En vista del inminente cambio climático global, es necesario contar con modelos matemáticos regio... more En vista del inminente cambio climático global, es necesario contar con modelos matemáticos regionales y globales que puedan proyectar con detalle las tendencias futuras de temperatura, humedad, precipitación, viento y absorción de radiación solar, entre otras. Con esta motivación, presentamos los resultados preliminares de un modelo físico cuantitativo que describe el movimiento, densidad y temperatura de masas de aire en la atmósfera. El modelo se basa en la solución numérica de las ecuaciones de Euler para aire seco, por medio del método de volúmenes finitos. El modelo es utilizado para describir la evolución en el tiempo de masas de aire tibio y frío en un perfil bidimensional que representa una sección vertical de la atmósfera. Se incluye también el efecto de la curvatura del suelo por medio de coordenadas que siguen el perfil topográfico del terreno. En los resultados de la simulación es posible observar que el movimiento del aire genera diferentes patrones en las corrientes...
Se presenta un análisis de de circulación del viento en la vecindad de la superficie terrestre, p... more Se presenta un análisis de de circulación del viento en la vecindad de la superficie terrestre, para una región centrada alrededor de Guatemala. Para tal fin se utilizó el modelo climático regional (RegCM), con el caul se simuló la dinámica atmosférica sobre dicha región durante todo el 2016. El propósito del estudio es obtener la variación de mesoescala (decenas de kilómetros) del campo de velocidad del viento. Se puede observar que a medida que la resolución se incrementa se obtiene una representación más precisa de los detalles y características de la topografía del terreno, la cual influye en los patrones de circulación del viento a escalas de pocos kilómetros. Con una resolución fina de 2 km es posible observar zonas de flujo intenso de viento sobre la superficie; como en Palín, Escuintla. También se logra ver la presencia de patrones de circulación diurna que son producto del ciclo diario de calentamiento del terreno debido al sol y el consecuente enfriamiento durante la noche...
Gravitational wave observations can be used to probe non-linear gravitational interactions and th... more Gravitational wave observations can be used to probe non-linear gravitational interactions and thus provide strong tests of Einstein's theory of general relativity. Using the tools of numerical relativity, we present results from the late inspiral and merger of a binary black hole system in Jordan-Brans-Dicke-Fierz theory. In particular, we address whether in this theory the gravitational waves produced during the
We present a microscopic driving algorithm that prescribes the acceleration using three parameter... more We present a microscopic driving algorithm that prescribes the acceleration using three parameters: the distance to the leading vehicle, to the next traffic light and to the nearest stopping point when the next traffic light is in the red phase. We apply this algorithm to construct decision trees that enable two driving behaviors: aggressive and careful. The focus of this study is to analyze the amount of aggressive drivers that are needed in order to generate a traffic gridlock in a portion of a city with signalized intersections. At rush hour, aggressive drivers will enter the intersection regardless if they have enough time or space to clear it. When their traffic light changes they block other drivers, thus providing the conditions for a gridlock to develop. We find that gridlocks emerge even with very few aggressive drivers present. These results support the idea of promoting good driving behavior to avoid heavy congestion during rush hours.
La región del Sur de México y América Central conforman lo que se conoce como Mesoamérica. El cic... more La región del Sur de México y América Central conforman lo que se conoce como Mesoamérica. El ciclo anual de precipitación característico de la vertiente del Pacífico de esta región presenta una distribución anual bimodal, con dos máximos y un mínimo relativo intraestacional que se conoce como veranillo o canícula. En este estudio se analiza la variabilidad a pequeña escala (decenas de kilómetros) del veranillo. Se realizaron simulaciones numéricas utilizando el modelo de área limitada RegCM4 sobre un dominio en la región de Mesoamérica, para un periodo de seis años. Se utilizaron los datos de reanálisis de ERA Interim como condiciones iniciales y de frontera lateral. El dominio fue subdividido en áreas más pequeñas y se calculó la precipitación promedio mensual para cada una de ellas. Los resultados muestran que la canícula o veranillo presenta una alta variabilidad espacial en la intensidad de sus dos máximos, e incluso la ausencia total del valor mínimo que la caracteriza. Tal comportamiento se atribuye a las interacciones de la atmósfera con el suelo y a la topografía del terreno que son mejor representadas en un modelo climático regional.
Within linearized perturbation theory, black holes decay to their final stationary state through ... more Within linearized perturbation theory, black holes decay to their final stationary state through the well-known spectrum of quasinormal modes. Here we numerically study whether nonlinearities change this picture. For that purpose we study the ringdown frequencies of gauge-invariant second-order gravitational perturbations induced by self-coupling of linearized perturbations of Schwarzschild black holes. We do so through high-accuracy simulations in the time domain of first and second-order Regge-Wheeler-Zerilli type equations, for a variety of initial data sets. We consider first-order even-parity $(\ell=2,m=\pm 2)$ perturbations and odd-parity $(\ell=2,m=0)$ ones, and all the multipoles that they generate through self-coupling. For all of them and all the initial data sets considered we find that ---in contrast to previous predictions in the literature--- the numerical decay frequencies of second-order perturbations are the same ones of linearized theory, and we explain the observe...
ABSTRACT Gravitational wave observations will probe non-linear gravitational interactions and thu... more ABSTRACT Gravitational wave observations will probe non-linear gravitational interactions and thus enable strong tests of Einstein's theory of general relativity. We present a numerical relativity study of the late inspiral and merger of binary black holes in scalar-tensor theories of gravity. We consider black hole binaries in an inhomogeneous scalar field, specifically binaries inside a scalar field bubble, in some cases with a potential. We calculate the emission of dipole radiation. We also show how these configurations trigger detectable differences between gravitational waves in scalar-tensor gravity and the corresponding waves in general relativity. We conclude that, barring an external mechanism to induce dynamics in the scalar field, scalar-tensor gravity binary black holes alone are not capable of awaking a dormant scalar field, and are thus observationally indistinguishable from their general relativistic counterparts.
This dissertation presents numerical studies of gravitational waves produced by black holes in tw... more This dissertation presents numerical studies of gravitational waves produced by black holes in two scenarios: perturbations of a single black hole, and the collision of a binary pair. Their detection plays a crucial roll in further testing General Relativity and opens a whole new field of observational astronomy. First, a technique called Cauchy--perturbative matching is revisited in one dimension through the use of new numerical methods, such as high order finite difference operators, constraint-preserving boundary conditions and, most important, a multi-domain decomposition (also referred to as multi-patch, or multi-block approach). These methods are then used to numerically solve the fully non-linear three-dimensional Einstein vacuum equations representing a non-rotating distorted black hole. In combination with a generalization of the Regge-Wheeler-Zerilli formalism, we quantify the effect of the background choice in the wave extraction techniques. It is found that a systematic error is introduced at finite distances. Furthermore, such error is found to be larger than those due to numerical discretization. Subsequently, the first simulations ever of binary black holes with a finite-difference multi-domain approach are presented. The case is one in which the black holes orbit for about twelve cycles before merging. The salient features of this multi-domain approach are: i) the complexity of the problem scales linearly with the size of the computational domain, ii) excellent scaling, in both weak and strong senses, for several thousand processors. As a next step, binary black hole simulations from inspiral to merger and ringdown are performed using a new technique, turduckening, and a standard finite difference, adaptive mesh- refinement code. The computed gravitational waveforms are compared to those obtained through evolution of the same exact initial configuration but with a pseudo-spectral collocation code. Both the gravitational waves extracted at finite locations and their extrapolated values to null infinity are compared. Finally, a numerical study of generic second order perturbations of Schwarzschild black holes is presented using a new gauge invariant high order perturbative formalism. A study of the self-coupling of first order modes and the resulting radiated energy, in particular its dependence on the type of initial perturbation, is detailed.
Gravitational wave observations can be used to probe non-linear gravitational interactions and th... more Gravitational wave observations can be used to probe non-linear gravitational interactions and thus provide strong tests of Einstein's theory of general relativity. Using the tools of numerical relativity, we present results from the late inspiral and merger of a binary black hole system in Jordan-Brans-Dicke-Fierz theory. In particular, we address whether in this theory the gravitational waves produced during the coalescence differ from those from general relativity. We discuss how future gravitational wave observations of binary black hole mergers could be used to place bounds on such scalar-tensor theories.
We compare waveforms for binary black hole simulations using finite difference with adaptive mesh... more We compare waveforms for binary black hole simulations using finite difference with adaptive mesh refinement and spectral methods with multiple domains. In both cases we use the exact same initial data, extracting waves at a fixed location and extrapolating them to infinity. )
A complete gauge invariant formalism for arbitrary second order perturbations of Schwarzschild bl... more A complete gauge invariant formalism for arbitrary second order perturbations of Schwarzschild black holes will be presented. We will then discuss numerical simulations using that formalism to study non-linear effects in the ringdown of Schwarzschild black holes due to mode-mode coupling and the dependence of these effects on the type and shape of initial perturbation. Finally we will compare results with numerical simulations of colliding binary black holes in their late stage (ringdown) phase. )
Multi-block (or multi-patch) systems are computational methods to discretise manifolds by coverin... more Multi-block (or multi-patch) systems are computational methods to discretise manifolds by covering them with several independent blocks. Each block is then discretised in a conventional way, e.g.using finite differences. Thus multi-block systems are a natural approach in general relativity, where they correspond to using several maps to cover a domain. Multi-block systems have several major advantages: They can be used to avoid coordinate singularities, to use coordinates that are adapted to a particular problem, and to place numerical resolution where desired. In particular, they can be used to model spherical boundaries in a smooth manner and to track gravitational radiation efficiently in the wave zone of compact sources. While adaptive mesh refinement is essential to achieve a necessary accuracy locally, multi-block methods are superior in adapting a discretisation globally to a given problem setup. We report on recent results of fully relativistic three-dimensional time-dependent black hole simulations using multi-block systems. We will compare accuracy and efficiency to mesh refinement methods, demonstrating certain advantages of multi-block discretisations.
Within linearized perturbation theory, black holes decay to their final stationary state through ... more Within linearized perturbation theory, black holes decay to their final stationary state through the well-known spectrum of quasinormal modes. Here we numerically study whether nonlinearities change this picture. For that purpose we study the ringdown frequencies of gauge-invariant second-order gravitational perturbations induced by self-coupling of linearized perturbations of Schwarzschild black holes. We do so through high-accuracy simulations in the time domain of first and second-order Regge-Wheeler-Zerilli type equations, for a variety of initial data sets. We consider first-order even-parity $(\ell=2,m=\pm 2)$ perturbations and odd-parity $(\ell=2,m=0)$ ones, and all the multipoles that they generate through self-coupling. For all of them and all the initial data sets considered we find that ---in contrast to previous predictions in the literature--- the numerical decay frequencies of second-order perturbations are the same ones of linearized theory, and we explain the observed behavior. This would indicate, in particular, that when modeling or searching for ringdown gravitational waves, appropriately including the standard quasinormal modes already takes into account nonlinear effects.
We present results from the simulation of equal mass binary black holes using a multiple block do... more We present results from the simulation of equal mass binary black holes using a multiple block domain decomposition. Our scheme makes use of high-order finite difference operators, excision and the generalized harmonic formulation of Einstein's equations. We are able to compute wave-forms and compare them with numerical solutions obtained by pseudo-spectral methods.
En vista del inminente cambio climático global, es necesario contar con modelos matemáticos regio... more En vista del inminente cambio climático global, es necesario contar con modelos matemáticos regionales y globales que puedan proyectar con detalle las tendencias futuras de temperatura, humedad, precipitación, viento y absorción de radiación solar, entre otras. Con esta motivación, presentamos los resultados preliminares de un modelo físico cuantitativo que describe el movimiento, densidad y temperatura de masas de aire en la atmósfera. El modelo se basa en la solución numérica de las ecuaciones de Euler para aire seco, por medio del método de volúmenes finitos. El modelo es utilizado para describir la evolución en el tiempo de masas de aire tibio y frío en un perfil bidimensional que representa una sección vertical de la atmósfera. Se incluye también el efecto de la curvatura del suelo por medio de coordenadas que siguen el perfil topográfico del terreno. En los resultados de la simulación es posible observar que el movimiento del aire genera diferentes patrones en las corrientes...
Se presenta un análisis de de circulación del viento en la vecindad de la superficie terrestre, p... more Se presenta un análisis de de circulación del viento en la vecindad de la superficie terrestre, para una región centrada alrededor de Guatemala. Para tal fin se utilizó el modelo climático regional (RegCM), con el caul se simuló la dinámica atmosférica sobre dicha región durante todo el 2016. El propósito del estudio es obtener la variación de mesoescala (decenas de kilómetros) del campo de velocidad del viento. Se puede observar que a medida que la resolución se incrementa se obtiene una representación más precisa de los detalles y características de la topografía del terreno, la cual influye en los patrones de circulación del viento a escalas de pocos kilómetros. Con una resolución fina de 2 km es posible observar zonas de flujo intenso de viento sobre la superficie; como en Palín, Escuintla. También se logra ver la presencia de patrones de circulación diurna que son producto del ciclo diario de calentamiento del terreno debido al sol y el consecuente enfriamiento durante la noche...
Gravitational wave observations can be used to probe non-linear gravitational interactions and th... more Gravitational wave observations can be used to probe non-linear gravitational interactions and thus provide strong tests of Einstein's theory of general relativity. Using the tools of numerical relativity, we present results from the late inspiral and merger of a binary black hole system in Jordan-Brans-Dicke-Fierz theory. In particular, we address whether in this theory the gravitational waves produced during the
We present a microscopic driving algorithm that prescribes the acceleration using three parameter... more We present a microscopic driving algorithm that prescribes the acceleration using three parameters: the distance to the leading vehicle, to the next traffic light and to the nearest stopping point when the next traffic light is in the red phase. We apply this algorithm to construct decision trees that enable two driving behaviors: aggressive and careful. The focus of this study is to analyze the amount of aggressive drivers that are needed in order to generate a traffic gridlock in a portion of a city with signalized intersections. At rush hour, aggressive drivers will enter the intersection regardless if they have enough time or space to clear it. When their traffic light changes they block other drivers, thus providing the conditions for a gridlock to develop. We find that gridlocks emerge even with very few aggressive drivers present. These results support the idea of promoting good driving behavior to avoid heavy congestion during rush hours.
La región del Sur de México y América Central conforman lo que se conoce como Mesoamérica. El cic... more La región del Sur de México y América Central conforman lo que se conoce como Mesoamérica. El ciclo anual de precipitación característico de la vertiente del Pacífico de esta región presenta una distribución anual bimodal, con dos máximos y un mínimo relativo intraestacional que se conoce como veranillo o canícula. En este estudio se analiza la variabilidad a pequeña escala (decenas de kilómetros) del veranillo. Se realizaron simulaciones numéricas utilizando el modelo de área limitada RegCM4 sobre un dominio en la región de Mesoamérica, para un periodo de seis años. Se utilizaron los datos de reanálisis de ERA Interim como condiciones iniciales y de frontera lateral. El dominio fue subdividido en áreas más pequeñas y se calculó la precipitación promedio mensual para cada una de ellas. Los resultados muestran que la canícula o veranillo presenta una alta variabilidad espacial en la intensidad de sus dos máximos, e incluso la ausencia total del valor mínimo que la caracteriza. Tal comportamiento se atribuye a las interacciones de la atmósfera con el suelo y a la topografía del terreno que son mejor representadas en un modelo climático regional.
Within linearized perturbation theory, black holes decay to their final stationary state through ... more Within linearized perturbation theory, black holes decay to their final stationary state through the well-known spectrum of quasinormal modes. Here we numerically study whether nonlinearities change this picture. For that purpose we study the ringdown frequencies of gauge-invariant second-order gravitational perturbations induced by self-coupling of linearized perturbations of Schwarzschild black holes. We do so through high-accuracy simulations in the time domain of first and second-order Regge-Wheeler-Zerilli type equations, for a variety of initial data sets. We consider first-order even-parity $(\ell=2,m=\pm 2)$ perturbations and odd-parity $(\ell=2,m=0)$ ones, and all the multipoles that they generate through self-coupling. For all of them and all the initial data sets considered we find that ---in contrast to previous predictions in the literature--- the numerical decay frequencies of second-order perturbations are the same ones of linearized theory, and we explain the observe...
ABSTRACT Gravitational wave observations will probe non-linear gravitational interactions and thu... more ABSTRACT Gravitational wave observations will probe non-linear gravitational interactions and thus enable strong tests of Einstein's theory of general relativity. We present a numerical relativity study of the late inspiral and merger of binary black holes in scalar-tensor theories of gravity. We consider black hole binaries in an inhomogeneous scalar field, specifically binaries inside a scalar field bubble, in some cases with a potential. We calculate the emission of dipole radiation. We also show how these configurations trigger detectable differences between gravitational waves in scalar-tensor gravity and the corresponding waves in general relativity. We conclude that, barring an external mechanism to induce dynamics in the scalar field, scalar-tensor gravity binary black holes alone are not capable of awaking a dormant scalar field, and are thus observationally indistinguishable from their general relativistic counterparts.
This dissertation presents numerical studies of gravitational waves produced by black holes in tw... more This dissertation presents numerical studies of gravitational waves produced by black holes in two scenarios: perturbations of a single black hole, and the collision of a binary pair. Their detection plays a crucial roll in further testing General Relativity and opens a whole new field of observational astronomy. First, a technique called Cauchy--perturbative matching is revisited in one dimension through the use of new numerical methods, such as high order finite difference operators, constraint-preserving boundary conditions and, most important, a multi-domain decomposition (also referred to as multi-patch, or multi-block approach). These methods are then used to numerically solve the fully non-linear three-dimensional Einstein vacuum equations representing a non-rotating distorted black hole. In combination with a generalization of the Regge-Wheeler-Zerilli formalism, we quantify the effect of the background choice in the wave extraction techniques. It is found that a systematic error is introduced at finite distances. Furthermore, such error is found to be larger than those due to numerical discretization. Subsequently, the first simulations ever of binary black holes with a finite-difference multi-domain approach are presented. The case is one in which the black holes orbit for about twelve cycles before merging. The salient features of this multi-domain approach are: i) the complexity of the problem scales linearly with the size of the computational domain, ii) excellent scaling, in both weak and strong senses, for several thousand processors. As a next step, binary black hole simulations from inspiral to merger and ringdown are performed using a new technique, turduckening, and a standard finite difference, adaptive mesh- refinement code. The computed gravitational waveforms are compared to those obtained through evolution of the same exact initial configuration but with a pseudo-spectral collocation code. Both the gravitational waves extracted at finite locations and their extrapolated values to null infinity are compared. Finally, a numerical study of generic second order perturbations of Schwarzschild black holes is presented using a new gauge invariant high order perturbative formalism. A study of the self-coupling of first order modes and the resulting radiated energy, in particular its dependence on the type of initial perturbation, is detailed.
Gravitational wave observations can be used to probe non-linear gravitational interactions and th... more Gravitational wave observations can be used to probe non-linear gravitational interactions and thus provide strong tests of Einstein's theory of general relativity. Using the tools of numerical relativity, we present results from the late inspiral and merger of a binary black hole system in Jordan-Brans-Dicke-Fierz theory. In particular, we address whether in this theory the gravitational waves produced during the coalescence differ from those from general relativity. We discuss how future gravitational wave observations of binary black hole mergers could be used to place bounds on such scalar-tensor theories.
We compare waveforms for binary black hole simulations using finite difference with adaptive mesh... more We compare waveforms for binary black hole simulations using finite difference with adaptive mesh refinement and spectral methods with multiple domains. In both cases we use the exact same initial data, extracting waves at a fixed location and extrapolating them to infinity. )
A complete gauge invariant formalism for arbitrary second order perturbations of Schwarzschild bl... more A complete gauge invariant formalism for arbitrary second order perturbations of Schwarzschild black holes will be presented. We will then discuss numerical simulations using that formalism to study non-linear effects in the ringdown of Schwarzschild black holes due to mode-mode coupling and the dependence of these effects on the type and shape of initial perturbation. Finally we will compare results with numerical simulations of colliding binary black holes in their late stage (ringdown) phase. )
Multi-block (or multi-patch) systems are computational methods to discretise manifolds by coverin... more Multi-block (or multi-patch) systems are computational methods to discretise manifolds by covering them with several independent blocks. Each block is then discretised in a conventional way, e.g.using finite differences. Thus multi-block systems are a natural approach in general relativity, where they correspond to using several maps to cover a domain. Multi-block systems have several major advantages: They can be used to avoid coordinate singularities, to use coordinates that are adapted to a particular problem, and to place numerical resolution where desired. In particular, they can be used to model spherical boundaries in a smooth manner and to track gravitational radiation efficiently in the wave zone of compact sources. While adaptive mesh refinement is essential to achieve a necessary accuracy locally, multi-block methods are superior in adapting a discretisation globally to a given problem setup. We report on recent results of fully relativistic three-dimensional time-dependent black hole simulations using multi-block systems. We will compare accuracy and efficiency to mesh refinement methods, demonstrating certain advantages of multi-block discretisations.
Within linearized perturbation theory, black holes decay to their final stationary state through ... more Within linearized perturbation theory, black holes decay to their final stationary state through the well-known spectrum of quasinormal modes. Here we numerically study whether nonlinearities change this picture. For that purpose we study the ringdown frequencies of gauge-invariant second-order gravitational perturbations induced by self-coupling of linearized perturbations of Schwarzschild black holes. We do so through high-accuracy simulations in the time domain of first and second-order Regge-Wheeler-Zerilli type equations, for a variety of initial data sets. We consider first-order even-parity $(\ell=2,m=\pm 2)$ perturbations and odd-parity $(\ell=2,m=0)$ ones, and all the multipoles that they generate through self-coupling. For all of them and all the initial data sets considered we find that ---in contrast to previous predictions in the literature--- the numerical decay frequencies of second-order perturbations are the same ones of linearized theory, and we explain the observed behavior. This would indicate, in particular, that when modeling or searching for ringdown gravitational waves, appropriately including the standard quasinormal modes already takes into account nonlinear effects.
We present results from the simulation of equal mass binary black holes using a multiple block do... more We present results from the simulation of equal mass binary black holes using a multiple block domain decomposition. Our scheme makes use of high-order finite difference operators, excision and the generalized harmonic formulation of Einstein's equations. We are able to compute wave-forms and compare them with numerical solutions obtained by pseudo-spectral methods.
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Papers by Enrique Pazos