Reconstructing the conformal mode in simplicial gravity

We verify that summing 2D DT geometries correctly reproduces the Polyakov action for the conformal mode, including all ghost contributions, at large volumes. The Gaussian action is reproduced even for central charges greater than one lending strong support to the hypothesis that the space of all possible dyamical triangulations approximates well the space of physically distinct metrics independent of the precise nature of the matter coupling.Comment: 3 pages, 4 figures, contribution to Lattice 9

Distributed Partial Differential Equation Solving with Julia Fast Fourier Transform Library

Scientific computing relies on advanced computational and mathematical techniques to solve complex problems in scientific domains. For the numerical rendering of spectral, nonlinear, and dynamic phenomena, there is a growing need for greater availability of a broad class of Fourier-based algorithms to perform large scale operations on multidimensional data in distributed and optimized ways. To this effect, the Julia programming language is new and has significant advantages compared to other common languages used in scientific computing. The research presented here formulates a basis for further development in high-performance scientific computing of periodic partial differential equations through the application of distributed Fast Fourier Transforms in Julia with the PencilFFTs.jl library

de Sitter Vacua, Renormalization and Locality

We analyze the renormalization properties of quantum field theories in de Sitter space and show that only two of the maximally invariant vacuum states of free fields lead to consistent perturbation expansions. One is the Euclidean vacuum, and the other can be viewed as an analytic continuation of Euclidean functional integrals on $RP^d$. The corresponding Lorentzian manifold is the future half of global de Sitter space with boundary conditions on fields at the origin of time. We argue that the perturbation series in this case has divergences at the origin, which render the future evolution of the system indeterminate without a better understanding of high energy physics.Comment: JHEP Latex, 13 pages, v2. references adde

Condensates and quasiparticles in inflationary cosmology: mass generation and decay widths

During de Sitter inflation massless particles of minimally coupled scalar fields acquire a mass and a decay width thereby becoming \emph{quasiparticles}. For bare massless particles non-perturbative infrared radiative corrections lead to a self-consistent generation of mass, for a quartic self interaction $M \propto \lambda^{1/4} H$, and for a cubic self-interaction the mass is induced by the formation of a non-perturbative \emph{condensate} leading to $M \propto \lambda^{1/3} H^{2/3}$. These radiatively generated masses restore de Sitter invariance and result in anomalous scaling dimensions of superhorizon fluctuations. We introduce a generalization of the non-perturbative Wigner-Weisskopf method to obtain the time evolution of quantum states that include the self-consistent generation of mass and regulate the infrared behavior. The infrared divergences are manifest as poles in $\Delta=M^2/3H^2$ in the single particle self-energies, leading to a re-arrangement of the perturbative series non-analytic in the couplings. A set of simple rules that yield the leading order infrared contributions to the decay width are obtained and implemented. The lack of kinematic thresholds entail that all particle states acquire a decay width, dominated by the emission and absorption of superhorizon quanta $\propto (\lambda/H)^{4/3}\,[H/k_{ph}(\eta)]^6 ; \lambda\,[H/k_{ph}(\eta)]^6$ for cubic and quartic couplings respectively to leading order in $M/H$. The decay of single particle quantum states hastens as their wavevectors cross the Hubble radius and their width is related to the highly squeezed limit of the bi- or tri-spectrum of scalar fluctuations respectively.Comment: 31 pages, 7 figures. Comments and references, matches published versio

A Probabilistic Approach for the Optimal Sizing of Storage Devices to Increase the Penetration of Plug-in Electric Vehicles in Direct Current Networks

The growing diffusion of electric vehicles connected to distribution networks for charging purposes is an ongoing problem that utilities must deal with. Direct current networks and storage devices have emerged as a feasible means of satisfying the expected increases in the numbers of vehicles while preserving the effective operation of the network. In this paper, an innovative probabilistic methodology is proposed for the optimal sizing of electrical storage devices with the aim of maximizing the penetration of plug-in electric vehicles while preserving efficient and effective operation of the network. The proposed methodology is based on an analytical solution of the problem concerning the power losses minimization in distribution networks equipped with storage devices. The closed-form expression that was obtained is included in a Monte Carlo simulation procedure aimed at handling the uncertainties in loads and renewable generation units. The results of several numerical applications are reported and discussed to demonstrate the validity of the proposed solution. Also, different penetration levels of generation units were analyzed in order to focus on the importance of renewable generation