977 resultados para Integrable equations in Physics
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This study explores the effects of modeling instruction on student learning in physics. Multiple representations grounded in physical contexts were employed by students to analyze the results of inquiry lab investigations. Class whiteboard discussions geared toward a class consensus following Socratic dialogue were implemented throughout the modeling cycle. Lab investigations designed to address student preconceptions related to Newton’s Third Law were implemented. Student achievement was measured based on normalized gains on the Force Concept Inventory. Normalized FCI gains achieved by students in this study were comparable to those achieved by students of other novice modelers. Physics students who had taken a modeling Intro to Physics course scored significantly higher on the FCI posttest than those who had not. The FCI results also provided insight into deeply rooted student preconceptions related to Newton’s Third Law. Implications for instruction and the design of lab investigations related to Newton’s Third Law are discussed.
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The conjugate gradient is the most popular optimization method for solving large systems of linear equations. In a system identification problem, for example, where very large impulse response is involved, it is necessary to apply a particular strategy which diminishes the delay, while improving the convergence time. In this paper we propose a new scheme which combines frequency-domain adaptive filtering with a conjugate gradient technique in order to solve a high order multichannel adaptive filter, while being delayless and guaranteeing a very short convergence time.
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O CERN - a Organização Europeia para a Investigação Nuclear - é um dos maiores centros de investigação a nível mundial, responsável por diversas descobertas na área da física bem como na área das ciências da computação. O CERN Document Server, também conhecido como CDS Invenio, é um software desenvolvido no CERN, que tem como objectivo fornecer um conjunto de ferramentas para gerir bibliotecas digitais. A fim de melhorar as funcionalidades do CDS Invenio foi criado um novo módulo, chamado BibCirculation, para gerir os livros (e outros itens) da biblioteca do CERN, funcionando como um sistema integrado de gestão de bibliotecas. Esta tese descreve os passos que foram dados para atingir os vários objectivos deste projecto, explicando, entre outros, o processo de integração com os outros módulos existentes bem como a forma encontrada para associar informações dos livros com os metadados do CDS lnvenio. É também possível encontrar uma apresentação detalhada sobre todo o processo de implementação e os testes realizados. Finalmente, são apresentadas as conclusões deste projecto e o trabalho a desenvolver futuramente. ABSTRACT: CERN - The European Organization for Nuclear Research - is one of the largest research centers worldwide, responsible for several discoveries in physics as well as in computer science. The CERN Document Server, also known as CDS Invenio, is a software developed at CERN, which aims to provide a set of tools for managing digital libraries. ln order to improve the functionalities of CDS Invenio a new module was developed, called BibCirculation, to manage books (and other items) from the CERN library, and working as an Integrated Library System. This thesis shows the steps that have been done to achieve the several goals of this project, explaining, among others aspects, the process of integration with other existing modules as well as the way to associate the information about books with the metadata from CDS lnvenio. You can also find detailed explanation of the entire implementation process and testing. Finally, there are presented the conclusions of this project and ideas for future development.
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This thesis provides a necessary and sufficient condition for asymptotic efficiency of a nonparametric estimator of the generalised autocovariance function of a Gaussian stationary random process. The generalised autocovariance function is the inverse Fourier transform of a power transformation of the spectral density, and encompasses the traditional and inverse autocovariance functions. Its nonparametric estimator is based on the inverse discrete Fourier transform of the same power transformation of the pooled periodogram. The general result is then applied to the class of Gaussian stationary ARMA processes and its implications are discussed. We illustrate that for a class of contrast functionals and spectral densities, the minimum contrast estimator of the spectral density satisfies a Yule-Walker system of equations in the generalised autocovariance estimator. Selection of the pooling parameter, which characterizes the nonparametric estimator of the generalised autocovariance, controlling its resolution, is addressed by using a multiplicative periodogram bootstrap to estimate the finite-sample distribution of the estimator. A multivariate extension of recently introduced spectral models for univariate time series is considered, and an algorithm for the coefficients of a power transformation of matrix polynomials is derived, which allows to obtain the Wold coefficients from the matrix coefficients characterizing the generalised matrix cepstral models. This algorithm also allows the definition of the matrix variance profile, providing important quantities for vector time series analysis. A nonparametric estimator based on a transformation of the smoothed periodogram is proposed for estimation of the matrix variance profile.
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The aim of this thesis project is to automatically localize HCC tumors in the human liver and subsequently predict if the tumor will undergo microvascular infiltration (MVI), the initial stage of metastasis development. The input data for the work have been partially supplied by Sant'Orsola Hospital and partially downloaded from online medical databases. Two Unet models have been implemented for the automatic segmentation of the livers and the HCC malignancies within it. The segmentation models have been evaluated with the Intersection-over-Union and the Dice Coefficient metrics. The outcomes obtained for the liver automatic segmentation are quite good (IOU = 0.82; DC = 0.35); the outcomes obtained for the tumor automatic segmentation (IOU = 0.35; DC = 0.46) are, instead, affected by some limitations: it can be state that the algorithm is almost always able to detect the location of the tumor, but it tends to underestimate its dimensions. The purpose is to achieve the CT images of the HCC tumors, necessary for features extraction. The 14 Haralick features calculated from the 3D-GLCM, the 120 Radiomic features and the patients' clinical information are collected to build a dataset of 153 features. Now, the goal is to build a model able to discriminate, based on the features given, the tumors that will undergo MVI and those that will not. This task can be seen as a classification problem: each tumor needs to be classified either as “MVI positive” or “MVI negative”. Techniques for features selection are implemented to identify the most descriptive features for the problem at hand and then, a set of classification models are trained and compared. Among all, the models with the best performances (around 80-84% ± 8-15%) result to be the XGBoost Classifier, the SDG Classifier and the Logist Regression models (without penalization and with Lasso, Ridge or Elastic Net penalization).
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This thesis work has been developed in collaboration between the Department of Physics and Astronomy of the University of Bologna and the IRCCS Rizzoli Orthopedic Institute during an internship period. The study aims to investigate the sensitivity of single-sided NMR in detecting structural differences of the articular cartilage tissue and their correlation with mechanical behavior. Suitable cartilage indicators for osteoarthritis (OA) severity (e.g., water and proteoglycans content, collagen structure) were explored through four NMR parameters: T2, T1, D, and Slp. Structural variations of the cartilage among its three layers (i.e., superficial, middle, and deep) were investigated performing several NMR pulses sequences on bovine knee joint samples using the NMR-MOUSE device. Previously, cartilage degradation studies were carried out, performing tests in three different experimental setups. The monitoring of the parameters and the best experimental setup were determined. An NMR automatized procedure based on the acquisition of these quantitative parameters was implemented, tested, and used for the investigation of the layers of twenty bovine cartilage samples. Statistical and pattern recognition analyses on these parameters have been performed. The results obtained from the analyses are very promising: the discrimination of the three cartilage layers shows very good results in terms of significance, paving the way for extensive use of NMR single-sided devices for biomedical applications. These results will be also integrated with analyses of tissue mechanical properties for a complete evaluation of cartilage changes throughout OA disease. The use of low-priced and mobile devices towards clinical applications could concern the screening of diseases related to cartilage tissue. This could have a positive impact both economically (including for underdeveloped countries) and socially, providing screening possibilities to a large part of the population.
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Sound radiators based on forced vibrations of plates are becoming widely employed, mainly for active sound enhancement and noise cancelling systems, both in music and automotive environment. Active sound enhancement solutions based on electromagnetic shakers hence find increasing interest. Mostly diffused applications deal with active noise control (ANC) and active vibration control systems for improving the acoustic experience inside or outside the vehicle. This requires investigating vibrational and, consequently, vibro-acoustic characteristics of vehicles. Therefore, simulation and processing methods capable of reducing the calculation time and providing high-accuracy results, are strongly demanded. In this work, an ideal case study on rectangular plates in fully clamped conditions preceded a real case analysis on vehicle panels. The sound radiation generated by a vibrating flat or shallow surface can be calculated by means of Rayleigh’s integral. The analytical solution of the problem is here calculated implementing the equations in MATLAB. Then, the results are compared with a numerical model developed in COMSOL Multiphysics, employing Finite Element Method (FEM). A very good matching between analytical and numerical solutions is shown, thus the cross validation of the two methods is achieved. The shift to the real case study, on a McLaren super car, led to the development of a mixed analytical-numerical method. Optimum results were obtained with mini shakers excitement, showing good matching of the recorded SPL with the calculated one over all the selected frequency band. In addition, a set of directivity measurements of the hood were realized, to start studying the spatiality of sound, which is fundamental to active noise control systems.
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Turbulent plasmas inside tokamaks are modeled and studied using guiding center theory, applied to charged test particles, in a Hamiltonian framework. The equations of motion for the guiding center dynamics, under the conditions of a constant and uniform magnetic field and turbulent electrostatic field are derived by averaging over the fast gyroangle, for the first and second order in the guiding center potential, using invertible changes of coordinates such as Lie transforms. The equations of motion are then made dimensionless, exploiting temporal and spatial periodicities of the model chosen for the electrostatic potential. They are implemented numerically in Python. Fast Fourier Transform and its inverse are used. Improvements to the original Python scripts are made, notably the introduction of a power-law curve fitting to account for anomalous diffusion, the possibility to integrate the equations in two steps to save computational time by removing trapped trajectories, and the implementation of multicolored stroboscopic plots to distinguish between trapped and untrapped guiding centers. The post-processing of the results is made in MATLAB. The values and ranges of the parameters chosen for the simulations are selected based on numerous simulations used as feedback tools. In particular, a recurring value for the threshold to detect trapped trajectories is evidenced. Effects of the Larmor radius, the amplitude of the guiding center potential and the intensity of its second order term are studied by analyzing their diffusive regimes, their stroboscopic plots and the shape of guiding center potentials. The main result is the identification of cases anomalous diffusion depending on the values of the parameters (mostly the Larmor radius). The transitions between diffusive regimes are identified. The presence of highways for the super-diffusive trajectories are unveiled. The influence of the charge on these transitions from diffusive to ballistic behaviors is analyzed.
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The hadrontherapy exploits beams of charged particles against deep cancers. These ions have a depth-dose profile in which there is a little release of energy at the beginning of their path, whereas there is a sharp maximum, the Bragg Peak, near its end path. However, if heavy ions are used, the fragmentation of the projectile can happen and the fragments can release some dose outside the treatment volume beyond the Bragg peak. The fragmentation process takes place also when the Galactic Cosmic Rays at high energy hit the spaceship during space missions. In both cases some neutrons can be produced and if they interact with the absorbing materials nuclei some secondary particles are generated which can release energy. For this reason, studies about the cross section measurements of the fragments generated during the collisions of heavy ions against the tissues nuclei are very important. In this context, the FragmentatiOn Of Target (FOOT) experiment was born, and aims at measuring the differential and double differential fragmentation cross sections for different kinetic energies relevant to hadrontherapy and space radioprotection with high accuracy. Since during fragmentation processes also neutrons are produced, tests of a neutron detection system are ongoing. In particular, recently a neutron detector made up of a liquid organic scintillator, BC-501A with neutrons/gammas discrimination capability was studied, and it represents the core of this thesis. More in details, an analysis of the data collected at the GSI laboratory, in Darmstadt, Germany, is effectuated which consists in discriminating neutral and charged particles and then to separate neutrons from gammas. From this analysis, a preliminary energy-differential reaction cross-section for the production of neutrons in the 16O + (C_2H_4)_(n) and 16O + C reactions was estimated.
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In this thesis we study the heat kernel, a useful tool to analyze various properties of different quantum field theories. In particular, we focus on the study of the one-loop effective action and the application of worldline path integrals to derive perturbatively the heat kernel coefficients for the Proca theory of massive vector fields. It turns out that the worldline path integral method encounters some difficulties if the differential operator of the heat kernel is of non-minimal kind. More precisely, a direct recasting of the differential operator in terms of worldline path integrals, produces in the classical action a non-perturbative vertex and the path integral cannot be solved. In this work we wish to find ways to circumvent this issue and to give a suggestion to solve similar problems in other contexts.
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We present a new quantum description for the Oppenheimer-Snyder model of gravitational collapse of a ball of dust. Starting from the geodesic equation for dust in spherical symmetry, we introduce a time-independent Schrödinger equation for the radius of the ball. The resulting spectrum is similar to that of the Hydrogen atom and Newtonian gravity. However, the non-linearity of General Relativity implies that the ground state is characterised by a principal quantum number proportional to the square of the ADM mass of the dust. For a ball with ADM mass much larger than the Planck scale, the collapse is therefore expected to end in a macroscopically large core and the singularity predicted by General Relativity is avoided. Mathematical properties of the spectrum are investigated and the ground state is found to have support essentially inside the gravitational radius, which makes it a quantum model for the matter core of Black Holes. In fact, the scaling of the ADM mass with the principal quantum number agrees with the Bekenstein area law and the corpuscular model of Black Holes. Finally, the uncertainty on the size of the ground state is interpreted within the framework of an Uncertainty Principle.
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In the upcoming years, various upgrades and improvements are planned for the CERN Large Hadron Collider (LHC) and represent the mandate of the High-Luminosity project. The upgrade will allow for a total stored beam energy of about 700 MJ, which will need, among others, an extremely efficient collimation system. This will be achieved with the addition of a hollow electron lens (HEL) system to help control the beam-halo depletion and mitigate the effects of fast beam losses. In this master thesis, we present a diffusion model of the HEL for HL-LHC. In particular, we explore several scenarios to use such a device, focusing on the halo depletion efficiency given by different noise regimes.
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Il passaggio dalla concezione delle forze come azioni a distanza a quella che le vede come azioni che avvengono per contatto, attraverso un mezzo descrivibile con una teoria di campo, costituisce un punto di svolta importante nell'evoluzione della fisica. Da un'analisi storica e filosofica, emerge una molteplicità di aspetti che hanno contribuito a questo cambiamento. Rivestono un ruolo importante le concezioni filosofiche che caratterizzano un periodo storico, gli strumenti matematici, i modelli e le analogie. Questa molteplicità rende il passaggio da un paradigma newtoniano a uno maxwelliano un tema significativo per la didattica. L'obiettivo di questo lavoro di tesi è quello di costruire un percorso didattico indirizzato agli studenti del quarto anno di Liceo Scientifico attraverso i concetti principali dell'elettrostatica, vista come punto di congiunzione tra diversi paradigmi concettuali e tra differenti metodi di rappresentazione matematica. Le ricerche sull'uso della storia della fisica come mezzo per la didattica mettono in luce il parallelismo tra i profili concettuali degli studenti di diverse età con i profili newtoniano e maxwelliano, e attribuiscono le difficoltà nel passaggio da un profilo a un altro a una didattica che non evidenzia la necessità di questo cambiamento. Attraverso un'analisi storica dello sviluppo dell'elettrostatica ho dunque identificato alcuni punti significativi per favorire il cambiamento concettuale, dai quali sono partita per costruire un percorso che si compone di 3 unità in cui sono rese esplicite le motivazioni che portano da un'azione a distanza al concetto di campo e di azione tramite un mezzo. I concetti dell'elettrostatica vengono così trattati attraverso una molteplicità di rappresentazioni e facendo uso di analogie tratte dalla storia della fisica, in maniera coerente con le indicazioni Nazionali per i Licei Scientifici e con le ricerche sulla didattica della fisica che riguardano i diversi aspetti toccati.
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In the ‘society of acceleration and uncertainty’ (Rosa, 2013), the young are struggling to interpret our complex and fast-changing world. The entity and the velocity of changes are so enormous that we need new narratives or languages to conceptualise them. Among those changes “Climate Change” is placed in a particular difficult position. As the writer A. Ghosh said: “The current climate crisis is also a crisis of culture, and thus of the imagination”. In fact, in today’s literature and cinema a strong dichotomy exists between fictional and non-fictional works, but none of those extremities seems suitable to picture an “adequate representation” of climate change issues, particularly those that are related to future. The main goal of my study, carried out within FEDORA EU project, was to understand to what extent the hybrid film form called “mockumentary” (a language that adopts the aesthetics of factual production to give an illusion of truth to invented stories) could inspire and help students in overcoming the mentioned dichotomy, working as a tool to foster the development of argumentative and imaginative skills needed to picture “immaginary yet realistic” climate change scenarios.
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In this master's thesis, the formation of Primordial Black Holes (PBHs) in the context of multi-field inflation is studied. In these models, the interaction of isocurvature and curvature perturbations can lead to a significant enhancement of the latter, and to the subsequent production of PBHs. Depending on their mass, these can account for a significant fraction (or, in some cases, the entirety) of the universe's Dark Matter content. After studying the theoretical framework of generic N-field inflationary models, the focus is restricted to the two-field case, for which a few concrete realisations are analysed. A numerical code (written in Wolfram Mathematica) is developed to make quantitative predictions for the main inflationary observables, notably the scalar power spectra. Parallelly, the production of PBHs due to the dynamics of 2-field inflation is examined: their mass, as well as the fraction of Dark Matter they represent, is calculated for the models considered previously.