Optimal boundary geometry in an elasticity problem: a systematic adjoint approach

p. 509-524In different problems of Elasticity the definition of the optimal geometry of the boundary, according to a given objective function, is an issue of great interest. Finding the shape of a hole in the middle of a plate subjected to an arbitrary loading such that the stresses along the hole minimizes some functional or the optimal middle curved concrete vault for a tunnel along which a uniform minimum compression are two typical examples. In these two examples the objective functional depends on the geometry of the boundary that can be either a curve (in case of 2D problems) or a surface boundary (in 3D problems). Typically, optimization is achieved by means of an iterative process which requires the computation of gradients of the objective function with respect to design variables. Gradients can by computed in a variety of ways, although adjoint methods either continuous or discrete ones are the more efficient ones when they are applied in different technical branches. In this paper the adjoint continuous method is introduced in a systematic way to this type of problems and an illustrative simple example, namely the finding of an optimal shape tunnel vault immersed in a linearly elastic terrain, is presented.Garcia-Palacios, J.; Castro, C.; Samartin, A. (2009). Optimal boundary geometry in an elasticity problem: a systematic adjoint approach. Editorial Universitat Politècnica de València. http://hdl.handle.net/10251/654

Kagome KMn3_3Sb5_5 metal: Magnetism, lattice dynamics, and anomalous Hall conductivity

Kagome metals are reported to exhibit remarkable properties, including superconductivity, charge density wave order, and a large anomalous Hall conductivity, which facilitate the implementation of spintronic devices. In this work, we study a novel kagome metal based on Mn magnetic sites in a KMn$_3$Sb$_5$ stoichiometry. By means of first-principles density functional theory calculations, we demonstrate that the studied compound is dynamically stable, locking the ferromagnetic order as the ground state configuration, thus preventing the charge-density-wave state as reported in its vanadium-based counterpart KV$_3$Sb$_5$. Our calculations predict that KMn$_3$Sb$_5$ exhibits an out-of-plane (001) ferromagnetic response as the ground state, allowing for the emergence of topologically protected Weyl nodes near the Fermi level and nonzero anomalous Hall conductivity ($\sigma_{ij}$) in this centrosymmetric system. We obtain a tangible $\sigma_{xy} = 314$ S$\cdot$cm$^{-1}$ component, which is comparable to that of other kagome metals. Finally, we explore the effect of the on-site Coulomb repulsion ($+U$) on the structural and electronic properties and find that, although the lattice parameters and $\sigma_{xy}$ moderately vary with increasing $+U$, KMn$_3$Sb$_5$ stands as an ideal stable ferromagnetic kagome metal with a large anomalous Hall conductivity response

Further ALMA observations and detailed modeling of the Red Rectangle

We present new high-quality ALMA observations of the Red Rectangle (a well known post-AGB object) in C17O J=6-5 and H13CN J=4-3 line emission and results from a new reduction of already published 13CO J=3-2 data. A detailed model fitting of all the molecular line data, including previous maps and single-dish spectra, was performed using a sophisticated code. These observations and the corresponding modeling allowed us to deepen the analysis of the nebular properties. We also stress the uncertainties in the model fitting. We confirm the presence of a rotating equatorial disk and an outflow, which is mainly formed of gas leaving the disk. The mass of the disk is ~ 0.01 Mo, and that of the CO-rich outflow is ~ 10 times smaller. High temperatures of ~ 100 K are derived for most components. From comparison of the mass values, we roughly estimate the lifetime of the rotating disk, which is found to be of about 10000 yr. Taking data of a few other post-AGB composite nebulae into account, we find that the lifetimes of disks around post-AGB stars typically range between 5000 and more than 20000 yr. The angular momentum of the disk is found to be high, ~ 9 Mo AU km/s, which is comparable to that of the stellar system at present. Our observations of H13CN show a particularly wide velocity dispersion and indicate that this molecule is only abundant in the inner Keplerian disk, at ~ 60 AU from the stellar system. We suggest that HCN is formed in a dense photodissociation region (PDR) due to the UV excess known to be produced by the stellar system, following chemical mechanisms that are well established for interstellar medium PDRs and disks orbiting young stars. We further suggest that this UV excess could lead to the efficient formation and excitation of PAHs and other C-bearing macromolecules, whose emission is very intense in the optical counterpart.Comment: Astronomy & Astrohysics, in press; 17 pages, 18 figures, 1 tabl

Geometric ferroelectricity in fluoroperovskites

We used first-principles calculations to investigate the existence and origin of the ferroelectric in- stability in the ABF3 fluoro-perovskites. We find that many fluoro-perovskites have a ferroelectric instability in their high symmetry cubic structure, which is of similar amplitude to that commonly found in oxide perovskites. In contrast to the oxides, however, the fluorides have nominal Born effective charges, indicating a different mechanism for the instability. We show that the instability originates from ionic size effects, and is therefore in most cases largely insensitive to pressure and strain, again in contrast to the oxide perovskites. An exception is NaMnF3, where coherent epitaxial strain matching to a substrate with equal in-plane lattice constants destabilizes the bulk Pnma structure leading to a ferroelectric, and indeed multiferroic, ground state with an unusual polarization/strain response

ALMA observations of the Red Rectangle, a preliminary analysis

We aim to study equatorial disks in rotation and axial outflows in post-AGB objects, as to disclose the formation and shaping mechanisms in planetary nebulae. So far, both disks and outflows had not been observed simultaneously. We have obtained high-quality ALMA observations of 12CO and 13CO J=3-2 and 12CO J=6-5 line emission in the Red Rectangle, the only post-AGB/protoplanetary object in which a disk in rotation has been mapped up to date. These observations provide an unprecedented description of the complex structure of this source. Together with an equatorial disk in rotation, we find a low-velocity outflow that occupies more or less the region placed between the disk and the optical X-shaped nebula. From our observations and preliminary modeling of the data, we confirm the previously known properties of the disk and obtain a first description of the structure, dynamics, and physical conditions of the outflow.Comment: 5 pages, 5 figure