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Inference for types and structured families of commutative orthogonal block structures

Publication . Carvalho, Francisco; Mexia, João T.; Santos, Carla; Nunes, Célia

Models with commutative orthogonal block structure, COBS, have orthogonal block structure, OBS, and their least square estimators for estimable vectors are, as it will be shown, best linear unbiased estimator, BLUE. Commutative Jordan algebras will be used to study the algebraic structure of the models and to define special types of models for which explicit expressions for the estimation of variance components are obtained. Once normality is assumed, inference using pivot variables is quite straightforward. To illustrate this class of models we will present unbalanced examples before considering families of models. When the models in a family correspond to the treatments of a base design, the family is structured. It will be shown how, under quite general conditions, the action of the factors in the base design on estimable vectors, can be studied.

2014Journal article

Open access

Semiclassical dynamics of horizons in spherically symmetric collapse

Publication . Tavakoli, Yaser; Marto, João; Dapor, Andrea

In this work, we consider a semiclassical description of the spherically symmetric gravitational collapse with a massless scalar field. In particular, we employ an effective scenario provided by holonomy corrections from loop quantum gravity, to the homogeneous interior spacetime. The singularity that would arise at the final stage of the corresponding classical collapse, is resolved in this context and is replaced by a bounce. Our main purpose is to investigate the evolution of trapped surfaces during this semiclassical collapse. Within this setting, we obtain a threshold radius for the collapsing shells in order to have horizons formation. In addition, we study the final state of the collapse by employing a suitable matching at the boundary shell from which quantum gravity effects are carried to the exterior geometry.

2013-03-25Journal article

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Improved dynamics and gravitational collapse of tachyon field coupled with a barotropic fluid

Publication . Marto, João; Tavakoli, Yaser; Moniz, Paulo

We consider a spherically symmetric gravitational collapse of a tachyon field with an inverse square potential, which is coupled with a barotropic fluid. By employing an holonomy correction imported from loop quantum cosmology, we analyse the dynamics of the collapse within a semiclassical description. Using a dynamical system approach, we find that the stable fixed points given by the standard general relativistic setting turn into saddle points in the present context. This provides a new dynamics in contrast to the black hole and naked singularities solutions appearing in the classical model. Our results suggest that classical singularities can be avoided by quantum gravity effects and are replaced by a bounce. By a thorough numerical studies we show that, depending on the barotropic parameter $\gamma$, there exists a class of solutions corresponding to either a fluid or a tachyon dominated regimes. Furthermore, for the case $\gamma \sim 1$, we find an interesting tracking behaviour between the tachyon and the fluid leading to a dust-like collapse. In addition, we show that, there exists a threshold scale which determines when an outward energy flux emerges, as a non-singular black hole is forming, at the corresponding collapse final stages.

2013-08-22Journal article

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A Note on Standard Composition Algebras of Types II and III

Publication . Beites, P. D.; Nicolás, Alejandro

Some identities satis ed by certain standard composition algebras, of types II and III, are studied and become candidates for the characterization of the mentioned types.[...]

2017Journal article

Open access

The Crank–Nicolson–Galerkin Finite Element Method for a Nonlocal Parabolic Equation with Moving Boundaries

Publication . Almeida, Rui M.P.; Duque, José C. M.; Ferreira, Jorge; Robalo, Rui J.

The aim of this article is to establish the convergence and error bounds for the fully discrete solutions of a class of nonlinear equations of reaction–diffusion nonlocal type with moving boundaries, using a linearized Crank–Nicolson–Galerkin finite element method with polynomial approximations of any degree. A coordinate transformation which fixes the boundaries is used. Some numerical tests to compare our Matlab code with some existing moving finite element methods are investigated.

2014-12-28Journal article

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