Dynamics of Patterns

Patterns and nonlinear waves arise in many applications. Mathematical descriptions and analyses draw from a variety of fields such as partial differential equations of various types, differential and difference equations on networks and lattices, multi-particle systems, time-delayed systems, and numerical analysis. This workshop brought together researchers from these diverse areas to bridge existing gaps and to facilitate interaction

Modeling and Adaptive Control of Magnetostrictive Actuators

In this dissertation, we propose a model and formulate a control methodology for a thin magnetostrictive rod actuator. The goal is to obtain a bulk, low dimensional model that can be used for real-time control purposes. Previous and concurrent research in the modeling of magnetostrictive actuators and the related area of electrostrictive actuators have produced models that are of low order and reproduce their quasi-static response reasonably well. But the main interest in using these and other smart actuators is at a high frequency -- for producing large displacements with mechanical rectification, producing sonar signals etc. The well known limitation of smart actuators that are based on electro-magneto-thermo-elastic behaviors of smart materials is the complex, input-rate dependent, hysteretic behavior of the latter. The model proposed in this dissertation is a bulk model and describes the behaviour of a magnetostrictive actuator by a system with 4 states. We develop this model using phenomenological arguments following the work done by Jiles and Atherton for describing bulk ferromagnetic hysteresis. The model accounts for magnetic hysteresis; eddy current effects; magneto-elastic effects; inertial effects; and mechanical damping. We show rigorously that the system with the intial state at the origin has a periodic orbit as its $Omega$ limit set. For the bulk ferromagnetic hysteresis model - a simplification of the magnetostrictive model, we show that all trajectories starting within a certain set approach this limit set. It is envisioned that the model will help application engineers to do simulation studies of structures with magnetostrictive actuators. Towards this end, an algorithm is proposed to identify the various parameters in the model. In control applications, one may require the actuator to follow a certain trajectory. The complex rate dependent behaviour of the actuator makes the design of a suitable control law a challenging one. As our system of equations do not model transient effects, they do not model the minor-loop closure property common to ferromagnetic materials. Therefore, the design of control laws making explicit use of the model (without modifications) is not possible. A major reason to use model free approaches to control design is that magnetostrictive actuators seem to have slight variations in their behavior with time. Therefore, we tried to use a direct adaptive control methodology that uses features of our model. The system is now looked at as a relative degree two linear system with set-valued input nonlinearity. Extensions of Eugene Ryan's work on universal tracking for a relative degree one linear system and Morse's work on stablization for relative degree two linear systems were sought. Experimental verification of our method confirmed our intuition about the model structure. Though the tracking results were not very satisfactory due to the presence of sensor noise, the experimental results, nevertheless validate our modeling effort

Fatigue of Structural and Additively Manufactured Steels: Damage Assessment and Modelling Techniques

PhD thesis in Offshore technologyThe topics of damage assessment by in situ measurements before a macroscopic crack has been initiated, nonlinear damage modelling and additive manufacturing are herein discussed and researched from the perspective of the maintenance of ageing structures and mechanical equipment subjected to fatigue loading. In relation to the aforementioned topics, the thesis can be categorized into three parts, all of which are related to the maintenance of ageing structures and mechanical equipment. These are: 1) Fatigue damage monitoring prior to macroscopic crack initiation, 2) Damage modelling based on S-N curves, and 3) Mechanical properties of additively manufactured steel. 1. Fatigue damage monitoring prior to macroscopic crack initiation A conceptual framework is developed to select a method to assess small fatigue crack propagation and fatigue damage accumulation. The framework is focused on the underlying fatigue mechanism which is correlated with the measurable change for each of the identified parameters throughout the fatigue life, and how the parameter will change. The framework is based on the literature and is useful for both research and development communities, for those who are involved in structural integrity assessment. An experimental study is also performed regarding the feasibility of adopting macroscopic hardness indentations and their correlation with fatigue damage accumulation. Both Brinell and Vickers were adopted, with Brinell being found to exhibit a more continuous change, in addition to being statistically significant. 2. Damage modelling based on S-N curves A new damage function is proposed herein, based on the damage theory known as the theory of the S-N fatigue damage envelope. The work can be considered a framework to develop S-N curve-specific damage functions, as the underlying theory can be applied to any S-N curve for materials or structural details. Furthermore, the proposed damage function is compared with other recently proposed functions, including Miner’s rule, using experimental data. The proposed function generally exhibits better prediction than Miner’s rule and some of the other models. A generalized expression/function for fatigue damage was also proposed by investigating the functional forms commonly adopted in the literature. The relation of the parameters or variables of the functional form can be represented in three dimensions, resulting in it being able to be evaluated in three dimensions with experimental data, where it will result in a surface. Herein, it is also shown that two special cases of the proposed function exist, where the parameters are reduced to a single ratio, which is subsequently evaluated based on experimental data. 3. Mechanical properties of additively manufactured steel An experimental study is performed regarding the mechanical properties of additively manufactured steel printed by the technology of Bound Metal Deposition. Specimens were printed in various directions, which were subsequently tension tested to develop stress-strain curves. It was found that the printing technology would result in the final product exhibiting anisotropic behaviour correlated to a mesh of crack-like defects. The crack like defects also result in the conclusion that the printed specimens are expected to exhibit very poor fatigue capacity in comparison to their traditionally manufactured counterparts and also to exhibit anisotropic behaviour in relation to fatigue. Keywords: Fatigue damage assessment, hardness-based fatigue damage, nonlinear damage modelling, additively manufactured stee

International Symposium on Magnetic Suspension Technology, Part 1

The goal of the symposium was to examine the state of technology of all areas of magnetic suspension and to review related recent developments in sensors and controls approaches, superconducting magnet technology, and design/implementation practices. The symposium included 17 technical sessions in which 55 papers were presented. The technical session covered the areas of bearings, sensors and controls, microgravity and vibration isolation, superconductivity, manufacturing applications, wind tunnel magnetic suspension systems, magnetically levitated trains (MAGLEV), space applications, and large gap magnetic suspension systems

Ferroelectrics

Ferroelectric materials exhibit a wide spectrum of functional properties, including switchable polarization, piezoelectricity, high non-linear optical activity, pyroelectricity, and non-linear dielectric behaviour. These properties are crucial for application in electronic devices such as sensors, microactuators, infrared detectors, microwave phase filters and, non-volatile memories. This unique combination of properties of ferroelectric materials has attracted researchers and engineers for a long time. This book reviews a wide range of diverse topics related to the phenomenon of ferroelectricity (in the bulk as well as thin film form) and provides a forum for scientists, engineers, and students working in this field. The present book containing 24 chapters is a result of contributions of experts from international scientific community working in different aspects of ferroelectricity related to experimental and theoretical work aimed at the understanding of ferroelectricity and their utilization in devices. It provides an up-to-date insightful coverage to the recent advances in the synthesis, characterization, functional properties and potential device applications in specialized areas

On the transition to turbulence of wall-bounded flows in general, and plane Couette flow in particular

The main part of this contribution to the special issue of EJM-B/Fluids dedicated to Patrick Huerre outlines the problem of the subcritical transition to turbulence in wall-bounded flows in its historical perspective with emphasis on plane Couette flow, the flow generated between counter-translating parallel planes. Subcritical here means discontinuous and direct, with strong hysteresis. This is due to the existence of nontrivial flow regimes between the global stability threshold Re_g, the upper bound for unconditional return to the base flow, and the linear instability threshold Re_c characterized by unconditional departure from the base flow. The transitional range around Re_g is first discussed from an empirical viewpoint ({\S}1). The recent determination of Re_g for pipe flow by Avila et al. (2011) is recalled. Plane Couette flow is next examined. In laboratory conditions, its transitional range displays an oblique pattern made of alternately laminar and turbulent bands, up to a third threshold Re_t beyond which turbulence is uniform. Our current theoretical understanding of the problem is next reviewed ({\S}2): linear theory and non-normal amplification of perturbations; nonlinear approaches and dynamical systems, basin boundaries and chaotic transients in minimal flow units; spatiotemporal chaos in extended systems and the use of concepts from statistical physics, spatiotemporal intermittency and directed percolation, large deviations and extreme values. Two appendices present some recent personal results obtained in plane Couette flow about patterning from numerical simulations and modeling attempts.Comment: 35 pages, 7 figures, to appear in Eur. J. Mech B/Fluid

Nanopositionnement 3D à base de mesure à courant tunnel et piezo-actionnement

The objective of this thesis was to elaborate high performance control strategies and their real-time validation on a tunneling current-based 3D nanopositioning system developed in GIPSA-lab. The thesis lies in the domain of micro-/nano mechatronic systems (MEMS) focused on applications of fast and precise positioning and scanning tunneling microscopy (STM). More precisely, the aim is to position the metallic tunneling tip (like in STM) over the metallic surface using piezoelectric actuators in X, Y and Z directions and actuated micro-cantilever (like in Atomic Force Microscope AFM), electrostatically driven in Z direction, with high precision, over possibly high bandwidth. However, the presence of different adverse effects appearing at such small scale (e.g. measurement noise, nonlinearities of different nature, cross-couplings, vibrations) strongly affect the overall performance of the 3D system. Therefore a high performance control is needed. To that end, a novel 3D model of the system has been developed and appropriate control methods for such a system have been elaborated. First the focus is on horizontal X and Y directions. The nonlinear hysteresis and creep effects exhibited by piezoelectric actuators have been compensated and a comparison between different compensation methods is provided. Modern SISO and MIMO robust control methods are next used to reduce high frequency effects of piezo vibration and cross-couplings between X and Y axes. Next, the horizontal motion is combined with the vertical one (Z axis) with tunneling current and micro-cantilever control. Illustrative experimental results for 3D nanopositioning of tunneling tip, as well as simulation results for surface topography reconstruction and multi-mode cantilever positioning, are finally given.L'objectif de la thèse est l'élaboration de lois de commande de haute performance et leur validation en temps réel sur une plateforme expérimentale 3D de nano-positionnement à base de courant à effet tunnel, développée au laboratoire GIPSA-lab. Elle s'inscrit donc dans le cadre des systèmes micro-/nano-mécatronique (MEMS), et de la commande. Plus précisément, le principal enjeu considéré est de positionner la pointe métallique à effet tunnel (comme en microscopie à effet tunnel STM) contre la surface métallique en utilisant des actionneurs piézoélectriques en X, Y et Z et un micro-levier (comme en microscopie à force atomique AFM) actionné électrostatiquement en Z avec une grande précision et une bande passante élevée. Cependant, la présence de différents effets indésirables apparaissant à cette petite échelle (comme le bruit de mesure, des non-linéarités de natures différentes, les couplages, les vibrations) affectent fortement la performance globale du système 3D. En conséquence, une commande de haute performance est nécessaire. Pour cela, un nouveau modèle 3D du système a été développé et des méthodes de contrôle appropriées pour un tel système ont été élaborées. Tout d'abord l'accent est mis sur de positionnement selon les axes X et Y. Les effets d'hystérésis et de fluage non linéaires présents dans les actionneurs piézoélectriques ont été compensés et une comparaison entre les différentes méthodes de compensation est effectuée. Des techniques modernes de commande robuste SISO et MIMO sont ensuite utilisées pour réduire les effets des vibrations piézoélectriques et des couplages entre les axes X et Y. Le mouvement horizontal est alors combiné avec le mouvement vertical (Axe Z) et une commande du courant tunnel et du micro-levier. Des résultats expérimentaux illustrent le nano positionnement 3D de la pointe, et des résultats de simulation pour la reconstruction de la topographie de la surface ainsi que le positionnement du micro-levier à base d'un modèle multi-modes

Nonlinear Systems

The editors of this book have incorporated contributions from a diverse group of leading researchers in the field of nonlinear systems. To enrich the scope of the content, this book contains a valuable selection of works on fractional differential equations.The book aims to provide an overview of the current knowledge on nonlinear systems and some aspects of fractional calculus. The main subject areas are divided into two theoretical and applied sections. Nonlinear systems are useful for researchers in mathematics, applied mathematics, and physics, as well as graduate students who are studying these systems with reference to their theory and application. This book is also an ideal complement to the specific literature on engineering, biology, health science, and other applied science areas. The opportunity given by IntechOpen to offer this book under the open access system contributes to disseminating the field of nonlinear systems to a wide range of researchers

Scanning Probe Microscopies for the Study at Nanoscale of Nanomaterials and Nanosystems: Magnetic Properties for Bio-applications

Magnetic nanomaterials due to their various features different from the ordinary bulk matter in their mechanical, thermal, magnetic, optical properties, are attracting more and more attention in both theoretical research and practical applications in various fields. Magnetic nanoparticles (MNPs) are a very important branch of magnetic nanomaterials due to their nanoscale sizes, being relatively long in vivo half-life and limited agglomeration. These make them ideal for biomedical applications such as magnetic labeling, hyperthermia cancer treatment, targeted drug delivery, and contrast enhancement agents in magnetic resonance imaging (MRI). In drug delivery applications, MNPs can be determined with high accuracy [1]. It would be of interest to localize and characterize MNPs at the nanoscale for biological applications. However, very limited studies exist on detecting and characterizing the magnetic signals of nanoparticles in biological science. Many methods in surface structure analysis are used as nano-characterization techniques, such as transmission electron microscopy (TEM), scanning electron microscopy (SEM), field electron microscopy (FEM), field ion microscope (FIM), low energy electron diffraction (LEED), Auger electron spectroscopy (AES), photoelectron spectroscopy (ESCA) and electron probe. These techniques detect the surface or interface to show the physical and chemical properties at the nanoscale. But any kind of these techniques has the limitations of one kind or another. For example, LEED and X-ray diffraction method require that the sample has a periodic structure; the resolution of optical microscopy and SEM are insufficient to distinguish surface atoms; high-resolution TEM is mainly used for thin bulk samples and interfacial studies to detect the magnetic properties, but the sample preparation process to get cell sections for TEM analysis is time consuming, and only a small part of cell section can be analyzed; FEM and FIM can only detect the tip radius of less than 100 nm of the atomic structure in two-dimensional geometry. Most commonly, studies which analyze the magnetic nature of MNPs use a superconducting quantum interference device (SQUID) and vibrating sample magnetometer (VSM). But due to low sensitivity and ultimately poor accuracy neither is an appropriate technique to measure the magnetic moment of individual MNPs, whatever in air or in liquid environment. Proper characterization and monitoring the properties of MNPs system are important for their potential applications. Currently, one of the most common methods for intracellular imaging of magnetic nanoparticles is fluorescence microscopy [2]. A disadvantage of this technique is that nanoparticles must first be labeled with fluorescent probes in order to be visualized. Due to the inherent limitations, the resolution of optical instruments is restricted by the wavelength of the light [3]. In 2010, Sun et al. conjugated fluorescent probes to the surface of magnetic nanoparticles to map cellular uptake pathways [4]. Relative to fluorescence microscopy, two-photon microscopy (TPM) offers improved resolution to study cellular interactions with magnetic nanoparticles, requiring the particles to be labeled with a two-photon fluorescent dye [5]. However it has been known that the imaging depth in TPM cannot be increased indefinitely, meanwhile optimization of the two-photon excitation efficiency is limited by the degree of damage the specimen can tolerate [6]. Due to the relatively poor resolution and reliability of these techniques, scanning probe microscopes (SPM) emerged out. SPM is a generation of scanning tunneling microscope based on a variety of new probe microscopes, such as atomic force microscopy (AFM), lateral force microscopy (LFM) and electrostatic force microscope (EFM). Among these techniques magnetic force microscope (MFM), a label-free in vitro detection method for magnetic materials, has the capability to detect nanoscale magnetic domains and simultaneously obtain atomic force microscopy topography images. Due to its ability to localize, characterize and distinguish magnetic materials from other materials at the nanoscale, as well as the advantage of three-dimensional information, MFM offers the great potential for the in vivo research. The scope for MFM lies in detecting the presence of magnetic nanomaterials and spatially localizing magnetic domains. It is likely that magnetic nanomaterials (occur in clusters or aggregates) are embedded in a biological matrix to different depth, and surrounded by bio-molecules. The development and application of MFM for detecting MNPs hold great promise in biology. Spatially localizing magnetic plaques, at nanometer resolution in ambient atmospheric environment, will provide a better understanding of the deposition mechanism of magnetic material derivatives in the biological tissues. The background on magnetic materials and nanoparticles is presented in chapter 1 and AFM/MFM experimental apparatus and technique is illustrated in chapter 2. In the last three chapters of the thesis the results of three different typologies of experiments are reported. The studies I have conducted are developed in the framework of the research activities of the laboratory of Scanning Probe Microscopy of EMiNaLab (coordinator prof. Marco Rossi), at the Department of Basic and Applied Sciences for Engineering of Sapienza University of Rome. In particular, in Chapter 3, we investigate bacterial biofilms at the first time, which are colonies of microbes embedded in a self-produced exopolysaccharides extracellular matrix presenting a major concern in health care. We will demonstrate an approach based on magnetic force microscopy to perform accurate measurement of the thickness of soft thin films - although it may easily extended even to stiff films - deposited on periodically patterned magnetic substrates. By detecting the biofilm thickness MFM will provide a novel method to study the thin film. In the second part of the thesis, MFM is applied to visualize and quantitatively measure magnetically labeled vesicular system. Vesicles containing magnetic nanoparticles as magnetic target carrier can be used for a wide range of biological application. The encapsulation of drugs in vesicles can minimize drug degradation and inactivation by increasing drug bioavailability and targeting to the pathological area. Many different non-contact techniques have been proposed. Nevertheless, MFM has never been used to study vesicular systems embedding MNPs, either qualitatively or quantitatively. MFM will be illustrated to evaluate the amount of MNPs incorporated in single vesicle, together with discussion on its merits and possible sources of uncertainty. In the last part of the thesis, we developed the capability of AFM/MFM to detect magnetically labeled materials of biological interest, which are magnetoferritin, APTES functionalized Fe3O4 nanoparticles and cells labeled Fe@Au nanoparticle. AFM/MFM will allow us to detect magnetic nanoparticles within submembranes and without severe deformation of samples. In our study, We expect to demonstrate the potential of MFM for the study of magnetic properties of different nano-biosystems, illustrating our approaches which aim at deducing quantitative information from MFM characterizations. Such a research is useful for future applications of MFM, indicating the potential to image magnetic nanoparticles unlabelled and unmodified in living cellular systems. The overall target of the thesis is to develop and standardize reliable innovative protocols, using scanning probe microscopy-based techniques that could be implemented in rapid and early theranostic methods