scholarly journals Scalar-Tensor Bianchi VI Models

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
J. A. Belinchón

We study how may vary the gravitational and the cosmological “constants,” ( and ) in several scalar-tensor theories with Bianchi III, , and symmetries. By working under the hypothesis of self-similarity we find exact solutions for two different theoretical models, which are the Jordan-Brans-Dicke (JBD) with and the usual JBD model with potential (that mimics the behaviour of . We compare both theoretical models, and some physical and geometrical properties of the solutions are also discussed putting special emphasis on the study of the isotropization of the solutions.

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Riccardo Cristoferi

AbstractA method for obtaining the exact solution for the total variation denoising problem of piecewise constant images in dimension one is presented. The validity of the algorithm relies on some results concerning the behavior of the solution when the parameter λ in front of the fidelity term varies. Albeit some of them are well-known in the community, here they are proved with simple techniques based on qualitative geometrical properties of the solutions.


2018 ◽  
Vol 8 (8) ◽  
pp. 1310
Author(s):  
Naoya Kihara ◽  
Osamu Sakai

Fractal-like nanoparticle two-dimensional patterns forming in diffusion-limited aggregation show variant spatial patterns. However, they have invariant statistical properties in their network topologies, even though their formation is completely in self-assembled processes. One of the outputs from these topological properties is optical resonances at invariant frequencies, which is a required feature of a metamaterial alternative. Fractal-like metallic patterns studied here in both experiments and theoretical models exhibit similar resonance frequencies in the infrared-ray range, and they depend on the unit length of nanoparticles composing arbitrary fractal-like structures. The scheme of analysis applied here using complex network theory does not only reveal the topological properties of the nanoparticle network, but points out their optical and possibly other physical potentials arising from their geometrical properties.


2001 ◽  
Vol 54 (6) ◽  
pp. B108-B109 ◽  
Author(s):  
PL Sachdev, ◽  
WS Janna,

Open Physics ◽  
2012 ◽  
Vol 10 (4) ◽  
Author(s):  
José Belinchón

AbstractWe study how the constants G and Λ may vary in different theoretical models (general relativity (GR) with a perfect fluid, scalar cosmological models (SM) (“quintessence”) with and without interacting scalar and matter fields and three scalar-tensor theories (STT) with a dynamical Λ) in order to explain some observational results. We apply the program outlined in section II to study the Bianchi I models, under the self-similarity hypothesis. We put special emphasis on calculating exact power-law solutions which allow us to compare the different models. In all the studied cases we conclude that the solutions are isotropic and noninflationary. We also arrive at the conclusion that in the GR model with time-varying constants, Λ vanishes while G is constant. In the SM all the solutions are massless i.e. the potential vanishes and all the interacting models are inconsistent from the thermodynamical point of view. The solutions obtained in the STT collapse to the perfect fluid one obtained in the GR model where G is a true constant and Λ vanishes as in the GR and SM frameworks.


Author(s):  
José Antonio Belinchón ◽  
Carlos González ◽  
Sami Dib

We study the [Formula: see text] cosmological models under the self-similarity hypothesis. We determine the exact form that each physical and geometrical quantity may take in order that the field equations (FE) admit exact self-similar (SS) solutions through the matter collineation approach. We study two models: the case[Formula: see text] and the case [Formula: see text]. In each case, we state general theorems which determine completely the form of the unknown functions [Formula: see text] such that the FE admit SS solutions. We also state some corollaries as limiting cases. These results are quite general and valid for any homogeneous SS metric[Formula: see text] In this way, we are able to generate new cosmological scenarios. As examples, we study two cases by finding exact solutions to these particular models.


Author(s):  
Nicolás Roa Rojas ◽  
Nívea Gabriela Benevides de Albuquerque ◽  
Guilherme Sales Soares de Azevedo Melo ◽  
Nathaly Sarasty Narváez

RESUMO: Este trabalho trata da análise de vigas de concreto armado reforçadas ao cortante através da colagem externa de compósitos de fibras poliméricas (EB-FRP), tomando-se por base os modelos teóricos propostos por autores como Chen et al. (2003) e Chen (2010) – cujas abordagens fundamentam-se na análise de resultados experimentais e computacionais – sendo contrastadas às previsões das contribuições estimadas por normas vigentes. Dessa forma, buscou-se realizar uma avaliação dos dados e modelos de cálculo sugeridos pelos autores, salientando a influência de parâmetros particulares nas capacidades dos reforços que geram resultados mais próximos aos obtidos experimentalmente. Nesta pesquisa também foi analisada a precisão das estimativas das contribuições dos reforços, em especial das fibras de carbono, determinadas pelos modelos e pela norma americana ACI 440.2R (2008) e italiana CNR DT200 (2004) em relação aos resultados de um banco de dados experimental selecionado, os quais conduzem a resultados ainda pouco precisos. Isto é atribuído principalmente a não consideração das interações existentes entre estribos e fibras de carbono como materiais de reforço, como também de algumas propriedades físicas, mecânicas e geométricas. Diante disso, constata-se a necessidade contínua de refinamento dos modelos teóricos para a obtenção de resultados mais satisfatórios.
 
 ABSTRACT: This work deals with the analysis of reinforced concrete beams strengthened to shear force by using externally bonded fiber reinforced polymer composites (EB-FRP), based upon the theoretical models proposed by authors such as Chen et al. (2003) and Chen (2010) – whose approaches are grounded on the analysis of experimental and computational results – and contrasted to the provisions of estimated contributions by current codes. Thus, it sought to conduct an assessment of the data and calculation models suggested by the authors, emphasizing the influence of particular parameters on reinforcement capabilities that generate results closer to those obtained experimentally. The accuracy of estimations, especially the carbon fiber’s contribution, is also analyzed through the American code ACI 440.2R (2008) and the Italian code CNR DT200 (2004) regarding selected experimental databases, which lead to results still not accurate. This is mainly attributed to non consideration of interactions between stirrups and fibers as reinforcing materials, as well as some physical, mechanical and geometrical properties. Thus, there has been a continued need for refinement of numerical and theoretical models to obtain more satisfactory results.


2012 ◽  
Vol 2012 ◽  
pp. 1-14
Author(s):  
Filipe C. Mena

We review recent results about the modelling of gravitational collapse to black holes in higher dimensions. The models are constructed through the junction of two exact solutions of the Einstein field equations: an interior collapsing fluid solution and a vacuum exterior solution. The vacuum exterior solutions are either static or containing gravitational waves. We then review the global geometrical properties of the matched solutions which, besides black holes, may include the existence of naked singularities and wormholes. In the case of radiating exteriors, we show that the data at the boundary can be chosen to be, in some sense, arbitrarily close to the data for the Schwarzschild-Tangherlini solution.


2014 ◽  
Vol 10 (S313) ◽  
pp. 346-351
Author(s):  
D. Emmanoulopoulos

AbstractMany theoretical models of Active Galactic Nuclei (AGN) predict that the X-ray corona, lying above the black hole, constitutes the base of the X-ray jet. Thus, by studying the exact geometry of the close black hole environment, we can pinpoint the launching site of the jet. Detection of negative X-ray reverberation time delays (i.e. soft band X-ray variations lagging behind the corresponding hard band X-ray variations) can yield significant information about the geometrical properties of the AGN, such as the location of the X-ray source, as well as the physical properties of the the black hole, such as its mass and spin. In the frame-work of the lamp-post geometry, I present the first systematic X-ray time-lag modelling results of an ensemble of 12 AGN, using a fully general relativistic (GR) ray tracing approach for the estimation of the systems' response functions. By combing these state-of-the art GR response models with statistically innovative fitting routines, I derive the geometrical layout of the close BH environment for each source, unveiling the position of the AGN jet-base.


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