Entanglement entropy from the holographic stress tensor

We consider entanglement entropy in the context of gauge/gravity duality for conformal field theories in even dimensions. The holographic prescription due to Ryu and Takayanagi (RT) leads to an equation describing how the entangling surface extends into the bulk geometry. We show that setting to zero, the timetime component of the Brown-York stress tensor evaluated on the co-dimension 1 entangling surface, leads to the same equation. By considering a spherical entangling surface as an example, we observe that the Euclidean actionmethods in AdS/CFT will lead to the RT area functional arising as a counterterm needed to regularize the stress tensor. We present arguments leading to a justification for the minimal area prescription.

Holographic stress tensor at finite coupling

We calculate one, two and three point functions of the holographic stress tensor for any bulk Lagrangian of the form L (g(ab), R-abcd, del(e) R-abcd). Using the first law of entanglement, a simple method has recently been proposed to compute the holographic stress tensor arising from a higher derivative gravity dual. The stress tensor is proportional to a dimension dependent factor which depends on the higher derivative couplings. In this paper, we identify this proportionality constant with a B-type trace anomaly in even dimensions for any bulk Lagrangian of the above form. This in turn relates to C-T, the coefficient appearing in the two point function of stress tensors. We use a background field method to compute the two and three point function of stress tensors for any bulk Lagrangian of the above form in arbitrary dimensions. As an application we consider general situations where eta/s for holographic plasmas is less than the KSS bound.

Approximation of Spatio-Temporal Random Processes Using Tensor Decomposition

A new representation of spatio-temporal random processes is proposed in this work. In practical applications, such processes are used to model velocity fields, temperature distributions, response of vibrating systems, to name a few. Finding an efficient representation for any random process leads to encapsulation of information which makes it more convenient for a practical implementations, for instance, in a computational mechanics problem. For a single-parameter process such as spatial or temporal process, the eigenvalue decomposition of the covariance matrix leads to the well-known Karhunen-Loeve (KL) decomposition. However, for multiparameter processes such as a spatio-temporal process, the covariance function itself can be defined in multiple ways. Here the process is assumed to be measured at a finite set of spatial locations and a finite number of time instants. Then the spatial covariance matrix at different time instants are considered to define the covariance of the process. This set of square, symmetric, positive semi-definite matrices is then represented as a third-order tensor. A suitable decomposition of this tensor can identify the dominant components of the process, and these components are then used to define a closed-form representation of the process. The procedure is analogous to the KL decomposition for a single-parameter process, however, the decompositions and interpretations vary significantly. The tensor decompositions are successfully applied on (i) a heat conduction problem, (ii) a vibration problem, and (iii) a covariance function taken from the literature that was fitted to model a measured wind velocity data. It is observed that the proposed representation provides an efficient approximation to some processes. Furthermore, a comparison with KL decomposition showed that the proposed method is computationally cheaper than the KL, both in terms of computer memory and execution time.

On the stability of the L-p-norm of the Riemannian curvature tensor

We consider the Riemannian functional defined on the space of Riemannian metrics with unit volume on a closed smooth manifold M where R(g) and dv (g) denote the corresponding Riemannian curvature tensor and volume form and p a (0, a). First we prove that the Riemannian metrics with non-zero constant sectional curvature are strictly stable for for certain values of p. Then we conclude that they are strict local minimizers for for those values of p. Finally generalizing this result we prove that product of space forms of same type and dimension are strict local minimizer for for certain values of p.

SOME UNSTABLE CRITICAL METRICS FOR THE L-n/2-NORM OF THE CURVATURE TENSOR

We consider the Riemannian functional defined on the space of Riemannian metrics with unit volume on a closed smooth manifold M given by R-n/2(g) := integral(M) vertical bar R(g)vertical bar(n//2) dv(g) where R(g), dv(g) denote the Riemannian curvature and volume form corresponding to g. We show that there are locally symmetric spaces which are unstable critical points for this functional.

Strain Regularity and Stiffness Tensor of Reinforcers in Dense Particle Reinforced Composites

针对高体积份数、随机分布、等轴状颗粒增强复合材料 ,研究了材料的应变分布规律 ,给出了基体和增强体应变平均值与材料微观结构参数之间的定量关系。结果表明 ,除应变平均值外 ,应变涨落是影响刚度张量的另一个重要因素 ,研究了应变涨落与材料微观结构参数之间的关系 ,并推导出了复合材料的刚度张量。与实验结果和以往的理论比较 ,预测结果与实验结果吻合良好

Moment Tensor Analysis of the Acoustic Emission Source in the Rock Damage Process

To further investigate the mechanism of acoustic emission (AE) in the rock fracture experiment, moment tensor analysis was carried out. The AE sources characterized by crack sizes, orientations and fracture modes, are represented by a time-dependent momen

Diagnóstico da gestão de resíduos na construção civil comparação de obras no Rio de Janeiro visando a certificação LEED e obras sem certificação.

A implantação de práticas de gestão ambiental nos canteiros de obras se tornou de fundamental importância para o setor da construção civil. Nas obras de edificação que visam obter a certificação LEED, são implementadas práticas que buscam a minimização e o reaproveitamento dos resíduos de construção civil, representando uma possibilidade de redução dos impactos ambientais produzidos pelo setor. Este trabalho apresenta um estudo comparativo sobre a geração de resíduos de quatro obras de edificações no município do Rio de Janeiro, sendo que duas delas implantaram práticas para obtenção da certificação LEED. Complementarmente, foi realizada uma pesquisa através de questionário com profissionais da construção civil buscando identificar a sua percepção sobre construções sustentáveis e gerenciamento de resíduos sólidos. Desconsiderando o solo de escavação, o entulho foi o resíduo mais gerado em todas as quatro obras, seguido pela sucata metálica, resíduos não recicláveis e madeira. A obra com certificação LEED apresentou o menor índice total de resíduos, 119,23 kg/m2, sendo este valor próximo às médias de países desenvolvidos.

Diseño del sistema de tensor de cadena y acople de pinza de freno trasero para moto de competición.

[ES]En este documento se propone el diseño de dos sistemas imprescindibles en el tren trasero de una moto de competición, el sistema de tensor de cadena y el del acople de pinza de freno trasero. Junto a estos sistemas se diseñará, dada su relevancia, el basculante de la moto. Estos diseños se realizarán de tal manera que cumplan una serie de requisitos geométricos y de resistencia, garantizando en todo momento la estabilidad y seguridad del piloto. Se realizará también el estudio de la fabricación de cada uno de los elementos que componen los sistemas, con el fin de realizar diseños viables, que resulten económicamente factibles y mantengan un alto grado de calidad. En el proyecto se analizarán las diferentes alternativas de los sistemas que se puedan adoptar, sus ventajas y desventajas, para así poder escoger, con un alto grado de seguridad, la opción que mejor cumpla los objetivos y condiciones establecidos. Cabe destacar que este proyecto se encuentra dentro de otro de mayor envergadura consistente en el diseño y la fabricación de una motocicleta de competición para participar en el campeonato internacional llamado “MotoStudent”. Esta competición se realiza entre universidades de todo el mundo y en ella los equipos de estudiantes se enfrentan al desafío de diseñar y desarrollar un prototipo de motocicleta de competición similar a la categoría mundialista de “Moto3”.