Area terms in entanglement entropy

We discuss area terms in entanglement entropy and show that a recent formula by Rosenhaus and Smolkin is equivalent to the term involving a correlator of traces of the stress tensor in Adler-Zee formula for the renormalization of the Newton constant. We elaborate on how to fix the ambiguities in these formulas: Improving terms for the stress tensor of free fields, boundary terms in the modular Hamiltonian, and contact terms in the Euclidean correlation functions. We make computations for free fields and show how to apply these calculations to understand some results for interacting theories which have been studied in the literature. We also discuss an application to the F-theorem.Comment: 26 pages, no figures, references adde

Multi-line Stokes inversion for prominence magnetic-field diagnostics

We present test results on the simultaneous inversion of the Stokes profiles of the He I lines at 587.6 nm (D_3) and 1083.0 nm in prominences (90-deg scattering). We created datasets of synthetic Stokes profiles for the case of quiescent prominences (B<200 G), assuming a conservative value of 10^-3 of the peak intensity for the polarimetric sensitivity of the simulated observations. In this work, we focus on the error analysis for the inference of the magnetic field vector, under the usual assumption that the prominence can be assimilated to a slab of finite optical thickness with uniform magnetic and thermodynamic properties. We find that the simultaneous inversion of the two lines significantly reduces the errors on the inference of the magnetic field vector, with respect to the case of single-line inversion. These results provide a solid justification for current and future instrumental efforts with multi-line capabilities for the observations of solar prominences and filaments.Comment: 14 pages, 5 figures, 1 tabl

Deformation induced by wetting: a simple model

This paper presents a simple model for predicting the deformation induced by wetting. The objective is to quantify the deformation induced by saturation of an unsaturated layer of homogeneous soil, causing variation of the initial void ratio and gravimetric water content. The soil is a low-plasticity silty sand. A simple expression for the normal compression line (NCL), which depends on the parameter χ and one more parameter, will be proposed. The model may capture the progressive degradation induced by loading and wetting by linking the dependency of NCL by the parameter χ and water retention curve by porosity

Effects of partial saturation on the behaviour of a compacted silt

The effects of partial saturation on the behaviour of a compacted silt was investigated. In the first part of the work the compatibility of the experimental data carried out at Università di Napoli Federico II to investigate the effects of partial saturation on the volumetric behaviour and on the initial shear stiffness of a compacted silt with a Bishop Stress Modeln (BSM) were discussed. In the second part of the work the results of a centrifuge model of a shallow foundation relying of a layer of unsaturated soil and submitted to axial load for different water level were discussed. The tested material is an eolian silt from Jossigny, East of Paris. This work was done with the support of MUSE network. The objective of the work was to represent a foundation of 1.5 m in diameter on a 15 m soil layer

Optimizing the computation of overriding

We introduce optimization techniques for reasoning in DLN---a recently introduced family of nonmonotonic description logics whose characterizing features appear well-suited to model the applicative examples naturally arising in biomedical domains and semantic web access control policies. Such optimizations are validated experimentally on large KBs with more than 30K axioms. Speedups exceed 1 order of magnitude. For the first time, response times compatible with real-time reasoning are obtained with nonmonotonic KBs of this size

Positivity, entanglement entropy, and minimal surfaces

The path integral representation for the Renyi entanglement entropies of integer index n implies these information measures define operator correlation functions in QFT. We analyze whether the limit $n\rightarrow 1$, corresponding to the entanglement entropy, can also be represented in terms of a path integral with insertions on the region's boundary, at first order in $n-1$. This conjecture has been used in the literature in several occasions, and specially in an attempt to prove the Ryu-Takayanagi holographic entanglement entropy formula. We show it leads to conditional positivity of the entropy correlation matrices, which is equivalent to an infinite series of polynomial inequalities for the entropies in QFT or the areas of minimal surfaces representing the entanglement entropy in the AdS-CFT context. We check these inequalities in several examples. No counterexample is found in the few known exact results for the entanglement entropy in QFT. The inequalities are also remarkable satisfied for several classes of minimal surfaces but we find counterexamples corresponding to more complicated geometries. We develop some analytic tools to test the inequalities, and as a byproduct, we show that positivity for the correlation functions is a local property when supplemented with analyticity. We also review general aspects of positivity for large N theories and Wilson loops in AdS-CFT.Comment: 36 pages, 10 figures. Changes in presentation and discussion of Wilson loops. Conclusions regarding entanglement entropy unchange

A procedure for the direct determination of Bishop's chi parameter from changes in pore size distribution

Permission is granted by ICE Publishing to print one copy for personal use. Any other use of these PDF files is subject to reprint fees.Most of the recent works relating to the concept of effective stress in unsaturated soils focus on the proposal by Bishop, and, more particularly, on the search for suitable relationships between Bishop's ¿ parameter and the main controlling variables. These relationships are generally formulated by theoretical derivations and back-analyses of the dependency of mechanical parameters on hydraulic variables such as suction or saturation. In this note, a new procedure is proposed to evaluate directly, and without any a priori assumptions, values for Bishop's ¿ parameter. In the first part, a general derivation based on the definition of work conjugated variables allows the ¿ parameter to be defined as the ratio of the change of water volume over the change in pore volume during a process at constant suction. This definition is further exploited to evaluate Bishop's parameter from the changes suffered by material pore size distribution during loading. The method is applied to data obtained by mercury intrusion porosimetry tests on low-plasticity silt (Jossigny silt), low-plasticity sandy clay (lean clay) and highly plastic clay (Febex clay). Values obtained for these materials show that the ¿ parameter is close to the effective degree of saturation rather than the total degree of saturation.Peer ReviewedPostprint (published version

Undrained loading and collapse of unsaturated soils during centrifuge testing. An experimental and numerical study

The paper presents the results of a centrifuge model of a shallow foundation relying of a layer of unsaturated soil and submitted to axial load for different water level. The objective of the work was to represent a foundation of 1.5 m in diameter on a 15 m soil layer. The model of foundation was a circular disk of 30 mm in diameter and the layer was a cylindrical container of 300 mm in diameter and height. In order to maintain similitude between prototype and model the tests were carried out at 50g. The tests were carried out at the LCPC facilities in Nantes (France). The tested material is an eolian silt from Jossigny, East of Paris. In order to decide the initial conditions of the model in terms of water content and void ratio it was performed a preliminary laboratory investigations. As the intention of the study was to examine the behaviour of a collapsible soil therefore it was decided to prepare the model with a low dry density (14.5 kN/m3 ). The evolution of pore water pressure during the tests are compared with the numerical simulation of the prototype with code brig

The Hydromechanical Interplay in the Simplified Three-Dimensional Limit Equilibrium Analyses of Unsaturated Slope Stability

This paper presents a three-dimensional slope stability limit equilibrium solution for translational planar failure modes. The proposed solution uses Bishop's average skeleton stress combined with the Mohr-Coulomb failure criterion to describe soil strength evolution under unsaturated conditions while its formulation ensures a natural and smooth transition from the unsaturated to the saturated regime and vice versa. The proposed analytical solution is evaluated by comparing its predictions with the results of the Ruedlingen slope failure experiment. The comparison suggests that, despite its relative simplicity, the analytical solution can capture the experimentally observed behaviour well and highlights the importance of considering lateral resistance together with a realistic interplay between mechanical parameters (cohesion) and hydraulic (pore water pressure) conditions

On reduced density matrices for disjoint subsystems

We show that spin and fermion representations for solvable quantum chains lead in general to different reduced density matrices if the subsystem is not singly connected. We study the effect for two sites in XX and XY chains as well as for sublattices in XX and transverse Ising chains.Comment: 10 pages, 4 figure