Casimir Energy and Entropy in the Sphere--Sphere Geometry

We calculate the Casimir energy and entropy for two spheres described by the perfect metal model, plasma model, and Drude model in the large separation limit. We obtain nonmonotonic behavior of the Helmholtz free energy with separation and temperature for the perfect metal and plasma models, leading to parameter ranges with negative entropy, and also nonmonotonic behavior of the entropy with temperature and the separation between the spheres. This nonmonotonic behavior has not been found for Drude model. The appearance of this anomalous behavior of the entropy is discussed as well as its thermodynamic consequences.Comment: 9 pages, 7 figure

On some spectral properties of pseudo-differential operators on T

In this paper we use Riesz spectral Theory and Gershgorin Theory to obtain explicit information concerning the spectrum of pseudo-differential operators defined on the unit circle $\mathbb{T} := \mathbb{R}/ 2 \pi \mathbb{ Z}$. For symbols in the H\"ormander class $S^m_{1 , 0} (\mathbb{T} \times \mathbb{Z})$, we provide a sufficient and necessary condition to ensure that the corresponding pseudo-differential operator is a Riesz operator in $L^p (\mathbb{T})$, $1< p < \infty$, extending in this way compact operators characterisation and Ghoberg's lemma to $L^p (\mathbb{T})$. We provide an example of a non-compact Riesz pseudo-differential operator in $L^p (\mathbb{T})$, $1<p<2$. Also, for pseudo-differential operators with symbol satisfying some integrability condition, it is defined its associated matrix in terms of the Fourier coefficients of the symbol, and this matrix is used to give necessary and sufficient conditions for $L^2$-boundedness without assuming any regularity on the symbol, and to locate the spectrum of some operators

Theory of the Strain-Induced Magnetoelectric Effect in Planar Dirac Systems

The magnetoelectric response in inversion-breaking two dimensional Dirac systems induced by strain is analyzed. It is shown that, in the same way that the piezoelectric response in these materials is related to the valley Chern number, the strain-induced magnetoelectric effect is related both to the non trivial Berry curvature and the derivative of the orbital magnetic moment per valley. This phenomenon allows to locally induce and control charge densities by an external magnetic field in strained zones of the sample.Comment: 7 pages, 2 figure

Explore what-if scenarios with SONG: Social Network Write Generator

Online Social Networks (OSNs) have witnessed a tremendous growth the last few years, becoming a platform for online users to communicate, exchange content and even find employment. The emergence of OSNs has attracted researchers and analysts and much data-driven research has been conducted. However, collecting data-sets is non-trivial and sometimes it is difficult for data-sets to be shared between researchers. The main contribution of this paper is a framework called SONG (Social Network Write Generator) to generate synthetic traces of write activity on OSNs. We build our framework based on a characterization study of a large Twitter data-set and identifying the important factors that need to be accounted for. We show how one can generate traces with SONG and validate it by comparing against real data. We discuss how one can extend and use SONG to explore different `what-if' scenarios. We build a Twitter clone using 16 machines and Cassandra. We then show by example the usefulness of SONG by stress-testing our implementation. We hope that SONG is used by researchers and analysts for their own work that involves write activity.Comment: 11 page

Non-harmonic Gohberg's lemma, Gershgorin theory and heat equation on manifolds with boundary

In this paper, following the works on non-harmonic analysis of boundary value problems by Tokmagambetov, Ruzhansky and Delgado, we use Operator Ideals Theory and Gershgorin Theory to obtain explicit information concerning the spectrum of pseudo-differential operators, on a smooth manifold $\Omega$ with boundary $\partial \Omega$, in the context of the non-harmonic analysis of boundary value problems, introduced by Tokmagambetov and Ruzhansky in terms of a model operator $\mathfrak{L}$. Under certain assumptions about the eigenfunctions of the model operator, for symbols in the H\"ormander class $S^0_{1,0} (\overline{\Omega} \times \mathcal{I} )$, we provide a "non-harmonic version" of Gohberg's Lemma, and a sufficient and necessary condition to ensure that the corresponding pseudo-differential operator is a compact operator in $L^2(\Omega)$. Also, for pseudo-differential operators with symbols satisfying some integrability condition, one defines its associated matrix in terms of the biorthogonal system associated to $\mathfrak{L}$, and this matrix is used to give necessary and sufficient conditions for the $L^2(\Omega)$-boundedness, and to locate the spectrum of some operators. After that, we extend to the context of the non-harmonic analysis of boundary value problems the well known theorems about the exact domain of elliptic operators, and discuss some applications of the obtained results to evolution equations. Specifically we provide sufficient conditions to ensure the smoothness and stability of solutions to a generalised version of the heat equation

Searching for a Unique Style in Soccer

Is it possible to have a unique, recognizable style in soccer nowadays? We address this question by proposing a method to quantify the motif characteristics of soccer teams based on their pass networks. We introduce the the concept of "flow motifs" to characterize the statistically significant pass sequence patterns. It extends the idea of the network motifs, highly significant subgraphs that usually consists of three or four nodes. The analysis of the motifs in the pass networks allows us to compare and differentiate the styles of different teams. Although most teams tend to apply homogenous style, surprisingly, a unique strategy of soccer exists. Specifically, FC Barcelona's famous tiki-taka does not consist of uncountable random passes but rather has a precise, finely constructed structure.Comment: 2014 KDD Workshop on Large-Scale Sports Analytic

Partially hyperbolic dynamics in dimension 3

Partial hyperbolicity appeared in the sixties as a natural generaliza- tion of hyperbolicity. In the last 20 years in this area there has been great activity. Here we survey the state of the art in some topics, focusing especially in partial hyperbolicity in dimension 3. The reason for this is not only that it is the smallest dimension in which non-degenerate partial hyperbolicity can occur, but also that the topology of 3-manifolds influences this dynamics in revealing ways.Comment: Updated version, to appear in Ergodic Theory and Dynamical System

Relativistic Quantum Optics: On the relativistic invariance of the light-matter interaction models

In this note we discuss the invariance under general changes of reference frame of all the physical predictions of particle detector models in quantum field theory in general and, in particular, of those used in quantum optics to model atoms interacting with light. We find explicitly how the light-matter interaction Hamiltonians change under general coordinate transformations, and analyze the subtleties of the Hamiltonians commonly used to describe the light-matter interaction when relativistic motion is taken into account.Comment: 11 pages. ReVteX 4.1. V2: Updated to match published versio

Morris-Thorne wormholes in static pseudo-spherically symmetric spacetimes

In this paper we study classical general relativistic static wormhole configurations with pseudo-spherical symmetry. We show that in addition to the hyperbolic wormhole solutions discussed by Lobo and Mimoso in the Ref. Phys.\ Rev.\ D {\bf 82}, 044034 (2010), there exists another wormhole class, which is truly pseudo-spherical counterpart of spherical Morris-Thorne wormhole (contrary to the Lobo-Mimoso wormhole class), since all constraints originally defined by Morris and Thorne for spherically symmetric wormholes are satisfied. We show that, for both classes of hyperbolic wormholes the energy density, at the throat, is always negative, while the radial pressure is positive, contrary to the spherically symmetric Morris-Thorne wormhole. Specific hyperbolic wormholes are constructed and discussed by imposing different conditions for the radial and lateral pressures, or by considering restricted choices for the redshift and the shape functions. In particular, we show that an hyperbolic wormhole can not be sustained at the throat by phantom energy, and that there are pseudo-spherically symmetric wormholes supported by matter with isotropic pressure and characterized by space sections with an angle deficit (or excess).Comment: 12 pages, 5 figure

Evolution of a modified binomial random graph by agglomeration

In the classical Erd\"os-R\'enyi random graph G(n,p) there are n vertices and each of the possible edges is independently present with probability p. The random graph G(n,p) is homogeneous in the sense that all vertices have the same characteristics. On the other hand, numerous real-world networks are inhomogeneous in this respect. Such an inhomogeneity of vertices may influence the connection probability between pairs of vertices. The purpose of this paper is to propose a new inhomogeneous random graph model which is obtained in a constructive way from the Erd\"os-R\'enyi random graph G(n,p). Given a configuration of n vertices arranged in N subsets of vertices (we call each subset a super-vertex), we define a random graph with N super-vertices by letting two super-vertices be connected if and only if there is at least one edge between them in G(n,p). Our main result concerns the threshold for connectedness. We also analyze the phase transition for the emergence of the giant component and the degree distribution. Even though our model begins with G(n,p), it assumes the existence of some community structure encoded in the configuration. Furthermore, under certain conditions it exhibits a power law degree distribution. Both properties are important for real applications.Comment: The definition of the threshold probability for connectivity has been slightly changed in order to remove the extra condition on Theorem 1. The presentation of the paper has been improve