Poincaré Inequality for a Mesh-Dependent 2-Norm on Piecewise Linear Surfaces with Boundary

We establish several useful estimates for a non-conforming 2-norm posed on piecewise linear surface triangulations with boundary, with the main result being a Poincaré inequality. We also obtain equivalence of the non-conforming 2-norm posed on the true surface with the norm posed on a piecewise linear approximation. Moreover, we allow for free boundary conditions. The true surface is assumed to be C 2 , 1 C^{2,1} when free conditions are present; otherwise, C 2 C^{2} is sufficient. The framework uses tools from differential geometry and the closest point map (see [G. Dziuk, Finite elements for the Beltrami operator on arbitrary surfaces, Partial Differential Equations and Calculus of Variations, Lecture Notes in Math. 1357, Springer, Berlin (1988), 142–155]) for approximating the full surface Hessian operator. We also present a novel way of applying the closest point map when dealing with surfaces with boundary. Connections with surface finite element methods for fourth-order problems are also noted.

Applying integrated seismic technology to complex foothill areas of foreland basins in China

Due to complicated near-surface conditions, including large elevation changes and complex geologic structures, accurate imaging of subsurface structures for hydrocarbon exploration in the foreland basins of western China has been challenging for many years. After decades of research and fieldwork, we developed an effective seismic exploration workflow that uses the latest technologies from acquisition to imaging. They include 3D high-density and wide-azimuth (WAZ) acquisition, 3D true-surface tilted transverse isotropy (TTI) anisotropic prestack depth migration, and dual-detachment structural modeling and interpretation. To further reduce uncertainty in velocity model building and improve imaging quality, our geologists, geophysicists, and reservoir engineers worked closely through the exploration cycle (seismic acquisition, processing, and interpretation). This exploration model has been used successfully in hydrocarbon exploration of many complex foothill areas in western China. Three-dimensional WAZ high-density seismic surveys have been conducted over 40,000 km2 of the foreland basins, greatly improving the field seismic data quality. After application of 3D true-surface TTI anisotropic depth model building and imaging with integrated structural interpretation, new discoveries of hydrocarbon reservoirs have increased. The application of new technologies not only increased drilling success but also reduced depth well-tie errors between seismic data and wells.

Characterising porosity in platinum nanoparticles

Accurately determining the morphology and hence the true surface areas of catalytic nanoparticles remains challenging.

The acoustics of primary and secondary stress in Modern Hebrew

This study investigates the acoustic realization of primary and secondary stress in polysyllabic words in Modern Hebrew (MH). The study focuses on the production of target words embedded in a meaningful carrier sentence, with three primary stress types: ultimate, penultimate and antepenultimate stress. We measured the duration, intensity and F0 of each vowel. Results show that duration is the sole reliable cue for stress in MH, and that there is no phonetic realization of secondary stress in MH, and therefore no true surface alternating pattern. These findings may have phonological implications regarding the prosodic organization of language, and provide a solid basis for future studies on the perception of primary and secondary stress by speakers.

Rayleigh wave at the surface of a general anisotropic poroelastic medium: derivation of real secular equation

A secular equation governs the propagation of Rayleigh wave at the surface of an anisotropic poroelastic medium. In the case of anisotropy with symmetry, this equation is obtained as a real irrational equation. But, in the absence of anisotropic symmetries, this secular equation is obtained as a complex irrational equation. True surface waves in non-dissipative materials decay only with depth. That means, propagation of Rayleigh wave in anisotropic poroelastic solid should be represented by a real phase velocity. In this study, the determinantal system leading to the complex secular equation is manipulated to obtain a transformed equation. Even for arbitrary (triclinic) anisotropy, this transformed equation remains real for the propagation of true surface waves. Such a real secular equation is obtained with the option of boundary pores being opened or sealed. A numerical example is solved to study the existence and propagation of Rayleigh waves in porous media for the top three (i.e. triclinic, monoclinic and orthorhombic) anisotropies.

Electrochemical oxidation of As(iii) on Pd immobilized Pt surface: kinetics and sensing performance

Amplification of true surface area can be improved when Pd particles are deposited on a substrate in the presence of sodium dodecyl sulfate (SDS) surfactant. In acidic medium, As(iii) undergoes a two-step oxidation process.

Methanol as a hydrate inhibitor and hydrate activator

Water–methane interface broadening by low-dose methanol addition highlights the need for true surface sampling on the atomistic level.