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

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

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

Efflorescence of Alkali-Activated Cements (Geopolymers) and the Impacts on Material Structures: A Critical Analysis

Even with the rapid development of the alkali-activated cement (AAC) technology in the past few years, some phenomena still needs to be better understood, that may alter the durability of the material. In many industrial uses and laboratory researches the formation of the salts on the surface alkali-activated type cements was observed, which was identified as efflorescence. This occurs due to the presence of an alkali transported in contact with the humidity and CO2 environment. It may present externally from the formation of salts on the surface and internally with the carbonation of the alkalis in capillary pores. The effects of efflorescence on the material in use, as well as all factors that can influence its formation are not yet fully understood or reported. The search for papers was conducted using the search words efflorescence and geopolymer/alkali-activated, combined in the electronic data base. Due to the limited quantity of papers published related to efflorescence in geopolymers, the review was complemented using papers that discuss this behavior in Portland cement (PC) and based on the main properties that can influence the formation of efflorescence. In this paper, to understand the nature of efflorescence, upon which proper methods of minimizing of this issue can be based, the following aspects are discussed and re-examined: (1) the development of efflorescence's in PC concrete, (2) the role of alkalis in AACs, (3) efflorescence in AACs, and (4) effect from a physical and microstructural point of view of efflorescence's on the ACCs. This paper highlights that the nature of the pore structure and the design parameters (such as alkali concentration, presence of soluble silicates, and water content in the activator) are the two most important factors that control efflorescence rate and changes in mechanical behavior. However, the stability of the alkalis and their relationship with the formed gel, which are determining factors in the formation of efflorescence, remain not completely understood. In the same way, the effect of efflorescence in tensile strength and shrinkage needs to be evaluated

Real-Time High-Resolution X-ray Imaging and Nuclear Magnetic Resonance Study of the Hydration of Pure and Na-Doped C 3

This study details the differences in real-time hydration between pure tricalcium aluminate (cubic C{sub 3}A or 3CaO {center_dot} Al{sub 2}O{sub 3}) and Na-doped tricalcium aluminate (orthorhombic C{sub 3}A or Na{sub 2}Ca{sub 8}Al{sub 6}O{sub 18}), in aqueous solutions containing sulfate ions. Pure phases were synthesized in the laboratory to develop an independent benchmark for the reactions, meaning that their reactions during hydration in a simulated early age cement pore solution (saturated with respect to gypsum and lime) were able to be isolated. Because the rate of this reaction is extremely rapid, most microscopy methods are not adequate to study the early phases of the reactions in the early stages. Here, a high-resolution full-field soft X-ray imaging technique operating in the X-ray water window, combined with solution analysis by {sup 27}Al nuclear magnetic resonance (NMR) spectroscopy, was used to capture information regarding the mechanism of C{sub 3}A hydration during the early stages. There are differences in the hydration mechanism between the two types of C{sub 3}A, which are also dependent on the concentration of sulfate ions in the solution. The reactions with cubic C{sub 3}A (pure) seem to be more influenced by higher concentrations of sulfate ions, forming smaller ettringite needles at a slower pace than the orthorhombic C{sub 3}A (Na-doped) sample. The rate of release of aluminate species into the solution phase is also accelerated by Na doping