Equilibrated tractions for the Hybrid High-Order method

We show how to recover equilibrated face tractions for the hybrid high-order method for linear elasticity recently introduced in [D. A. Di Pietro and A. Ern, A hybrid high-order locking-free method for linear elasticity on general meshes, Comput. Meth. Appl. Mech. Engrg., 2015, 283:1-21], and prove that these tractions are optimally convergent

A Hybrid High-Order method for Leray-Lions elliptic equations on general meshes

In this work, we develop and analyze a Hybrid High-Order (HHO) method for steady non-linear Leray-Lions problems. The proposed method has several assets, including the support for arbitrary approximation orders and general polytopal meshes. This is achieved by combining two key ingredients devised at the local level: a gradient reconstruction and a high-order stabilization term that generalizes the one originally introduced in the linear case. The convergence analysis is carried out using a compactness technique. Extending this technique to HHO methods has prompted us to develop a set of discrete functional analysis tools whose interest goes beyond the specific problem and method addressed in this work: (direct and) reverse Lebesgue and Sobolev embeddings for local polynomial spaces, $L^{p}$-stability and $W^{s,p}$-approximation properties for $L^{2}$-projectors on such spaces, and Sobolev embeddings for hybrid polynomial spaces. Numerical tests are presented to validate the theoretical results for the original method and variants thereof

An advection-robust Hybrid High-Order method for the Oseen problem

In this work, we study advection-robust Hybrid High-Order discretizations of the Oseen equations. For a given integer $k\ge 0$, the discrete velocity unknowns are vector-valued polynomials of total degree $\le k$ on mesh elements and faces, while the pressure unknowns are discontinuous polynomials of total degree $\le k$ on the mesh. From the discrete unknowns, three relevant quantities are reconstructed inside each element: a velocity of total degree $\le(k+1)$, a discrete advective derivative, and a discrete divergence. These reconstructions are used to formulate the discretizations of the viscous, advective, and velocity-pressure coupling terms, respectively. Well-posedness is ensured through appropriate high-order stabilization terms. We prove energy error estimates that are advection-robust for the velocity, and show that each mesh element $T$ of diameter $h_T$ contributes to the discretization error with an $\mathcal{O}(h_T^{k+1})$-term in the diffusion-dominated regime, an $\mathcal{O}(h_T^{k+\frac12})$-term in the advection-dominated regime, and scales with intermediate powers of $h_T$ in between. Numerical results complete the exposition

Spectral weight redistribution in (LaNiO3)n/(LaMnO3)2 superlattices from optical spectroscopy

We have studied the optical properties of four (LaNiO$_3$)$_n$/(LaMnO$_3$)$_2$ superlattices (SL) ($n$=2, 3, 4, 5) on SrTiO$_3$ substrates. We have measured the reflectivity at temperatures from 20 K to 400 K, and extracted the optical conductivity through a fitting procedure based on a Kramers-Kronig consistent Lorentz-Drude model. With increasing LaNiO$_3$ thickness, the SLs undergo an insulator-to-metal transition (IMT) that is accompanied by the transfer of spectral weight from high to low frequency. The presence of a broad mid-infrared band, however, shows that the optical conductivity of the (LaNiO$_3$)$_n$/(LaMnO$_3$)$_2$ SLs is not a linear combination of the LaMnO$_3$ and LaNiO$_3$ conductivities. Our observations suggest that interfacial charge transfer leads to an IMT due to a change in valence at the Mn and Ni sites.Comment: Accepted for publication in Phys. Rev. Lett. 5 pages, 5 figure

Scale-factor duality in string Bianchi cosmologies

We apply the scale factor duality transformations introduced in the context of the effective string theory to the anisotropic Bianchi-type models. We find dual models for all the Bianchi-types [except for types $VIII$ and $IX$] and construct for each of them its explicit form starting from the exact original solution of the field equations. It is emphasized that the dual Bianchi class $B$ models require the loss of the initial homogeneity symmetry of the dilatonic scalar field.Comment: 18 pages, no figure

An arbitrary-order discrete rot-rot complex on polygonal meshes with application to a quad-rot problem

In this work, following the discrete de Rham (DDR) approach, we develop a discrete counterpart of a two-dimensional de Rham complex with enhanced regularity. The proposed construction supports general polygonal meshes and arbitrary approximation orders. We establish exactness on a contractible domain for both the versions of the complex with and without boundary conditions and, for the former, prove a complete set of Poincar\'e-type inequalities. The discrete complex is then used to derive a novel discretisation method for a quad-rot problem which, unlike other schemes in the literature, does not require the forcing term to be prepared. We carry out complete stability and convergence analyses for the proposed scheme and provide numerical validation of the results

Uranium Fate and Mineral Transformations upon Remediation with Ammonia (NH3) Gas

The fission of uranium (U) for plutonium production was a major activity at the U.S. Department of Energy’s (DOE) Hanford Site in Washington State during World War II and Cold War. This endeavor resulted in the generation of over two million liters of high-level radioactive waste, most of which still remains in 177 underground storage tanks. Due to the improper storage and aging of these tanks in addition to other waste releases across the Site, approximately 200,000 kg of U have been released into the vadose zone. The objective of this study was to determine whether the application of the reactive gas, ammonia (NH3), could be effective for sequestration of U in vadose zone conditions such as those at the Hanford Site. The goal of this novel technique is to elevate the pH and induce mineral dissolution. As the NH3 dissipates and the pH returns to neutral conditions, adsorption and co-precipitation processes are expected to immobilize U. The targeted mineral dissolution and secondary precipitate formation processes are not well understood at these conditions including their impact on U behavior. The experimental results suggest that, as a result of pH manipulation with NH3, investigated minerals (illite, muscovite, and montmorillonite) undergo incongruent dissolution. In addition, several analytical techniques were applied to compare ammonia-treated and circumneutral pH-treated minerals. Characterization studies showed that physicochemical transformations occurred, such as recrystallization of mineral edges and particle size and surface area increase. These behaviors are indicative of secondary precipitate formation, which was confirmed by comparisons of Al:Si ratios in solution and the solid phase, suggesting U sequestration. Furthermore, U distribution calculations between the solid and liquid phases indicate a significant increase in solid phase U with treatment, while geochemical software modeling provided a way to predict U species and secondary mineral phases upon alkaline treatment. These findings show the scientific community that NH3 gas injection is an effective technology to decrease the mobility of the uranyl ion. This technology may be particularly valuable to unsaturated areas where contamination remedies are needed in situ without the addition of liquid amendments

Numerical approximation of poroelasticity with random coefficients using Polynomial Chaos and Hybrid High-Order methods

In this work, we consider the Biot problem with uncertain poroelastic coefficients. The uncertainty is modelled using a finite set of parameters with prescribed probability distribution. We present the variational formulation of the stochastic partial differential system and establish its well-posedness. We then discuss the approximation of the parameter-dependent problem by non-intrusive techniques based on Polynomial Chaos decompositions. We specifically focus on sparse spectral projection methods, which essentially amount to performing an ensemble of deterministic model simulations to estimate the expansion coefficients. The deterministic solver is based on a Hybrid High-Order discretization supporting general polyhedral meshes and arbitrary approximation orders. We numerically investigate the convergence of the probability error of the Polynomial Chaos approximation with respect to the level of the sparse grid. Finally, we assess the propagation of the input uncertainty onto the solution considering an injection-extraction problem.Comment: 30 pages, 15 Figure