Dissertations / Theses on the topic 'Beams dynamics'

The extreme electron beams are characterized by parameters that are comparable or superior to the state of the art. The beams parameters proposed in the more advanced machines under development or in operation demonstrate that extreme beam qualities are necessary to conceive experiments meeting the demands of cutting-edge research. The optimization of parameters such as brightness, beam current or energy spread plays a major role in the design choices of new and competitive machines. A large amount of simulations of beam dynamics is required, accompanied later by a specific R&D of machine components and demonstration experiments. In the field of beam dynamics, the development and improvement of tracking simulators and optimization tools is a main topic. For this reason, in the beam physics group of INFN & University of Milan the code GIOTTO, based on a genetic algorithm, is being developed for years specifically for this purpose. During the work of PhD, I developed new features in the GIOTTO code that allowed me to apply it to new type of problems: simulation of a beam based method for the increase of the brightness of linac beams, design from scratch of matching lines for plasma driven FELs (Free Electron Lasers), the study of new linear acceleration and compression techniques and a preliminary study on how to produce an ultra-cold beam for a quantum-FEL. All these works are united by being applied to linear machines dedicated to the production of high-brightness electron beams for various purposes. During the last year of PhD, I had the opportunity to participate in the design of an FEL source, named MariX. MariX is based on a compact acceleration scheme where the electron beam propagates twice through a superconducting standing wave linac thanks to an arc compressor that reverses the direction of the beam and compresses it.

A methodology to study the impact dynamics of rods, beams and panels using modern numerical solution technique and instrumentation is developed. The numerical study is carried out using the commercial finite element package ABAQUS. The general approach of this tool is illustrated and verified for the static analysis of the stress distribution in a castellated beam and for the dynamic analysis of a cantilevered beam subjected to multiple impact loading. The finite element analysis technique is used to assess the optimal performance of steel plate panels of different cross-sections and thicknesses under the same blast loading conditions. Also, the structural response of folded plate panels of different cross-sections and thicknesses subjected to various blast pressures is studied numerically and compared with the existing experimental measurements. It is shown that the strength to weight ratio of the folded plate panels is higher than those of the single and double plate panels and that the folded plate panel is the more blast-resistant design. Stress wave propagation in circular mild steel rods is studied both numerically and experimentally. The rods are impacted longitudinally using spherical balls. The Hertzian law of impact and the associated non-linear ordinary differential equation of motion are used to determine the force-time history of impact. This force-time history is used in a finite element analysis of the rods to predict the propagation of pulses in the rods. The use of finite element simulation in predicting the wave propagation phenomena and its application to non-destructive testing (NDT) of rods and bars is demonstrated. For the experimental measurements, the stress waves propagated in rods and bars are monitored using PZT patches of size 5x3 mm which are calibrated by means of a finite element approach and by the use of a standard wire-resistance strain gauge. A time domain, frequency domain, regression analysis and autocorrelation procedures are developed to detect defects in rods and bars using wave propagation data. The defects are introduced in the form of slots. By analysing the stress wave data for the defect-free rods and bars and for the rods and bars with defects, it is possible to pinpoint the location of the defects. The results show that defects can be identified using any of the procedures and that their location can be estimated using the time domain technique. It is also shown that a high degree of correlation is obtained between measured and predicted characteristics.

Ce travail de thèse est une contribution au projet national AMOCOPS, financé par l’ANR. Le thème central du projet est la diffusion de lumière par des particules de formes complexes et de grandes tailles (plusieurs dizaines de µm au moins), domaine où les méthodes de simulation numérique existantes trouvent leurs limites d’applicabilité. Nous abordons le problème par le biais des effets mécaniques de la lumière, autrement dit les forces et couples créés par la pression de radiation. Etant la conséquence du transfert d’impulsion entre l’onde et la matière, ces effets sont directement liés à la diffusion de lumière. La thèse comprend une partie expérimentale –majoritaire- concernant les réponses mécaniques de particules de polystyrène de forme ellipsoïdale et d’allongement variable sous illumination par un ou deux faisceaux laser. Les cas de faisceaux faiblement focalisés (lévitation optique) et d’un faisceau très fortement focalisé (pincette optique) sont examinés successivement. Nous caractérisons différents types d’équilibre statique, certains d’entre eux non décrits auparavant, obtenus dans les deux géométries. Par ailleurs nous confirmons l’existence de réponses purement dynamiques, où la particule oscille en permanence. Trois nouveaux modes sont observés, deux dans la géométrie lévitation optique et un autre sous pincette optique. Cette étude nous permet de distinguer les oscillations dites de Simpson-Hanna dans le régime linéaire de celles non linéaires mises en évidence avant nous par Mihiretie et al..Les résultats de nos expériences sont comparés à ceux obtenus par les simulations de J.C. Loudet, sur la base de la simple optique géométrique (OG) et limitées à 2 dimensions (2d). Nous montrons que ces simulations permettent de reproduire qualitativement et comprendre physiquement la plupart des comportements observés dans nos expériences. La principale limitation de ces calculs tient à ce que l’OG ignore le caractère ondulatoire de la lumière. Pour faire mieux et aller vers des simulations fiables quantitativement, il faut développer un modèle alliant optique géométrique et optique ondulatoire. C’est la fonction du modèle VCRM (Vectorial Complex Ray Model) développé récemment par K.F. Ren en 2d. Le but du projet Amocops est de mettre au point la version 3d de la méthode et de la valider sur la base d’expériences comme celles que nous avons conduites. La deuxième partie de la thèse est consacrée à la méthode VCRM. Nous en exposons les principes, et nous présentons quelques résultats des travaux en cours avec une version intermédiaire entre 2d et 3d, dite « 2d+ ». Quelques illustrations sont proposées sur des exemples impliquant des sphères et ellipsoïdes de grandes tailles
This work is a contribution to the “AMOCOPS” project, funded by Agence Nationale de la Recherche. AMOCOPS is dedicated to the development of new computation schemes to simulate the light scattering patterns of large complexly shaped particles. Particle sizes are of the order of several 10s of micrometres, which is at the limit, or beyond the capabilities of currently available computation techniques.Our work indirectly deals with light scattering through the corresponding mechanical effects of light. Light scattering is the source of momentum transfer between light and matter, and therefore of the forces and torques acting on the exposed particles. The majority of Part A of this thesis is about the mechanical responses of ellipsoidal polystyrene particles of varying aspect ratios, under illumination by one or two laser beams. We investigate the case of weakly focused beams (optical levitation), and that of a single large aperture beam (optical tweezers). Different types of static equilibria, some of which are new, are observed and characterized in both geometries. We confirm the existence of dynamic states, whereby the particle permanently oscillates within the laser beam(s). Three new oscillation modes are observed, two of them in the conditions of optical levitation, and another one in the optical tweezer geometry. The study allows us to make a distinction between noise-driven oscillations in the linear regime, of the type predicted by Simpson and Hanna, and nonlinear oscillations such as those evidenced prior to this work, by Mihiretie et al..Results from our experiments are compared to simulations by J.C. Loudet, using simple ray-optics (RO) in two dimensions (2D). We show that results from 2D-RO qualitatively match most of our observations, and allow us to physically understand the main mechanisms at work in the observed phenomena. The simulations cannot be quantitatively exact, due to the 2D limitation, and because RO essentially ignores the wave nature of light. In Part B of the manuscript, we present the principles of the Vectorial Complex Ray Model (VCRM), which was recently developed by K.F. Ren in 2d. The goal of AMOCOPS is to develop a full 3D version of VCRM, able to simulate light scattering by particles of any shape with a smooth surface. We explain the basics of the model, as well as the “2D+” version, which is an extension of the basic 2D-VCRM. A few illustrative examples of light scattering patterns computed with 2d+-VCRM for large-sizes spheres and ellipsoids are presented

Thesis (Ph. D.) -- University of Maryland, College Park, 2008.
Thesis research directed by: Dept. of Electrical and Computer Engineering. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.

Many steel railway bridges in Europe are older than 50 years whilethey are subjected to higher loads than they were originally designedfor. As many of these bridges are approaching the end of their designlife it is crucial to carry out accurate fatigue assessments in order toensure their safety and keep them in service. Usually the influence ofdynamics on fatigue damage is taken into account using dynamicamplification factors from design codes whereas the actual influenceof dynamics has not been thoroughly studied.   During this study the importance of dynamics on fatigue damage isexamined on two specific examples, namely the Söderstöm Bridgeand the Åby älv bridge, which are good examples of open deckbridges that are common among steel railway bridge population.   Different train speeds, the cross beam effect and load distributionwere studied in order to assess the importance of dynamics on fatiguedamage. Three dimensional finite element models were created andlater modified to perform dynamic analysis. Moving point loads wereused to simulate the loading of moving trains. Fatigue damages werecalculated at the various locations to evaluate the influence ofdynamics on fatigue damage.   The results show that the dynamics has small influence on fatiguedamage at studied speeds and damage is not dependent on speed.Assessed cross beam effect was not detected on studied bridges interms of dynamics, but has great influence in terms of statics.

A combination of Newton's second law, a transformation using three consecutive Euler angles, and Taylor expansions is used to develop three nonlinear integro-differential equations describing the flexural-flexural-torsional vibration of metallic and composite beams. The twisting curvature is used to define a physical twisting variable which makes the equations of motion unique and independent of the rotation sequence of the Euler angles. A numerical-perturbation approach is used to analyze the response of metallic and composite beams to parametric and external excitations. First, the linear eigenfunctions and natural frequencies are calculated using a combination of the state-space concept and the fundamental-matrix method. Then, the method of multiple scales is used to construct a set of nonlinear autonomous first-order ordinary-differential equations describing the slow-time modulation of the amplitudes and phases of the interacting modes in the presence of one-to-one and/or two-to-one internal resonances. The inversion symmetry, D, symmetry, and 0(2) symmetry of the system are studied using the modulation equations. The solutions of the modulation equations may be fixed points, limit cycles, or chaotic solutions.
Ph. D.

To investigate the device which is capable of generate and amplify a coherent electromagnetic radiation in the millimeter and submillimeter wavelength ranges is extremely important today. In the research under discussion the model of a plasma-beam superheterodyne free electron laser (SFEL) is the following. Plasma is located in the longitudinal focusing magnetic field with strength H0. Relativistic electron beam is injected into this plasma environment at an angle α with respect to the magnetic field strength vector. We chose a circularly polarized intense low-frequency electromagnetic wave as a pump. This wave propagates along the guiding magnetic field and in the opposite direction to the electron beam. Also we feed a weak high-frequency circularly polarized electromagnetic wave (signal wave) into the system. The direction of the wave signal may be different, so the wave number can either positive or negative. The parametric resonance between the signal wave and the pump wave results in excitation of a space-charge wave (SCW).

Uncertainties in load and system properties play a significant role in reliability analysis of vibrating structural systems. The subject of random vibrations has evolved over the last few decades to deal with uncertainties in external loads. A well developed body of literature now exists which documents the status of this subject. Studies on the influ­ence of system property uncertainties on reliability of vibrating structures is, however, of more recent origin. Currently, the problem of dynamic response characterization of sys­tems with parameter uncertainties has emerged as a subject of intensive research. The motivation for this research activity arises from the need for a more accurate assess­ment of the safety of important and high cost structures like nuclear plant installations, satellites and long span bridges. The importance of the problem also lies in understand­ing phenomena like mode localization in nearly periodic structures and deviant system behaviour at high frequencies. It is now well established that these phenomena are strongly influenced by spatial imperfections in the vibrating systems. Design codes, as of now, are unable to systematically address the influence of scatter and uncertainties. Therefore, there is a need to develop robust design algorithms based on the probabilistic description of the uncertainties, leading to safer, better and less over-killed designs. Analysis of structures with parameter uncertainties is wrought with diffi­culties, which primarily arise because the response variables are nonlinearly related to the stochastic system parameters; this being true even when structures are idealized to display linear material and deformation characteristics. The problem is further com­pounded when nonlinear structural behaviour is included in the analysis. The analysis of systems with parameter uncertainties involves modeling of random fields for the system parameters, discretization of these random fields, solutions of stochastic differential and algebraic eigenvalue problems, inversion of random matrices and differential operators, and the characterization of random matrix products. It should be noted that the mathematical nature of many of these problems is substantially different from those which are encountered in the traditional random vibration analysis. The basic problem lies in obtaining the solution of partial differential equations with random coefficients which fluctuate in space. This has necessitated the development of methods and tools to deal with these newer class of problems. An example of this development is the generalization of the finite element methods of structural analysis to encompass problems of stochastic material and geometric characteristics. The present thesis contributes to the development of methods and tools to deal with structural uncertainties in the analysis of vibrating structures. This study is a part of an ongoing research program in the Department, which is aimed at gaining insights into the behaviour of randomly parametered dynamical systems and to evolve computational methods to assess the reliability of large scale engineering structures. Recent studies conducted in the department in this direction, have resulted in the for­mulation of the stochastic dynamic stiffness matrix for straight Euler-Bernoulli beam elements and these results have been used to investigate the transient and the harmonic steady state response of simple built-up structures. In the present study, these earlier formulations are extended to derive the stochastic dynamic stiffness matrix for a more general beam element, namely, the curved Timoshenko beam element. Furthermore, the method has also been extended to study the mean and variance of the stationary response of built-up structures when excited by stationary stochastic forces. This thesis is organized into five chapters and four appendices. The first chapter mainly contains a review of the developments in stochas­tic finite element method (SFEM). Also presented is a brief overview of the dynamics of curved beams and the essence of the dynamic stiffness matrix method. This discussion also covers issues pertaining to modeling rotary inertia and shear deformations in the study of curved beam dynamics. In the context of SFEM, suitability of different methods for modeling system uncertainties, depending on the type of problem, is discussed. The relative merits of several schemes of discretizing random fields, namely, local averaging, series expansions using orthogonal functions, weighted integral approach and the use of system Green functions, are highlighted. Many of the discretization schemes reported in the literature have been developed in the context of static problems. The advantages of using the dynamic stiffness matrix approach in conjunction with discretization schemes based on frequency dependent shape functions, are discussed. The review identifies the dynamic analysis of structures built-up of randomly parametered curved beams, using dynamic stiffness matrix method, as a problem requiring further research. The review also highlights the need for studies on the treatment of non-Gaussian nature of system parameters within the framework of stochastic finite element analysis and simulation methods. The problem of deterministic analysis of curved beam elements is consid­ered first. Chapter 2 reports on the development of the dynamic stiffness matrix for a curved Timoshenko beam element. It is shown that when the beam is uniformly param-etered, the governing field equations can be solved in a closed form. These closed form solutions serve as the basis for the formulation of damping and frequency dependent shape functions which are subsequently employed in the thesis to develop the dynamic stiffness matrix of stochastically inhomogeneous, curved beams. On the other hand, when the beam properties vary spatially, the governing equations have spatially varying coefficients which discount the possibility of closed form solutions. A numerical scheme to deal with this problem is proposed. This consists of converting the governing set of boundary value problems into a larger class of equivalent initial value problems. This set of Initial value problems can be solved using numerical schemes to arrive at the element dynamic stiffness matrix. This algorithm forms the basis for Monte Carlo simulation studies on stochastic beams reported later in this thesis. Numerical results illustrating the formulations developed in this chapter are also presented. A satisfactory agreement of these results has been demonstrated with the corresponding results obtained from independent finite element code using normal mode expansions. The formulation of the dynamic stiffness matrix for a curved, randomly in-homogeneous, Timoshenko beam element is considered in Chapter 3. The displacement fields are discretized using the frequency dependent shape functions derived in the pre­vious chapter. These shape functions are defined with respect to a damped, uniformly parametered beam element and hence are deterministic in nature. Lagrange's equations are used to derive the 6x6 stochastic dynamic stiffness matrix of the beam element. In this formulation, the system property random fields are implicitly discretized as a set of damping and frequency dependent Weighted integrals. The results for a straight Timo- shenko beam are obtained as a special case. Numerical examples on structures made up of single curved/straight beam elements are presented. These examples also illustrate the characterization of the steady state response when excitations are modeled as stationary random processes. Issues related to ton-Gaussian features of the system in-homogeneities are also discussed. The analytical results are shown to agree satisfactorily with corresponding results from Monte Carlo simulations using 500 samples. The dynamics of structures built-up of straight and curved random Tim-oshenko beams is studied in Chapter 4. First, the global stochastic dynamic stiffness matrix is assembled. Subsequently, it is inverted for calculating the mean and variance, of the steady state stochastic response of the structure when subjected to stationary random excitations. Neumann's expansion method is adopted for the inversion of the stochastic dynamic stiffness matrix. Questions on the treatment of the beam characteris­tics as non-Gaussian random fields, are addressed. It is shown that the implementation of Neumann's expansion method and Monte-Carlo simulation method place distinc­tive demands on strategy of modeling system parameters. The Neumann's expansion method, on one hand, requires the knowledge of higher order spectra of beam properties so that the non-Gaussian features of beam parameters are reflected in the analysis. On the other hand, simulation based methods require the knowledge of the range of the stochastic variations and details of the probability density functions. The expediency of implementing Gaussian closure approximation in evaluating contributions from higher order terms in the Neumann expansion is discussed. Illustrative numerical examples comparing analytical and Monte-Carlo simulations are presented and the analytical so­lutions are found to agree favourably with the simulation results. This agreement lends credence to the various approximations involved in discretizing the random fields and inverting the global dynamic stiffness matrix. A few pointers as to how the methods developed in the thesis can be used in assessing the reliability of these structures are also given. A brief summary of contributions made in the thesis together with a few suggestions for further research are presented in Chapter 5. Appendix A describes the models of non-Gaussian random fields employed in the numerical examples considered in this thesis. Detailed expressions for the elements of the covariance matrix of the weighted integrals for the numerical example considered in Chapter 5, are presented in Appendix B; A copy of the paper, which has been ac­cepted for publication in the proceedings of IUTAM symposium on 'Nonlinearity and Stochasticity in Structural Mechanics' has been included as Appendix C.

Uncertainties in load and system properties play a significant role in reliability analysis of vibrating structural systems. The subject of random vibrations has evolved over the last few decades to deal with uncertainties in external loads. A well developed body of literature now exists which documents the status of this subject. Studies on the influ­ence of system property uncertainties on reliability of vibrating structures is, however, of more recent origin. Currently, the problem of dynamic response characterization of sys­tems with parameter uncertainties has emerged as a subject of intensive research. The motivation for this research activity arises from the need for a more accurate assess­ment of the safety of important and high cost structures like nuclear plant installations, satellites and long span bridges. The importance of the problem also lies in understand­ing phenomena like mode localization in nearly periodic structures and deviant system behaviour at high frequencies. It is now well established that these phenomena are strongly influenced by spatial imperfections in the vibrating systems. Design codes, as of now, are unable to systematically address the influence of scatter and uncertainties. Therefore, there is a need to develop robust design algorithms based on the probabilistic description of the uncertainties, leading to safer, better and less over-killed designs. Analysis of structures with parameter uncertainties is wrought with diffi­culties, which primarily arise because the response variables are nonlinearly related to the stochastic system parameters; this being true even when structures are idealized to display linear material and deformation characteristics. The problem is further com­pounded when nonlinear structural behaviour is included in the analysis. The analysis of systems with parameter uncertainties involves modeling of random fields for the system parameters, discretization of these random fields, solutions of stochastic differential and algebraic eigenvalue problems, inversion of random matrices and differential operators, and the characterization of random matrix products. It should be noted that the mathematical nature of many of these problems is substantially different from those which are encountered in the traditional random vibration analysis. The basic problem lies in obtaining the solution of partial differential equations with random coefficients which fluctuate in space. This has necessitated the development of methods and tools to deal with these newer class of problems. An example of this development is the generalization of the finite element methods of structural analysis to encompass problems of stochastic material and geometric characteristics. The present thesis contributes to the development of methods and tools to deal with structural uncertainties in the analysis of vibrating structures. This study is a part of an ongoing research program in the Department, which is aimed at gaining insights into the behaviour of randomly parametered dynamical systems and to evolve computational methods to assess the reliability of large scale engineering structures. Recent studies conducted in the department in this direction, have resulted in the for­mulation of the stochastic dynamic stiffness matrix for straight Euler-Bernoulli beam elements and these results have been used to investigate the transient and the harmonic steady state response of simple built-up structures. In the present study, these earlier formulations are extended to derive the stochastic dynamic stiffness matrix for a more general beam element, namely, the curved Timoshenko beam element. Furthermore, the method has also been extended to study the mean and variance of the stationary response of built-up structures when excited by stationary stochastic forces. This thesis is organized into five chapters and four appendices. The first chapter mainly contains a review of the developments in stochas­tic finite element method (SFEM). Also presented is a brief overview of the dynamics of curved beams and the essence of the dynamic stiffness matrix method. This discussion also covers issues pertaining to modeling rotary inertia and shear deformations in the study of curved beam dynamics. In the context of SFEM, suitability of different methods for modeling system uncertainties, depending on the type of problem, is discussed. The relative merits of several schemes of discretizing random fields, namely, local averaging, series expansions using orthogonal functions, weighted integral approach and the use of system Green functions, are highlighted. Many of the discretization schemes reported in the literature have been developed in the context of static problems. The advantages of using the dynamic stiffness matrix approach in conjunction with discretization schemes based on frequency dependent shape functions, are discussed. The review identifies the dynamic analysis of structures built-up of randomly parametered curved beams, using dynamic stiffness matrix method, as a problem requiring further research. The review also highlights the need for studies on the treatment of non-Gaussian nature of system parameters within the framework of stochastic finite element analysis and simulation methods. The problem of deterministic analysis of curved beam elements is consid­ered first. Chapter 2 reports on the development of the dynamic stiffness matrix for a curved Timoshenko beam element. It is shown that when the beam is uniformly param-etered, the governing field equations can be solved in a closed form. These closed form solutions serve as the basis for the formulation of damping and frequency dependent shape functions which are subsequently employed in the thesis to develop the dynamic stiffness matrix of stochastically inhomogeneous, curved beams. On the other hand, when the beam properties vary spatially, the governing equations have spatially varying coefficients which discount the possibility of closed form solutions. A numerical scheme to deal with this problem is proposed. This consists of converting the governing set of boundary value problems into a larger class of equivalent initial value problems. This set of Initial value problems can be solved using numerical schemes to arrive at the element dynamic stiffness matrix. This algorithm forms the basis for Monte Carlo simulation studies on stochastic beams reported later in this thesis. Numerical results illustrating the formulations developed in this chapter are also presented. A satisfactory agreement of these results has been demonstrated with the corresponding results obtained from independent finite element code using normal mode expansions. The formulation of the dynamic stiffness matrix for a curved, randomly in-homogeneous, Timoshenko beam element is considered in Chapter 3. The displacement fields are discretized using the frequency dependent shape functions derived in the pre­vious chapter. These shape functions are defined with respect to a damped, uniformly parametered beam element and hence are deterministic in nature. Lagrange's equations are used to derive the 6x6 stochastic dynamic stiffness matrix of the beam element. In this formulation, the system property random fields are implicitly discretized as a set of damping and frequency dependent Weighted integrals. The results for a straight Timo- shenko beam are obtained as a special case. Numerical examples on structures made up of single curved/straight beam elements are presented. These examples also illustrate the characterization of the steady state response when excitations are modeled as stationary random processes. Issues related to ton-Gaussian features of the system in-homogeneities are also discussed. The analytical results are shown to agree satisfactorily with corresponding results from Monte Carlo simulations using 500 samples. The dynamics of structures built-up of straight and curved random Tim-oshenko beams is studied in Chapter 4. First, the global stochastic dynamic stiffness matrix is assembled. Subsequently, it is inverted for calculating the mean and variance, of the steady state stochastic response of the structure when subjected to stationary random excitations. Neumann's expansion method is adopted for the inversion of the stochastic dynamic stiffness matrix. Questions on the treatment of the beam characteris­tics as non-Gaussian random fields, are addressed. It is shown that the implementation of Neumann's expansion method and Monte-Carlo simulation method place distinc­tive demands on strategy of modeling system parameters. The Neumann's expansion method, on one hand, requires the knowledge of higher order spectra of beam properties so that the non-Gaussian features of beam parameters are reflected in the analysis. On the other hand, simulation based methods require the knowledge of the range of the stochastic variations and details of the probability density functions. The expediency of implementing Gaussian closure approximation in evaluating contributions from higher order terms in the Neumann expansion is discussed. Illustrative numerical examples comparing analytical and Monte-Carlo simulations are presented and the analytical so­lutions are found to agree favourably with the simulation results. This agreement lends credence to the various approximations involved in discretizing the random fields and inverting the global dynamic stiffness matrix. A few pointers as to how the methods developed in the thesis can be used in assessing the reliability of these structures are also given. A brief summary of contributions made in the thesis together with a few suggestions for further research are presented in Chapter 5. Appendix A describes the models of non-Gaussian random fields employed in the numerical examples considered in this thesis. Detailed expressions for the elements of the covariance matrix of the weighted integrals for the numerical example considered in Chapter 5, are presented in Appendix B; A copy of the paper, which has been ac­cepted for publication in the proceedings of IUTAM symposium on 'Nonlinearity and Stochasticity in Structural Mechanics' has been included as Appendix C.

We investigate theoretically and experimentally the nonlinear responses of a clamped-clamped buckled beam to a variety of external harmonic excitations and internal resonances. We assume that the beam geometry is uniform and its material is homogeneous. We initially buckle the beam by an axial force beyond the critical load of the first buckling mode, and then we apply a transverse harmonic excitation that is uniform over its span. The beam is modeled according to the Euler-Bernoulli beam theory and small strains and moderate rotation approximations are assumed. We derive the equation of motion governing the nonlinear transverse planar vibrations and associated boundary conditions using the extended Hamilton's principle. The governing equation is a nonlinear integral-partial-differential equation in space and time that possesses quadratic and cubic nonlinearities. A closed-form solution for such equations is not available and hence we seek approximate solutions. We use perturbation methods to investigate the slow dynamics in the neighborhood of an equilibrium configuration. A Galerkin approximation is used to discretize the nonlinear partial-differential equation governing the beam's response and obtain a set of nonlinearly coupled ordinary-differential equations governing the time evolution of the response. We based our theory on a multi-mode Galerkin discretization. To investigate the large-amplitude dynamics, we use a shooting method to numerically integrate the discretized equations and obtain periodic orbits. The stability and bifurcations of these periodic orbits are investigated using Floquet theory. We solve the nonlinear buckling problem to determine the buckled configurations as a function of the applied axial load. We compare the static buckled configurations obtained from the discretized equations with the exact ones. We find out that the number of modes retained in the discretization has a significant effect on these static configurations. We consider three cases: primary resonance, subharmonic resonance of order one-half of the first vibration mode, and one-to-one internal resonance between the first and second modes. We obtain interesting dynamics, such as phase-locked and quasiperiodic motions, resulting from a Hopf bifurcation, snapthrough motions, and a sequence of period-doubling bifurcations leading to chaos. To validate our theoretical results, we ran an experiment, which is a modified version of the experiment designed by Kreider and Nayfeh. We find that the obtained theoretical results are in good qualitative agreement with the experimental results. In the case of one-to-one internal resonance, we report, theoretically and experimentally, energy transfer between the first mode, which is externally excited, and the second mode.
Ph. D.

This work is done as a small facet of a much larger study on efficient control of indoor air environments. Halton passive chilled beams are used to cool rooms and the focus of this work is to model the beams. This work also reviews the mesh making process in Gmsh. ANSYS Fluent was used throughout the entire research and this thesis describes the software and a careful description of the case study.
Master of Science

A system is presented that is capable of confining an ion beam or plasma within a region that is essentially free of applied fields. An Artificially Structured Boundary (ASB) produces a spatially periodic set of magnetic field cusps that provides charged particle confinement. Electrostatic plugging of the magnetic field cusps enhances confinement. An ASB that has a small spatial period, compared to the dimensions of a confined plasma, generates electro- magneto-static fields with a short range. An ASB-lined volume thus constructed creates an effectively field free region near its center. It is assumed that a non-neutral plasma confined within such a volume relaxes to a Maxwell-Boltzmann distribution. Space charge based confinement of a second species of charged particles is envisioned, where the second species is confined by the space charge of the first non-neutral plasma species. An electron plasma confined within an ASB-lined volume can potentially provide confinement of a positive ion beam or positive ion plasma. Experimental as well as computational results are presented in which a plasma or charged particle beam interact with the electro- magneto-static fields generated by an ASB. A theoretical model is analyzed and solved via self-consistent computational methods to determine the behavior and equilibrium conditions of a relaxed plasma. The equilibrium conditions of a relaxed two species plasma are also computed. In such a scenario, space charge based electrostatic confinement is predicted to occur where a second plasma species is confined by the space charge of the first plasma species. An experimental apparatus with cylindrical symmetry that has its interior surface lined with an ASB is presented. This system was developed by using a simulation of the electro- magneto-static fields present within the trap to guide mechanical design. The construction of the full experimental apparatus is discussed. Experimental results that show the characteristics of electron beam transmission through the experimental apparatus are presented. A description of the experimental hardware and software used for trapping a charged particle beam or plasma is also presented.

Based on a refined analytical anisotropic thin-walled beam model, aeroelastic instability, dynamic aeroelastic response, active/passive aeroelastic control of advanced aircraft wings modeled as thin-walled beams are systematically addressed. The refined thin-walled beam model is based on an existing framework of the thin-walled beam model and a couple of non-classical effects that are usually also important are incorporated and the model herein developed is validated against the available experimental, Finite Element Anaylsis (FEA), Dynamic Finite Element (DFE), and other analytical predictions. The concept of indicial functions is used to develop unsteady aerodynamic model, which broadly encompasses the cases of incompressible, compressible subsonic, compressible supersonic and hypersonic flows. State-space conversion of the indicial function based unsteady aerodynamic model is also developed. Based on the piezoelectric material technology, a worst case control strategy based on the minimax theory towards the control of aeroelastic systems is further developed. Shunt damping within the aeroelastic tailoring environment is also investigated. The major part of this dissertation is organized in the form of self-contained chapters, each of which corresponds to a paper that has been or will be submitted to a journal for publication. In order to fullfil the requirement of having a continuous presentation of the topics, each chapter starts with the purely structural models and is gradually integrated with the involved interactive field disciplines.
Ph. D.

Dans cette thèse, nous présentons des résultats concernant la propagation d’un faisceau Airy dans un cristal photoréfractif. Le faisceau Airy est un faisceau à plusieurs lobes qui conserve la même forme tout en se propageant sur une trajectoire courbe. Le cristal photoréfractif est un milieu non linéaire. La lumière peut être imprimée à l’intérieur du cristal et/ou un faisceau lumineux peut y créer son propre guide d’ondes. La propagation du faisceau Airy est modifiée lors du passage dans le cristal. La trajectoire parabolique se transforme alors partiellement ou complètement en un faisceau solitaire. Ce phénomène s’imprime à l’intérieur du cristal et créé un guide d’onde complexe. En modifiant les paramètres du faisceau Airy et la réponse non linéaire du cristal, différents type de guides d’ondes peuvent être obtenues. Nous pouvons donc créer et contrôler un dispositif de routage tout-optique pouvant avoir des applications dans le domaine des télécommunications
In this thesis we present results concerning the propagation of an Airy beam in a photorefractive crystal. The Airy beam is a multi-lobed beam that keeps the same shape while propagating along a curved trajectory. It can also regenerate its profile while propagating if it is partially blocked. The photorefractive crystal is a nonlinear media. Light can imprint its intensity distribution inside the crystal and a light beam can create its own waveguide. The Airy beam propagation is changed When going through the crystal. The parabolic trajectory changes partially or completely to a solitary straight beam. Furthermore, this propagation behavior is imprinted inside the crystal and this creates a complex waveguiding structure. By changing the Airy beam parameters and the nonlinear response of the crystal, different waveguiding configurations can be obtained. We can therefore create and control an all-optical routing device with potential applications in the field of telecommunications

Dans la première partie de la thèse, les schémas d’intégration conservatifs sont appliqués aux poutres co-rotationnelles 2D. Les cinématiques d'Euler-Bernoulli et de Timoshenko sont abordées. Ces formulations produisent des expressions de l'énergie interne et l'énergie cinétique complexe et fortement non-linéaires. L’idée centrale de l’algorithme consiste à définir, par intégration, le champ des déformations en fin de pas à partir du champ de vitesses de déformations et non à partir du champ des déplacements au travers de la relation déplacement-déformation. La même technique est appliquée aux termes d’inerties. Ensuite, une poutre co-rotationnelle plane avec rotules généralisées élasto-(visco)-plastiques aux extrémités est développée et comparée au modèle fibre avec le même comportement pour des problèmes d'impact. Des exemples numériques montrent que les effets de la vitesse de déformation influencent sensiblement la réponse de la structure. Dans la seconde partie de cette thèse, une théorie de poutre spatiale d’Euler-Bernoulli géométriquement exacte est développée. Le principal défi dans la construction d’une telle théorie réside dans le fait qu’il n’existe aucun moyen naturel de définir un trièdre orthonormé dans la configuration déformée. Une nouvelle méthodologie permettant de définir ce trièdre et par conséquent de développer une théorie de poutre spatiale en incorporant l'hypothèse d'Euler- Bernoulli est fournie. Cette approche utilise le processus d'orthogonalisation de Gram-Schmidt couplé avec un paramètre rotation qui complète la description cinématique et décrit la rotation associée à la torsion. Ce processus permet de surmonter le caractère non-unique de la procédure de Gram-Schmidt. La formulation est étendue au cas dynamique et un schéma intégration temporelle conservant l'énergie est également développé. De nombreux exemples démontrent l’efficacité de cette formulation
In the first part of the thesis, energymomentum conserving algorithms are designed for planar co-rotational beams. Both Euler-Bernoulli and Timoshenko kinematics are addressed. These formulations provide us with highly complex nonlinear expressions for the internal energy as well as for the kinetic energy which involve second derivatives of the displacement field. The main idea of the algorithm is to circumvent the complexities of the geometric non-linearities by resorting to strain velocities to provide, by means of integration, the expressions for the strain measures themselves. Similarly, the same strategy is applied to the highly nonlinear inertia terms. Next, 2D elasto-(visco)-plastic fiber co-rotational beams element and a planar co-rotational beam with generalized elasto-(visco)-plastic hinges at beam ends have been developed and compared against each other for impact problems. In the second part of this thesis, a geometrically exact 3D Euler-Bernoulli beam theory is developed.The main challenge in defining a three-dimensional Euler-Bernoulli beam theory lies in the fact that there is no natural way of defining a base system at the deformed configuration. A novel methodology to do so leading to the development of a spatial rod formulation which incorporates the Euler-Bernoulli assumption is provided. The approach makes use of Gram-Schmidt orthogonalisation process coupled to a one-parametric rotation to complete the description of the torsional cross sectional rotation and overcomes the non-uniqueness of the Gram-Schmidt procedure. Furthermore, the formulation is extended to the dynamical case and a stable, energy conserving time-stepping algorithm is developed as well. Many examples confirm the power of the formulation and the integration method presented

A pulsed supersonic molecular beam apparatus has been constructed for the investigation of atomic and molecular van der Waals clusters. The apparatus was characterized by investigating supersonic beam intensities as a function of reservoir pressure and nozzle to skimmer separation, and by measuring supersonic beam speed distributions for various monatomic and diatomic gases and binary monatomic gas mixtures using time-of-flight methods. A new technique for deconvolving badly convoluted time-of-flight data was developed and successfully applied to the deconvolution of time-of-flight waveforms measured for unchopped pulsed supersonic beams of argon, krypton, CHCl₃ and CH₃Cl. Size distributions of van der Waals cluster species were investigated for supersonic expansions of pure argon and for seeded helium expansions containing 8O₂, N₂O and H₂O, NO and NO₂ and NH₃. Appearance potentials of the cluster ions (CO₂)n⁺, (N₂O) n⁺ (2 ≤ n ≤ 4) and (NH₃)nH⁺ (1 ≤ n ≤ 8), and the cluster ion fragments (N₂O∙O)+ and (N₂O∙NO)+ have been determined by electron impact ionization of neutral clusters formed in the supersonic beam. The measured appearance potential data were used to estimate cluster ion binding energies, and possible mechanisms for the formation of the cluster fragment ions (N₂O∙O)+ and (N₂O∙NO)+ are discussed. Computational procedures have been developed for the calculation of supersonic beam properties as a function of distance along the expansion axis. Collision frequency, flow velocity, particle density, mean free path, and axial and radial temperatures in supersonic atomic and homonuclear diatomic beams have been calculated for various species using realistic interaction potentials and collision cross sections obtained from scattering theory. A simple approach to the estimation of rotational relaxation times and collision numbers in supersonic expansions was developed and used to calculate rotational relaxation times and rotational collision numbers for H₂, N ₂, O ₂ and Cl₂. A sophisticated direct simulation Monte Carlo procedure was devised for the investigation of rotational relaxation in small molecules. The devised relaxation model has been used to calculate rotational relaxation data for the homonuclear diatomic molecules H₂, N₂, O ₂ and Cl₂, and for the polyatomic species CO₂, OCS, NH₃, CH₄, CH₃Cl and C₂H₄. Results obtained using the Monte Carlo procedure were used to investigate the breakdown of translational and rotational equilibrium in supersonic expansions of CO₂, OCS and CH₃Cl.

Cette thèse se concentre sur la contrôlabilité de l'indice de réfraction au niveau sub-micronique par changements d'indice induits par laser sur de longues dimensions i.e., avec des hauts rapports d'aspect élevés et des sections à l'échelle nanométrique. À cette fin, nous explorons les faisceaux ultracourts de Bessel non-diffractifs d'ordre zéro et les facteurs qui contribuent au confinement de l'énergie au-delà de la limite de diffraction. Le traitement par laser de matériaux transparents à l'aide de faisceaux non diffractifs offre un avantage important pour les structures sub-microniques en volume de haut rapport d'aspect à des fins applicatives en nanophotonique et en nanofluidique. Nous présentons l'effet de différentes conditions de focalisation et de paramètres laser sur la modification de la silice fondue, explorant ainsi les différents régimes d'interaction. Cette thèse aborde essentiellement des conditions modérées de focalisation car elles offrent un régime d'interaction stable sur une large gamme de paramètres laser, permettant l'ingénierie de la dispersion. La durée de l'impulsion laser s'est révélée être essentielle dans la définition du type de modification de l'indice de réfraction ou de modification structurale. Par exemple, l'usinage utilisant des impulsions laser femtosecondes entraîne une augmentation des structures d'indice de réfraction alors que les impulsions laser picosecondes engendrent une cavité uniforme i.e., des structures de faible indice. Pour acquérir un meilleur contrôle et une meilleure précision du dépôt d'énergie laser, un ensemble de mécanismes physiques responsables des dommages induits par laser dans des conditions d'excitation non-diffractives a été observé expérimentalement et examiné par des simulations indiquant le rôle essentiel de la diffusion de la lumière sur les électrons. Des mesures de microscopie pompe-sonde résolues en temps avec une résolution temporelle sub-picoseconde et spatiale sub-micronique donnent accès à l'excitation et à la relaxation dynamique instantanées. La transmission optique dynamique et le contraste de phase offrent des informations complémentaires sur la réponse électronique ou sur celle de la matrice vitreuse. La dynamique ultrarapide des porteurs libres a été particulièrement étudiée puisque le transfert d'énergie des électrons vers le réseau est la clé de transformation ultérieure du matériau. Le rôle de l'excitation instantanée pour différentes durées et énergie d'impulsion laser est exposé. Ainsi, la dynamique complète des porteurs de charge est présentée pour différents paramètres du laser. En particulier, la dynamique d'obtention de structures d'indice de réfraction positif et des cavités uniformes indique deux chemins différents de relaxation électronique et de dépôt de l'énergie: une relaxation rapide par l'intermédiaire de défauts pour les structures d'indice positif et une relaxation thermomécanique lente pour les cavités nanométriques. Enfin, en corrélant les résultats des études résolues en temps, les simulations et les résultats de photoluminescence après irradiation, nous formulons des scénarios potentiels de formation de l'indice de réfraction positif ainsi que des structures d'indice faible ou de vides uniformes
This thesis is focused on the controllability of laser-induced refractive index changes at sub-micron level over long dimensions i.e., with high aspect ratios and sections on the nanoscale. To this end, we explore non-diffractive zerothorder ultrafast Bessel beams and factors contributing to energy confinement beyond the diffraction limit. Laser processing of transparent materials using non-diffracting beams offers a strong advantage for high aspect ratio submicron structures inside the bulk in view of nanophotonics and nanouidics applications. We present the role of various focusing conditions and laser parameters on material modification in bulk fused silica and explore the different interaction regimes. This thesis tackles mostly the moderate focusing conditions as they offer a stable interaction regime backed up dispersion engineering over a large range of laser parameters. The laser pulse duration was found to be key in defining the type of laser induced refractive index or structural modification. For instance, machining using femtosecond laser pulses results in increased refractive index structures whereas picosecond laser pulses result in uniform void i.e., low index structures. To acquire better control over the laser energy deposition and precision, a range of physical mechanisms responsible for the laser induced damage in non-diffractive excitation conditions have been observed experimentally and further interrogated by simulations indicating a critical role of light scattering on carriers. Time-resolved pump-probe microscopy measurements with a sub-picosecond temporal and sub-micron spatial resolution allow access to the instantaneous excitation and relaxation dynamics. Dynamic optical transmission and phase contrast o_er complementary information of either electronic and glass matrix response. Primarily, ultrafast dynamics of free carriers was studied as the electron mediated energy transfer to the lattice is key to the subsequent material transformation. Role of instantaneous excitation at different laser pulse durations and energies is outlined. Then complete carrier dynamics is presented at different laser parameters. Particularly dynamics in conditions of positive refractive index structures and uniform voids is indicating two different paths of electronic relaxation and energy deposition: a fast defect mediated relaxation for positive index structures and slow thermomechanical relaxation for nanosize void structures. Finally, by correlating the results of time resolved studies, simulations and post-irradiated photoluminescence results, we formulate potential formation scenarios for the positive refractive index and low index or uniform void structures

We study numerical methods for time-dependent partial differential equations describing wave propagation, primarily applied to problems in quantum dynamics governed by the time-dependent Schrödinger equation (TDSE). We consider both methods for spatial approximation and for time stepping. In most settings, numerical solution of the TDSE is more challenging than solving a hyperbolic wave equation. This is mainly because the dispersion relation of the TDSE makes it very sensitive to dispersion error, and infers a stringent time step restriction for standard explicit time stepping schemes. The TDSE is also often posed in high dimensions, where standard methods are intractable. The sensitivity to dispersion error makes spectral methods advantageous for the TDSE. We use spectral or pseudospectral methods in all except one of the included papers. In Paper III we improve and analyse the accuracy of the Fourier pseudospectral method applied to a problem with limited regularity, and in Paper V we construct a matrix-free spectral method for problems with non-trivial boundary conditions. Due to its stiffness, the TDSE is most often solved using exponential time integration. In this thesis we use exponential operator splitting and Krylov subspace methods. We rigorously prove convergence for force-gradient operator splitting methods in Paper IV. One way of making high-dimensional problems computationally tractable is low-rank approximation. In Paper VI we prove that a splitting method for dynamical low-rank approximation is robust to singular values in the approximation approaching zero, a situation which is difficult to handle since it implies strong curvature of the approximation space.
eSSENCE

A mechanical wave is generated as a result of an external force interacting with the well-defined medium and it propagates through that medium transferring energy from one location to another. The ability to generate and control the motion of the mechanical waves through the finite medium opens up the opportunities for creating novel actuation mechanisms not possible before. However, any impedance to the path of these waves, especially in the form of finite boundaries, disperses this energy in the form of reflections. Therefore, it is impractical to achieve steady state traveling waves in finite structures without any reflections. In-spite of all these conditions, is it possible to generate waveforms that travel despite reflections at the boundaries? The work presented in this thesis develops a framework to answer this question by leveraging the dynamics of the finite structures without any active control. Therefore, this work investigates how mechanical waves are developed in finite structures and identifies the factors that influence steady state wave characteristics. Theoretical and experimental analysis is conducted on 1D and 2D structures to realize different type of traveling waves. Owing to the robust characteristics of the piezo-ceramics (PZTs) in vibrational studies, we developed piezo-coupled structures to develop traveling waves through experiments.The results from this study provided the fundamental physics behind the generation of mechanical waves and their propagation through finite mediums. This research will consolidate the outcomes and develop a structural framework that will aid with the design of adaptable structural systems built for the purpose. The present work aims to generate and harness structural traveling waves for various applications.
Ph. D.

The nuclear research carried out at the LNS laboratory in Catania is mainly allowed by the ion beams delivered by two ion accelerators, a 15 MV Tandem and a k800 Superconducting Cyclotron (the so-called CS). These accelerators deliver to the INFN-LNS scientific community a large variety of stable ion beams with energies ranging from a few MeV/amu to 80 MeV/amu. NUMEN, a nuclear physics project born recently at INFN-LNS, proposes the use of the heavy ion induced double charge exchange reactions as a tool to access quantitative information relevant for nuclear matrix elements for neutrinoless double beta decay. The pilot experiment carried out by the NUMEN team at LNS in Catania has already demonstrated that beam power of the order of 1-10 kW of Carbon, Oxigen and Neon with energies in the range 15-70 MeV/amu are mandatory for the NUMEN reaction study. An additional requirement is that the beam energy resolution should not overcome 1/1000 FWHM. Currently, the maximum CS beam power does not exceed 100 W, so a substantial upgrade of the CS is needed to fulfil the NUMEN requirements. In the frame of the CS upgrade, this thesis is devoted to the simulations of beam dynamics in the LNS cyclotron, with the aim to overcome the current CS limitations and to propose innovative solutions for achieving the beam characteristics in terms of beam power and energy resolution required by the NUMEN project. In this thesis, one of the main topic is the stripping extraction from the CS. The study has allowed to individuate: i) the stripper foil position for each ion to be extracted by stripping, ii) the transverse dimension and direction of the new extraction channel in the CS to be used for all the ions to be extracted by stripping and iii) the features of the magnetic channels to be installed inside the new extraction channel. The second subject of this thesis is the beam injection and acceleration up to the extraction in the LNS cyclotron. This study has been possible thanks to the development of the beam tracking model of the INFN-LNS Superconducting Cyclotron, performed in collaboration with the Ion Beam Applications company. This work has shown that the total transmission efficiency from the CS bore injection up to the extraction system, simulating also a process of energy selection outside the CS according to the NUMEN requirement, is only around the 2.7%, a low value compared to the expected value of 15%. The energy selection process is the main cause of the low total efficiency. We demonstrated that the major contribution to the beam energy spread at the extraction in the LNS cyclotron is due to the large emittance circulating in the LNS cyclotron. The energy gain per turn contributes only partially to the energy spread at the extraction but, in any case, it sets an inferior limit on the minimum energy spread obtainable in the CS cyclotron. This value stays around 0.2%, about the twice of the NUMEN requirement. This thesis allows also to establish a roadmap of the goals and milestones to be achieved in next months/years. According to the simulation results, the goal of reduction of the beam energy spread at the extraction can be achieved only paying attention on the ion beam production and transport to the CS, since these processes determine the emittance in the horizontal and vertical phase spaces of the beam entering the CS central region. Also a good quality of the accelerated beam will be necessary since an initial beam offset in the central region implies a further increase of the beam energy spread at the extraction. This work has also shown that an increase of the injection efficiency is possible by applying higher dee voltages than the nominal one and modifying slightly the existing central region design. These changes have allowed to increase the injection efficiency up to a factor of about 1.7.

Cette thèse se concentre sur le développement de faisceaux de positrons polarisés et non polarisés pour le futur programme expérimental en physique hadronique au Thomas Jefferson National Accelerator Facility (JLab). Le défi principal consiste à produire des faisceaux de positrons polarisés à haute intensité et à cycle de service élevé (Duty cycle). La source de positrons du JLab, basée sur la technique PEPPo (Polarized Electrons for Polarized Positrons), vise à utiliser un faisceau continu d'électrons de haute intensité (1 mA) et hautement polarisés (90%) d'énergie modérée (120 MeV) pour produire soit un faisceau de positrons de faible intensité (>100nA) et hautement polarisés (60%), soit un faisceau de positrons de haute intensité (>3 μA) et non polarisés.L'optimisation de la disposition et des performances de la source de positrons est examinée dans cette thèse. La source est conçue avec un second injecteur spécialisé pour générer, transporter, accélérer et façonner les faisceaux de positrons. Elle est compatible avec l'accélération au Continuous Electron Beam Accelerator Facility (CEBAF), et les résultats de l'investigation sont présentés dans ce document
This thesis focuses on the development of polarized and unpolarized positronbeams for the future experimental program in hadronic physics at the Thomas Jefferson National Accelerator Facility (JLab). The primary challenge is to produce high-duty-cycle and high-intensity polarized positron beams. The JLab positron source, which is based on the PEPPo (Polarized Electrons for Polarized Positrons) technique, aims to use a high-intensity (1 mA) and highly polarized (90%) continuous electron beam of moderate energy (120 MeV) to produce either a low intensity (>100nA), highly polarized (60%) positron beam or a high intensity (>3 μA), unpolarized positron beam.The optimization of the layout and performance of the positron source is examined in this thesis. The source is designed with a specialized second injector to generate, transport, accelerate, and shape positron beams. It is compatible with acceleration at the Continuous Electron Beam Accelerator Facility (CEBAF), and the investigation results are presented in this document

In this thesis the Ramberg-Osgood nonlinear model for describing the behavior of many different materials is investigated. A brief overview of the model as it is currently used in the literature is undertaken and several misunderstandings and possible pitfalls in its application is pointed out, especially as it pertains to more recent approaches to finding solutions involving the model. There is an investigation of the displacement of a cantilever beam under a combined loading consisting of a distributed load across the entire length of the beam and a point load at its end and new solutions to this problem are provided with a mixture of numerical techniques, which suggest strong mathematical consistency within the model for all theoretical assumptions made. A physical experiment was undertaken and the results prove to be inaccurate when using parameters derived from tensile tests, but when back calculating parameters from the beam test the model has a 14.40% error at its extreme against the experimental data suggesting the necessity for further testing.

Multislice HAADF - STEM image simulations of SrTiO 3 are performed at 300 K.The procedure of these simulations and the used techniques are briefly ex-plained and reasoned. The results are presented and discussed in a conciseway and in an attached paper a comparison to experimental images is made.The paper proofs that the electron optical setup developed in Dresden is indeed capable of producing atomic-sized EVBs, a precondition for measuring EMCD with atomic resolution.

Thesis: S.M., Massachusetts Institute of Technology, Computation for Design and Optimization Program, May, 2020
Cataloged from the official PDF of thesis.
Includes bibliographical references (pages 172-178).
With the rapid rise in the use of air conditioning systems and technological advancements, there is an ever-increasing need for optimizing the HVAC systems for energy efficiency while maintaining adequate occupant thermal comfort. HVAC systems in buildings alone contribute to almost 15% of the overall energy consumption across all sectors in the world and optimizing this would contribute positively towards overcoming climate change and reducing the global carbon footprint. A relatively modern solution is to implement a smart building-based control system and one of the objectives of this study is to understand the physical phenomenon associated with workspaces conditioned by chilled beams and evaluated the methods to reduce energy consumption.
Building upon the initial work aimed at creating a workflow for a smart building, this thesis presents the results of both experimental and computational studies of occupant thermal comfort with chilled beams (primarily in conference rooms) and the various inefficiencies associated. Results from these studies have helped to inform an optimum location for the installation of a chilled beam to counter the effects of incoming solar irradiation through an external window while keeping the energy consumption low. A detailed understanding of the various parameters influencing the temperature distribution in a room with chilled beams is achieved using CFD studies and data analysis of experimental data logging.
The work converges into a fundamental question of where, how, and what to measure to best monitor and control the human thermal comfort, and a novel technique was presented using the existing sensors which would provide a significant improvement over other existing methods in practice. This technique was validated using a series of experiments. The thesis concludes by presenting early works on hybrid HVAC systems including chilled beams and ceiling fans for higher economic gains. Future work should seek to perform CFD simulations for a better understanding of hybrid HVAC systems, both in conference rooms and open-plan office spaces, and also to design a new sensor that could better estimate human thermal comfort.
by Nikhilesh Ghanta.
S.M.
S.M. Massachusetts Institute of Technology, Computation for Design and Optimization Program

Nesta tese, estudamos feixes intensos não-contínuos de partículas carregadas. Na primeira parte, analisamos um feixe com simetria esférica e a sua relaxação para um estado quase-estacionário. Por ser um sistema com interação de longo alcance, a evolução do feixe e dominado pela dinâmica de Vlasov-Maxwell. Mostramos que o mecanismo de relaxação e a ressonância entre o movimento coletivo e o individual de algumas partículas. Fazemos uma analogia entre a dinâmica de Vlasov e um gás de férmions para modelar o estado quase estacionário. Os parâmetros do modelo são calculados usando princípios básicos, como os de conservação de energia e de partículas no transporte. Os resultados quando comparados com simulação mostram uma boa concordância. Na segunda parte, verificamos a estabilidade do modo de oscilação simétrico para um feixe esférico. Argumentamos que, quando esse modo for estável, o modelo para o estado quase-estacionário pode descrever feixes levemente anisotrópicos, o que e uma situação mais realista em experimentos. Constatamos que, num regime de interesse prático, esse modo e sempre estável. Por fim, estudamos um caso em que as forças focalizadoras externas são anisotrópicas, e o feixe tem simetria elipsoidal. Mostramos que, para certos valores dos parâmetros, há um forte acoplamento entre a dinâmica não-linear dos envelopes, o que causa uma troca de energia entre os graus de liberdade. Os resultados quando comparados com dinâmica molecular mostraram uma boa concordância.
In this thesis, we study intense bunched charged particle beams. In the rst part, we analyze a beam with spherical symmetry and its relaxation to a stationary state. The beam evolution follows the Vlasov-Maxwell dynamics since it is a system of long range interaction. We show that the main mechanism for the beam relaxation is a resonance between the collective beam motion and individual particle motion. We make an analogy between Vlasov dynamics and a Fermi gas to model the beam quasistationary state. The parameters of the model are calculated using basic principles, such as energy and particle conservation in the beam transport. The results compared with simulation showed a good agreement. In the second part, we verify the symmetric oscillation mode stability for a spherical beam. We argue that when this mode is stable, our model for the quasistationary state can also describe slightly anisotropic beams, a situation more realistic in experiments. We nd out that in situations of practical interest the mode is always stable. Finally, we study a situation in which the external focusing forces are anisotropic, and the beam has ellipsoidal symmetry. We show that, for certain values of the parameters, there is a strong coupling between the nonlinear envelopes dynamics, which causes exchange of energy between the degrees of freedom. The results compared with molecular dynamics showed a good agreement.

Les Structures atomiques Quasi-périodiques (QP) possèdent des propriétés particulières, notamment dans le domaine vibrationnel. Il pourrait être intéressant de pouvoir transférer ces propriétés à des méta-matériaux macroscopiques. Des réseaux de poutres quasi-périodiques 2D sont étudiés dans cette thèse dans le cadre du modèle élément finis (EF) poutre Euler Bernoulli. Ces réseaux de poutres peuvent facilement être produits par fabrication additive ou par découpe laser. Il est possible de faire varier l'élancement des poutres (le ratio hauteur sur longueur) qui est un paramètre intéressant pour modifier la réponse mécanique du réseau. En utilisant la méthode EF, l'influence de l'élancement des poutres sur la réponse vibratoire des réseaux de poutres QP est étudiée. La méthode numérique Kernel Polynomial (KPM) est adaptée avec succès de la dynamique moléculaire aux réseaux de poutres pour étudier leurs modes de vibration sans avoir à diagonaliser complètement la matrice dynamique. Les réseaux de poutres QP présentent des propriétés similaires à leur compère atomique: en particulier la localisation de modes sur des sous-structures et une relation de dispersion hiérarchisée. Le comportement à la fracture est aussi étudié étant donné que les symétries présentes dans les QP pourraient permettre des réseaux de poutres ne présentant pas de plans faibles pour la propagation de fissures. Cela a été démontré d'après des calculs EF statiques avec un critère de fracture fragile sur l'énergie de déformation. Les simulations statiques ne suffisent pas car elles ne peuvent pas capturer les phénomènes dynamiques complexes qui apparaissent lors de la fissuration fragile. Les propriétés de vibration du QP pourraient aussi avoir un impact sur la propagation dynamique de fissure. Un modèle dynamique de fissuration est développé afin d'étudier l'impact de l'élancement sur la capacité des réseaux de poutres QP à dissiper de l'énergie par fissuration. Finalement une méthode Coarse Graining est développée pour identifier un milieu Cosserat continu équivalant au réseau de poutres QP pour différentes échelles. Cette méthode permet d'identifier la densité, les déformations, les contraintes et donc les modules d'élasticité du milieu Cosserat équivalent, permettant ainsi une meilleure compréhension du rôle des sous structures précédemment identifiées
Quasi periodic (QP) structures have shown peculiar properties in the atomistic domain, especially the vibrational one. It could be interesting to be able to transpose these properties in macroscopic meta-materials. Quasi periodic 2D beam lattices are studied in this thesis due to the simplicity of the Euler Bernoulli finite element (FE) model. These beam lattices can easily be produced by additive manufacturing or by laser cutting. It is possible to vary the beam slenderness (i.e the ratio of height over length) that is a interesting parameter to modify the mechanical response of the lattice. Using finite element method, the influence of the beam slenderness over the vibration behavior of the QP beam lattices will be studied. The Kernel Polynomial numerical Method (KPM) is successfully adapted from molecular dynamics simulations in order to study vibrational modes of FE beam lattices without having to fully diagonalize the dynamical matrix. The QP lattices show similar properties as their atomic counterpart e.g mode localization over sub-stuctures and hierarchical dispersion relation. The fracture behavior is also studied, as the special symmetries allowed by the quasi periodicity could result in beam lattices without weak planes for crack propagation. It was proved to be true from static FE simulations with a brittle strain energy breaking criterion. Static simulations were not enough and do not grasp the complex dynamical phenomena taking place in brittle fracture. A dynamic crack propagation model was thus developed. The vibrational properties of quasi periodic structures could also have an impact on the dynamic crack propagation. Several simulations are run in order to study the impact of the slenderness on the energy dissipated by fracture of QP lattices. Finally, a coarse graining method (CG) was developed to identify a continuous Cosserat medium at different scales from the FE beam model. This CG method allows to identify, density, strain, stress and elastic moduli of an equivalent continuous Cosserat. This allows a better understanding of the role of previously identified characteristic sub structures

Les accélérateurs de particules sont aujourd’hui un des moyens les plus efficaces pour sonder la matière et les éléments qui la composent.La collaboration JEDI propose de mesurer la valeur du moment électrique dipolaire (EDM) du proton (voire deuton) avec une précision plusieurs ordre de grandeur supérieure au limites actuelles, par le moyen d’un anneau de stockage.La mesure d’un moment électrique dipolaire permanent permettrait l’ajout de sources de violation de CP supplémentaires. La violation de la symétrie CP est une des trois conditions nécessaires à l’explication de l’asymétrie matière/antimatière de l’Univers.En vue de parvenir à une telle précision, les particules doivent être stockées pendant une longue durée dans des champs électriques et/ou magnétiques : dans le cas de particules chargées, un anneau de stockage se présente comme une excellente solution.Un des principaux défis consiste à conserver la polarisation en spin du faisceau pendant toute la durée de l’expérience. Un excellent contrôle des systématiques et de la dynamique de spin sont alors obligatoires.Les déflecteurs électrostatiques utilisés dans l’expérience à la fois pour guider les particules et pour entraîner la précession du spin liée à la présence d’EDM, sont source d’erreurs systématiques et de décohérence de spin. La partie interne des déflecteurs, et aussi leurs champs de fuite doivent être compris et maîtrisés, en termes de trajectoires et de dynamique de spin. Ma thèse fournit un modèle pour le calcul de champ, trajectoires et dynamique de spin dans un déflecteur électrostatique.La première partie est dédiée au contexte autour de la mesure d’EDM, et se précisera sur le cas particulier de la mesure proposée par JEDI. L’équation de précession du spin sera présentée ainsi que les objectifs de la thèse.La seconde partie décrit en détails tous les outils analytiques ou semi-analytiques qui ont été développés pour répondre à nos besoins spécifiques. Ces outils seront ensuite utilisés dans la partie suivante.La troisième partie concerne les résultats et l’élaboration du modèle de champs, de trajectoire et de spin. Le modèle de champ, établi part transformation conformes, est un modèle universel dépendant uniquement du ration gap/rayon du déflecteur.Il prend en compte les conditions aux limites telles qu’une chambre à vide ou un diaphragme.Le résolution des équations du mouvement se fait à partir des équations d’Hamilton, au second order, par une méthode perturbative et en utilisant la méthode de la variation des constantes.La dynamique de spin, quant à elle, est obtenue par la résolution de l’équation Thomas-BMT par une méthode perturbative. Les fonctions de transfert obtenues dépendent des coordonnées de l’espace des phases à l’entrée du déflecteur. Elles sont totalement analytiques dans le cas de la partie centrale du déflecteur, et semi-analytiques pour les champs de fuites, où elles font intervenir une liste d’intégrales particulières, calculées avant la simulation.La dernière partie concerne l’analyse et le test du modèle à l’aide d’un code de calcul appelé BMAD
Particle accelerators are one of the most efficient ways to study matter andelementary particles, as proved by the recent discovery of the Higgs Bosonon the Large Hadron Collider.The JEDI collaboration propose to measurethe value of the proton electric dipole moment (EDM) with a precision of〖10〗^(-29) e.cm using a storage ring.A measurement of such a value of EDM, above the extremely small predictionof Standard Model would lead to new physics, by adding an additionalsource of CP violation. The CP violation is one of the three conditionsnecessary to explain the un-understanded asymetry between matter andantimatter in the universe.In order to achieve this 〖10〗^(-29)e.cm precision, one need to store the measuredparticles for many seconds in an electric field : a storage ring appearsas an ideal solution for charged particles. One of the main issues consistsin keeping the beam spin-coherent during the whole duration of the measurement.An excellent control of systematics and understanding of thespin dynamics to perform this measurement are mandatory.The electrostatic deflectors used in the experiment to provide both bendingand EDM-induced spin precession could lead to systematic errors andspin decoherence. The internal part of the deflectors and especially theirfringe fields need to be understand, in terms of trajectories and spin dynamics.This thesis provide models for fields, trajectories, spin dynamics and alsoresults about the spin decoherence induced by the deflectors.The first part is dedicated to the context around EDM measurements,and will then focus on the storage ring method. Also a first approach tothe spin precession equation and spin coherence time will be done, and theproblematic about the electrostatic deflectors exposed.The second part describes in details the analytic or semi-analytic modelswe developed. The first model describes the electric fringe field of thedeflector, using conformal mapping.This model takes into account boundary conditions like the vacuum chamberor a diaphragm and propose universal formulas as a function of theratio between gap and radius. The second model concerns trajectories inthe deflector and the fringe fields.It is using an Hamiltonian integration, variation of parameters and quadratureformulas to integrate the previously found field. This is done at thesecond order.The last model is about spin dynamics and allows the user to compute thespin total precession in the deflector or the fringe fields by using a list ofintegrals of the field. The final spin transfer solution is a function of theinitial conditions (x,px,y,py,dz,_P/P) at the second order.The last part shows the implementation on BMAD and the differenteffects of deflectors/fringe fields on the spin coherence time

A novel apparatus, combining buffer-gas cooling, electrostatic velocity selection and ion trapping, has been constructed and characterised. This apparatus is designed to investigate cold ion-molecule chemistry in the laboratory, at a variable translational and internal (rotational) temperature. This improves on previous experiments with translationally cold but rotationally hot molecule sources. The ability to vary the rotational temperature of cold molecules will allow for the experimental investigation of post-Langevin capture theories.

Dynamical maps for magnetic components are fundamental to studies of beam dynamics in accelerators. However, it is usually not possible to write down maps in closed form for anything other than simplified models of standard accelerator magnets. In the work presented here, the magnetic field is expressed in analytical form obtained from fitting Fourier series to a 3D numerical solution of Maxwell’s equations. Dynamical maps are computed for a particle moving through this field by applying a second order (with the paraxial approximation) explicit symplectic integrator. These techniques are used to study the beam dynamics in the first non-scaling FFAG ever built, EMMA, especially challenging regarding the validity of the paraxial approximation for the large excursion of particle trajectories. The EMMA lattice has four degrees of freedom (strength and transverse position of each of the two quadrupoles in each periodic cell). Dynamical maps, computed for a set of lattice configurations, may be efficiently used to predict the dynamics in any lattice configuration. We interpolate the coefficients of the generating function for the given configuration, ensuring the symplecticity of the solution. An optimisation routine uses this tool to look for a lattice defined by four constraints on the time of flight at different beam energies. This provides a way to determine the tuning of the lattice required to produce a desired variation of time of flight with energy, which is one of the key characteristics for beam acceleration in EMMA. These tools are then benchmarked against data from the recent EMMA commissioning.

Experiments and numerical investigations on trapped electron plasmas and traveling electron bunches are discussed. A Thomson backscattering diagnostics set up was installed in the ELTRAP (Electron TRAP) device, a Penning-Malmberg trap operating at the Department of Physics of the University of Milano since 2001. Here, an infrared (IR) laser pulse collides with nanosecond electron bunches with an energy of 1-20 keV traveling through a longitudinal magnetic field in a dynamical regime where space-charge effects play a significant role. The backscattered radiation is optically filtered and detected by means of a photomultiplier tube. The minimum sensitivity of the backscattering diagnostics has been estimated for the present set-up configuration. Constraints on the number of photons and thus on the information one can obtain with the Thomson backscattering technique are determined by the relatively low density of the electron beam as well as by noise issues. Solutions to increase the signal level and to reduce the noise are briefly discussed. The generation of an electron plasma by stochastic heating was realized in ELTRAP under ultra-high vacuum conditions by means of the application of low power RF (1-20 MHz) drives on one of the azimuthally sectored electrodes of the trap. The relevant experimental results are reviewed. The electron heating mechanism has been studied by means of a two-dimensional (2D) particle-in-cell (PIC) code, starting with a very low electron density, and applying RF drives of various amplitudes in the range 1-15 MHz on different electrodes. The axial kinetic energy of the electrons is in general increasing for all considered cases. Of course, higher temperature increments are obtained by increasing the amplitude of the RF excitation. The simulation results indicate in particular that the heating is initially higher close to the cylindrical wall of the device. These results on the electron heating point in the same direction of the experimental findings, where the plasma formation due to the ionization of the residual gas is found to be localized close to the trap wall. The simulations indicate also major heating effects when the RF drive is applied close to one end of the trap. Similar results are obtained for an electron plasma at higher densities, simulating a situation in which the RF is applied to an already formed plasma. With the aim to extend these RF studies to the microwave range, a bench test analysis has been performed of the transmission efficiency of a microwave injection system up to a few GHz. The test was based on the use of a prototype circular waveguide with the same diameter and length of the ELTRAP electrode stack and of a coupled rectangular waveguide with dimensions suitable for a future installation in the device. Electromagnetic PIC simulations have also been performed of the electron heating effect, again both at very low and relatively high electron densities, applying a microwave drive with a frequency of approximately 3 GHz close to the center and close to one end of the trap. Both the bench test of the injection system and the numerical simulations indicate that the new microwave heating system will allow the extension of the previous RF studies to the GHz range. In particular, the electron cyclotron resonance heating of the electrons will be aimed to increasing the electron temperature, and possibly its density as a consequence of a higher ionization rate of the residual gas. The installation of the new RF system will open up the possibility to study, e.g., the interaction between the confined plasma and traveling electron bunches.

This thesis presents an investigation into the behaviour of a laser beam of finite diameter in a plasma with respect to forces and optical properties, which lead to self-focusing of the beam. The transient setting of ponderomotive nonlinearity in a collisionless plasma has been studied, and consequently the self- focusing of the pulse, and the focusing of the plasma wave occurs. The description of a self-focusing mechanism of laser radiation in the plasma due to nonlinear forces acting on the plasma in the lateral direction, relative to the laser has been investigated in the non-relativistic regime. The behaviour of the laser beams in plasma, which is the domain of self-focusing at high or moderate intensity, is dominated by the nonlinear force. The investigation of self-focusing processes of laser beams in plasma result from the relativistic mass and energy dependency of the refractive index at high laser intensities. Here the relativistic effects are considered to evaluate the relativistic self-focusing lenghts for the neodymium glass radiation, at different plasma densities of various laser intensities. A sequence of code in C++ has been developed to explore in depth self-focusing over a wide range of parameters. The nonlinear plasma dielectric function to relativistic electron motion will be derived in the latter part of this thesis. From that, one can obtain the nonlinear refractive index of the plasma and estimate the importance of relativistic self-focusing as compared to ponderomotive non-relativistic self-focusing, at very high laser intensities. When the laser intensity is very high, pondermotive self-focusing will be dominant. But at some point, when the oscillating velocity of the plasma electron becomes very large, relativistic effects will also play a role in self-focusing. A numerical and theoretical study of the generation and propagation of oscillation in the semiclassical limit of the nonlinear paraxial equation is presented in this thesis. In a general setting of both dimension and nonlinearity, the essential differences between the 'defocusing' and 'focusing' cases hence is identified. Presented in this thesis are the nonlinearity and dispersion effects involved in the propagation of solitions which can be understood by using a numerical routines were implemented through the use of the mathematica program, and results give a very clear idea of this interesting phenomena

The research reviews the various methods, accurate and approximate, analytical and numerical, used for the analysis of beams that are subjected to dynamic loads. A review of previous research is presented. A detailed description of one of the methods, the Simplified Elastic Plastic Method (the SEP Method), a well-developed approximate method, is given. A finite element model, built with the aid of the computer software ABAQUS, is described. Results of 20 experiments made by others are provided and used as a benchmark for the finite element analysis. The methodology used for the validation of the ABAQUS Model and the SEP Method is to do, for various study cases, a comparison between the experimental results, those computed using the ABAQUS Model and those predicted using the SEP Method. Having validated the ABAQUS Model, it has been used as a benchmark with which to check the SEP Method. Therefore, additional cases have been analysed using the ABAQUS Model in order to cover a more comprehensive range of variables. A good agreement has been found between the results. The accuracy of the ABAQUS model and the conservatism of the SEP Method are shown. A design procedure using the SEP Method has been developed. Calibration factors are also proposed in order to reduce the conservatism in the SEP Method. The results and recommendations of the research can be employed in the defence industry, civil and structural engineering.

Les calculs théoriques prévoient que la dynamique d’excitation rotationnelle desmolécules CO et O2, induite par collision avec H2, est dominée par des résonancesquantiques aux très basses énergies. Leur mise en évidence expérimentale estrendue difficile par la nécessité d’obtenir des énergies de collision très faibles et unegrande résolution en énergie. Les expériences menées grâce à un montage defaisceaux moléculaires croisés à angle d’intersection variable, nous permettent ainsid’observer le seuil des transitions j = 0  1 de CO à 3,85 cm-1 et Nj = 10  11 de O2à 3,96 cm-1. Ces énergies correspondent à l’énergie cinétique moyenne d’un gaz àune température inférieure à 4 K. Les pics dans le tracé des sections efficacesintégrales en fonction de l’énergie de collision, constituent la première observationexpérimentale de résonances pour des processus inélastiques. Le bon accord avecles calculs théoriques permet de valider les potentiels d’interaction et ainsi dedéduire les constantes de vitesse pour la modélisation du milieu interstellaire. Nosrésultats expérimentaux mettent en relief la nature quantique des interactionsmoléculaires aux très basses énergies
Theoretical calculations predict that the dynamics of rotational excitation of CO or O2molecules, induced by collisions with H2, are dominated by quantum scatteringresonances at very low energies. However, experimental observation of these effectsis challenging: very low collision energies and high energy resolution are bothrequired. Experiments performed with a crossed molecular beam apparatus withvariable intersection angle allow us to observe the thresholds of the CO (j = 0  1)transition at 3.85 cm-1 and the O2 (Nj = 10  11) transition at 3.96 cm-1, whichcorrespond to the average kinetic energy of a gas below 4 K. The peaks in theintegral cross section’s collision energy dependence constitute the first experimentalobservation of resonances in an inelastic process. The good agreement betweentheory and experiment reinforces the confidence in the interaction potentials used todeduce rate coefficients for modeling the interstellar medium in the 1-20 K range. Ourexperimental results highlight the quantum nature of molecular interactions at verylow energies