Spectral dimension in graph models of causal quantum gravity

The phenomenon of scale dependent spectral dimension has attracted special interest in the quantum gravity community over the last eight years. It was first observed in computer simulations of the causal dynamical triangulation (CDT) approach to quantum gravity and refers to the reduction of the spectral dimension from 4 at classical scales to 2 at short distances. Thereafter several authors confirmed a similar result from different approaches to quantum gravity. Despite the contribution from different approaches, no analytical model was proposed to explain the numerical results as the continuum limit of CDT. In this thesis we introduce graph ensembles as toy models of CDT and show that both the continuum limit and a scale dependent spectral dimension can be defined rigorously. First we focus on a simple graph ensemble, the random comb. It does not have any dynamics from the gravity point of view, but serves as an instructive toy model to introduce the characteristic scale of the graph, study the continuum limit and define the scale dependent spectral dimension. Having defined the continuum limit, we study the reduction of the spectral dimension on more realistic toy models, the multigraph ensembles, which serve as a radial approximation of CDT. We focus on the (recurrent) multigraph approximation of the two-dimensional CDT whose ensemble measure is analytically controlled. The latter comes from the critical Galton-Watson process conditioned on non-extinction. Next we turn our attention to transient multigraph ensembles, corresponding to higher-dimensional CDT. Firstly we study their fractal properties and secondly calculate the scale dependent spectral dimension and compare it to computer simulations. We comment further on the relation between Horava-Lifshitz gravity, asymptotic safety, multifractional spacetimes and CDT-like models.Comment: DPhil (Phd) thesis (2013), University of Oxford, 145 pages, 18 figures, new results/analysis on 2+1 model, comments are welcom

VI Workshop on Computational Data Analysis and Numerical Methods: Book of Abstracts

The VI Workshop on Computational Data Analysis and Numerical Methods (WCDANM) is going to be held on June 27-29, 2019, in the Department of Mathematics of the University of Beira Interior (UBI), Covilhã, Portugal and it is a unique opportunity to disseminate scientific research related to the areas of Mathematics in general, with particular relevance to the areas of Computational Data Analysis and Numerical Methods in theoretical and/or practical field, using new techniques, giving especial emphasis to applications in Medicine, Biology, Biotechnology, Engineering, Industry, Environmental Sciences, Finance, Insurance, Management and Administration. The meeting will provide a forum for discussion and debate of ideas with interest to the scientific community in general. With this meeting new scientific collaborations among colleagues, namely new collaborations in Masters and PhD projects are expected. The event is open to the entire scientific community (with or without communication/poster)

PREDICTING INTERNET TRAFFIC BURSTS USING EXTREME VALUE THEORY

Computer networks play an important role in today’s organization and people life. These interconnected devices share a common medium and they tend to compete for it. Quality of Service (QoS) comes into play as to define what level of services users get. Accurately defining the QoS metrics is thus important. Bursts and serious deteriorations are omnipresent in Internet and considered as an important aspects of it. This thesis examines bursts and serious deteriorations in Internet traffic and applies Extreme Value Theory (EVT) to their prediction and modelling. EVT itself is a field of statistics that has been in application in fields like hydrology and finance, with only a recent introduction to the field of telecommunications. Model fitting is based on real traces from Belcore laboratory along with some simulated traces based on fractional Gaussian noise and linear fractional alpha stable motion. QoS traces from University of Napoli are also used in the prediction stage. Three methods from EVT are successfully used for the bursts prediction problem. They are Block Maxima (BM) method, Peaks Over Threshold (POT) method, and RLargest Order Statistics (RLOS) method. Bursts in internet traffic are predicted using the above three methods. A clear methodology was developed for the bursts prediction problem. New metrics for QoS are suggested based on Return Level and Return Period. Thus, robust QoS metrics can be defined. In turn, a superior QoS will be obtained that would support mission critical applications

Analysis of Wake Vortices of a Medium Range Twin-Propeller Military Cargo Aircraft Using Statistically Designed Experiments

An experimental study was initiated to analyze the trajectories of the streamwise vortices behind the wing tip and flap of a medium range and propeller driven twin-engine military cargo aircraft. The model used for the experimental study was a generic, high wing and half model of a propeller driven aircraft and mounted within Old Dominion University\u27s Low Speed Wind Tunnel where the wind tunnel flow speed was set to constant value of 9 m/sec. The main purpose of the study was to reach regression models for the motion and vorticity strength of both vortices under varying factors such as angle of attack, flap angle, propeller pitch angle and downstream distance. Velocity measurements of the flow fields were accomplished using both Particle Image Velocimetry (PIV) and Hotwire Anemometry (HWA) to yield average velocities, turbulence levels, vorticity strengths and Reynolds shear stresses in the wake of the model. The results of measurements showed that the vertical motions, horizontal motions, and vorticity strengths of both vortices as well as the shortest distance between both vortices depend on the aforementioned factors and the interactions of some factors. It can be concluded that propeller pitch angle mainly affects the behaviors of the vortices as much as angle of attack to the extent that their second order terms take place in some of the regression models

AFIT School of Engineering Contributions to Air Force Research and Technology. Calendar Year 1972

This report contains abstracts of Master of Science Theses, Doctoral Dissertations, and faculty publications completed during the 1972 calendar year at the School of Engineering, Air Force Institute of Technology, at Wright-Patterson Air Force Base, Ohio