Topological volumes of fibrations: a note on open covers

We establish a straightforward estimate for the number of open sets with fundamental group constraints needed to cover the total space of fibrations. This leads to vanishing results for simplicial volume and minimal volume entropy, e.g., for certain mapping tori.

On Scalar and Ricci Curvatures

The purpose of this report is to acknowledge the influence of M. Gromov's vision of geometry on our own works. It is two-fold: in the first part we aim at describing some results, in dimension 3, around the question: which open 3-manifolds carry a complete Riemannian metric of positive or non negative scalar curvature? In the second part we look for weak forms of the notion of ''lower bounds of the Ricci curvature'' on non necessarily smooth metric measure spaces. We describe recent results some of which are already posted in [arXiv:1712.08386] where we proposed to use the volume entropy. We also attempt to give a new synthetic version of Ricci curvature bounded below using Bishop-Gromov's inequality.

Structural, mechanical and thermodynamic properties study on Mg–Y alloys from first-principles calculations

The structures with different compositions of the binary Mg–Y alloys have been predicted by first-principles calculations combined with an unbiased Crystal structure Analysis by Particle Swarm Optimization (CALYPSO) structure searching method. The two already known stoichiometries alloys of Mg1Y1 with Pm-[Formula: see text] symmetry and Mg3Y1 with Fm-[Formula: see text] are confirmed, and a new stoichiometry alloy of Mg1Y3 with [Formula: see text] symmetry is proposed. The dynamical and mechanical stabilities for the three alloys at different pressures are investigated by phonon spectra and mechanical stability criteria, respectively. Subsequently, the bulk modulus, shear modulus, Young’s modulus, the brittleness/ductile behavior, the elastic anisotropy as well as Vickers hardness for the three alloys at 0 GPa are discussed in detail. The results show that the Mg1Y1, Mg3Y1 and Mg1Y3 alloys improve the hardness and stiffness compared with pure Mg, and Mg1Y3 alloy is of the best ductility in the three alloys. Meanwhile, the three alloys exhibit anisotropic. Moreover, the thermodynamic properties, such as Debye temperature, heat capacity at constant volume, entropy and Helmholtz free energy for the three stable alloys, are predicted and discussed.

Comparative Thermodynamic Analysis of the Behavior of C60 and C28 Fullerenes when Heated in an Inert Medium

The structural changes of condensed fullerenes C60 and C28 at a temperature increase from 200 K to 2000 K have been studied by computational methods using the TERRA software for carbon-argon systems. The processes of destruction of fullerenes C60 and C28 molecules are presented, and the temperature ranges of their thermal stability are determined: up to 1000 K and up to 400 K, respectively. The following thermophysical parameters of the C60-Ar and C28-Ar systems are considered: specific volume, entropy, total enthalpy, total internal energy, equilibrium specific heat, molar mass of the gas phase, gas constant, and mass fraction of the condensed phase. A comparative analysis of their changes with increasing temperature is carried out. The results obtained in the course of thermodynamic modeling are similar to the results of a full-scale experiment conducted under similar conditions. In the future, the obtained data can be used to determine the explosive and fire-hazardous properties of fullerenes as a dispersed solid.

Systolic Aspects of Black Hole Entropy

We attempt to provide a mesoscopic treatment of the origin of black hole entropy in (3 + 1)-dimensional spacetimes. We ascribe this entropy to the non-trivial topology of the space-like sections Σ of the horizon. This is not forbidden by topological censorship, since all the known energy inequalities needed to prove the spherical topology of Σ are violated in quantum theory. We choose the systoles of Σ to encode its complexity, which gives rise to the black hole entropy. We present hand-waving reasons why the entropy of the black hole can be considered as a function of the volume entropy of Σ . We focus on the limiting case of Σ having a large genus.