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arXiv 2020年

作者： Lemos-Paião, Ana P. Silva, Cristiana J. Torres, Delfim F.M. Venturino, Ezio Center for Research and Development in Mathematics and Applications CIDMA Department of Mathematics University of Aveiro Aveiro3810-193 Portugal Department of Mathematics Giuseppe Peano Università di Torino via Carlo Alberto 10 Torino10123 Italy INdAM research group GNCS

We propose a mathematical model for the transmission dynamics of some strains of the bacterium Vibrio cholerae, responsible for the cholera disease in humans. We prove that, when the basic reproduction number is equal to one, a transcritical bifurcation occurs for which the endemic equilibrium emanates from the disease-free point. A control function is introduced into the model, representing the distribution of chlorine water tablets for water purification. An optimal control problem is then proposed and analyzed, where the goal is to determine the fraction of susceptible individuals who should have access to chlorine water tablets in order to minimize the total number of new infections plus the total cost associated with the distribution of chlorine water tablets, over the considered period of time. Finally, we consider real data of the cholera outbreak in Yemen, from 27 April 2017 to 15 April 2018, choosing the values of the parameters of the uncontrolled model that fit the real data. Using our optimal control results, we show, numerically, that the distribution of chlorine water tablets could have stopped, in a fast way, the worst cholera outbreak that ever occurred in human history. Due to the critical situation of Yemen, we also simulate the case where only a small percentage of susceptible individuals has access to chlorine water tablets and obtain an optimal control solution that decreases, substantially, the maximum number of infective individuals attained at the *** Codes 34C60, 49K15, 92D30 Copyright © 2020, The Authors. All rights reserved.

关键词： Diseases

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Compactness bounds in general relativity

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Physical Review D 2022年第4期106卷 L041502-L041502页

作者： Artur Alho José Natário Paolo Pani Guilherme Raposo Center for Mathematical Analysis Geometry and Dynamical Systems Instituto Superior Técnico Universidade de Lisboa Av. Rovisco Pais 1049-001 Lisboa Portugal Dipartimento di Fisica Sapienza Università di Roma & INFN Roma1 Piazzale Aldo Moro 5 00185 Roma Italy CENTRA Instituto Superior Técnico Universidade de Lisboa Av. Rovisco Pais 1049-001 Lisboa Portugal Centre for Research and Development in Mathematics and Applications (CIDMA) Campus de Santiago 3810-183 Aveiro Portugal

A foundational theorem due to Buchdahl states that, within general relativity (GR), the maximum compactness C≡GM/(Rc2) of a static, spherically symmetric, perfect fluid object of mass M and radius R is C=4/9. As a corollary, there exists a compactness gap between perfect fluid stars and black holes (where C=1/2). Here we generalize Buchdahl’s result by introducing the most general equation of state for elastic matter with constant longitudinal wave speeds and apply it to compute the maximum compactness of regular, self-gravitating objects in GR. We show that: (i) the maximum compactness grows monotonically with the longitudinal wave speed; (ii) elastic matter can exceed Buchdahl’s bound and reach the black hole compactness C=1/2 continuously; (iii) however, imposing subluminal wave propagation lowers the maximum compactness bound to C≈0.462, which we conjecture to be the maximum compactness of any static elastic object satisfying causality; (iv) imposing also radial stability further decreases the maximum compactness to C≈0.389. Therefore, although anisotropies are often invoked as a mechanism for supporting horizonless ultracompact objects, we argue that the black hole compactness cannot be reached with physically reasonable matter within GR and that true black hole mimickers require either exotic matter or beyond-GR effects.

关键词： General relativity Gravitation

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On the Randić energy of caterpillar graphs

arXiv

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arXiv 2021年

作者： Cardoso, Domingos M. Carvalho, Paula Martínez, Roberto Carlos Díaz Rama, Paula Center for Research and Development in Mathematics and Applications Department of Mathematics Universidade de Aveiro Aveiro Portugal Department of Mathematics Universidade de Aveiro Aveiro Portugal Departamento de Matematicas Universidad de La Serena Cisternas 1200 La Serena Chile

A caterpillar graph T (p1,..., pr) of order n = r + ∑ri=1 pi, r ≥ 2, is a tree such that removing all its pendent vertices gives rise to a path of order r. In this paper we establish a necessary and sufficient condition for a real number to be an eigenvalue of the Randić matrix of T (p1,..., pr). This result is applied to determine the extremal caterpillars for the Randić energy of T (p1,..., pr) for cases r = 2 (the double star) and r = 3. We characterize the extremal caterpillars for r = 2. Moreover, we study the family of caterpillars T (p, n−p−q−3, q) of order n, where q is a function of p, and we characterize the extremal caterpillars for three cases: q = p, q = n − p − b − 3 and q = b, for b ∈ {1,..., n − 6} fixed. Some illustrative examples are included. Copyright © 2021, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

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Precessing binary black holes as engines of electromagnetic helicity

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Physical Review D 2023年第4期108卷 044052-044052页

作者： Nicolas Sanchis-Gual Adrian del Rio Departament d’Astronomía i Astrofísica Universitat de València Dr. Moliner 50 46100 Burjassot València Spain Departamento de Matemática Universidade de Aveiro and Centre for Research and Development in Mathematics and Applications (CIDMA) Campus de Santiago 3810-183 Aveiro Portugal Departamento de Física Teórica and IFIC Universitat de Valencia-CSIC Dr. Moliner 50 46100 Burjassot Valencia Spain

We show that binary black hole mergers with precessing evolution can potentially excite photons from the quantum vacuum in such a way that total helicity is not preserved in the process. Helicity violation is allowed by quantum fluctuations that spoil the electric-magnetic duality symmetry of the classical Maxwell theory without charges. We show here that precessing binary black hole systems in astrophysics generate a flux of circularly polarized gravitational waves which, in turn, provides the required helical background that triggers this quantum effect. Solving the fully nonlinear Einstein’s equations with numerical relativity we explore the parameter space of binary systems and extract the detailed dependence of the quantum effect with the spins of the two black holes. We also introduce a set of diagrammatic techniques that allows us to predict when a binary black hole merger can or cannot emit circularly polarized gravitational radiation, based on mirror-symmetry considerations. This framework allows to understand and to interpret correctly the numerical results, and to predict the outcomes in potentially interesting astrophysical systems.

关键词： Gravitational wave sources Quantum aspects of black holes Quantum fields in curved spacetime Numerical relativity Numerical simulations in gravitation & astrophysics

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Binary superradiance: A numerical study

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Physical Review D 2022年第8期105卷 084004-084004页

作者： Diogo C. Ribeiro Miguel Zilhão Vitor Cardoso Centro de Astrofísica e Gravitação-CENTRA Departamento de Física Instituto Superior Técnico-IST Universidade de Lisboa-UL Avenida Rovisco Pais 1 1049-001 Lisboa Portugal Departamento de Matemática da Universidade de Aveiro and Centre for Research and Development in Mathematics and Applications (CIDMA) Campus de Santiago 3810-183 Aveiro Portugal Niels Bohr International Academy Niels Bohr Institute Blegdamsvej 17 2100 Copenhagen Denmark

Rotating axisymmetric objects amplify incoming waves by superradiant scattering. When enclosed in a cavity, the repeated interaction of a confined field with the object may trigger superradiant instabilities. Rotating binaries are ubiquitous in physics, and play a fundamental role in astrophysics and in everyday life instruments. Such binaries may be prone to superradiant phenomena as well, but their inherent complexity makes it challenging to study how exactly such instabilities can be triggered. Here, we study a binary of two absorbing objects (mimicking black hole binaries, blades of a helicopter, etc.) revolving around a common center, and show that superradiant instabilities do occur, on expected timescales and frequency range. Our results provide the first demonstration that superradiance also occurs for highly asymmetric systems, and may have a wealth of applications in fluid dynamics and astrophysics. Extrapolating to astrophysical black holes, our findings indicate that compact binaries may be used as interesting particle detectors, depositing a fraction of their energy into putative new fundamental ultralight degrees of freedom.

关键词： Classical black holes Fluids & classical fields in curved spacetime General relativity

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Full 3D nonlinear dynamics of charged and magnetized boson stars

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Physical Review D 2025年第2期111卷 024070-024070页

作者： Víctor Jaramillo Darío Núñez Milton Ruiz Miguel Zilhão Department of Astronomy University of Science and Technology of China Hefei Anhui 230026 China Department of Modern Physics University of Science and Technology of China Hefei Anhui 230026 China Instituto de Ciencias Nucleares Universidad Nacional Autónoma de México Circuito Exterior Ciudad Universitaria A.P. 70-543 Coyoacán México 04510 CdMx México Centre for Research and Development in Mathematics and Applications (CIDMA) Department of Mathematics University of Aveiro 3810-193 Aveiro Portugal Departament d’Astronomia i Astrofísica Universitat de València C/ Dr Moliner 50 46100 Burjassot (València) Spain

Gauged boson stars are exotic compact objects that can potentially mimic black holes or magnetized neutron stars in both their gravitational and electromagnetic signatures, offering a compelling new description or even an alternative explanation for various multimessenger phenomena. As a crucial step toward establishing boson stars as viable multimessenger sources, we perform 3D numerical simulations of the fully nonlinear Einstein-Maxwell-Klein-Gordon system, focusing on both spherical and axisymmetric boson star configurations that vary in their electromagnetic coupling between the neutral case up to values close to the critical case, and thus their magnetic field content. For spherical configurations, we consistently find stable solutions. In contrast, for axially symmetric, electrically neutral, magnetized configurations, the dynamics are highly sensitive to the electromagnetic coupling. Configurations with stronger coupling develop a one-armed mode instability, which leads to collapse into black holes. Configurations with weaker coupling undergo a two-stage process: an initial bar-mode instability that triggers a one-armed spiral deformation. This eventually also results in black hole formation, accompanied by emissions of both gravitational and electromagnetic radiation. A similar instability and two-stage pattern is observed in all charged rotating boson stars analyzed. However, all of these configurations become stable when self-interactions are introduced.

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Ultralight bosonic dark matter in white dwarfs and potential observational consequences

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Physical Review D 2022年第8期105卷 084023-084023页

作者： Nicolas Sanchis-Gual Paula Izquierdo Departamento de Astronomía y Astrofísica Universitat de València Doctor Moliner 50 Burjassot (València) 46100 Spain Departamento de Matemática Universidade de Aveiro and Centre for Research and Development in Mathematics and Applications (CIDMA) Campus de Santiago Aveiro 3810-183 Portugal Instituto de Astrofísica de Canarias La Laguna Tenerife 38205 Spain Department of Physics University of Warwick Coventry CV4 7AL United Kingdom

Fluid and ultralight bosonic dark matter can interact through gravity to form stable fermion-boson stars, which are static and regular mixed solutions of the Einstein-Euler-(complex, massive)-Klein-Gordon system. In this work we study the dynamical formation via gravitational cooling of a spherical mixed white-dwarf–boson star, whose properties depend on the boson particle mass and the mass of the boson star. Due to the accretion of bosonic dark matter, the white dwarf migrates to a denser and more compact object with a boson star core, thus modifying its gravitational redshift and altering the electromagnetic radiation emitted from the photosphere. We discuss the implications of the changes in the gravitational redshift that in principle could be produced by any type of dark matter and that might lead to small discrepancies in the estimation of masses and radii derived from white-dwarf observations.

关键词： Dark matter Fluids & classical fields in curved spacetime General relativity Numerical relativity

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Compact elastic objects in general relativity

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Physical Review D 2022年第4期105卷 044025-044025页

We introduce a rigorous and general framework to study systematically self-gravitating elastic materials within general relativity, and apply it to investigate the existence and viability, including radial stability, of spherically symmetric elastic stars. We present the mass-radius (M−R) diagram for various families of models, showing that elasticity contributes to increasing the maximum mass and the compactness up to ≈22%, thus supporting compact stars with mass well above two solar masses. Some of these elastic stars can reach compactness as high as GM/(c2R)≈0.35 while remaining stable under radial perturbations and satisfying all energy conditions and subluminal wave propagation, thus being physically realizable models of stars with a light ring. We provide numerical evidence that radial instability occurs for central densities larger than that corresponding to the maximum mass, as in the perfect-fluid case. Elasticity may be a key ingredient to building consistent models of exotic ultracompact objects and black hole mimickers, and can also be relevant for a more accurate modeling of the interior of neutron stars.

关键词： Fluids & classical fields in curved spacetime General relativity

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Traversable Wormholes in Einstein-Dirac-Maxwell Theory

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Physical Review Letters 2021年第10期126卷 101102-101102页

作者： Jose Luis Blázquez-Salcedo Christian Knoll Eugen Radu Departamento de Física Teórica and IPARCOS Universidad Complutense de Madrid E-28040 Madrid Spain Institut für Physik Universität Oldenburg Postfach 2503 D-26111 Oldenburg Germany Departamento de Matemática da Universidade de Aveiro and Centre for Research and Development in Mathematics and Applications (CIDMA) Campus de Santiago 3810-183 Aveiro Portugal

We construct a specific example of a class of traversable wormholes in Einstein-Dirac-Maxwell theory in four spacetime dimensions, without needing any form of exotic matter. Restricting to a model with two massive fermions in a singlet spinor state, we show the existence of spherically symmetric asymptotically flat configurations which are free of singularities, representing localized states. These solutions satisfy a generalized Smarr relation, being connected with the extremal Reissner-Nordström black holes. They also possess a finite mass M and electric charge Qe, with Qe/M>1. An exact wormhole solution with ungauged, massless fermions is also reported.

关键词： General relativity General relativity equations & solutions

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Spinning gauged boson and Dirac stars: A comparative study

arXiv

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arXiv 2021年

作者： Herdeiro, Carlos Perapechka, Ilya Radu, Eugen Shnir, Yakov Departamento de Matemática Universidade de Aveiro Center for Research and Development in Mathematics and Applications - CIDMA Campus de Santiago Aveiro3810-183 Portugal Department of Theoretical Physics and Astrophysics Belarusian State University Nezavisimosti Avenue 4 Minsk220004 Belarus BLTP JINR Joliot-Curie 6 Moscow Region Dubna141980 Russia

Scalar boson stars and Dirac stars are solitonic solutions of the Einstein-Klein-Gordon and Einstein-Dirac classical equations, respectively. Despite the different bosonic vs. fermionic nature of the matter field, these solutions to the classical field equations have been shown to have qualitatively similar features [1]. In particular, for spinning stars the most fundamental configurations can be in both cases toroidal, unlike spinning Proca stars that are spheroidal [2]. In this paper we gauge the scalar and Dirac fields, by minimally coupling them to standard electromagnetism. We explore the impact of the gauge coupling on the resulting solutions. One of the most relevant difference concerns the gyromagnetic ratio, which for the scalar stars takes values around 1, whereas for Dirac stars takes values around 2. Copyright © 2021, The Authors. All rights reserved.

关键词： Stars

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