626 research outputs found

    A virtual element method for the solution of 2D time-harmonic elastic wave equations via scalar potentials

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    In this paper, we propose and analyse a numerical method to solve 2D Dirichlet timeharmonic elastic wave equations. The procedure is based on the decoupling of the elastic vector field into scalar Pressure (P-) and Shear (S-) waves via a suitable Helmholtz– Hodge decomposition. For the approximation of the two scalar potentials we apply a virtual element method associated with different mesh sizes and degrees of accuracy. We provide for the stability of the method and a convergence error estimate in the L 2 -norm for the displacement field, in which the contributions to the error associated with the P- and S- waves are separated. In contrast to standard approaches that are directly applied to the vector formulation, this procedure allows for keeping track of the two different wave numbers, that depend on the P- and S- speeds of propagation and, therefore, for using a high-order method for the approximation of the wave associated with the higher wave number. Some numerical tests, validating the theoretical results and showing the good performance of the proposed approach, are presented

    Numerical resolution of the Navier-Stokes equations with parallel programming for the analysis of heat and mass transfer phenomena.

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    Aquesta tesi analitza mètodes numèrics per resoldre les equacions de Navier-Stokes en dinàmica de fluids computacional (CFD, per les sigles en anglès). La investigació es centra a des- envolupar una visió profunda de diferents mètodes numèrics i la seva aplicació a diversos fenòmens de transport. S’aplica una metodologia pas a pas, que abarca l’anàlisi de volums fi- nits i mètodes espectrals, la validació de models i la verificació de codis a través de l’anàlisi de casos d’estudi de convecció-difusió, flux de fluids i turbulència. La investigació revela l’efecte de diferents esquemes d’aproximació a la solució numèrica i emfatitza la importància d’una representació física precisa juntament amb la solidesa matemàtica. S’examina la convergència del mètode de resolució d’equacions iteratiu pel que fa a la naturalesa de la física de l’estudi, i cal destacar la necessitat de tècniques de relaxació apropiades. A més, s’explora el mètode de passos fraccionats per resoldre el fort acoblament de pressió-velocitat a les equacions de Navier-Stokes, mentre es considera l’addició d’altres fenòmens de transport. L’anàlisi de fluxes turbulents mostra la cascada d’energia a l’espai de Fourier i l’efecte del truncament a causa de la discretització espacial o espectral, abordat per l’aplicació de models simplificats, com ara Large Eddy Simulation (LES), aconseguint una solució aproximada amb un menor cost computacional. A més, s’analitza la implementació de la computació en paral·lel utilitzant l’estàndard MPI, emfatitzant-ne l’escalabilitat i el potencial per abordar les demandes creixents de l’anàlisi CFD en els camps de l’enginyeria. En general, aquesta recerca proporciona informació valuosa sobre els mètodes numèrics per a les equacions de Navier-Stokes, la seva aplicació a CFD i les implicacions pràctiques per als processos d’enginyeriaEsta tesis analiza métodos numéricos para resolver las ecuaciones de Navier-Stokes en dinámica de fluidos computacional (CFD, por sus siglas en Inglés). La investigación se centra en desarrollar una visión profunda de distintos métodos numéricos y su aplicación a diversos fenómenos de transporte. Se aplica una metodología paso a paso, que abarca el análisis de volúmenes finitos y métodos espectrales, validación de modelos y verificación de códigos a través del analisis de casos de estudio de convección-difusión, flujo de fluidos y turbulencia. La investigación revela el efecto de diferentes esquemas de aproximación en la solución numérica y enfatiza la importancia de una representación física precisa junto con la solidez matemática. Se examina la convergencia del método de resolución de equaciones iterativo con respecto a la naturaleza de la física del estudio, destacando la necesidad de técnicas de relajación apropiadas. Además, se explora el método de pasos fraccionados para resolver el fuerte acoplamiento de presión-velocidad en las ecuaciones de Navier-Stokes, mientras se considera la adición de otros fenómenos de transporte. El análisis de flujos turbulentos muestra la cascada de energía en el espacio de Fourier y el efecto del truncamiento debido a la discretización espacial o espectral, abordado por la aplicación de modelos simplificados, como Large Eddy Simulation (LES), logrando una solución aproximada con un menor costo computacional. Además, se analiza la implementación de la computación en paralelo utilizando el estándar MPI, enfatizando su escalabilidad y potencial para abordar las crecientes demandas del análisis CFD en los campos de la ingeniería. En general, esta investigación proporciona información valiosa sobre los métodos numéricos para las ecuaciones de Navier-Stokes, su aplicación a CFD y sus implicaciones prácticas para los procesos de ingenieríaThis thesis analyzes numerical methods for solving the Navier-Stokes equations in computational fluid dynamics (CFD). The research focuses on developing a deep insight into different numerical techniques and their application to various transport phenomena. A step-by-step methodology is applied, encompassing the analysis of finite volume and spectral methods, model validation, and code verification with the study of convection-diffusion, fluid flow, and turbulence study cases. The investigation reveals the effect of different approximation schemes on the numerical solution and emphasizes the importance of accurate physics representation alongside mathematical robustness. The convergence of the numerical solver is examined concerning the nature of the studied physics, highlighting the need for appropriate relaxation techniques. Additionally, the fractional step method is explored to solve the strong pressure-velocity coupling in the Navier-Stokes equations while considering the addition of other transport phenomena. The analysis of turbulent flows showcases the energy cascade in the Fourier space and its truncation effect due to spatial or spectral discretization, addressed by the application of simplified models, such as Large Eddy Simulation (LES), capable of approximating the solution with reduced computational cost. Furthermore, the implementation of parallel computing using the MPI standard is discussed, emphasizing its scalability and potential for addressing the growing demands of CFD analysis in engineering fields. Overall, this research provides valuable insights into numerical methods for the Navier-Stokes equations, their application to CFD, and their practical implications for engineering processe

    Novel 129Xe Magnetic Resonance Imaging and Spectroscopy Measurements of Pulmonary Gas-Exchange

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    Gas-exchange is the primary function of the lungs and involves removing carbon dioxide from the body and exchanging it within the alveoli for inhaled oxygen. Several different pulmonary, cardiac and cardiovascular abnormalities have negative effects on pulmonary gas-exchange. Unfortunately, clinical tests do not always pinpoint the problem; sensitive and specific measurements are needed to probe the individual components participating in gas-exchange for a better understanding of pathophysiology, disease progression and response to therapy. In vivo Xenon-129 gas-exchange magnetic resonance imaging (129Xe gas-exchange MRI) has the potential to overcome these challenges. When participants inhale hyperpolarized 129Xe gas, it has different MR spectral properties as a gas, as it diffuses through the alveolar membrane and as it binds to red-blood-cells. 129Xe MR spectroscopy and imaging provides a way to tease out the different anatomic components of gas-exchange simultaneously and provides spatial information about where abnormalities may occur. In this thesis, I developed and applied 129Xe MR spectroscopy and imaging to measure gas-exchange in the lungs alongside other clinical and imaging measurements. I measured 129Xe gas-exchange in asymptomatic congenital heart disease and in prospective, controlled studies of long-COVID. I also developed mathematical tools to model 129Xe MR signals during acquisition and reconstruction. The insights gained from my work underscore the potential for 129Xe gas-exchange MRI biomarkers towards a better understanding of cardiopulmonary disease. My work also provides a way to generate a deeper imaging and physiologic understanding of gas-exchange in vivo in healthy participants and patients with chronic lung and heart disease

    Application of multi-scale computational techniques to complex materials systems

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    The applications of computational materials science are ever-increasing, connecting fields far beyond traditional subfields in materials science. This dissertation demonstrates the broad scope of multi-scale computational techniques by investigating multiple unrelated complex material systems, namely scandate thermionic cathodes and the metallic foam component of micrometeoroid and orbital debris (MMOD) shielding. Sc-containing scandate cathodes have been widely reported to exhibit superior properties compared to previous thermionic cathodes; however, knowledge of their precise operating mechanism remains elusive. Here, quantum mechanical calculations were utilized to map the phase space of stable, highly-faceted and chemically-complex W nanoparticles, accounting for both finite temperature and chemical environment. The precise processing conditions required to form the characteristic W nanoparticle observed experimentally were then distilled. Metallic foams, a central component of MMOD shielding, also represent a highly-complex materials system, albeit at a far higher length scale than W nanoparticles. The non-periodic, randomly-oriented constituent ligaments of metallic foams and similar materials create a significant variability in properties that is generally difficult to model. Rather than homogenizing the material such that its unique characteristic structural features are neglected, here, a stochastic modeling approach is applied that integrates complex geometric structure and utilizes continuum calculations to predict the resulting probabilistic distributions of elastic properties. Though different in many aspects, scandate cathodes and metallic foams are united by complexity that is impractical, even dangerous, to ignore and well-suited to exploration with multi-scale computational methods

    Realising Global Water Futures: a Summary of Progress in Delivering Solutions to Water Threats in an Era of Global Change

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    Canada First Research Excellence FundNon-Peer ReviewedOver the past six years the Global Water Futures program has produced a wide range of scientific findings and engagements with multiple types of potential users of the research. This briefing book provides a snapshot of some of the science advancements and user engagement that have taken place to date. Annual reports to the funding agency are the most up to date source of information: this compilation has been created from reports submitted by projects in 2022, representing both completed and current project work. The briefing book aims to provide quick access to information about GWF projects in a single place for GWF’s User Advisory Panel: we hope that knowing more about the research being produced will spark conversations about how to make the best use of the new knowledge in both policy and practice

    Precision spectroscopy of the 2S-6P transition in atomic deuterium

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    Die Quantenelektrodynamik (QED) bildet die Grundlage aller anderen Quantenfeldtheorien, auf denen das Standardmodell der Teilchenphysik aufgebaut ist. Derzeit ist klar, dass unser fundamentales Naturverständnis unvollständig ist, sodass erwartet wird, dass das Standardmodell um neue Teilchen oder Wechselwirkungen verändert oder erweitert werden muss. Eine Möglichkeit, diese Grenzen der Grundlagenphysik zu erforschen, ist die Durchführung von Präzisionsmessungen. Diese Arbeit untersucht die Präzisionslaserspektroskopie von Deuterium, wo die Übergangsenergien zwischen verschiedenen Energiezuständen des an den Kern gebundenen Elektrons mit Techniken wie ultrastabilen Lasern und dem Frequenzkamm genau gemessen werden können. Aufgrund der Einfachheit der wasserstoffähnlichen Atome können ihre Energieniveaus anhand der QED-Theorie für gebundene Zustände genau berechnet werden, und mit dem Experiment mit der relativen Genauigkeit in der Größenordnung von 10−1210^{-12} verglichen werden. Ein solcher Vergleich zwischen Theorie und Experiment ist mit der Bestimmung von Naturkonstanten verbunden, die als Parameter in die Theorie eingehen. Erst wenn mehr unabhängige Messungen als Parameter vorliegen, kann die Theorie überprüft werden. Der Vergleich zwischen Theorie und Laser-Spektroskopie im Deuterium betrifft die Ryd-berg-Konstante R∞R_\infty und den Deuteronen-Ladungsradius rdr_d. Dies erfordert mindestens zwei Messungen der verschiedenen Übergangsfrequenzen, um diese Konstanten zu bestimmen, und mehr Messungen, um die Theorie zu testen. Im Gegensatz zum Wasserstoff gibt es bei Deuterium nur wenige ausreichend genaue Messungen der Übergänge. In dieser Arbeit wird die erste Untersuchung des 2S-6P-Übergangs in Deuterium vorgestellt, die mit der bestehenden Frequenzmessung des 1S-2S-Übergangs kombiniert werden kann, um R∞R_\infty und rdr_d zu erhalten. Zusammen mit der Messung des 2S-2P-Übergangs von myonischem Deuterium stellt diese Bestimmung einen Theorietest dar. Ein solcher Vergleich ist wichtig, um die anhaltende Diskrepanz zwischen dem Ergebnis aus myonischem Deuterium und dem Durchschnitt früherer Daten aus elektronischem Deuterium, sowie die Spannungen zwischen den jüngsten Ergebnissen aus der Wasserstoffspektroskopie, zu beleuchten. Im Gegensatz zu Wasserstoff wird die Präzisionsspektroskopie des 2S-6P-Übergangs in Deuterium durch die gleichzeitige Anregung unaufgelöster Hyperfeinstruktur-Komponenten erschwert, was zur unaufgelösten Quanteninterferenz führen kann. Diese Arbeit untersucht die möglichen systematischen Effekte, die mit dieser Komplikation verbunden sind. Zusammen mit analytischen störungstheoretischen Modellen werden Supercomputersimulationen durchgeführt, um diese Effekte zu analysieren. Es wird gezeigt, dass die Quanteninterferenz für alle 2S-nnP-Übergänge in Deuterium stark unterdrückt wird, wodurch Präzisionsmessungen dieser Übergänge möglich werden. Darüber hinaus wird ein weiterer Effekt in Deuterium im Vergleich zu Wasserstoff untersucht, der sich aus der Lichtkraft ergibt, die auf die Atome in der stehenden Welle des Spektroskopielichts wirkt. Trotz zusätzlicher Zustandsvielfalt durch die gleichzeitige Anregung unaufgelöster Hyperfeinkomponenten wird gezeigt, dass diese sogenannte ``Lichtkraftverschiebung'' mit dem gut verstandenen Effekt im Wasserstoff vergleichbar ist. Die größte Herausforderung bei der Messung des 2S-6P-Ein-Photonen-Übergangs in Deuterium ist die Doppler-Verschiebung erster Ordnung. Ein großer Teil dieser Arbeit befasst sich daher mit dem verbesserten aktiven faserbasierten Retroreflektor (AFR), der eine Technik zur Unterdrückung dieser Verschiebung darstellt. Der zentrale Teil des AFR ist der Faserkollimator, der für die Erzeugung hochwertiger gegenläufiger Laserstrahlen erforderlich ist. Die Entwicklung und Charakterisierung eines solchen Kollimators für die nahe ultraviolette Wellenlänge des 2S-6P-Übergangs ist eine der wichtigsten Errungenschaften des verbesserten AFR. Die Ergebnisse dieser Arbeit können für andere Anwendungen von Interesse sein, bei denen eine hohe Strahlqualität oder wellenfront-zurückverfolgende Strahlen wichtig sind. Darüber hinaus werden die Einschränkungen der AFR untersucht, die sich aus polarisationserhaltenden Singlemode-Fasern ergeben. Neben anderen Verbesserungen wurde eine Polarisationsüberwachung der Spektroskopielaserstrahlen implementiert. Es werden verschiedene Charakterisierungsmessungen vorgestellt, um die Leistungsfähigkeit des verbesserten AFR zu demonstrieren. Schließlich wird in dieser Arbeit eine vorläufige Messung des 2S-6P-Übergangs in Deuterium vorgestellt. Für diese Messung wurde ein neuer Kryostat in die Apparatur eingebaut, der die Stabilität des Spektroskopiesignals durch reduzierte Temperaturschwankungen verbessert. Die Erzeugung des kryogenen Deuterium-Atomstrahls wurde in Abhängigkeit von der Düsentemperatur analysiert, was eine wichtige Studie für künftige Spektroskopiemessungen darstellt. Darüber hinaus wurden für die Präzisionsmessung verschiedene systematische Effekte untersucht, darunter die Fehlausrichtung des Atomstrahls und die elektrischen Streufelder. Es wird gezeigt, dass eine Präzisionsmessung des 2S-6P-Übergangs in Deuterium mit einer ähnlichen Unsicherheit wie in Wasserstoff machbar ist. Nach der vorläufigen Unsicherheitsabschätzung kann die 2S1/2_{1/2}-6P1/2_{1/2}-Übergangsfrequenz in Deuterium auf \SI{1.7}{kHz} bestimmt werden, was einer relativen Genauigkeit von 2.3×10−122.3 \times 10^{-12} entspricht. Zusammen mit der 1S-2S-Messung kann dieses Ergebnis bereits die genauesten Bestimmungen des Deuteronenradius und der Rydberg-Konstante aus dem elektronischen Deuterium ermöglichen, sodass die Unsicherheiten für die Rydberg-Konstante und den Deuteronenradius δR∞≃5×10−5 m−1\delta R_\infty \simeq 5\times 10^{-5}\,\text{m}^{-1} bzw.~\delta r_d \simeq \SI{0.002}{fm} betragen. Dieses Ergebnis bildet die Grundlage für eine zukünftige Präzisionsmessung, bei der die 2S-6P-Übergangsfrequenz mit ähnlicher Genauigkeit wie bei Wasserstoff bestimmt werden soll, was δR∞≃2×10−5 m−1\delta R_\infty \simeq 2\times 10^{-5}\,\text{m}^{-1} und \delta r_d \simeq \SI{0.0007}{fm} entsprechen würde. Der Vergleich mit dem Ergebnis von myonischem Deuterium würde es dann erlauben, die QED-Theorie für gebundene Zustände auf dem Niveau von 9×10−139 \times 10^{-13} zu testen.Quantum electrodynamics (QED) forms the basis for all other quantum field theories, upon which the Standard Model of particle physics is constructed. Currently, it is clear that our fundamental understanding of nature is incomplete, such that the Standard Model is expected to be modified or extended by new particles or interactions. One way to explore these frontiers of fundamental physics is to perform precision measurements. This thesis studies the precision laser spectroscopy of deuterium, where the transition energies between different energy states of the electron bound to the nucleus can be accurately measured with techniques such as ultra-stable lasers and the frequency comb. Due to the simplicity of hydrogen-like atoms, their energy levels can be precisely calculated from bound-state QED and confronted with the experiment with the relative accuracy on the order of 10−1210^{-12}. Such a comparison between theory and experiment is linked to the determination of fundamental constants, which enter the theory as parameters. Only if more indepedendent measurements are available than there are parameters, the theory can be tested. The comparison between theory and laser spectroscopy in deuterium concerns the Rydberg constant R∞R_\infty and the deuteron charge radius rdr_d. This requires at least two different transition frequency measurements to determine those constants, and more measurements to test the theory. Contrary to hydrogen, only few accurate enough transition frequency measurements are available in deuterium. This thesis presents the first study of the 2S-6P transition in deuterium, which can be combined with the existing 1S-2S transition frequency measurement to obtain R∞R_\infty and rdr_d. Together with the 2S-2P transition measurement from muonic deuterium, this determination provides a theory test. Such a comparison is important to shine light on the persisting discrepancy between the result from muonic deuterium and the average of previous data from electronic deuterium, as well as tensions between the recent results from hydrogen spectroscopy. In contrast to hydrogen, precision spectroscopy of the 2S-6P transition in deuterium is complicated by the simultaneous excitation of unresolved hyperfine components, possibly leading to unresolved quantum interference. This thesis studies the possible systematic effects associated with this complication. Along with analytical perturbative models, supercomputer simulations are performed to analyze these effects. It is shown, that quantum interference is strongly suppressed for all 2S-nnP transitions in deuterium, making precision measurements of these transitions possible. Furthermore, another effect is studied in deuterium compared to hydrogen, which arises from the light force acting on the atoms in the standing wave of the spectroscopy light. Despite additional state manifolds from the simultaneous excitation of unresolved hyperfine components, it is shown that this so-called ``light force shift'' is comparable to the well understood effect in hydrogen. The main challenge of measuring the one-photon 2S-6P transition in deuterium is the first-order Doppler shift. Therefore, a large part of this thesis contributes to the improved active fiber-based retroreflector (AFR), which is a technique to suppress this shift. The central part of the AFR is the fiber collimator, which is required to produce high-quality counter-propagating laser beams. Designing and characterizing such a collimator for the near ultra-violet wavelength of the 2S-6P transition is one of the main achievements of the improved AFR. The results of this work can be of interest to other applications where a high beam quality or wavefront-retracing beams are important. Furthermore, the limitations of the AFR arising from single-mode polarization-maintaining fibers are investigated. Along with other improvements, a polarization monitor of the spectroscopy laser beams has been implemented. Various characterization measurements are presented to demonstrate the performance of the improved AFR. Finally, this thesis presents a preliminary measurement of the 2S-6P transition in deuterium. For this measurement, a new cryostat has been installed in the apparatus, which improves the stability of the spectroscopy signal due to reduced temperature fluctuations. The cryogenic deuterium atomic beam generation has been analyzed in dependence on the nozzle temperature, which is an important study for future spectroscopy measurements. Furthermore, for the precision measurement different systematic effects have been investigated, including the atomic beam misalignment and the stray electric fields. It is demonstrated that a precision measurement of the 2S-6P transition in deuterium with a similar uncertainty than in hydrogen is feasible. According to the preliminary uncertainty budget, the 2S1/2_{1/2}-6P1/2_{1/2} transition frequency in deuterium can be determined to \SI{1.7}{kHz}, which corresponds to 2.3×10−122.3 \times 10^{-12} relative accuracy. Together with the 1S-2S measurement, already this result can enable the most accurate determinations of the deuteron radius and the Rydberg constant from the electronic deuterium with the uncertainties on the Rydberg constant and the deuteron radius of δR∞≃5×10−5 m−1\delta R_\infty \simeq 5\times 10^{-5}\,\text{m}^{-1} and \delta r_d \simeq \SI{0.002}{fm}, respectively. This result sets the stage for a future precision measurement, where the 2S-6P transition frequency is expected to be determined with the similar accuracy as in hydrogen, which would correspond to δR∞≃2×10−5 m−1\delta R_\infty \simeq 2\times 10^{-5}\,\text{m}^{-1} and \delta r_d \simeq \SI{0.0007}{fm}. The comparison to the result from muonic deuterium would then allow to test bound-state QED at the level of 9×10−139 \times 10^{-13}

    LIPIcs, Volume 261, ICALP 2023, Complete Volume

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    LIPIcs, Volume 261, ICALP 2023, Complete Volum

    Localizations with noncompact transverse spaces and covert symmetry breaking in supergravity

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    The focus of my doctoral work has been answering the question: Can lower-dimensional effective gravitational theories be found in a higher-dimensional theory with a non-compact transverse space? To answer this question this thesis is divided into two parts. First, I explore supergravity solutions on warped product manifolds and argue that they correspond to solutions of a modified Laplacian. I pay special attention to Type III † solutions, or solutions characterized by the presence of non-constant transverse zero modes, and emphasize that these are the only higher dimensional solutions corresponding to localized sources that yield effectively lower-dimensional physics when the transverse space has infinite volume. Second, I derive the lower dimensional effective field theory about such backgrounds. I discover that these effective field theories have covert symmetry breaking, spontaneous breaking of gauge symmetry which only appears at quartic order. I show this explicitly for D = d + 1 scalar electrodynamics with any boundary condition that corresponds to a non-constant transverse zero mode. The mathematical prerequisite for both of these conclusions is Sturm–Liouville theory with precise manipulations of Green’s formula. To support this I derive the fundamental conclusions of Sturm–Liouville theory for a restricted class of operator, that is the Laplacian, which relaxes some requirements for permissible boundary conditions of Sturm–Liouville theory. The answer to my focal question is: Yes; however, the lower-dimensional theory has novel corrections which were previously unexplored, and further research is indicated.Open Acces

    Noncommutative Geometry and Gauge theories on AF algebras

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    Non-commutative geometry (NCG) is a mathematical discipline developed in the 1990s by Alain Connes. It is presented as a new generalization of usual geometry, both encompassing and going beyond the Riemannian framework, within a purely algebraic formalism. Like Riemannian geometry, NCG also has links with physics. Indeed, NCG provided a powerful framework for the reformulation of the Standard Model of Particle Physics (SMPP), taking into account General Relativity, in a single "geometric" representation, based on Non-Commutative Gauge Theories (NCGFT). Moreover, this accomplishment provides a convenient framework to study various possibilities to go beyond the SMPP, such as Grand Unified Theories (GUTs). This thesis intends to show an elegant method recently developed by Thierry Masson and myself, which proposes a general scheme to elaborate GUTs in the framework of NCGFTs. This concerns the study of NCGFTs based on approximately finite C∗C^*-algebras (AF-algebras), using either derivations of the algebra or spectral triples to build up the underlying differential structure of the Gauge Theory. The inductive sequence defining the AF-algebra is used to allow the construction of a sequence of NCGFTs of Yang-Mills Higgs types, so that the rank n+1n+1 can represent a grand unified theory of the rank nn. The main advantage of this framework is that it controls, using appropriate conditions, the interaction of the degrees of freedom along the inductive sequence on the AF algebra. This suggests a way to obtain GUT-like models while offering many directions of theoretical investigation to go beyond the SMPP

    The role of turbulence and winding in the development of large-scale, strong magnetic fields in long-lived remnants of binary neutron star mergers

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    We perform a long and accurate Large-Eddy Simulation of a binary neutron star merger, following the newly formed remnant up to 110 milliseconds. The combination of high-order schemes, high-resolution and the gradient subgrid-scale model allow us to have among the highest effective resolutions ever achieved. Our results show that, although the magnetic fields are strongly amplified by the Kelvin-Helmholtz instability, they are coherent only over very short spatial scales until t \gtrsim 30 ms. Around that time, magnetic winding becomes more efficient leading to a linear growth of the toroidal component and slowly ordering the field to more axisymmetric, large scales. The poloidal component only starts to grow at small scales at much later times t \gtrsim 90 ms, in a way compatible with the magneto-rotational instability. No strong large-scale poloidal field or jet is produced in the timescales spanned by our simulation, although there is an helicoidal structure gradually developing at late times. We highlight that soon after the merger the topology is always strongly dominated by toroidal structures, with a complex distribution in the meridional plane and highly turbulent perturbations. Thus, starting with strong purely dipolar fields before the merger is largely inconsistent with the outcomes of a realistic evolution. Finally, we confirm the universality of the evolved topology, even when starting with very different magnetic fields confined to the outermost layers of each neutron star.Comment: 18 pages, 14 figures. arXiv admin note: text overlap with arXiv:2112.0841
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