7,456 research outputs found
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, -stability and -approximation properties for
-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 , the discrete velocity
unknowns are vector-valued polynomials of total degree on mesh elements
and faces, while the pressure unknowns are discontinuous polynomials of total
degree on the mesh. From the discrete unknowns, three relevant
quantities are reconstructed inside each element: a velocity of total degree
, 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 of diameter contributes to the discretization error with
an -term in the diffusion-dominated regime, an
-term in the advection-dominated regime, and
scales with intermediate powers of 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)/(LaMnO) superlattices (SL) (=2, 3, 4, 5) on
SrTiO 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 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)/(LaMnO) SLs is not a linear
combination of the LaMnO and LaNiO 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 and ] 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
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
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