3,085 research outputs found

    Complexity & wormholes in holography

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    Holography has proven to be a highly successful approach in studying quantum gravity, where a non-gravitational quantum field theory is dual to a quantum gravity theory in one higher dimension. This doctoral thesis delves into two key aspects within the context of holography: complexity and wormholes. In Part I of the thesis, the focus is on holographic complexity. Beginning with a brief review of quantum complexity and its significance in holography, the subsequent two chapters proceed to explore this topic in detail. We study several proposals to quantify the costs of holographic path integrals. We then show how such costs can be optimized and match them to bulk complexity proposals already existing in the literature. In Part II of the thesis, we shift our attention to the study of spacetime wormholes in AdS/CFT. These are bulk spacetime geometries having two or more disconnected boundaries. In recent years, such wormholes have received a lot of attention as they lead to interesting implications and raise important puzzles. We study the construction of several simple examples of such wormholes in general dimensions in the presence of a bulk scalar field and explore their implications in the boundary theory

    Symmetries of Riemann surfaces and magnetic monopoles

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    This thesis studies, broadly, the role of symmetry in elucidating structure. In particular, I investigate the role that automorphisms of algebraic curves play in three specific contexts; determining the orbits of theta characteristics, influencing the geometry of the highly-symmetric Bring’s curve, and in constructing magnetic monopole solutions. On theta characteristics, I show how to turn questions on the existence of invariant characteristics into questions of group cohomology, compute comprehensive tables of orbit decompositions for curves of genus 9 or less, and prove results on the existence of infinite families of curves with invariant characteristics. On Bring’s curve, I identify key points with geometric significance on the curve, completely determine the structure of the quotients by subgroups of automorphisms, finding new elliptic curves in the process, and identify the unique invariant theta characteristic on the curve. With respect to monopoles, I elucidate the role that the Hitchin conditions play in determining monopole spectral curves, the relation between these conditions and the automorphism group of the curve, and I develop the theory of computing Nahm data of symmetric monopoles. As such I classify all 3-monopoles whose Nahm data may be solved for in terms of elliptic functions

    Computational Modelling of the Plasma in the Charge Exchange Thruster

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    The Charge Exchange Thruster (CXT) is a novel plasma thruster that produces thrust via energetic neutrals leaving the device. This is done by accelerating ions with an electrostatic potential inside of a so-called hollow cathode device: some of these ions then undergo charge exchange and leave the thruster as energetic neutrals whilst others contribute to the formation of an electrical discharge inside the thruster. In this thesis a new 2D-3V particle-in-cell-Monte Carlo (PIC-MCC) simulation code is developed and tested with the purpose of modelling the plasma inside the CXT. This code includes multiple chemical processes involving hydrogen ions, atoms, and molecular species, an external circuit simulation, probabilistic reflections from boundaries, and the generation of secondary electrons, all of which are found to be vital in the plasma initiation and development. The new PIC-MCC code is benchmarked successfully against the theoretical plasma sheath width as well as experimental Paschen curves for a parallel plate discharge, being found to reproduce these results well. Similarly, by modelling hollow cathode discharge systems it is found that the code can reproduce two effects specific to hollow cathode devices, a higher plasma density inside the cathode than outside, as well as beams of energetic neutrals. The code was able to reproduce the experimental results of the original CXT paper reasonably well but suffered from numerical instabilities that prevented the simulation from modelling the discharge in a steady state. It was found that simulating the thruster in a lower pressure discharge mode did not produce as much thrust but was able to reach a steady state and was numerically stable over timescales of tens of microseconds. Future work on investigating the cause of the numerical instabilities at high pressures, as well as a more complex model for the background gas dynamics in the thruster are recommended

    Exact steady states of minimal models of nonequilibrium statistical mechanics

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    Systems out of equilibrium with their environment are ubiquitous in nature. Of particular relevance to biological applications are models in which each microscopic component spontaneously generates its own motion. Known collectively as active matter, such models are natural effective descriptions of many biological systems, from subcellular motors to flocks of birds. One would like to understand such phenomena using the tools of statistical mechanics, yet the inherent nonequilibrium setting means that the most powerful classical results of that field cannot be applied. This circumstance has fuelled interest in exactly solvable models of active matter. The aim in studying such models is twofold. Firstly, as exactly solvable model are often minimal, it makes them good candidates as generic coarse-grained descriptions of real-world processes. Secondly, even if the model in question does not correspond directly to some situation realizable in experiment, its exact solution may suggest some general principles, which could also apply to more complex phenomena. A typical tool to investigate the properties of a large system is to study the behaviour of a probe particle placed in such an environment. In this context, cases of interest are both an active particle in a passive environment or an active particle in an active environment. One model that has attracted much attention in this regard is the asymmetric simple exclusion process (ASEP), which is a prototypical minimal model of driven diffusive transport. In this thesis, I consider two variations of the ASEP on a ring geometry. The first is a system of symmetrically diffusing particles with one totally asymmetric (driven) defect particle. The second is a system of partially asymmetric particles, with one defect that may overtake the other particles. I analyze the steady states of these systems using two exact methods: the matrix product ansatz, and, for the second model the Bethe ansatz. This allows me to derive the exact density profiles and mean currents for these models, and, for the second model, the diffusion constant. Moreover, I use the Yang-Baxter formalism to study the general class of two-species partially asymmetric processes with overtaking. This allows me to determine conditions under which such models can be solved using the Bethe ansatz

    New techniques for integrable spin chains and their application to gauge theories

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    In this thesis we study integrable systems known as spin chains and their applications to the study of the AdS/CFT duality, and in particular to N “ 4 supersymmetric Yang-Mills theory (SYM) in four dimensions.First, we introduce the necessary tools for the study of integrable periodic spin chains, which are based on algebraic and functional relations. From these tools, we derive in detail a technique that can be used to compute all the observables in these spin chains, known as Functional Separation of Variables. Then, we generalise our methods and results to a class of integrable spin chains with more general boundary conditions, known as open integrable spin chains.In the second part, we study a cusped Maldacena-Wilson line in N “ 4 SYM with insertions of scalar fields at the cusp, in a simplifying limit called the ladders limit. We derive a rigorous duality between this observable and an open integrable spin chain, the open Fishchain. We solve the Baxter TQ relation for the spin chain to obtain the exact spectrum of scaling dimensions of this observable involving cusped Maldacena-Wilson line.The open Fishchain and the application of Functional Separation of Variables to it form a very promising road for the study of the three-point functions of non-local operators in N “ 4 SYM via integrability

    MECHANICAL ENERGY HARVESTER FOR POWERING RFID SYSTEMS COMPONENTS: MODELING, ANALYSIS, OPTIMIZATION AND DESIGN

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    Finding alternative power sources has been an important topic of study worldwide. It is vital to find substitutes for finite fossil fuels. Such substitutes may be termed renewable energy sources and infinite supplies. Such limitless sources are derived from ambient energy like wind energy, solar energy, sea waves energy; on the other hand, smart cities megaprojects have been receiving enormous amounts of funding to transition our lives into smart lives. Smart cities heavily rely on smart devices and electronics, which utilize small amounts of energy to run. Using batteries as the power source for such smart devices imposes environmental and labor cost issues. Moreover, in many cases, smart devices are in hard-to-access places, making accessibility for disposal and replacement difficult. Finally, battery waste harms the environment. To overcome these issues, vibration-based energy harvesters have been proposed and implemented. Vibration-based energy harvesters convert the dynamic or kinetic energy which is generated due to the motion of an object into electric energy. Energy transduction mechanisms can be delivered based on piezoelectric, electromagnetic, or electrostatic methods; the piezoelectric method is generally preferred to the other methods, particularly if the frequency fluctuations are considerable. In response, piezoelectric vibration-based energy harvesters (PVEHs), have been modeled and analyzed widely. However, there are two challenges with PVEH: the maximum amount of extractable voltage and the effective (operational) frequency bandwidth are often insufficient. In this dissertation, a new type of integrated multiple system comprised of a cantilever and spring-oscillator is proposed to improve and develop the performance of the energy harvester in terms of extractable voltage and effective frequency bandwidth. The new energy harvester model is proposed to supply sufficient energy to power low-power electronic devices like RFID components. Due to the temperature fluctuations, the thermal effect over the performance of the harvester is initially studied. To alter the resonance frequency of the harvester structure, a rotating element system is considered and analyzed. In the analytical-numerical analysis, Hamilton’s principle along with Galerkin’s decomposition approach are adopted to derive the governing equations of the harvester motion and corresponding electric circuit. It is observed that integration of the spring-oscillator subsystem alters the boundary condition of the cantilever and subsequently reforms the resulting characteristic equation into a more complicated nonlinear transcendental equation. To find the resonance frequencies, this equation is solved numerically in MATLAB. It is observed that the inertial effects of the oscillator rendered to the cantilever via the restoring force effects of the spring significantly alter vibrational features of the harvester. Finally, the voltage frequency response function is analytically and numerically derived in a closed-from expression. Variations in parameter values enable the designer to mutate resonance frequencies and mode shape functions as desired. This is particularly important, since the generated energy from a PVEH is significant only if the excitation frequency coming from an external source matches the resonance (natural) frequency of the harvester structure. In subsequent sections of this work, the oscillator mass and spring stiffness are considered as the design parameters to maximize the harvestable voltage and effective frequency bandwidth, respectively. For the optimization, a genetic algorithm is adopted to find the optimal values. Since the voltage frequency response function cannot be implemented in a computer algorithm script, a suitable function approximator (regressor) is designed using fuzzy logic and neural networks. The voltage function requires manual assistance to find the resonance frequency and cannot be done automatically using computer algorithms. Specifically, to apply the numerical root-solver, one needs to manually provide the solver with an initial guess. Such an estimation is accomplished using a plot of the characteristic equation along with human visual inference. Thus, the entire process cannot be automated. Moreover, the voltage function encompasses several coefficients making the process computationally expensive. Thus, training a supervised machine learning regressor is essential. The trained regressor using adaptive-neuro-fuzzy-inference-system (ANFIS) is utilized in the genetic optimization procedure. The optimization problem is implemented, first to find the maximum voltage and second to find the maximum widened effective frequency bandwidth, which yields the optimal oscillator mass value along with the optimal spring stiffness value. As there is often no control over the external excitation frequency, it is helpful to design an adaptive energy harvester. This means that, considering a specific given value of the excitation frequency, energy harvester system parameters (oscillator mass and spring stiffness) need to be adjusted so that the resulting natural (resonance) frequency of the system aligns with the given excitation frequency. To do so, the given excitation frequency value is considered as the input and the system parameters are assumed as outputs which are estimated via the neural network fuzzy logic regressor. Finally, an experimental setup is implemented for a simple pure cantilever energy harvester triggered by impact excitations. Unlike the theoretical section, the experimental excitation is considered to be an impact excitation, which is a random process. The rationale for this is that, in the real world, the external source is a random trigger. Harmonic base excitations used in the theoretical chapters are to assess the performance of the energy harvester per standard criteria. To evaluate the performance of a proposed energy harvester model, the input excitation type consists of harmonic base triggers. In summary, this dissertation discusses several case studies and addresses key issues in the design of optimized piezoelectric vibration-based energy harvesters (PVEHs). First, an advanced model of the integrated systems is presented with equation derivations. Second, the proposed model is decomposed and analyzed in terms of mechanical and electrical frequency response functions. To do so, analytic-numeric methods are adopted. Later, influential parameters of the integrated system are detected. Then the proposed model is optimized with respect to the two vital criteria of maximum amount of extractable voltage and widened effective (operational) frequency bandwidth. Corresponding design (influential) parameters are found using neural network fuzzy logic along with genetic optimization algorithms, i.e., a soft computing method. The accuracy of the trained integrated algorithms is verified using the analytical-numerical closed-form expression of the voltage function. Then, an adaptive piezoelectric vibration-based energy harvester (PVEH) is designed. This final design pertains to the cases where the excitation (driving) frequency is given and constant, so the desired goal is to match the natural frequency of the system with the given driving frequency. In this response, a regressor using neural network fuzzy logic is designed to find the proper design parameters. Finally, the experimental setup is implemented and tested to report the maximum voltage harvested in each test execution

    Map enumeration from a dynamical perspective

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    This contribution summarizes recent work of the authors that combines methods from dynamical systems theory (discrete Painlev\'e equations) and asymptotic analysis of orthogonal polynomial recurrences, to address long-standing questions in map enumeration. Given a genus gg, we present a framework that provides the generating function for the number of maps that can be realized on a surface of that genus. In the case of 4-valent maps, our methodology leads to explicit expressions for map counts. For general even or mixed valence, the number of vertices of the map specifies the relevant order of the derivatives of the generating function that needs to be considered. Beyond summarizing our own results, we provide context for the program highlighted in this article through a brief review of the literature describing advances in map enumeration. In addition, we discuss open problems and challenges related to this fascinating area of research that stands at the intersection of statistical physics, random matrices, orthogonal polynomials, and discrete dynamical systems theory

    From a causal representation of multiloop scattering amplitudes to quantum computing in the Loop-Tree Duality

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    La teoría cúantica de campos con enfoque perturbativo ha logrado de manera exitosa proporcionar predicciones teóricas increíblemente precisas en física de altas energías. A pesar del desarrollo de diversas técnicas con el objetivo de incrementar la eficiencia de estos cálculos, algunos ingredientes continuan siendo un verdadero reto. Este es el caso de las amplitudes de dispersión con lazos múltiples, las cuales describen las fluctuaciones cuánticas en los procesos de dispersión a altas energías. La Dualidad Lazo-Árbol (LTD) es un método innovador, propuesto con el objetivo de afrontar estas dificultades abriendo las amplitudes de lazo a amplitudes conectadas de tipo árbol. En esta tesis presentamos tres logros fundamentales: la reformulación de la Dualidad Lazo-Árbol a todos los órdenes en la expansión perturbativa, una metodología general para obtener expresiones LTD con un comportamiento manifiestamente causal, y la primera aplicación de un algoritmo cuántico a integrales de lazo de Feynman. El cambio de estrategia propuesto para implementar la metodología LTD, consiste en la aplicación iterada del teorema del residuo de Cauchy a un conjunto de topologías con lazos m\'ultiples y configuraciones internas arbitrarias. La representación LTD que se obtiene, sigue una estructura factorizada en términos de subtopologías más simples, caracterizada por un comportamiento causal bien conocido. Además, a través de un proceso avanzado desarrollamos representaciones duales analíticas explícitamente libres de singularidades no causales. Estas propiedades permiten escribir cualquier amplitud de dispersión, hasta cinco lazos, de forma factorizada con una mejor estabilidad numérica en comparación con otras representaciones, debido a la ausencia de singularidades no causales. Por último, establecemos la conexión entre las integrales de lazo de Feynman y la computación cuántica, mediante la asociación de los dos estados sobre la capa de masas de un propagador de Feynman con los dos estados de un qubit. Proponemos una modificación del algoritmo cuántico de Grover para encontrar las configuraciones singulares causales de los diagramas de Feynman con lazos múltiples. Estas configuraciones son requeridas para establecer la representación causal de topologías con lazos múltiples.The perturbative approach to Quantum Field Theories has successfully provided incredibly accurate theoretical predictions in high-energy physics. Despite the development of several techniques to boost the efficiency of these calculations, some ingredients remain a hard bottleneck. This is the case of multiloop scattering amplitudes, describing the quantum fluctuations at high-energy scattering processes. The Loop-Tree Duality (LTD) is a novel method aimed to overcome these difficulties by opening the loop amplitudes into connected tree-level diagrams. In this thesis we present three core achievements: the reformulation of the Loop-Tree Duality to all orders in the perturbative expansion, a general methodology to obtain LTD expressions which are manifestly causal, and the first flagship application of a quantum algorithm to Feynman loop integrals. The proposed strategy to implement the LTD framework consists in the iterated application of the Cauchy's residue theorem to a series of mutiloop topologies with arbitrary internal configurations. We derive a LTD representation exhibiting a factorized cascade form in terms of simpler subtopologies characterized by a well-known causal behaviour. Moreover, through a clever approach we extract analytic dual representations that are explicitly free of noncausal singularities. These properties enable to open any scattering amplitude of up to five loops in a factorized form, with a better numerical stability than in other representations due to the absence of noncausal singularities. Last but not least, we establish the connection between Feynman loop integrals and quantum computing by encoding the two on-shell states of a Feynman propagator through the two states of a qubit. We propose a modified Grover's quantum algorithm to unfold the causal singular configurations of multiloop Feynman diagrams used to bootstrap the causal LTD representation of multiloop topologies
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