arXiv subjects

Jaume Amorós

Publications and source records attributed to Jaume Amorós.

At least 19 recordsLinked to original sources

arXiv2025

A Dynamic Similarity Index for Assessing Voltage Source Behaviour in Power Systems

Due to the fundamental transition to a power electronic dominated power system, the increasing diversity of dynamic elements underscores the need to assess their similarity to mature electrical engineering models. This article addresses the concept of the Dynamic Similarity Index (DSI) for its use in, power electronics-dominated networks. The DSI is a multipurpose tool developed to be used by different stakeholders (e.g., converter manufacturers and system operators). Such an index is calculated per frequency, which serves to anticipate potential differences in particular frequency ranges of interest between the model under study and the reference model. Within the scope of this study, the dynamic similarity of inverter-based generators to an ideal voltage source behind an impedance is assessed, due to the relevance of this fundamental circuit in the representation of generation units in power system studies. The article presents two potential applications based on this mathematical framework. First, for manufacturers to evaluate control performance compared to a reference model and second, it enables operators to diagnose buses with voltage vulnerability based on a user-defined reference Short-Circuit Ratio (SCR) value. The DSI results for these two case studies are validated using Matlab Simulink simulations.

eess.SY↗

arXiv2024

Topological reconstruction of sampled surfaces via Morse theory

In this work, we study the perception problem for sampled surfaces (possibly with boundary) using tools from computational topology, specifically, how to identify their underlying topology starting from point-cloud samples in space, such as those obtained with 3D scanners. We present a reconstruction algorithm based on a careful topological study of the point sample that allows us to obtain a cellular decomposition of it using a Morse function. No triangulation or local implicit equations are used as intermediate steps, avoiding in this way reconstruction-induced artifices. The algorithm can be run without any prior knowledge of the surface topology, density or regularity of the point-sample. The results consist of a piece-wise decomposition of the given surface as a union of Morse cells (i.e. topological disks), suitable for tasks such as mesh-independent reparametrization or noise-filtering, and a small-rank cellular complex determining the topology of the surface. The algorithm, which we test with several real and synthetic surfaces, can be applied to smooth surfaces with or without boundary, embedded in an ambient space of any dimension.

cs.CG↗

arXiv2024

Symplectized Torelli mapping tori

Examples of aspherical closed symplectic 4-manifolds are presented whose Sullivan minimal models are (1,n)-formal for any n, without being formal. They have as cohomology algebra, signature, canonical class, those of a product of a closed Riemann surface of genus g>1 and an elliptic curve, and the fundamental group, resp. $A_{\infty}$ category defined by their de Rham complex, is isomorphic to that of the product of surfaces up to brackets of order n+1, resp. products of order n+1. Nevertheless, the manifolds do not admit any holomorphic structure. These examples are derived from the fact that the Torelli groups are pro-unipotent. The mapping tori for representatives of suitable classes in the Torelli group are considered, and their product with $S^1$ is symplectized a la Thurston.

math.SG↗

arXiv2023

A novel collision model for inextensible textiles and its experimental validation

In this work, we introduce a collision model specifically tailored for the simulation of inextensible textiles. The model considers friction, contacts, and inextensibility constraints all at the same time without any decoupling. Self-collisions are modeled in a natural way that allows considering the thickness of cloth without introducing unwanted oscillations. The discretization of the equations of motion leads naturally to a sequence of quadratic problems with inequality and equality constraints. In order to solve these problems efficiently, we develop a novel active-set algorithm that takes into account past active constraints to accelerate the resolution of unresolved contacts. We put to a test the developed collision procedure with diverse scenarios involving static and dynamic friction, sharp objects, and complex-topology folding sequences. Finally, we perform an experimental validation of the collision model by comparing simulations with recordings of real textiles as given by a $\textit{Motion Capture System}$. The results are very accurate, having errors around 1 cm for DIN A2 textiles (42 x 59.4 cm) even in difficult scenarios involving fast and strong hits with a rigid object.

cs.RO↗

arXiv2022

The dGLI Cloth Coordinates: A Topological Representation for Semantic Classification of Cloth States

Robotic manipulation of cloth is a highly complex task because of its infinite-dimensional shape-state space that makes cloth state estimation very difficult. In this paper we introduce the dGLI Cloth Coordinates, a low-dimensional representation of the state of a rectangular piece of cloth that allows to efficiently distinguish key topological changes in a folding sequence, opening the door to efficient learning methods for cloth manipulation planning and control. Our representation is based on a directional derivative of the Gauss Linking Integral and allows us to represent both planar and spatial configurations in a consistent unified way. The proposed dGLI Cloth Coordinates are shown to be more accurate in the classification of cloth states and significantly more sensitive to changes in grasping affordances than other classic shape distance methods. Finally, we apply our representation to real images of a cloth, showing we can identify the different states using a simple distance-based classifier.

cs.RO↗

arXiv2021

An Inextensible Model for Robotic Simulations of Textiles

We introduce a new isometric strain model for the study of the dynamics of cloth garments in a moderate stress environment, such as robotic manipulation in the neighborhood of humans. This model treats textiles as surfaces which are inextensible, admitting only isometric motions. Inextensibility is imposed in a continuous setting, prior to any discretization, which gives consistency with respect to re-meshing and prevents the problem of locking even with coarse meshes. The simulations of robotic manipulation using the model are compared to the actual manipulation in the real world, finding that the error between the simulated and real position of each point in the garment is lower than 1cm in average, even when a coarse mesh is used. Aerodynamic contributions to motion are incorporated to the model through the virtual uncoupling of the inertial and gravitational mass of the garment. This approach results in an accurate, as compared to reality, description of cloth motion incorporating aerodynamic effects by using only two parameters.

cs.RO↗

arXiv2021

Developable surfaces with prescribed boundary

It is proved that a generic simple, closed, piecewise regular curve in space can be the boundary of only finitely many developable surfaces with nonvanishing mean curvature. The relevance of this result in the context of the dynamics of developable surfaces is discussed.

math.DG↗

arXiv2020

Understanding the phenomenology of interacting dark energy scenarios and their theoretical bounds

Non-gravitational interaction between dark matter and dark energy has been considered in a spatially flat Friedmann-Lemaître-Robertson-Walker (FLRW) universe. The interaction rate is assumed to be linear in the energy densities of dark matter and dark energy and it is also proportional to the Hubble rate of the FLRW universe. This kind of interaction model leads to an autonomous linear dynamical system, and depending on the coupling parameters, could be solved analytically by calculating the exponential of the matrix, defining the system. We show here that such interaction rate has a very deep connection with some well known cosmological theories. We then investigate the theoretical bounds on the coupling parameters of the interaction rate in order that the energy densities of the dark sector remain positive throughout the evolution of the universe and asymptotically converge to zero at very late times. Our analyses also point out that such linear interacting model may encounter with finite time future singularities depending on the coupling parameters as well as the dark energy state parameter.

gr-qc↗

arXiv2020

Scaling solutions in quintessential inflation

In quintessence scalar field theories, the presence of scaling solutions are important during the radiation and matter epoch due to having their attractor character. Usually, it is assumed that the initial conditions of the quintessence field are in the basin of attraction of the scaling solutions. However, in order to reproduce the current cosmic acceleration, at late times, a mechanism to exit this behavior is needed. In the present work we show that the quintessential inflation models could be an excellent candidate to exhibit the above behavior. However, the crucial point of quintessential inflation is that the initial conditions has to be taken during the inflation, and at the beginning of the radiation era, the scalar field does not belong to the basin of attraction of the scaling solution. This means that, in the case where quintessence is depicted via exponential potentials, only a single exponential in the tail of the { quintessential inflation} potential is enough to depict the evolution of our universe.

gr-qc↗

arXiv2019

The Peebles -- Vilenkin quintessential inflation model revisited

We review the well-known Peebles-Vilenkin (PV) quintessential inflation model and discuss its possible improvements in agreement with the recent observations. The improved PV model depends only on two parameters: the inflaton mass $m$, and another smaller mass $M$; where the latter has to be chosen in order to undertake that, at present time, the dark energy density of the universe is approximately about 70\% of the total energy budget of the universe. The value of the inflaton mass $m$ is calculated using the observational value of the power spectrum of the scalar perturbations, and the value of mass $M$, which depends on the reheating temperature, is calculated by solving the corresponding dynamical system whose initial conditions are taken at the matter-radiation equality and are obtained from three observational data: the red shift at the matter-radiation equality, the ratio of the matter energy density to the critical one at the present time and the current value of the Hubble parameter.

gr-qc↗

arXiv2018

Bouncing cosmologies via modified gravity in the ADM formalism: Application to Loop Quantum Cosmology

We consider the ADM formalism as a tool to build bouncing cosmologies. In this approach, the foliation of the spacetime has to be fixed in order to go beyond General Relativity modifying the gravitational sector. Once a preferred slicing, which we choose based on the matter content of the universe following the spirit of Weyl's postulate, has been fixed, $f$ theories depending on the extrinsic and intrinsic curvature of the slicing are covariant for all the reference frames preserving the foliation, i.e., the constraint and dynamical equations have the same form for all these observers. Moreover, choosing multivalued $f$ functions, bouncing backgrounds emerge in a natural way. In fact, the simplest is the one corresponding to holonomy corrected Loop Quantum Cosmology. The final goal of this work is to provide the equations of perturbations which, unlike the full equations, become gauge invariant in this theory, and apply them to the so-called matter bounce scenario.

gr-qc↗

arXiv2017

Qualitative study in Loop Quantum Cosmology

This work contains a detailed qualitative analysis, in General Relativity and in Loop Quantum Cosmology, of the dynamics in the associated phase space of a scalar field minimally coupled with gravity, whose potential mimics the dynamics of a perfect fluid with a linear Equation of State (EoS). Dealing with the orbits (solutions) of the system, we will see that there are analytic ones, which lead to the same dynamics as the perfect fluid, and our goal is to check their stability, depending on the value of the EoS parameter, i.e., to show whether the other orbits converge or diverge to these analytic solutions at early and late times.

gr-qc↗

arXiv2017

The matter-ekpyrotic bounce scenario in Loop Quantum Cosmology

We will perform a detailed study of the matter-ekpyrotic bouncing scenario in Loop Quantum Cosmology using the methods of the dynamical systems theory. We will show that when the background is driven by a single scalar field, at very late times, in the contracting phase, all orbits depict a matter dominated Universe, which evolves to an ekpyrotic phase. After the bounce the Universe enters in the expanding phase, where the orbits leave the ekpyrotic regime going to a kination (also named deflationary) regime. Moreover, this scenario supports the production of heavy massive particles conformally coupled with gravity, which reheats the universe at temperatures compatible with the nucleosynthesis bounds and also the production of massless particles non-conformally coupled with gravity leading to very high reheating temperatures but ensuring the nucleosynthesis success. Dealing with cosmological perturbations, these background dynamics produce a nearly scale invariant power spectrum for the modes that leave the Hubble radius, in the contracting phase, when the Universe is quasi-matter dominated, whose spectral index and corresponding running is compatible with the recent experimental data obtained by PLANCK's team.

gr-qc↗

arXiv2016

Simple inflationary quintessential model II: Power law potentials

The present work is a sequel of our previous work Phys.Rev.D { 93}, 084018 (2016) [arXiv:1601.08175 [gr-qc]] cite{hap} which depicted a simple version of an inflationary quintessential model whose inflationary stage was described by a Higgs type potential and the quintessential phase was responsible due to an exponential potential. Additionally, the model predicted a nonsingular universe in past which was geodesically past incomplete. Further, it was also found that the model is in agreement with the Planck 2013 data when running is allowed. But, this model was found to be unsuccessful with Planck 2015 data with or without running. However, in this sequel we propose a family of models runs by a single parameter $alpha in [0, 1]$ which proposes another "inflationary quintessential model" where the inflation and the quintessence regimes are respectively described by a power law potential and a cosmological constant. The model is also nonsingular although geodesically past incomplete as in the cited model. However, the present one is found to be more simple in compared to the previous model and it is in excellent agreement with the observational data. We note that unlike the previous model which matched only with Planck 2013 data in presence of running, a large number of the models of this family with $alpha in [0,1/2)$ matches with both Planck 2013 and Planck 2015 data whether the running is allowed or not. Thus, the properties in the current family of models in compared to its past companion justify its need for a better cosmological model with the successive improvement of the observational data.1

gr-qc↗

arXiv2016

Discrepancies between observational data and theoretical forecast in single field slow roll inflation

The PLANCK collaboration has determined values for the spectral parameters of the CMB radiation, namely the spectral index $n_s$, its running $α_s$, the running of the running $β_s$, using a growing body of measurements of CMB anisotropies by the Planck satellite and other missions. These values do not follow the hierarchy of sizes predicted by single field, slow roll inflationary theory, and are thus difficult to fit for such inflation models. In this work we present first a study of 49 single field, slow roll inflationary potentials in which we assess the likelyhood of these models fitting the spectral parameters to their currently most accurate determination given by the PLANCK collaboration. We check numerically with a MATLAB program the spectral parameters that each model can yield for a very broad, comprehensive list of possible parameter and field values. The comparison of spectral parameter values supported by the models with their determinations by the PLANCK collaboration leads to the conclusion that the data provided by PLANCK2015 TT+lowP and PLANCK2015 TT,TE,EE+lowP taking into account the running of the running disfavours 40 of the 49 models with confidence level at least 92.8\%. Next, we discuss the reliability of the current computations of these spectral parameters. We identify a bias in the method of determination of the spectral parameters by least residue parameter fitting (using MCMC or any other scheme) currently used to reconstruct the power spectrum of scalar perturbations. This bias can explain the observed contradiction between theory and observations. Its removal is computationally costly, but necessary in order to compare the forecasts of single field, slow roll theories with observations.

gr-qc↗

arXiv2016

A simple nonsingular inflationary quintessential model

In the framework of a flat Friedmann-Lema{\^ı}tre-Robertson-Walker (FLRW) geometry, we present a nonsingular model (no big bang singularity at finite time) of our universe describing its evolution starting from its early inflationary era up to the present accelerating phase. We found that a hydrodynamical fluid with nonlinear equation of state could result in such a non singular scenario, which after the end of this inflationary stage, suffers a sudden phase transition and enters into the stiff matter dominated era, and the universe becomes reheated due to a huge amount of particle production. Finally, it asymptotically enters into the de Sitter phase concluding the present accelerated expansion. We show that the background providing an inflationary potential leads to a power spectrum of the cosmological perturbations which fit well with the latest Planck estimations. At the end, we compared our viable potential with some known inflationary quintessential potentials, which shows that, our model is an improved version of them because it contains an analytic solution that allows us to perform analytic calculations.

gr-qc↗

arXiv2015

Matter Bounce Scenario in F(T) gravity

It is shown that teleparallel $F(T)$ theories of gravity combined with holonomy corrected Loop Quantum Cosmology (LQC) support a Matter Bounce Scenario (MBS) which is a potential alternative to the inflationary paradigm. The Matter Bounce Scenario is reviewed and, according to the current observational data provided by PLANCK's team, we have summarized all the conditions that it has to satisfy in order to be a viable alternative to inflation, such as to provide a theoretical value of the spectral index and its running compatible with the latest PLANCK data, to have a reheating process via gravitational particle production, or to predict some signatures in the non-gaussianities of the power spectrum. The calculation of the power spectrum for scalar perturbations and the ratio of tensor to scalar perturbations has been done, in the simplest case of an exact matter dominated background, for both holonomy corrected LQC and teleparallel $F(T)$ gravity. Finally, we have discussed the challenges (essentially, dealing with non-gaussianities, the calculation of the 3-point function in flat spatial geometries for theories beyond General Relativity) and problems (Jeans instabilities in the case of holonomy corrected LQC or local Lorentz dependence in teleparallelism) that arise in either bouncing scenario.

gr-qc↗

arXiv2014

Viability of the matter bounce scenario in Loop Quantum Cosmology for general potentials

We consider the matter bounce scenario in Loop Quantum Cosmology (LQC) for physical potentials that at early times provide a nearly matter dominated Universe in the contracting phase, having a reheating mechanism in the expanding phase, i.e., being able to release the energy of the scalar field creating particles that thermalize in order to match with the hot Friedmann Universe, and finally at late times leading to the current cosmic acceleration. For these models, numerically solving the dynamical equations we have seen that the teleparallel version of LQC leads to theoretical results that fit well with current observational data. More precisely, in teleparallel LQC there is a set of solutions which leads to theoretical results that match correctly with last BICEP2 data, and there is another set whose theoretical results fit well with {\it Planck's} experimental data. On the other hand, in holonomy corrected LQC the theoretical value of the tensor/scalar ratio is smaller than in teleparallel LQC, which means that there is always a set of solutions that matches with {\it Planck's} data, but for some potentials BICEP2 experimental results disfavours holonomy corrected LQC.

gr-qc↗