476 research outputs found

    Electron Thermal Runaway in Atmospheric Electrified Gases: a microscopic approach

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    Thesis elaborated from 2018 to 2023 at the Instituto de AstrofĂ­sica de AndalucĂ­a under the supervision of Alejandro Luque (Granada, Spain) and Nikolai Lehtinen (Bergen, Norway). This thesis presents a new database of atmospheric electron-molecule collision cross sections which was published separately under the DOI : With this new database and a new super-electron management algorithm which significantly enhances high-energy electron statistics at previously unresolved ratios, the thesis explores general facets of the electron thermal runaway process relevant to atmospheric discharges under various conditions of the temperature and gas composition as can be encountered in the wake and formation of discharge channels

    Data analysis with merge trees

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    Today’s data are increasingly complex and classical statistical techniques need growingly more refined mathematical tools to be able to model and investigate them. Paradigmatic situations are represented by data which need to be considered up to some kind of trans- formation and all those circumstances in which the analyst finds himself in the need of defining a general concept of shape. Topological Data Analysis (TDA) is a field which is fundamentally contributing to such challenges by extracting topological information from data with a plethora of interpretable and computationally accessible pipelines. We con- tribute to this field by developing a series of novel tools, techniques and applications to work with a particular topological summary called merge tree. To analyze sets of merge trees we introduce a novel metric structure along with an algorithm to compute it, define a framework to compare different functions defined on merge trees and investigate the metric space obtained with the aforementioned metric. Different geometric and topolog- ical properties of the space of merge trees are established, with the aim of obtaining a deeper understanding of such trees. To showcase the effectiveness of the proposed metric, we develop an application in the field of Functional Data Analysis, working with functions up to homeomorphic reparametrization, and in the field of radiomics, where each patient is represented via a clustering dendrogram

    Intertwining the Busemann process of the directed polymer model

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    We study the Busemann process of the planar directed polymer model with i.i.d. weights on the vertices of the planar square lattice, both the general case and the solvable inverse-gamma case. We demonstrate that the Busemann process intertwines with an evolution obeying a version of the geometric Robinson-Schensted-Knuth correspondence. In the inverse-gamma case this relationship enables an explicit description of the distribution of the Busemann process: the Busemann function on a nearest-neighbor edge has independent increments in the direction variable, and its distribution comes from an inhomogeneous planar Poisson process. Various corollaries follow, including that each nearest-neighbor Busemann function has the same countably infinite dense set of discontinuities in the direction variable. This contrasts with the known zero-temperature last-passage percolation cases, where the analogous sets are nowhere dense but have a dense union. The distribution of the asymptotic competition interface direction of the inverse-gamma polymer is discrete and supported on the Busemann discontinuities. Further implications follow for the eternal solutions and the failure of the one force-one solution principle for the discrete stochastic heat equation solved by the polymer partition function.Comment: 79 page

    Controls that expedite first passage times in disordered systems

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    First passage time statistics in disordered systems exhibiting scale invariance are studied widely. In particular, long trapping times in energy or entropic traps are fat-tailed distributed, which slow the overall transport process. We study the statistical properties of the first passage time of biased processes in different models, and employ the big jump principle that shows the dominance of the maximum trapping time on the first passage time. Inspired by the restart paradigm, we demonstrate that the removal of this maximum significantly expedites transport. As the disorder increases, the system enters a phase where the removal shows a dramatic effect. Our results show how we may speed up transport in strongly disordered systems exploiting scale invariance. In contrast to the disordered systems studied here, the removal principle has essentially no effect in homogeneous systems; this indicates that improving the conductance of a poorly conducting system is, theoretically, relatively easy as compared to a homogeneous system

    Traffic Management System for the combined optimal routing, scheduling and motion planning of self-driving vehicles inside reserved smart road networks

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    The topic discussed in this thesis belongs to the field of automation of transport systems, which has grown in importance in the last decade, both in the innovation field (where different automation technologies have been gradually introduced in different sectors of road transport, in the promising view of making it more efficient, safer, and greener) and in the research field (where different research activities and publications have addressed the problem under different points of view). More in detail, this work addresses the problem of autonomous vehicles coordina tion inside reserved road networks by proposing a novel Traffic Management System (TMS) for the combined routing, scheduling and motion planning of the vehicles. To this aim, the network is assumed to have a modular structure, which results from a certain number of roads and intersections assembled together. The way in which roads and intersections are put together defines the network layout. Within such a system architecture, the main tasks addressed by the TMS are: (1) at the higher level, the optimal routing of the vehicles in the network, exploiting the available information coming from the vehicles and the various elements of the network; (2) at a lower level, the modeling and optimization of the vehicle trajectories and speeds for each road and for each intersection in the network; (3) the coordination between the vehicles and the elements of the network, to ensure a combined approach that considers, in a recursive way, the scheduling and motion planning of the vehicles in the various elements when solving the routing problem. In particular, the routing and the scheduling and motion planning problems are formulated as MILP optimization problems, aiming to maximize the performance of the entire network (routing model) and the performance of its single elements - roads and intersections (scheduling and motion planning model) while guaranteeing the requested level of safety and comfort for the passengers. Besides, one of the main features of the proposed approach consists of the integration of the scheduling decisions and the motion planning computation by means of constraints regarding the speed limit, the acceleration, and the so-called safety dynamic constraints on incompatible positions of conflicting vehicles. In particular, thanks to these last constraints, it is possible to consider the real space occupancy of the vehicles avoiding collisions. After the theoretical discussion of the proposed TMS and of its components and models, the thesis presents and discusses the results of different numerical experiments, aimed at testing the TMS in some specific scenarios. In particular, the routing model and the scheduling and motion planning model are tested on different scenarios, which demonstrate the effectiveness and the validity of such approach in performing the addressed tasks, also compared with more traditional methods. Finally, the computational effort needed for the problem solution, which is a key element to take into account, is discussed both for the road element and the intersection element

    Deep learning applied to computational mechanics: A comprehensive review, state of the art, and the classics

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    Three recent breakthroughs due to AI in arts and science serve as motivation: An award winning digital image, protein folding, fast matrix multiplication. Many recent developments in artificial neural networks, particularly deep learning (DL), applied and relevant to computational mechanics (solid, fluids, finite-element technology) are reviewed in detail. Both hybrid and pure machine learning (ML) methods are discussed. Hybrid methods combine traditional PDE discretizations with ML methods either (1) to help model complex nonlinear constitutive relations, (2) to nonlinearly reduce the model order for efficient simulation (turbulence), or (3) to accelerate the simulation by predicting certain components in the traditional integration methods. Here, methods (1) and (2) relied on Long-Short-Term Memory (LSTM) architecture, with method (3) relying on convolutional neural networks. Pure ML methods to solve (nonlinear) PDEs are represented by Physics-Informed Neural network (PINN) methods, which could be combined with attention mechanism to address discontinuous solutions. Both LSTM and attention architectures, together with modern and generalized classic optimizers to include stochasticity for DL networks, are extensively reviewed. Kernel machines, including Gaussian processes, are provided to sufficient depth for more advanced works such as shallow networks with infinite width. Not only addressing experts, readers are assumed familiar with computational mechanics, but not with DL, whose concepts and applications are built up from the basics, aiming at bringing first-time learners quickly to the forefront of research. History and limitations of AI are recounted and discussed, with particular attention at pointing out misstatements or misconceptions of the classics, even in well-known references. Positioning and pointing control of a large-deformable beam is given as an example.Comment: 275 pages, 158 figures. Appeared online on 2023.03.01 at CMES-Computer Modeling in Engineering & Science

    Operational research:methods and applications

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    Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order

    Selected Topics in Gravity, Field Theory and Quantum Mechanics

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    Quantum field theory has achieved some extraordinary successes over the past sixty years; however, it retains a set of challenging problems. It is not yet able to describe gravity in a mathematically consistent manner. CP violation remains unexplained. Grand unified theories have been eliminated by experiment, and a viable unification model has yet to replace them. Even the highly successful quantum chromodynamics, despite significant computational achievements, struggles to provide theoretical insight into the low-energy regime of quark physics, where the nature and structure of hadrons are determined. The only proposal for resolving the fine-tuning problem, low-energy supersymmetry, has been eliminated by results from the LHC. Since mathematics is the true and proper language for quantitative physical models, we expect new mathematical constructions to provide insight into physical phenomena and fresh approaches for building physical theories

    Stochastic Transport in Upper Ocean Dynamics

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    This open access proceedings volume brings selected, peer-reviewed contributions presented at the Stochastic Transport in Upper Ocean Dynamics (STUOD) 2021 Workshop, held virtually and in person at the Imperial College London, UK, September 20–23, 2021. The STUOD project is supported by an ERC Synergy Grant, and led by Imperial College London, the National Institute for Research in Computer Science and Automatic Control (INRIA) and the French Research Institute for Exploitation of the Sea (IFREMER). The project aims to deliver new capabilities for assessing variability and uncertainty in upper ocean dynamics. It will provide decision makers a means of quantifying the effects of local patterns of sea level rise, heat uptake, carbon storage and change of oxygen content and pH in the ocean. Its multimodal monitoring will enhance the scientific understanding of marine debris transport, tracking of oil spills and accumulation of plastic in the sea. All topics of these proceedings are essential to the scientific foundations of oceanography which has a vital role in climate science. Studies convened in this volume focus on a range of fundamental areas, including: Observations at a high resolution of upper ocean properties such as temperature, salinity, topography, wind, waves and velocity; Large scale numerical simulations; Data-based stochastic equations for upper ocean dynamics that quantify simulation error; Stochastic data assimilation to reduce uncertainty. These fundamental subjects in modern science and technology are urgently required in order to meet the challenges of climate change faced today by human society. This proceedings volume represents a lasting legacy of crucial scientific expertise to help meet this ongoing challenge, for the benefit of academics and professionals in pure and applied mathematics, computational science, data analysis, data assimilation and oceanography

    The width of curves in Riemannian manifolds

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    We develop a Morse-Lusternik-Schnirelmann theory for the distance between two points of a smoothly embedded circle in a complete Riemannian manifold. This theory suggests very naturally a definition of width that generalises the classical definition of the width of plane curves. Pairs of points of the circle realising the width bound one or more minimising geodesics that intersect the curve in special configurations. When the circle bounds a totally convex disc, we classify the possible configurations under a further geometric condition. We also investigate properties and characterisations of curves that can be regarded as the Riemannian analogues of plane curves of constant width.Comment: 49 pages, 3 figure
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