No-pole condition in Landau gauge: Properties of the Gribov ghost form factor and a constraint on the 2d gluon propagator

We study general properties of the Landau-gauge Gribov ghost form factor sigma(p(2)) for SU(N-c) Yang-Mills theories in the d-dimensional case. We find a qualitatively different behavior for d = 3, 4 with respect to the d = 2 case. In particular, considering any (sufficiently regular) gluon propagator D(p(2)) and the one-loop-corrected ghost propagator, we prove in the 2d case that the function sigma(p(2)) blows up in the infrared limit p -> 0 as -D(0) ln(p(2)). Thus, for d = 2, the no-pole condition sigma(p(2)) < 1 (for p(2) > 0) can be satisfied only if the gluon propagator vanishes at zero momentum, that is, D(0) = 0. On the contrary, in d = 3 and 4, sigma(p(2)) is finite also if D(0) > 0. The same results are obtained by evaluating the ghost propagator G(p(2)) explicitly at one loop, using fitting forms for D(p(2)) that describe well the numerical data of the gluon propagator in two, three and four space-time dimensions in the SU(2) case. These evaluations also show that, if one considers the coupling constant g(2) as a free parameter, the ghost propagator admits a one-parameter family of behaviors (labeled by g(2)), in agreement with previous works by Boucaud et al. In this case the condition sigma(0) <= 1 implies g(2) <= g(c)(2), where g(c)(2) is a "critical" value. Moreover, a freelike ghost propagator in the infrared limit is obtained for any value of g(2) smaller than g(c)(2), while for g(2) = g(c)(2) one finds an infrared-enhanced ghost propagator. Finally, we analyze the Dyson-Schwinger equation for sigma(p(2)) and show that, for infrared-finite ghost-gluon vertices, one can bound the ghost form factor sigma(p(2)). Using these bounds we find again that only in the d = 2 case does one need to impose D(0) = 0 in order to satisfy the no-pole condition. The d = 2 result is also supported by an analysis of the Dyson-Schwinger equation using a spectral representation for the ghost propagator. Thus, if the no-pole condition is imposed, solving the d = 2 Dyson-Schwinger equations cannot lead to a massive behavior for the gluon propagator. These results apply to any Gribov copy inside the so-called first Gribov horizon; i.e., the 2d result D(0) = 0 is not affected by Gribov noise. These findings are also in agreement with lattice data.

An in vitro comparison of subjective image quality of panoramic views acquired via 2D or 3D imaging

Objectives: The objective of this study is to compare subjective image quality and diagnostic validity of cone-beam CT (CBCT) panoramic reformatting with digital panoramic radiographs. Materials and methods: Four dry human skulls and two formalin-fixed human heads were scanned using nine different CBCTs, one multi-slice CT (MSCT) and one standard digital panoramic device. Panoramic views were generated from CBCTs in four slice thicknesses. Seven observers scored image quality and visibility of 14 anatomical structures. Four observers repeated the observation after 4 weeks. Results: Digital panoramic radiographs showed significantly better visualization of anatomical structures except for the condyle. Statistical analysis of image quality showed that the 3D imaging modalities (CBCTs and MSCT) were 7.3 times more likely to receive poor scores than the 2D modality. Yet, image quality from NewTom VGi® and 3D Accuitomo 170® was almost equivalent to that of digital panoramic radiographs with respective odds ratio estimates of 1.2 and 1.6 at 95% Wald confidence limits. A substantial overall agreement amongst observers was found. Intra-observer agreement was moderate to substantial. Conclusions: While 2D-panoramic images are significantly better for subjective diagnosis, 2/3 of the 3D-reformatted panoramic images are moderate or good for diagnostic purposes. Clinical relevance: Panoramic reformattings from particular CBCTs are comparable to digital panoramic images concerning the overall image quality and visualization of anatomical structures. This clinically implies that a 3D-derived panoramic view can be generated for diagnosis with a recommended 20-mm slice thickness, if CBCT data is a priori available for other purposes.

Weighted Fourier–Laplace transforms in reproducing kernel Hilbert spaces on the sphere

We study the action of a weighted Fourier–Laplace transform on the functions in the reproducing kernel Hilbert space (RKHS) associated with a positive definite kernel on the sphere. After defining a notion of smoothness implied by the transform, we show that smoothness of the kernel implies the same smoothness for the generating elements (spherical harmonics) in the Mercer expansion of the kernel. We prove a reproducing property for the weighted Fourier–Laplace transform of the functions in the RKHS and embed the RKHS into spaces of smooth functions. Some relevant properties of the embedding are considered, including compactness and boundedness. The approach taken in the paper includes two important notions of differentiability characterized by weighted Fourier–Laplace transforms: fractional derivatives and Laplace–Beltrami derivatives.

Electronic Structure Calculations in a 2D SixGe1-x Alloy Under an Applied Electric Field.

The recent advances and promises in nanoscience and nanotechnology have been focused on hexagonal materials, mainly on carbon-based nanostructures. Recently, new candidates have been raised, where the greatest efforts are devoted to a new hexagonal and buckled material made of silicon, named Silicene. This new material presents an energy gap due to spin-orbit interaction of approximately 1.5 meV, where the measurement of quantum spin Hall effect(QSHE) can be made experimentally. Some investigations also show that the QSHE in 2D low-buckled hexagonal structures of germanium is present. Since the similarities, and at the same time the differences, between Si and Ge, over the years, have motivated a lot of investigations in these materials. In this work we performed systematic investigations on the electronic structure and band topology in both ordered and disordered SixGe1-x alloys monolayer with 2D honeycomb geometry by first-principles calculations. We show that an applied electric field can tune the gap size for both alloys. However, as a function of electric field, the disordered alloy presents a W-shaped behavior, similarly to the pure Si or Ge, whereas for the ordered alloy a V-shaped behavior is observed.

Desarrollo de videojuegos en 2D usando Simple DirectMedia

[ES]Los Indie games, o videojuegos independientes, son aplicaciones creadas por individuos o pequeños grupos sin apoyo financiero de distribuidores. A menudo se centran en la innovación, y se basan en la distribución digital. En los últimos años han visto un gran aumento principalmente debido a; nuevos métodos de distribución en línea (Steam Greenlight1, Xbox Live2, Playstation Store3, Android Market, Apple Store), nuevas formas de financiación como Kickstarter4 y potentes herramientas gratuitas para el desarrollo. Este proyecto se puede considerar como uno de los primeros pasos en el desarrollo de videojuegos independientes o Indie. Usando SDL como base se pretende diseñar y desarrollar dos prototipos de videojuego, el primero será un clon del conocido Tetris, aprovechando la poca complejidad de las mecánicas del juego para tener un primer contacto con las herramientas. El segundo, de mayor complejidad, se centrará en desarrollar las principales características de un juego tipo plataformas en 2D, del estilo Super Mario, Sonic o los anteriormente mencionados Super Meat Boy y Braid. La Simple DirectMedia Layer (SDL) es un conjunto de bibliotecas desarrolladas en el lenguaje de programación C, que proporcionan funciones básicas para realizar operaciones de dibujo en dos dimensiones, gestión de efectos de sonido y música, además de carga y gestión de imágenes. Fueron desarrolladas inicialmente por Sam Lantinga en 1998, en este proyecto se ha usado la versión 1.2.15 y se espera que este año se termine la versión 2.0, el uno de Junio de este año ha alcanzado el estado Release Candidate.

Paralelización de métodos de optimización de mallas 2D

Máster Universitario en Sistemas Inteligentes y Aplicaciones Numéricas en Ingeniería (SIANI)

Diseño y desarrollo de un prototipo básico de un videojuego plataformas en 2D

Análisis, diseño, prototipado y desarrollo de un prototipo de videojuego del género plataformas en 2D. El análisis comienza a partir de una idea original, por lo que se incluye un estudio y prototipado de las mecánicas candidatas. Siguiendo los principios de la Ingeniería del Software, se lleva a cabo un documento de diseño y de arquitectura del software. La implementación se desarrolla siguiendo la arquitectura previamente establecida y se han añadido diferentes plataformas de control (mando, teclado y ratón) para enriquecer la experiencia de usuario. El desarrollo de este trabajo incluye un fuerte componente de diseño de videojuegos, incluyendo el estudio de referencias, análisis de mecánicas, evaluación de la experiencia del jugador y diseño de niveles. Nos centraremos en la preproducción de un juego, fase en la que se toman todas las decisiones sobre todos los aspectos finales de un videojuego. Tras un estudio de los motores de videojuego disponibles para el público, se ha utilizado el motor Unity 3D para la implementación final, llevando a cabo el desarrollo en la versión beta de Unity 4.6. A través del motor de videojuego podemos trabajar con animaciones, audio, interfaz, etc.  El lenguaje utilizado es C#. Como complemento se incluye un breve estudio de la historia de los videojuegos, los diferentes motores de videojuegos actuales y nociones del diseño de videojuegos.

Análisis, diseño y desarrollo de un videojuego en 2D con perspectiva top-down

[ES]En este proyecto la alumna ha desarrollado la demo jugable de un videojuego en 2D con perspectiva top-down. El juego transcurre en un zoológico, con un mono como protagonista, y el objetivo del mismo es lograr escapar al tiempo que se evita a los empleados del zoo. Para conseguir huir, el jugador tendrá que obtener algunos objetos y liberar a otros animales. En la propia demo se pueden consultar los controles y las distintas opciones disponibles. Para la creación del juego se ha utilizado el motor de juegos Unity 5 (edición personal) y recursos obtenidos de diversas fuentes de contenido gratuito.

Simulación URANS 2D del flujo alrededor de un cilindro para 104 ≤ Re ≤ 106 con tratamiento de paredes

Máster Universitario en Sistemas Inteligentes y Aplicaciones Numéricas en Ingeniería (SIANI)

A 2D BEM-FEM approach for time harmonic fluid-structure interaction analysis of thin elastic bodies.

[EN]This paper deals with two-dimensional time harmonic fluid-structure interaction problems when the fluid is at rest, and the elastic bodies have small thicknesses. A BEM-FEM numerical approach is used, where the BEM is applied to the fluid, and the structural FEM is applied to the thin elastic bodies.

A new method for T-spline parameterization of complex 2D geometries

[EN]We present a new strategy, based on the idea of the meccano method and a novel T-mesh optimization procedure, to construct a T-spline parameterization of 2D geometries for the application of isogeometric analysis. The proposed method only demands a boundary representation of the geometry as input data. The algorithm obtains, as a result, high quality parametric transformation between 2D objects and the parametric domain, the unit square. First, we define a parametric mapping between the input boundary of the object and the boundary of the parametric domain. Then, we build a T-mesh adapted to the geometric singularities of the domain in order to preserve the features of the object boundary with a desired tolerance...

T-spline parameterization of 2D geometries based on the meccano method with a new T-mesh optimization algorithm

[EN]We present a new method, based on the idea of the meccano method and a novel T-mesh optimization procedure, to construct a T-spline parameterization of 2D geometries for the application of isogeometric analysis. The proposed method only demands a boundary representation of the geometry as input data. The algorithm obtains, as a result, high quality parametric transformation between 2D objects and the parametric domain, the unit square. First, we define a parametric mapping between the input boundary of the object and the boundary of the parametric domain. Then, we build a T-mesh adapted to the geometric singularities of the domain in order to preserve the features of the object boundary with a desired tolerance…

Design and Computation of Warped Time-Frequency Transforms

In this work we introduce an analytical approach for the frequency warping transform. Criteria for the design of operators based on arbitrary warping maps are provided and an algorithm carrying out a fast computation is defined. Such operators can be used to shape the tiling of time-frequency plane in a flexible way. Moreover, they are designed to be inverted by the application of their adjoint operator. According to the proposed mathematical model, the frequency warping transform is computed by considering two additive operators: the first one represents its nonuniform Fourier transform approximation and the second one suppresses aliasing. The first operator is known to be analytically characterized and fast computable by various interpolation approaches. A factorization of the second operator is found for arbitrary shaped non-smooth warping maps. By properly truncating the operators involved in the factorization, the computation turns out to be fast without compromising accuracy.