Numerical wave propagation for the triangular P1DGP1_{DG}-P2P2 finite element pair

Inertia-gravity mode and Rossby mode dispersion properties are examined for discretisations of the linearized rotating shallow-water equations using the $P1_{DG}$-$P2$ finite element pair on arbitrary triangulations in planar geometry. A discrete Helmholtz decomposition of the functions in the velocity space based on potentials taken from the pressure space is used to provide a complete description of the numerical wave propagation for the discretised equations. In the $f$-plane case, this decomposition is used to obtain decoupled equations for the geostrophic modes, the inertia-gravity modes, and the inertial oscillations. As has been noticed previously, the geostrophic modes are steady. The Helmholtz decomposition is used to show that the resulting inertia-gravity wave equation is third-order accurate in space. In general the \pdgp finite element pair is second-order accurate, so this leads to very accurate wave propagation. It is further shown that the only spurious modes supported by this discretisation are spurious inertial oscillations which have frequency $f$, and which do not propagate. The Helmholtz decomposition also allows a simple derivation of the quasi-geostrophic limit of the discretised $P1_{DG}$-$P2$ equations in the $\beta$-plane case, resulting in a Rossby wave equation which is also third-order accurate.Comment: Revised version prior to final journal submissio

The atomic structure of large-angle grain boundaries Σ5\Sigma 5 and Σ13\Sigma 13 in YBa2Cu3O7−δ{\rm YBa_2Cu_3O_{7-\delta}} and their transport properties

We present the results of a computer simulation of the atomic structures of large-angle symmetrical tilt grain boundaries (GBs) $\Sigma 5$ (misorientation angles \q{36.87}{^{\circ}} and \q{53.13}{^{\circ}}), $\Sigma 13$ (misorientation angles \q{22.62}{^{\circ}} and \q{67.38}{^{\circ}}). The critical strain level $\epsilon_{crit}$ criterion (phenomenological criterion) of Chisholm and Pennycook is applied to the computer simulation data to estimate the thickness of the nonsuperconducting layer ${\rm h_n}$ enveloping the grain boundaries. The ${\rm h_n}$ is estimated also by a bond-valence-sum analysis. We propose that the phenomenological criterion is caused by the change of the bond lengths and valence of atoms in the GB structure on the atomic level. The macro- and micro- approaches become consistent if the $\epsilon_{crit}$ is greater than in earlier papers. It is predicted that the symmetrical tilt GB $\Sigma5$ \theta = \q{53.13}{^{\circ}} should demonstrate a largest critical current across the boundary.Comment: 10 pages, 2 figure

Relaxation volumes of microscopic and mesoscopic irradiation-induced defects in tungsten

The low-energy structures of irradiation-induced defects in materials have been studied extensively over several decades, as these determine the available modes by which a defect can diffuse or relax, and how the microstructure of an irradiated material evolves as a function of temperature and time. Consequently, many studies concern the relative energies of possible defect structures, and empirical potentials are commonly fitted to or evaluated with respect to these. But recently [S. L. Dudarev et al., Nucl. Fusion 58, 126002 (2018)], we have shown that other parameters of defects not directly related to defect energies, namely, their elastic dipole tensors and relaxation volumes, determine the stresses, strains, and swelling of reactor components under irradiation. These elastic properties of defects have received comparatively little attention. In this study, we compute relaxation volumes of irradiation-induced defects in tungsten using empirical potentials and compare to density functional theory results. Different empirical potentials give different results, but some clear potential-independent trends can be identified. We show that the relaxation volume of a small defect cluster can be predicted to within 10% from its point-defect count. For larger defect clusters, we provide empirical fits as a function of defect cluster size. We demonstrate that the relaxation volume associated with a single primary-damage cascade can be estimated from the primary knock-on atom energy. We conclude that while annihilation of defects invariably reduces the total relaxation volume of the cascade debris, there is still no conclusive verdict about whether coalescence of defects reduces or increases the total relaxation volume. Published under license by AIP Publishing.Peer reviewe