Holographic Entanglement Entropy for General Higher Derivative Gravity

We propose a general formula for calculating the entanglement entropy in theories dual to higher derivative gravity where the Lagrangian is a contraction of Riemann tensors. Our formula consists of Wald's formula for the black hole entropy, as well as corrections involving the extrinsic curvature. We derive these corrections by noting that they arise from naively higher order contributions to the action which are enhanced due to would-be logarithmic divergences. Our formula reproduces the Jacobson-Myers entropy in the context of Lovelock gravity, and agrees with existing results for general four-derivative gravity. We emphasize that the formula should be evaluated on a particular bulk surface whose location can in principle be determined by solving the equations of motion with conical boundary conditions. This may be difficult in practice, and an alternative method is desirable. A natural prescription is simply minimizing our formula, analogous to the Ryu-Takayanagi prescription for Einstein gravity. We show that this is correct in several examples including Lovelock and general four-derivative gravity.Comment: 1+35 pages, 2 figures; v2: typos fixed, references added, and other improvements; v3: corrected a previous omission in counting, other clarifications; v4: minor clarifications, references added, published versio

J2EE application for clustered servers : focus on balancing workloads among clustered servers : a thesis presented in partial fulfilment of the requirements for the degree of Master of Information Science in Computer Science at Massey University, Albany, New Zealand

J2EE has become a de facto platform for developing enterprise applications not only by its standard based methodology but also by reducing the cost and complexity of developing multi-tier enterprise applications. J2EE based application servers keep business logic separate from the front-end applications (client-side) and back-end database servers. The standardized components and containers simplify J2EE application design. The containers automatically manage the fundamental system level services for its components, which enable the components design to focus on the business requirement and business logic. This study applies the latest J2EE technologies to configure an online benchmark enterprise application - MG Project. The application focuses on three types of components design including Servlet, entity bean and session bean. Servlets run on the web server Tomcat, EJB components, session beans and entity beans run on the application server JBoss and the database runs on the database server Postgre SQL. This benchmark application is used for testing the performance of clustered JBoss due to various load-balancing policies applied at the EJB level. This research also focuses on studying the various load-balancing policies effect on the performance of clustered JBoss. As well as the four built-in load-balancing policies i.e. First Available, First Available Identical All Proxies, Random Robin and Round Robin, the study also extend the JBoss Load balance Policy interface to design two dynamic load-balancing policies. They are dynamic and dynamic weight-based load-balancing policies. The purpose of dynamic load-balancing policies design is to ensure minimal response time and obtain better performance by dispatching incoming requests to the appropriate server. However, a more accurate policy usually means more communications and calculations, which give an extra burden to a heavily loaded application server that can lead to drops in the performance

Resolving the problem of galaxy clustering on small scales: any new physics needed?

Galaxy clustering sets strong constraints on the physics governing galaxy formation and evolution. However, most current models fail to reproduce the clustering of low-mass galaxies on small scales ($r<1Mpc/h$). In this paper we study the galaxy clusterings predicted from a few semi-analytical models. We firstly compare two Munich versions, Guo et al. (2011, Guo11) and De Lucia \& Blazoit (2007, DLB07). The Guo11 model well reproduces the galaxy stellar mass function, but over-predicts the clustering of low-mass galaxies on small scales. The DLB07 model provides a better fit to the clustering on small scales, but over-predicts the stellar mass function. These seem to be puzzling. We find that there is slightly more fraction of satellite galaxies residing in massive haloes in the Guo11 model, which is the dominant contribution to the clustering discrepancy between the two models. However, both models still over-predict the clustering at $0.1Mpc/h<r<10Mpc/h$ for low mass galaxies. This is because both models over-predict the number of satellites by $30\%$ in massive halos than the data. Actually, the better agreement of DLB07 model with the data on small scales comes as a coincidence as it predicts too many low-mass central galaxies which are less clustered and thus bring down the total clustering. Finally, we show the predictions from the semi-analytical of Kang et al. (2012). We find that this model can simultaneously fit the stellar mass function and galaxy clustering if the supernova feedback in satellite galaxies is stronger. We conclude that semi-analytical models are now able to solve the small-scales clustering problem, without invoking of any other new physics or changing the dark matter properties, such as the recent favored warm dark matter.Comment: 12 pages, 8 figures. Accepted for publication in MNRA