Some theoretical aspects of elastic wave modeling with a recently developed spectral element method

A spectral element method has been recently developed for solving elastodynamic problems. The numerical solutions are obtained by using the weak formulation of the elastodynamic equation for heterogeneous media, based on the Galerkin approach applied to a partition, in small subdomains, of the original physical domain. In this work, some mathematical aspects of the method and the associated algorithm implementation are systematically investigated. Two kinds of orthogonal basis functions, constructed with Legendre and Chebyshev polynomials, and their related Gauss-Lobatto collocation points are introduced. The related integration formulas are obtained. The standard error estimations and expansion convergence are discussed. An element-by-element pre-conditioned conjugate gradient linear solver in the space domain and a staggered predictor/multi-corrector algorithm in the time integration are used for strong heterogeneous elastic media. As a consequence, neither the global matrices nor the effective force vector is assembled. When analytical formulas are used for the element quadrature, there is even no need for forming element matrix in order to further save memory without losing much in computational efficiency. The element-by-element algorithm uses an optimal tensor product scheme which makes this method much more efficient than finite-element methods from the point of view of both memory storage and computational time requirements. This work is divided into two parts. The first part mainly focuses on theoretical studies with a simple numerical result for the Che-byshev spectral element, and the second part, mainly with the Legendre spectral element, will give the algorithm implementation, numerical accuracy and efficiency analyses, and then the detailed modeling example comparisons of the proposed spectral element method with a pseudo-spectral method, which will be seen in another work by Lin, Wang and Zhang.     

Ab initio parameterization of an all-atom polarizable and dissociable force field for water

A novel all-atom, dissociative, and polarizable force field for water is presented. The force field is parameterized based on forces, stresses, and energies obtained form ab initio calculations of liquid water at ambient conditions. The accuracy of the force field is tested by calculating structural and dynamical properties of liquid water and the energetics of small water clusters. The transferability of the force field to dissociated states is studied by considering the solvation of a proton and the ionization of water at extreme conditions of pressure and temperature. In the case of the solvated proton, the force field properly describes the presence of both Eigen and Zundel configurations. In the case of the pressure-induced ice VIII/ice X transition and the temperature-induced transition to a superionic phase, the force field is found to describe accurately the proton symmetrization and the melting of the proton sublattice, respectively.     

Defective α‐Fe2O3(0001): An ab Initio Study

By using density functional theory calculations at the PBE+U level, we investigated the properties of hematite (0001) surfaces decorated with adatoms/vacancies/substituents. For the most stable surface termination over a large range of oxygen chemical potentials (${\mu _{\rm{O}} }$ ), the vacancy formation and adsorption energies were determined as a function of ${\mu _{\rm{O}} }$ . Under oxygen‐rich conditions, all defects are metastable with respect to the ideal surface. Under oxygen‐poor conditions, O vacancies and Fe adatoms become stable. Under ambient conditions, all defects are metastable; in the bulk, O vacancies form more easily than Fe vacancies, whereas at the surface the opposite is true. All defects, that is, O and Fe vacancies, Fe and Al adatoms, and Al substituents, induce important modifications to the geometry of the surface in their vicinity. Dissociative adsorption of molecular oxygen is likely to be exothermic on surfaces with Fe/Al adatoms or O vacancies.     

Spectral element method for acoustic wave simulation in heterogeneous media

In this paper, we present a spectral element method for studying acoustic wave propagation in complex geological structures. Due to complexity (both lithological and stratigraphical), the use of numerical methods of higher accuracy and flexibility is needed to achieve the correct results. The spectral element method shows more accurate results compared to the low-order finite element, the conventional finite difference and the pseudospectral methods. High accuracy is reached even for rather long wave propagation times and dispersion errors are essentially eliminated; pirregular interfaces between different media can be well described so that numerical artifacts or noises are not at all introduced. The method is tested against analytical solutions both in the two-dimensional homogenous and heterogeneous media. The results of different simulations are presented.     

Double-grid Chebyshev spectral elements for acoustic wave modeling

Highly accurate algorithms are needed for modeling wave propagation phenomena in realistic media. The spectral element methods, either based on a Chebyshev or a Legendre polynomial basis, have shown their excellent properties of high accuracy and flexibility in describing complex models outperforming other techniques. In contrast with standard grid methods, which use dense spatial meshes, spectral element methods discretize the computational domain in a very coarse mesh. With constant-property elements, this fact may in some cases reduce seriously the computational efficiency. For instance, if the medium is finely heterogeneous, it may need to be described in a much finer way than the acoustic wave field. The double-grid approach presented in this work is a viable way for overcoming this lack of the method and for handling problems where the medium changes continuously or even sharply on the small scale. The variation in the properties is taken into account by using an independent set of shape functions defined on a temporary local grid in such a way that either the small scale fluctuations are accurately handled, without the need of a global finer grid, and the macroscopic wave field propagation is solved with no loose of computational efficiency.     

Explicit secular equations of Stoneley waves in a non-homogeneous orthotropic elastic medium under the influence of gravity

The problem of Stoneley waves in a non-homogeneous orthotropic elastic medium under the influence of gravity was studied recently by Abd-Alla and Ahmed [A.M. Abd-Alla, S.M. Ahmed, Stoneley waves and Rayleigh waves in a non-homogeneous orthotropic elastic medium under the influence of gravity, Appl. Math. Comput. 135 (2003) 187–200], who derived the secular equation of the wave in the implicit form. In this paper, by using an appropriate representation of the solution, we obtain the secular equation of the wave in the explicit form. Moreover, considering its special cases, we derive explicit secular equations for a number of investigations of Stoneley waves under the influence of gravity, for which only the implicit dispersion equations were previously obtained.     

Wave Simulation in Frozen Porous Media

We propose a numerical algorithm for simulation of wave propagation in frozen porous media, where the pore space is filled with ice and water. The model, based on a Biot-type three-phase theory, predicts three compressional waves and two shear waves and models the attenuation level observed in rocks. Attenuation is modeled with exponential relaxation functions which allow a differential formulation based on memory variables. The wavefield is obtained using a grid method based on the Fourier differential operator and a Runge–Kutta time-integration algorithm. Since the presence of slow quasistatic modes makes the differential equations stiff, a time-splitting integration algorithm is used to solve the stiff part analytically. The modeling is second-order accurate in the time discretization and has spectral accuracy in the calculation of the spatial derivatives.     

Investigation of optoelectronic properties of triphenylamine-based dyes featuring heterocyclic anchoring groups for DSSCs’ applications: a theoretical study

Structural Chemistry - Design and synthesis of new potent sensitizers are of interest for realization of high-efficiency Dye Sensitized Solar Cells (DSSCs). Modification of the...     

Catalytic oxidation activity of Pt3O4 surfaces and thin films

The catalytic oxidation activity of platinum particles in automobile catalysts is thought to originate from the presence of highly reactive superficial oxide phases which form under oxygen-rich reaction conditions. Here we study the thermodynamic stability of platinum oxide surfaces and thin films and their reactivities toward oxidation of carbon compounds by means of first-principles atomistic thermodynamics calculations and molecular dynamics simulations based on density functional theory. On the Pt(111) surface the most stable superficial oxide phase is found to be a thin layer of alpha-PtO2, which appears not to be reactive toward either methane dissociation or carbon monoxide oxidation. A PtO-like structure is most stable on the Pt(100) surface at oxygen coverages of one monolayer, while the formation of a coherent and stress-free Pt3O4 film is favored at higher coverages. Bulk Pt3O4 is found to be thermodynamically stable in a region around 900 K at atmospheric pressure. The computed net driving force for the dissociation of methane on the Pt3O4(100) surface is much larger than that on all other metallic and oxide surfaces investigated. Moreover, the enthalpy barrier for the adsorption of CO molecules on oxygen atoms of this surface is as low as 0.34 eV, and desorption of CO2 is observed to occur without any appreciable energy barrier in molecular dynamics simulations. These results, combined, indicate a high catalytic oxidation activity of Pt3O4 phases that can be relevant in the contexts of Pt-based automobile catalysts and gas sensors.