Dissipative continuous Euler flows

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

In-situ laboratory X-ray diffraction applied to assess cement hydration

In-situ X-ray diffraction (XRD) is a powerful tool to assess the hydration of cementitious materials, providing time-resolved quantitative analysis with reasonable accuracy without disturbing sample. However, the lack of guidelines and well-established procedures for data collection and analysis is the limiting factor for spreading this technique. This paper discussed using in-situ laboratory XRD to assess cement hydration. The first part was dedicated to a literature review on the topic. Then, experimental strategies were discussed, and recommendations related to the data analysis routine were drawn; the advantages and limitations of this technique were also discussed. We can conclude that the critical factors for a successful analysis are the choice of an adequate experimental setup with good statistics and low measurement time, the proper consideration of different amorphous contributions in the XRD pattern, and a good data analysis routine. Independent techniques are highly recommended to support the in-situ XRD data.PID2020-114650RB-I0

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

Characterizing the nano and micro structure of concrete to improve its durability

New and advanced methodologies have been developed to characterize the nano and microstructure of cement paste and concrete exposed to aggressive environments. High resolution full-field soft X-ray imaging in the water window is providing new insight on the nano scale of the cement hydration process, which leads to a nano-optimization of cement-based systems. Hard X-ray microtomography images on ice inside cement paste and cracking caused by the alkali-silica reaction (ASR) enables three-dimensional structural identification. The potential of neutron diffraction to determine reactive aggregates by measuring their residual strains and preferred orientation is studied. Results of experiments using these tools will be shown on this paper

Characterizing the Nano and Micro Structure of Concrete toImprove its Durability

New and advanced methodologies have been developed to characterize the nano and microstructure of cement paste and concrete exposed to aggressive environments. High resolution full-field soft X-ray imaging in the water window is providing new insight on the nano scale of the cement hydration process, which leads to a nano-optimization of cement-based systems. Hard X-ray microtomography images of ice inside cement paste and cracking caused by the alkali?silica reaction (ASR) enables three-dimensional structural identification. The potential of neutron diffraction to determine reactive aggregates by measuring their residual strains and preferred orientation is studied. Results of experiments using these tools are shown on this paper

BV functions and sets of finite perimeters in sub-Riemannian manifolds

We give a notion of BV function on an oriented manifold where a volume form and a family of lower semicontinuous quadratic forms are given. When we consider sub-Riemannian manifolds, our definition coincides with the one given in the more general context of metric measure spaces which are doubling and support a Poincaré inequality. We focus on finite perimeter sets, i.e., sets whose characteristic function is BV, in sub-Riemannian manifolds. Under an assumption on the nilpotent approximation, we prove a blowup theorem, generalizing the one obtained for step-2 Carnot groups

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