the recent state-of-the-art.Comment: NeurIPS 202