On a differential inclusion related to the Born-Infeld equations

We study a partial differential relation that arises in the context of the Born-Infeld equations (an extension of the Maxwell's equations) by using Gromov's method of convex integration in the setting of divergence free fields

A Scanning Transmission X-ray Microscopy Study of Cubic and Orthorhombic C₃A and Their Hydration Products in the Presence of Gypsum.

This paper shows the microstructural differences and phase characterization of pure phases and hydrated products of the cubic and orthorhombic (Na-doped) polymorphs of tricalcium aluminate (C₃A), which are commonly found in traditional Portland cements. Pure, anhydrous samples were characterized using scanning transmission X-ray microscopy (STXM), X-ray photoelectron spectroscopy (XPS) and X-ray diffraction (XRD) and demonstrated differences in the chemical and mineralogical composition as well as the morphology on a micro/nano-scale. C₃A/gypsum blends with mass ratios of 0.2 and 1.9 were hydrated using a water/C₃A ratio of 1.2, and the products obtained after three days were assessed using STXM. The hydration process and subsequent formation of calcium sulfate in the C₃A/gypsum systems were identified through the changes in the LIII edge fine structure for Calcium. The results also show greater Ca LII binding energies between hydrated samples with different gypsum contents. Conversely, the hydrated samples from the cubic and orthorhombic C₃A at the same amount of gypsum exhibited strong morphological differences but similar chemical environments

Dissipative continuous Euler flows

We show the existence of continuous periodic solutions of the 3D incompressible Euler equations which dissipate the total kinetic energy

Effect of Gypsum on the Early Hydration of Cubic and Na-Doped Orthorhombic Tricalcium Aluminate

The tricalcium aluminate (C3A) and sulfate content in cement influence the hydration chemistry, setting time and rheology of cement paste, mortar and concrete. Here, in situ experiments are performed to better understand the effect of gypsum on the early hydration of cubic (cub-)C3A and Na-doped orthorhombic (orth-)C3A. The isothermal calorimetry data show that the solid-phase assemblage produced by the hydration of C3A is greatly modified as a function of its crystal structure type and gypsum content, the latter of which induces non-linear changes in the heat release rate. These data are consistent with the in situ X-ray diffraction results, which show that a higher gypsum content accelerates the consumption of orth-C3A and the subsequent precipitation of ettringite, which is contrary to the cub-C3A system where gypsum retarded the hydration rate. These in situ results provide new insight into the relationship between the chemistry and early-age properties of cub- and orth-C3A hydration and corroborate the reported ex situ findings of these systems

Mappings of least Dirichlet energy and their Hopf differentials

The paper is concerned with mappings between planar domains having least Dirichlet energy. The existence and uniqueness (up to a conformal change of variables in the domain) of the energy-minimal mappings is established within the class $\bar{\mathscr H}_2(X, Y)$ of strong limits of homeomorphisms in the Sobolev space $W^{1,2}(X, Y)$, a result of considerable interest in the mathematical models of Nonlinear Elasticity. The inner variation leads to the Hopf differential $h_z \bar{h_{\bar{z}}} dz \otimes dz$ and its trajectories. For a pair of doubly connected domains, in which $X$ has finite conformal modulus, we establish the following principle: A mapping $h \in \bar{\mathscr H}_2(X, Y)$ is energy-minimal if and only if its Hopf-differential is analytic in $X$ and real along the boundary of $X$. In general, the energy-minimal mappings may not be injective, in which case one observes the occurrence of cracks in $X$. Nevertheless, cracks are triggered only by the points in the boundary of $Y$ where $Y$ fails to be convex. The general law of formation of cracks reads as follows: Cracks propagate along vertical trajectories of the Hopf differential from the boundary of $X$ toward the interior of $X$ where they eventually terminate before making a crosscut.Comment: 51 pages, 4 figure

Ab initio study of the modification of elastic properties of alpha-iron by hydrostatic strain and by hydrogen interstitials

The effect of hydrostatic strain and of interstitial hydrogen on the elastic properties of $\alpha$-iron is investigated using \textit{ab initio} density-functional theory calculations. We find that the cubic elastic constants and the polycrystalline elastic moduli to a good approximation decrease linearly with increasing hydrogen concentration. This net strength reduction can be partitioned into a strengthening electronic effect which is overcome by a softening volumetric effect. The calculated hydrogen-dependent elastic constants are used to determine the polycrystalline elastic moduli and anisotropic elastic shear moduli. For the key slip planes in $\alpha$-iron, $[1\bar{1}0]$ and $[11\bar{2}]$, we find a shear modulus reduction of approximately 1.6% per at.% H.Comment: Updated first part of 1009.378

Regularity of harmonic discs in spaces with quadratic isoperimetric inequality

We study harmonic and quasi-harmonic discs in metric spaces admitting a uniformly local quadratic isoperimetric inequality for curves. The class of such metric spaces includes compact Lipschitz manifolds, metric spaces with upper or lower curvature bounds in the sense of Alexandrov, some sub-Riemannian manifolds, and many more. In this setting, we prove local Hölder continuity and continuity up to the boundary of harmonic and quasi-harmonic discs

Kaolin mining waste to produce geopolymers: Physicomechanical properties and susceptibility to efflorescence formation

The kaolin mining waste (KW) is a residue generated during the purification process of extracting high purity kaolin used in different industries. KW is mainly constituted by kaolinite-rich clay and other secondary minerals such as anatase and quartz. With the appropriated and controlled process, calcined kaolin mining waste (CKW). It can be thermally activated by calcination to obtain a highly reactive metakaolinite rich material, which exhibits interesting pozzolanic properties. According to its chemical composition and high reactivity, this material is used as an aluminosilicate precursor in the production of geopolymers. One of the negative effects may be the formation of efflorescence. This paper evaluated geopolymer produced with CKW at different activation conditions (alkali concentration and sodium silicate content). The leaching of alkalis was studied through the development of efflorescence on the surface of hardened samples exposed to efflorescence formation conditions (contact with air and water). The results indicated that a larger activator provided a higher compressive strength and reduced the capillary absorption and the efflorescence formation. The data showed that the efflorescence formation can be appropriately controlled by adjusting the mix design parameters, especially the sodium silicate content