On shape dependence of holographic entanglement entropy in AdS4/CFT3

We study the finite term of the holographic entanglement entropy of finite domains with smooth shapes and for four dimensional gravitational backgrounds. Analytic expressions depending on the unit vectors normal to the minimal area surface are obtained for both stationary and time dependent spacetimes. The special cases of AdS4, asymptotically AdS4 black holes, domain wall geometries and Vaidya-AdS backgrounds have been analysed explicitly. When the bulk spacetime is AdS4, the finite term is the Willmore energy of the minimal area surface viewed as a submanifold of the three dimensional flat Euclidean space. For the static spacetimes, some numerical checks involving spatial regions delimited by ellipses and non convex domains have been performed. In the case of AdS4, the infinite wedge has been also considered, recovering the known analytic formula for the coefficient of the logarithmic divergence

Corner contributions to holographic entanglement entropy in AdS4/BCFT3

We study the holographic entanglement entropy of spatial regions with corners in the AdS4/BCFT3correspondence by considering three dimensional boundary conformal field theories whose boundary is a timelike plane. We compute analytically the corner function corresponding to an infinite wedge having one edge on the boundary. A relation between this corner function and the holographic one point function of the stress tensor is observed. An analytic expression for the corner function of an infinite wedge having only its tip on the boundary is also provided. This formula requires to find the global minimum among two extrema of the area functional. The corresponding critical configurations of corners are studied. The results have been checked against a numerical analysis performed by computing the area of the minimal surfaces anchored to some finite domains containing corners

Holographic entanglement entropy in AdS4/BCFT3 and the Willmore functional

We study the holographic entanglement entropy of spatial regions having arbitrary shapes in the AdS4/BCFT3 correspondence with static gravitational backgrounds, focusing on the subleading term with respect to the area law term in its expansion as the UV cutoff vanishes. An analytic expression depending on the unit vector normal to the minimal area surface anchored to the entangling curve is obtained. When the bulk spacetime is a part of AdS4, this formula becomes the Willmore functional with a proper boundary term evaluated on the minimal surface viewed as a submanifold of a three dimensional flat Euclidean space with boundary. For some smooth domains, the analytic expressions of the finite term are reproduced, including the case of a disk disjoint from a boundary which is either flat or circular. When the spatial region contains corners adjacent to the boundary, the subleading term is a logarithmic divergence whose coefficient is determined by a corner function that is known analytically, and this result is also recovered. A numerical approach is employed to construct extremal surfaces anchored to entangling curves with arbitrary shapes. This analysis is used both to check some analytic results and to find numerically the finite term of the holographic entanglement entropy for some ellipses at finite distance from a flat boundary

On shape dependence of holographic mutual information in AdS4

We study the holographic mutual information in AdS(4) of disjoint spatial domains in the boundary which are delimited by smooth closed curves. A numerical method which approximates a local minimum of the area functional through triangulated surfaces is employed. After some checks of the method against existing analytic results for the holographic entanglement entropy, we compute the holographic mutual information of equal domains delimited by ellipses, superellipses or the boundaries of two dimensional spherocylinders, finding also the corresponding transition curves along which the holographic mutual information vanishes

Modeling the interactions between river morphodynamics and riparian vegetation

The study of river-riparian vegetation interactions is an important and intriguing research field in geophysics. Vegetation is an active element of the ecological dynamics of a floodplain which interacts with the fluvial processes and affects the flow field, sediment transport, and the morphology of the river. In turn, the river provides water, sediments, nutrients, and seeds to the nearby riparian vegetation, depending on the hydrological, hydraulic, and geomorphological characteristic of the stream. In the past, the study of this complex theme was approached in two different ways. On the one hand, the subject was faced from a mainly qualitative point of view by ecologists and biogeographers. Riparian vegetation dynamics and its spatial patterns have been described and demonstrated in detail, and the key role of several fluvial processes has been shown, but no mathematical models have been proposed. On the other hand, the quantitative approach to fluvial processes, which is typical of engineers, has led to the development of several morphodynamic models. However, the biological aspect has usually been neglected, and vegetation has only been considered as a static element. In recent years, different scientific communities (ranging from ecologists to biogeographers and from geomorphologists to hydrologists and fluvial engineers) have begun to collaborate and have proposed both semiquantitative and quantitative models of river-vegetation interconnections. These models demonstrate the importance of linking fluvial morphodynamics and riparian vegetation dynamics to understand the key processes that regulate a riparian environment in order to foresee the impact of anthropogenic actions and to carefully manage and rehabilitate riparian areas. In the first part of this work, we review the main interactions between rivers and riparian vegetation, and their possible modeling. In the second part, we discuss the semiquantitative and quantitative models which have been proposed to date, considering both multi- and single-thread river

Evolution of microstructure and crystallographic texture during dissimilar friction stir welding of duplex stainless steel to low carbon-manganese structural steel

Electron backscattered diffraction (EBSD) was used to analyze the evolution of microstructure and crystallographic texture during friction stir welding of dissimilar type 2205 duplex stainless steel (DSS) to type S275 low carbon-manganese structural steel. The results of microstructural analyses show that the temperature in the center of stirred zone reached temperatures between Ac 1 and Ac 3 during welding, resulting in a minor ferrite-to-austenite phase transformation in the S275 steel, and no changes in the fractions of ferrite and austenite in the DSS. Temperatures in the thermomechanically affected and shoulder-affected zones of both materials, in particular toward the root of the weld, did not exceed the Ac 1 of S275 steel. The shear generated by the friction between the material and the rotating probe occurred in austenitic/ferritic phase field of the S275 and DSS. In the former, the transformed austenite regions of the microstructure were transformed to acicular ferrite, on cooling, while the dual-phase austenitic/ferritic structure of the latter was retained. Studying the development of crystallographic textures with regard to shear flow lines generated by the probe tool showed the dominance of simple shear components across the whole weld in both materials. The ferrite texture in S275 steel was dominated by D 1, D 2, E, E¯ , and F, where the fraction of acicular ferrite formed on cooling showed a negligible deviation from the texture for the ideal shear texture components of bcc metals. The ferrite texture in DSS was dominated by D 1, D 2, I, I¯ , and F, and that of austenite was dominated by the A, A¯ , B, and B¯ of the ideal shear texture components for bcc and fcc metals, respectively. While D 1, D 2, and F components of the ideal shear texture are common between the ferrite in S275 steel and that of dual-phase DSS, the preferential partitioning of strain into the ferrite phase of DSS led to the development of I and I¯ components in DSS, as opposed to E and E¯ in the S275 steel. The formations of fine and ultrafine equiaxed grains were observed in different regions of both materials that are believed to be due to strain-induced continuous dynamic recrystallization (CDRX) in ferrite of both DSS and S275 steel, and discontinuous dynamic recrystallization (DDRX) in austenite phase of DSS