Comments on the Quantum Potential Approach to a Class of Quantum Cosmological Models

In this comment we bring attention to the fact that when we apply the ontological interpretation of quantum mechanics, we must be sure to use it in the coordinate representation. This is particularly important when canonical tranformations that mix momenta and coordinates are present. This implies that some of the results obtained by A. B\l aut and J. Kowalski-Glikman are incorrect.Comment: 7 pages, LaTe

Gaussian superpositions in scalar-tensor quantum cosmological models

A free scalar field minimally coupled to gravity model is quantized and the Wheeler-DeWitt equation in minisuperspace is solved analytically, exhibiting positive and negative frequency modes. The analysis is performed for positive, negative and zero values of the curvature of the spatial section. Gaussian superpositions of the modes are constructed, and the quantum bohmian trajectories are determined in the framework of the Bohm-de Broglie interpretation of quantum cosmology. Oscillating universes appear in all cases, but with a characteristic scale of the order of the Planck scale. Bouncing regular solutions emerge for the flat curvature case. They contract classically from infinity until a minimum size, where quantum effects become important acting as repulsive forces avoiding the singularity and creating an inflationary phase, expanding afterwards to an infinite size, approaching the classical expansion as long as the scale factor increases. These are non-singular solutions which are viable models to describe the early Universe.Comment: 14 pages, LaTeX, 3 Postscript figures, uses graficx.st

Study on the influence of orthotropy and tension–compression asymmetry of metal sheets in springback and formability predictions

Most yield criteria possess a point-symmetry with respect to its center, meaning that a stress state and its reverse state have the same absolute value. However, this can be an unrealistic approximation, even for cubic metals (both face-centered cubic and body center cubic)), which can present a small asymmetry between the yield stress in tension and compression, i.e. a strength differential (SD) effect. This work analyzes the influence of taking or not into account the SD effect in the modeling of the sheet orthotropic behavior in the numerical simulation of a cylindrical cup drawing process. The yield criterion adopted is the CPB06 [1], including its version with two linear transformations [2], allowing a better fitting of the experimental data available. The material analyzed presents a quite small tension-compression ratio of 0.963. However, this small SD effect leads to a slightly higher punch force during the bending dominated stage, resulting in a very small influence on the springback prediction. The influence on the thickness evolution during the process is negligible.Fundação para a Ciência e a Tecnologia(SFRH/BPD/101334/2014

Study of the frictional contact conditions in the hole expansion test

The adoption of advanced high-strength steels is growing in the automotive industry due to their good strength-to-weight ratio. However, the frictional contact conditions differ from the ones arising in mild steels due to the high values of contact pressure. The objective of this study is the detailed numerical analysis of the frictional contact conditions in the hole expansion test. The Coulomb friction law is adopted in the finite element model, using different values for the (constant) friction coefficient, as well as a pressure dependent friction coefficient. The increase of the friction coefficient leads to an increase of the punch force and a slight decrease of the hole expansion. The results show that increasing the friction coefficient postpones the onset of necking, but the localization does not change.Fundação para a Ciência e a Tecnologia(SFRH/BPD/101334/2014

The Consistency of Causal Quantum Geometrodynamics and Quantum Field Theory

We consider quantum geometrodynamics and parametrized quantum field theories in the framework of the Bohm-de Broglie interpretation. In the first case, and following the lines of our previous work [1], where a hamiltonian formalism for the bohmian trajectories was constructed, we show the consistency of the theory for any quantum potential, completing the scenarios for canonical quantum cosmology presented there. In the latter case, we prove the consistency of scalar field theory in Minkowski spacetime for any quantum potential, and we show, using this alternative hamiltonian method, a concrete example where Lorentz invariance of individual events is broken.Comment: Final version. See also http://www.cosmologia.cbpf.b

The Bohm Interpretation of Quantum Cosmology

I make a review on the aplications of the Bohm-De Broglie interpretation of quantum mechanics to quantum cosmology. In the framework of minisuperspaces models, I show how quantum cosmological effects in Bohm's view can avoid the initial singularity, isotropize the Universe, and even be a cause for the present observed acceleration of the Universe. In the general case, we enumerate the possible structures of quantum space and time.Comment: 28 pages, 1 figure, contribution to the James Cushing festschrift to appear in Foundations of Physic

Troubles with quantum anistropic cosmological models: Loss of unitarity

The anisotropic Bianchi I cosmological model coupled with perfect fluid is quantized in the minisuperspace. The perfect fluid is described by using the Schutz formalism which allows to attribute dynamical degrees of freedom to matter. A Schr\"odinger-type equation is obtained where the matter variables play the role of time. However, the signature of the kinetic term is hyperbolic. This Schr\"odinger-like equation is solved and a wave packet is constructed. The norm of the resulting wave function comes out to be time dependent, indicating the loss of unitarity in this model. The loss of unitarity is due to the fact that the effective Hamiltonian is hermitian but not self-adjoint. The expectation value and the bohmian trajectories are evaluated leading to different cosmological scenarios, what is a consequence of the absence of a unitary quantum structure. The consistency of this quantum model is discussed as well as the generality of the absence of unitarity in anisotropic quantum models.Comment: Latex file, 18 pages. To appear in General Relativity and Gravitatio