Diffusive models and chaos indicators for non-linear betatron motion in circular hadron accelerators

Understanding the complex dynamics of beam-halo formation and evolution in circular particle accelerators is crucial for the design of current and future rings, particularly those utilizing superconducting magnets such as the CERN Large Hadron Collider (LHC), its luminosity upgrade HL-LHC, and the proposed Future Circular Hadron Collider (FCC-hh). A recent diffusive framework, which describes the evolution of the beam distribution by means of a Fokker-Planck equation, with diffusion coefficient derived from the Nekhoroshev theorem, has been proposed to describe the long-term behaviour of beam dynamics and particle losses. In this thesis, we discuss the theoretical foundations of this framework, and propose the implementation of an original measurement protocol based on collimator scans in view of measuring the Nekhoroshev-like diffusive coefficient by means of beam loss data. The available LHC collimator scan data, unfortunately collected without the proposed measurement protocol, have been successfully analysed using the proposed framework. This approach is also applied to datasets from detailed measurements of the impact on the beam losses of so-called long-range beam-beam compensators also at the LHC. Furthermore, dynamic indicators have been studied as a tool for exploring the phase-space properties of realistic accelerator lattices in single-particle tracking simulations. By first examining the classification performance of known and new indicators in detecting the chaotic character of initial conditions for a modulated Hénon map and then applying this knowledge to study the properties of realistic accelerator lattices, we tried to identify a connection between the presence of chaotic regions in the phase space and Nekhoroshev-like diffusive behaviour, providing new tools to the accelerator physics community.

On the effect of confounding in linear regression models: an approach based on the theory of quadratic forms

The main topic of this thesis is confounding in linear regression models. It arises when a relationship between an observed process, the covariate, and an outcome process, the response, is influenced by an unmeasured process, the confounder, associated with both. Consequently, the estimators for the regression coefficients of the measured covariates might be severely biased, less efficient and characterized by misleading interpretations. Confounding is an issue when the primary target of the work is the estimation of the regression parameters. The central point of the dissertation is the evaluation of the sampling properties of parameter estimators. This work aims to extend the spatial confounding framework to general structured settings and to understand the behaviour of confounding as a function of the data generating process structure parameters in several scenarios focusing on the joint covariate-confounder structure. In line with the spatial statistics literature, our purpose is to quantify the sampling properties of the regression coefficient estimators and, in turn, to identify the most prominent quantities depending on the generative mechanism impacting confounding. Once the sampling properties of the estimator conditionally on the covariate process are derived as ratios of dependent quadratic forms in Gaussian random variables, we provide an analytic expression of the marginal sampling properties of the estimator using Carlson’s R function. Additionally, we propose a representative quantity for the magnitude of confounding as a proxy of the bias, its first-order Laplace approximation. To conclude, we work under several frameworks considering spatial and temporal data with specific assumptions regarding the covariance and cross-covariance functions used to generate the processes involved. This study allows us to claim that the variability of the confounder-covariate interaction and of the covariate plays the most relevant role in determining the principal marker of the magnitude of confounding.

Data driven regularization models of non-linear ill-posed inverse problems in imaging

Imaging technologies are widely used in application fields such as natural sciences, engineering, medicine, and life sciences. A broad class of imaging problems reduces to solve ill-posed inverse problems (IPs). Traditional strategies to solve these ill-posed IPs rely on variational regularization methods, which are based on minimization of suitable energies, and make use of knowledge about the image formation model (forward operator) and prior knowledge on the solution, but lack in incorporating knowledge directly from data. On the other hand, the more recent learned approaches can easily learn the intricate statistics of images depending on a large set of data, but do not have a systematic method for incorporating prior knowledge about the image formation model. The main purpose of this thesis is to discuss data-driven image reconstruction methods which combine the benefits of these two different reconstruction strategies for the solution of highly nonlinear ill-posed inverse problems. Mathematical formulation and numerical approaches for image IPs, including linear as well as strongly nonlinear problems are described. More specifically we address the Electrical impedance Tomography (EIT) reconstruction problem by unrolling the regularized Gauss-Newton method and integrating the regularization learned by a data-adaptive neural network. Furthermore we investigate the solution of non-linear ill-posed IPs introducing a deep-PnP framework that integrates the graph convolutional denoiser into the proximal Gauss-Newton method with a practical application to the EIT, a recently introduced promising imaging technique. Efficient algorithms are then applied to the solution of the limited electrods problem in EIT, combining compressive sensing techniques and deep learning strategies. Finally, a transformer-based neural network architecture is adapted to restore the noisy solution of the Computed Tomography problem recovered using the filtered back-projection method.

Comparative study of dental arch width in plaster models, photocopies and digitized images

The aim of this study was to comparatively assess dental arch width, in the canine and molar regions, by means of direct measurements from plaster models, photocopies and digitized images of the models. The sample consisted of 130 pairs of plaster models, photocopies and digitized images of the models of white patients (n = 65), both genders, with Class I and Class II Division 1 malocclusions, treated by standard Edgewise mechanics and extraction of the four first premolars. Maxillary and mandibular intercanine and intermolar widths were measured by a calibrated examiner, prior to and after orthodontic treatment, using the three modes of reproduction of the dental arches. Dispersion of the data relative to pre- and posttreatment intra-arch linear measurements (mm) was represented as box plots. The three measuring methods were compared by one-way ANOVA for repeated measurements (α = 0.05). Initial / final mean values varied as follows: 33.94 to 34.29 mm / 34.49 to 34.66 mm (maxillary intercanine width); 26.23 to 26.26 mm / 26.77 to 26.84 mm (mandibular intercanine width); 49.55 to 49.66 mm / 47.28 to 47.45 mm (maxillary intermolar width) and 43.28 to 43.41 mm / 40.29 to 40.46 mm (mandibular intermolar width). There were no statistically significant differences between mean dental arch widths estimated by the three studied methods, prior to and after orthodontic treatment. It may be concluded that photocopies and digitized images of the plaster models provided reliable reproductions of the dental arches for obtaining transversal intra-arch measurements.

Allometric models for estimating the phytomass of a secondary Atlantic Forest area of southeastern Brazil

The purpose of this study was to develop and validate equations to estimate the aboveground phytomass of a 30 years old plot of Atlantic Forest. In two plots of 100 m², a total of 82 trees were cut down at ground level. For each tree, height and diameter were measured. Leaves and woody material were separated in order to determine their fresh weights in field conditions. Samples of each fraction were oven dried at 80 °C to constant weight to determine their dry weight. Tree data were divided into two random samples. One sample was used for the development of the regression equations, and the other for validation. The models were developed using single linear regression analysis, where the dependent variable was the dry mass, and the independent variables were height (h), diameter (d) and d²h. The validation was carried out using Pearson correlation coefficient, paired t-Student test and standard error of estimation. The best equations to estimate aboveground phytomass were: lnDW = -3.068+2.522lnd (r² = 0.91; s y/x = 0.67) and lnDW = -3.676+0.951ln d²h (r² = 0.94; s y/x = 0.56).

Comparison of some theoretical models for fittings of the temperature dependence of the fundamental energy gap in GaAs

In this work we report on a comparison of some theoretical models usually used to fit the dependence on temperature of the fundamental energy gap of semiconductor materials. We used in our investigations the theoretical models of Viña, Pässler-p and Pässler-ρ to fit several sets of experimental data, available in the literature for the energy gap of GaAs in the temperature range from 12 to 974 K. Performing several fittings for different values of the upper limit of the analyzed temperature range (Tmax), we were able to follow in a systematic way the evolution of the fitting parameters up to the limit of high temperatures and make a comparison between the zero-point values obtained from the different models by extrapolating the linear dependence of the gaps at high T to T = 0 K and that determined by the dependence of the gap on isotope mass. Using experimental data measured by absorption spectroscopy, we observed the non-linear behavior of Eg(T) of GaAs for T > ΘD.

Data collapse, scaling functions, and analytical solutions of generalized growth models

We consider a nontrivial one-species population dynamics model with finite and infinite carrying capacities. Time-dependent intrinsic and extrinsic growth rates are considered in these models. Through the model per capita growth rate we obtain a heuristic general procedure to generate scaling functions to collapse data into a simple linear behavior even if an extrinsic growth rate is included. With this data collapse, all the models studied become independent from the parameters and initial condition. Analytical solutions are found when time-dependent coefficients are considered. These solutions allow us to perceive nontrivial transitions between species extinction and survival and to calculate the transition's critical exponents. Considering an extrinsic growth rate as a cancer treatment, we show that the relevant quantity depends not only on the intensity of the treatment, but also on when the cancerous cell growth is maximum.

Newtonian perturbations on models with matter creation

Creation of cold dark matter (CCDM) can macroscopically be described by a negative pressure, and, therefore, the mechanism is capable to accelerate the Universe, without the need of an additional dark energy component. In this framework, we discuss the evolution of perturbations by considering a Neo-Newtonian approach where, unlike in the standard Newtonian cosmology, the fluid pressure is taken into account even in the homogeneous and isotropic background equations (Lima, Zanchin, and Brandenberger, MNRAS 291, L1, 1997). The evolution of the density contrast is calculated in the linear approximation and compared to the one predicted by the Lambda CDM model. The difference between the CCDM and Lambda CDM predictions at the perturbative level is quantified by using three different statistical methods, namely: a simple chi(2)-analysis in the relevant space parameter, a Bayesian statistical inference, and, finally, a Kolmogorov-Smirnov test. We find that under certain circumstances, the CCDM scenario analyzed here predicts an overall dynamics (including Hubble flow and matter fluctuation field) which fully recovers that of the traditional cosmic concordance model. Our basic conclusion is that such a reduction of the dark sector provides a viable alternative description to the accelerating Lambda CDM cosmology.

Directed Abelian algebras and their application to stochastic models

With each directed acyclic graph (this includes some D-dimensional lattices) one can associate some Abelian algebras that we call directed Abelian algebras (DAAs). On each site of the graph one attaches a generator of the algebra. These algebras depend on several parameters and are semisimple. Using any DAA, one can define a family of Hamiltonians which give the continuous time evolution of a stochastic process. The calculation of the spectra and ground-state wave functions (stationary state probability distributions) is an easy algebraic exercise. If one considers D-dimensional lattices and chooses Hamiltonians linear in the generators, in finite-size scaling the Hamiltonian spectrum is gapless with a critical dynamic exponent z=D. One possible application of the DAA is to sandpile models. In the paper we present this application, considering one- and two-dimensional lattices. In the one-dimensional case, when the DAA conserves the number of particles, the avalanches belong to the random walker universality class (critical exponent sigma(tau)=3/2). We study the local density of particles inside large avalanches, showing a depletion of particles at the source of the avalanche and an enrichment at its end. In two dimensions we did extensive Monte-Carlo simulations and found sigma(tau)=1.780 +/- 0.005.

Treatment of Obese Adolescents: The Influence of Periodization Models and ACE Genotype

The aims of the present study were to compare the effects of two periodization models on metabolic syndrome risk factors in obese adolescents and verify whether the angiotensin-converting enzyme (ACE) genotype is important in establishing these effects. A total of 32 postpuberty obese adolescents were submitted to aerobic training (AT) and resistance training (RT) for 14 weeks. The subjects were divided into linear periodization (LP, n = 16) or daily undulating periodization (DUP, n = 16). Body composition, visceral and subcutaneous fat, glycemia, insulinemia, homeostasis model assessment of insulin resistance (HOMA-IR), lipid profiles, blood pressure, maximal oxygen consumption (VO(2max)), resting metabolic rate (RMR), muscular endurance were analyzed at baseline and after intervention. Both groups demonstrated a significant reduction in body mass, BMI, body fat, visceral and subcutaneous fat, total and low-density lipoprotein cholesterol, blood pressure and an increase in fat-free mass, VO(2max), and muscular endurance. However, only DUP promoted a reduction in insulin concentrations and HOMA-IR. It is important to emphasize that there was no statics difference between LP and DUP groups; however, it appears that there may be bigger changes in the DUP than LP group in some of the metabolic syndrome risk factors in obese adolescents with regard to the effect size (ES). Both periodization models presented a large effect on muscular endurance. Despite the limitation of sample size, our results suggested that the ACE genotype may influence the functional and metabolic characteristics of obese adolescents and may be considered in the future strategies for massive obesity control.

A simple way to introduce fibers into FEM models

This communication proposes a simple way to introduce fibers into finite element modelling. This is a promising formulation to deal with fiber-reinforced composites by the finite element method (FEM), as it allows the consideration of short or long fibers placed arbitrarily inside a continuum domain (matrix). The most important feature of the formulation is that no additional degree of freedom is introduced into the pre-existent finite element numerical system to consider any distribution of fiber inclusions. In other words, the size of the system of equations used to solve a non-reinforced medium is the same as the one used to solve the reinforced counterpart. Another important characteristic is the reduced work required by the user to introduce fibers, avoiding `rebar` elements, node-by-node geometrical definitions or even complex mesh generation. An additional characteristic of the technique is the possibility of representing unbounded stresses at the end of fibers using a finite number of degrees of freedom. Further studies are required for non-linear applications in which localization may occur. Along the text the linear formulation is presented and the bounded connection between fibers and continuum is considered. Four examples are presented, including non-linear analysis, to validate and show the capabilities of the formulation. Copyright (c) 2007 John Wiley & Sons, Ltd.

A FEM procedure based on positions and unconstrained vectors applied to non-linear dynamic of 3D frames

This study presents an alternative three-dimensional geometric non-linear frame formulation based on generalized unconstrained vector and positions to solve structures and mechanisms subjected to dynamic loading. The formulation is classified as total Lagrangian with exact kinematics description. The resulting element presents warping and non-constant transverse strain modes, which guarantees locking-free behavior for the adopted three-dimensional constitutive relation, Saint-Venant-Kirchhoff, for instance. The application of generalized vectors is an alternative to the use of finite rotations and rigid triad`s formulae. Spherical and revolute joints are considered and selected dynamic and static examples are presented to demonstrate the accuracy and generality of the proposed technique. (C) 2010 Elsevier B.V. All rights reserved.

Robust integration of real time optimization with linear model predictive control

Here, we study the stable integration of real time optimization (RTO) with model predictive control (MPC) in a three layer structure. The intermediate layer is a quadratic programming whose objective is to compute reachable targets to the MPC layer that lie at the minimum distance to the optimum set points that are produced by the RTO layer. The lower layer is an infinite horizon MPC with guaranteed stability with additional constraints that force the feasibility and convergence of the target calculation layer. It is also considered the case in which there is polytopic uncertainty in the steady state model considered in the target calculation. The dynamic part of the MPC model is also considered unknown but it is assumed to be represented by one of the models of a discrete set of models. The efficiency of the methods presented here is illustrated with the simulation of a low order system. (C) 2010 Elsevier Ltd. All rights reserved.

Discrete-time mean variance optimal control of linear systems with Markovian jumps and multiplicative noise

In this article, we consider the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noise under three kinds of performance criterions related to the final value of the expectation and variance of the output. In the first problem it is desired to minimise the final variance of the output subject to a restriction on its final expectation, in the second one it is desired to maximise the final expectation of the output subject to a restriction on its final variance, and in the third one it is considered a performance criterion composed by a linear combination of the final variance and expectation of the output of the system. We present explicit sufficient conditions for the existence of an optimal control strategy for these problems, generalising previous results in the literature. We conclude this article presenting a numerical example of an asset liabilities management model for pension funds with regime switching.

Non-linear modal analysis for beams subjected to axial loads: Analytical and finite-element solutions

A rigorous derivation of non-linear equations governing the dynamics of an axially loaded beam is given with a clear focus to develop robust low-dimensional models. Two important loading scenarios were considered, where a structure is subjected to a uniformly distributed axial and a thrust force. These loads are to mimic the main forces acting on an offshore riser, for which an analytical methodology has been developed and applied. In particular, non-linear normal modes (NNMs) and non-linear multi-modes (NMMs) have been constructed by using the method of multiple scales. This is to effectively analyse the transversal vibration responses by monitoring the modal responses and mode interactions. The developed analytical models have been crosschecked against the results from FEM simulation. The FEM model having 26 elements and 77 degrees-of-freedom gave similar results as the low-dimensional (one degree-of-freedom) non-linear oscillator, which was developed by constructing a so-called invariant manifold. The comparisons of the dynamical responses were made in terms of time histories, phase portraits and mode shapes. (C) 2008 Elsevier Ltd. All rights reserved.