Isomorphism test for digraphs with weighted edges

Colour refinement is at the heart of all the most efficient graph isomorphism software packages. In this paper we present a method for extending the applicability of refinement algorithms to directed graphs with weighted edges. We use Traces as a reference software, but the proposed solution is easily transferrable to any other refinement-based graph isomorphism tool in the literature. We substantiate the claim that the performances of the original algorithm remain substantially unchanged by showing experiments for some classes of benchmark graphs

Scaling behavior in the adiabatic Dicke Model

We analyze the quantum phase transition for a set of $N$-two level systems interacting with a bosonic mode in the adiabatic regime. Through the Born-Oppenheimer approximation, we obtain the finite-size scaling expansion for many physical observables and, in particular, for the entanglement content of the system.Comment: 4 pages, 3 figure

Conflict vs causality in event structures

Event structures are one of the best known models for concurrency. Many variants of the basic model and many possible notions of equivalence for them have been devised in the literature. In this paper, we study how the spectrum of equivalences for Labelled Prime Event Structures built by Van Glabbeek and Goltz changes if we consider two simplified notions of event structures: the first is obtained by removing the causality relation (Coherence Spaces) and the second by removing the conflict relation (Elementary Event Structures). As expected, in both cases the spectrum turns out to be simplified, since some notions of equivalence coincide in the simplified settings; actually, we prove that removing causality simplifies the spectrum considerably more than removing conflict. Furthermore, while the labeling of events and their cardinality play no role when removing causality, both the labeling function and the cardinality of the event set dramatically influence the spectrum of equivalences in the conflict-free setting

On the finite size behavior of quantum collective spin systems

We discuss the finite size behavior of the adiabatic Dicke model, describing the collective coupling of a set of N-two level atoms (qubits) to a faster (electromagnetic) oscillator mode. The energy eigen-states of this system are shown to be directly related to those of another widely studied collective spin model, the uniaxial one. By employing an approximate continuum approach, we obtain a complete characterization of the properties of the latter, which we then use to evaluate the scaling properties of various observables for the original Dicke model near its quantum phase transition.Comment: 8 pages, 4 figure

Stabilité L2 de schémas volumes finis pour les équations de Maxwell en 2D et 3D sur maillage non-structuré quelconque

Dans ce rapport, nous cherchons à établir des conditions suffisantes et éventuellement nécessaires de stabilité L2 pour des méthodes de volumes finis du premier ordre en temps et en espace, appliquées aux équations de Maxwell. En deux dimensions d'espace, nous proposons une condition suffisante de stabilité d'une grande généralité, puisqu'elle est valable pour toute forme de volumes finis, avec des conditions aux limites absorbantes ou métalliques. Nous montrons que cette condition est également nécessaire pour une classe de maillages réguliers. En trois dimensions d'espace, la condition suffisante prend une form similaire. Cependant, cette condition n'est jamais nécessaire. Nous indiquons une nouvelle condition suffisante de stabilité, plus large, et qui s'avère nécessaire pour des maillages en parallélépipèdes rectangle

Schémas en éléments finis discontinus localement raffinés en espace et en temps pour les équations de Maxwell 1D

Dans ce rapport, on fait un tour d'horizon des méthodes numériques disponibles pour la simulation numérique d'équations de propagation d'ondes (électromagnétisme, acoustique) en une dimension d'espace. On s'intéresse uniquement aux méthodes susceptibles d'être étendues en trois dimensions d'espace sur maillages non-structurés (on compare néanmoins celles-ci au schéma de Yee en une dimension) et qui conservent une énergie discrète : méthodes de volumes finis, méthodes de type Galerkin Discontinu. On étudie en détail leurs propriétés et on montre la possibilité de les utiliser sur des maillages localement raffinés en temps et en espace, notamment en conservant leur nature totalement explicite

Symplectic local time-stepping in non-dissipative DGTD methods applied to wave propagation problems

The Discontinuous Galerkin Time Domain (DGTD) methods are now popular for the solution of wave propagation problems. Able to deal with unstructured, possibly locally-refined meshes, they handle easily complex geometries and remain fully explicit with easy parallelization and extension to high orders of accuracy. Non-dissipative versions exist, where some discrete electromagnetic energy is exactly conserved. However, the stability limit of the methods, related to the smallest elements in the mesh, calls for the construction of local-time stepping algorithms. These schemes have already been developed for N-body mechanical problems and are known as symplectic schemes. They are applied here to DGTD methods on wave propagation problems

Numerical Simulation of Aeroelastic Instabilities of Elementary Bridge Decks

In this report, we propose a global methodology for the numerical simulation of wind effects on elementary bridge profiles, particularly possible aeroelast- ic instabilities. This methodology is based on an efficient coupling algorithm- , a finite-element solver for three-dimensional incompressible Navier-Stokes equations in a moving domain and a structural solver. The fluid solver is detailed, the emphasis being put on the ALE formulation. Numerical and experimental results are compared for cases with a structural rigid motion. On a rectangle, numerical simulations for forced oscillation (heaving or rotation) are qualitatively correct, rather inaccurate, but in good agreements with free oscillation numerical simulations though. On a H-shaped section close to the Tacoma Narrows bridge profile, numerical results are both qualitatively and quantitatively very satisfactory and promising

Cesarotti all’opera. Appunti sulla librettistica ossianica

Studio sulla fortuna operistica dei Canti di Ossian di Melchiorre Cesarotti

First characterisation of the PADME electromagnetic calorimeter

The PADME experiment, hosted at the LNF Beam Test Facility, is searching for a dark photon that decays into dark matter particles. This search is performed looking for the reaction e+ + e− → A0 + γ, where A' is the dark photon, which cannot be observed directly or via its decay products. A key role in the experiment is played by the electromagnetic calorimeter, which measures the energy and the position of the γ in the final state. From this, the missing four-momentum carried away by the A' can be evaluated and the particle mass can be inferred. This article will present the process followed for the construction and calibration of the electromagnetic calorimeter of the experiment. The results achieved in terms of equalisation, detection efficiency and energy resolution during the first phase of the experiment, demonstrate the effectiveness of the various devices used to improve the calorimeter performance with respect to first prototypes