Simplicial minisuperspace models in the presence of a massive scalar field with arbitrary scalar coupling

We extend previous simplicial minisuperspace models to account for arbitrary scalar coupling \eta R\phi^2.Comment: 24 pages and 9 figures. Accepted for publication by Classical and Quantum Gravit

Anisotropic simplicial minisuperspace model

The computation of the simplicial minisuperspace wavefunction in the case of anisotropic universes with a scalar matter field predicts the existence of a large classical Lorentzian universe like our own at late timesComment: 19 pages, Latex, 6 figure

Smoothed Analysis of Dynamic Networks

We generalize the technique of smoothed analysis to distributed algorithms in dynamic network models. Whereas standard smoothed analysis studies the impact of small random perturbations of input values on algorithm performance metrics, dynamic graph smoothed analysis studies the impact of random perturbations of the underlying changing network graph topologies. Similar to the original application of smoothed analysis, our goal is to study whether known strong lower bounds in dynamic network models are robust or fragile: do they withstand small (random) perturbations, or do such deviations push the graphs far enough from a precise pathological instance to enable much better performance? Fragile lower bounds are likely not relevant for real-world deployment, while robust lower bounds represent a true difficulty caused by dynamic behavior. We apply this technique to three standard dynamic network problems with known strong worst-case lower bounds: random walks, flooding, and aggregation. We prove that these bounds provide a spectrum of robustness when subjected to smoothing---some are extremely fragile (random walks), some are moderately fragile / robust (flooding), and some are extremely robust (aggregation).Comment: 20 page

SZ scaling relations in Galaxy Clusters: results from hydrodynamical N-body simulations

Observations with the SZ effect constitute a powerful new tool for investigating clusters and constraining cosmological parameters. Of particular interest is to investigate how the SZ signal correlates with other cluster properties, such as the mass, temperature and X-ray luminosities. In this presentation we quantify these relations for clusters found in hydrodynamical simulations of large scale structure and investigate their dependence on the effects of radiative cooling and pre-heating.Comment: 10 pages, 3 figures, LaTeX. To appear in proceedings of the JENAM 2002 conference. For a more detailed analysis see astro-ph/0308074, whose simulations supersede those presented at this conferenc

Characterization of curves that lie on a geodesic sphere or on a totally geodesic hypersurface in a hyperbolic space or in a sphere

The consideration of the so-called rotation minimizing frames allows for a simple and elegant characterization of plane and spherical curves in Euclidean space via a linear equation relating the coefficients that dictate the frame motion. In this work, we extend these investigations to characterize curves that lie on a geodesic sphere or totally geodesic hypersurface in a Riemannian manifold of constant curvature. Using that geodesic spherical curves are normal curves, i.e., they are the image of an Euclidean spherical curve under the exponential map, we are able to characterize geodesic spherical curves in hyperbolic spaces and spheres through a non-homogeneous linear equation. Finally, we also show that curves on totally geodesic hypersurfaces, which play the role of hyperplanes in Riemannian geometry, should be characterized by a homogeneous linear equation. In short, our results give interesting and significant similarities between hyperbolic, spherical, and Euclidean geometries.Comment: 15 pages, 3 figures; comments are welcom

Characterization of manifolds of constant curvature by spherical curves

It is known that the so-called rotation minimizing (RM) frames allow for a simple and elegant characterization of geodesic spherical curves in Euclidean, hyperbolic, and spherical spaces through a certain linear equation involving the coefficients that dictate the RM frame motion (da Silva, da Silva in Mediterr J Math 15:70, 2018). Here, we shall prove the converse, i.e., we show that if all geodesic spherical curves on a Riemannian manifold are characterized by a certain linear equation, then all the geodesic spheres with a sufficiently small radius are totally umbilical and, consequently, the given manifold has constant sectional curvature. We also furnish two other characterizations in terms of (i) an inequality involving the mean curvature of a geodesic sphere and the curvature function of their curves and (ii) the vanishing of the total torsion of closed spherical curves in the case of three-dimensional manifolds. Finally, we also show that the same results are valid for semi-Riemannian manifolds of constant sectional curvature.Comment: To appear in Annali di Matematica Pura ed Applicat

A Generalized Approach to Complex Networks

This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the network topology to new network growth models. First, the concepts of node degree and clustering coefficient are extended in order to characterize not only specific nodes, but any generic subnetwork. Second, the consideration of distance transform and rings are used to further extend those concepts in order to obtain a signature, instead of a single scalar measurement, ranging from the single node to whole graph scales. The enhanced discriminative potential of such extended measurements is illustrated with respect to the identification of correspondence between nodes in two complex networks, namely a protein-protein interaction network and a perturbed version of it. The use of other measurements derived from mathematical morphology are also suggested as a means to characterize complex networks connectivity in a more comprehensive fashion.Comment: 10 pages, 2 figur

Coherent phonon transport in short-period two-dimensional superlattices of graphene and boron nitride

Promoting coherent transport of phonons at material interfaces is a promising strategy for controlling thermal transport in nanostructures and an alternative to traditional methods based on structural defects. Coherent transport is particularly relevant in short-period heterostructures with smooth interfaces and long-wavelength heat-carrying phonons, such as two-dimensional superlattices of graphene and boron nitride. In this work, we predict phonon properties and thermal conductivities in these superlattices using a normal mode decomposition approach. We study the variation of the frequency dependence of these properties with the periodicity and interface configuration (zigzag and armchair) for superlattices with period lengths within the coherent regime. Our results showed that the thermal conductivity decreases significantly from the first period length (0.44 nm) to the second period length (0.87 nm), 13% across the interfaces and 16% along the interfaces. For greater periods, the conductivity across the interfaces continues decreasing at a smaller rate of 11 W/mK per period length increase (0.43 nm), driven by changes in the phonon group velocities (coherent effects). In contrast, the conductivity along the interfaces slightly recovers at a rate of 2 W/mK per period, driven by changes in the phonon relaxation times (diffusive effects). By changing the interface configuration from armchair to zigzag, the conductivities for all period lengths increase by approximately 7% across the interfaces and 19% along the interfaces