L. Fernández-Jambrina

Geodesic behavior of sudden future singularities

In this paper we analyze the effect of recently proposed classes of sudden future singularities on causal geodesics of FLRW spacetimes. Geodesics are shown to be extendible and just the equations for geodesic deviation are singular, although tidal forces are not strong enough to produce a Big Rip. For the sake of completeness, we compare with the typical sudden future singularities of phantom cosmologies.

Classification of cosmological milestones

In this paper causal geodesic completeness of Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological models is analyzed in terms of generalized power expansions of the scale factor in coordinate time. The strength of the found singularities is discussed following the usual definitions due to Tipler and Krolak. It is shown that while classical cosmological models are both timelike and lightlike geodesically incomplete, certain observationally allowed models which have been proposed recently are lightlike geodesically complete.

Singular fate of the universe in modified theories of gravity

In this Letter we study the final fate of the universe in modified theories of gravity. As compared with general relativistic formulations, in these scenarios the Friedmann equation has additional terms which are relevant for low density epochs. We analyze the sort of future singularities to be found under the usual assumption the expanding Universe is solely filled with a pressureless component. We report our results using two schemes: one concerned with the behavior of curvature scalars, and a more refined one linked to observers. Some examples with a very solid theoretical motivation and some others with a more phenomenological nature are used for illustration.

Automatic surface modelling of a ship hull

When defining a ship hull surface, the main objective is to obtain a faired surface or surfaces that contain some specific points of the hull, that have been selected in the design process and give the ship its hydrodynamic, stability and other properties. So, the hull surface should be a compromise between fairness and precision, and this is not and easy task. In this paper, authors present a thorough procedure for automatic modelling with a fair NURBS surface, having lists of points on the stations of the vessel as initial data. The construction of spline curves, and their application in the definition of ship lines is reviewed. Approximation of spline curves fitting the data on the stations is made, with special emphasis on the choice of parametrization, which is relevant to increase the accuracy of the splines. NURBS surfaces modelling the hull of the vessel are constructed and the fairing process adapted to maintain certain ship characteristics is described.

Singularity-free space-time

We show that the solution published in the paper by Senovilla [Phys. Rev. Lett. 64, 2219 (1990)] is geodesically complete and singularity-free. We also prove that the solution satisfies the stronger energy and causality conditions, such as global hyperbolicity, the strong energy condition, causal symmetry, and causal stability. A detailed discussion about which assumptions in the singularity theorems are not satisfied is performed, and we show explicitly that the solution is in accordance with those theorems. A brief discussion of the results is given.

Exterior differential system for cosmological perfect fluids and geodesic completeness

In this paper a new formalism based on exterior differential systems is derived for perfect-fluid spacetimes endowed with an Abelian orthogonally transitive group of motions acting on spacelike surfaces. This formulation allows simplifications of Einstein equations and it can be applied for different purposes. As an example a singularity-free metric is rederived in this framework. A sufficient condition for a diagonal metric to be geodesically complete is also provided.

Hidden past of dark energy cosmological models

Abstract In this Letter we analyse the possibility of having homogeneous isotropic cosmological models with observers reaching t = ∞ in finite proper time. It is shown that just observationally-suggested dark energy models with w ∈ ( − 5 / 3 , − 1 ) show this feature and that they are endowed with an exotic curvature singularity. Furthermore, it is shown that non-accelerated observers in these models may experience a duration of the universe as short as desired by increasing their linear momentum. A subdivision of phantom models in two families according to this behavior is suggested.

Programmed design of ship forms

This paper describes a new category of CAD applications devoted to the definition and parameterization of hull forms, called programmed design. Programmed design relies on two prerequisites. The first one is a product model with a variety of types large enough to face the modeling of any type of ship. The second one is a design language dedicated to create the product model. The main purpose of the language is to publish the modeling algorithms of the application in the designer knowledge domain to let the designer create parametric model scripts. The programmed design is an evolution of the parametric design but it is not just parametric design. It is a tool to create parametric design tools. It provides a methodology to extract the design knowledge by abstracting a design experience in order to store and reuse it. Programmed design is related with the organizational and architectural aspects of the CAD applications but not with the development of modeling algorithms. It is built on top and relies on existing algorithms provided by a comprehensive product model. Programmed design can be useful to develop new applications, to support the evolution of existing applications or even to integrate different types of application in a single one. A three-level software architecture is proposed to make the implementation of the programmed design easier. These levels are the conceptual level based on the design language, the mathematical level based on the geometric formulation of the product model and the visual level based on the polyhedral representation of the model as required by the graphic card. Finally, some scenarios of the use of programmed design are discussed. For instance, the development of specialized parametric hull form generators for a ship type or a family of ships or the creation of palettes of hull form components to be used as parametric design patterns. Also two new processes of reverse engineering which can considerably improve the application have been detected: the creation of the mathematical level from the visual level and the creation of the conceptual level from the mathematical level.

A wide family of singularity-free cosmological models

In this paper a family of non-singular cylindrical perfect fluid cosmologies is derived. The equation of state corresponds to a stiff fluid. The family depends on two independent functions under very simple conditions. A sufficient condition for geodesic completeness is provided.

Curves with rational chord-length parametrization

It has been recently proved that rational quadratic circles in standard Bezier form are parameterized by chord-length. If we consider that standard circles coincide with the isoparametric curves in a system of bipolar coordinates, this property comes as a straightforward consequence. General curves with chord-length parametrization are simply the analogue in bipolar coordinates of nonparametric curves. This interpretation furnishes a compact explicit expression for all planar curves with rational chord-length parametrization. In addition to straight lines and circles in standard form, they include remarkable curves, such as the equilateral hyperbola, Lemniscate of Bernoulli and Limacon of Pascal. The extension to 3D rational curves is also tackled.