Mechanized instrumentation of root canals oscillating systems

Cleaning and shaping are important steps in the root canal treatment. Despite the technological advances in endodontics, K and Hedströen files are still widely used. In an attempt to be more effective in preparing the root canals, faster and more cutting efficient kinematic, alloys and design alternatives utilizing mechanically oscillating or rotary files are proposed. Even with all these technological innovating alternatives, the preparation of root canals remains a challenge.

Oscillating systems damped by resistance proportional to the square of the velocity,

"Reprinted from the Physical review, n. s., vol. X, no. 5, November, 1917."

Performance analysis of adaptive lattice filters for FM signals and alpha-stable processes

The performance of an adaptive filter may be studied through the behaviour of the optimal and adaptive coefficients in a given environment. This thesis investigates the performance of finite impulse response adaptive lattice filters for two classes of input signals: (a) frequency modulated signals with polynomial phases of order p in complex Gaussian white noise (as nonstationary signals), and (b) the impulsive autoregressive processes with alpha-stable distributions (as non-Gaussian signals). Initially, an overview is given for linear prediction and adaptive filtering. The convergence and tracking properties of the stochastic gradient algorithms are discussed for stationary and nonstationary input signals. It is explained that the stochastic gradient lattice algorithm has many advantages over the least-mean square algorithm. Some of these advantages are having a modular structure, easy-guaranteed stability, less sensitivity to the eigenvalue spread of the input autocorrelation matrix, and easy quantization of filter coefficients (normally called reflection coefficients). We then characterize the performance of the stochastic gradient lattice algorithm for the frequency modulated signals through the optimal and adaptive lattice reflection coefficients. This is a difficult task due to the nonlinear dependence of the adaptive reflection coefficients on the preceding stages and the input signal. To ease the derivations, we assume that reflection coefficients of each stage are independent of the inputs to that stage. Then the optimal lattice filter is derived for the frequency modulated signals. This is performed by computing the optimal values of residual errors, reflection coefficients, and recovery errors. Next, we show the tracking behaviour of adaptive reflection coefficients for frequency modulated signals. This is carried out by computing the tracking model of these coefficients for the stochastic gradient lattice algorithm in average. The second-order convergence of the adaptive coefficients is investigated by modeling the theoretical asymptotic variance of the gradient noise at each stage. The accuracy of the analytical results is verified by computer simulations. Using the previous analytical results, we show a new property, the polynomial order reducing property of adaptive lattice filters. This property may be used to reduce the order of the polynomial phase of input frequency modulated signals. Considering two examples, we show how this property may be used in processing frequency modulated signals. In the first example, a detection procedure in carried out on a frequency modulated signal with a second-order polynomial phase in complex Gaussian white noise. We showed that using this technique a better probability of detection is obtained for the reduced-order phase signals compared to that of the traditional energy detector. Also, it is empirically shown that the distribution of the gradient noise in the first adaptive reflection coefficients approximates the Gaussian law. In the second example, the instantaneous frequency of the same observed signal is estimated. We show that by using this technique a lower mean square error is achieved for the estimated frequencies at high signal-to-noise ratios in comparison to that of the adaptive line enhancer. The performance of adaptive lattice filters is then investigated for the second type of input signals, i.e., impulsive autoregressive processes with alpha-stable distributions . The concept of alpha-stable distributions is first introduced. We discuss that the stochastic gradient algorithm which performs desirable results for finite variance input signals (like frequency modulated signals in noise) does not perform a fast convergence for infinite variance stable processes (due to using the minimum mean-square error criterion). To deal with such problems, the concept of minimum dispersion criterion, fractional lower order moments, and recently-developed algorithms for stable processes are introduced. We then study the possibility of using the lattice structure for impulsive stable processes. Accordingly, two new algorithms including the least-mean P-norm lattice algorithm and its normalized version are proposed for lattice filters based on the fractional lower order moments. Simulation results show that using the proposed algorithms, faster convergence speeds are achieved for parameters estimation of autoregressive stable processes with low to moderate degrees of impulsiveness in comparison to many other algorithms. Also, we discuss the effect of impulsiveness of stable processes on generating some misalignment between the estimated parameters and the true values. Due to the infinite variance of stable processes, the performance of the proposed algorithms is only investigated using extensive computer simulations.

Monotonous trend estimation using recursive prony analysis

This paper presents a solution to the problem of estimating the monotonous tendency of a slow-varying oscillating system. A recursive Prony Analysis (PA) scheme is developed which involves obtaining a dynamic model with parameters identified by implementing the forgetting factor recursive least square (FFRLS) method. A box threshold principle is proposed to separate the dominant components, which results in an accurate estimation of the trend of oscillating systems. Performance of the proposed PA is evaluated using real-time measurements when random noise and vibration effects are present. Moreover, the proposed method is used to estimate monotonous tendency of deck displacement to assist in a safe landing of an unmanned aerial vehicle (UAV). It is shown that the proposed method can estimate instantaneous mean deck satisfactorily, making it well suited for integration into ship-UAV approach and landing guidance systems.

(Table 2) Age determination of Irminger Basin sediment cores

High-resolution records of coarse lithic content and oxygen isotope have been obtained in a piston core from the Irminger Basin. The last glacial period is characterized by numerous periods of increased iceberg discharges originating partly from Iceland and corresponding to millennial-scale instabilities of the coastal ice sheets and ice shelves in the Nordic area. A comparison with midlatitude sediment cores shows that ice-rafted material corresponding to the Heinrich events was deposited synchronously from 40° to 60°N. There are thus two oscillating systems: every 5-10 kyr massive iceberg armadas are released from large continental ice caps, whereas more frequent instabilities of the coastal ice sheets in the high latitude regions occur every 1.2-3.8 kyr. At the time of the Heinrich events the synchroneity of the response from all the northern hemisphere ice sheets attests the existence of strong interactions between the two systems.

Hydrodynamic forces on heave plates for offshore systems oscillating close to the seabed or the free surface

La energía eólica marina es uno de los recursos energéticos con mayor proyección pudiendo contribuir a reducir el consumo de combustibles fósiles y a cubrir la demanda de energía en todo el mundo. El concepto de aerogenerador marino está basado en estructuras fijas como jackets o en plataformas flotantes, ya sea una semisumergible o una TLP. Se espera que la energía eólica offshore juegue un papel importante en el perfil de producción energética de los próximos años; por tanto, las turbinas eólicas deben hacerse más fables y rentables para ser competitivas frente a otras fuentes de energía. Las estructuras flotantes pueden experimentar movimientos resonantes en estados de la mar con largos períodos de oleaje. Estos movimientos disminuyen su operatividad y pueden causar daños en los componentes eléctricos de las turbinas y en las palas, también en los risers y moorings. La respuesta de la componente vertical del movimiento puede reducirse mediante diferentes actuaciones: (1) aumentando la amortiguación del sistema, (2) manteniendo el período del movimiento vertical fuera del rango de la energía de la ola, y (3) reduciendo las fuerzas de excitación verticales. Un ejemplo típico para llevar a cabo esta reducción son las "Heave Plates". Las heave plates son placas que se utilizan en la industria offshore debido a sus características hidrodinámicas, ya que aumentan la masa añadida y la amortiguación del sistema. En un análisis hidrodinámico convencional, se considera una estructura sometida a un oleaje con determinadas características y se evalúan las cargas lineales usando la teoría potencial. El amortiguamiento viscoso, que juega un papel crucial en la respuesta en resonancia del sistema, es un dato de entrada para el análisis. La tesis se centra principalmente en la predicción del amortiguamiento viscoso y de la masa añadida de las heave plates usadas en las turbinas eólicas flotantes. En los cálculos, las fuerzas hidrodinámicas se han obtenido con el f n de estudiar cómo los coeficientes hidrodinámicos de masa añadida5 y amortiguamiento varían con el número de KC, que caracteriza la amplitud del movimiento respecto al diámetro del disco. Por otra parte, se ha investigado la influencia de la distancia media de la ‘heave plate’ a la superficie libre o al fondo del mar, sobre los coeficientes hidrodinámicos. En este proceso, un nuevo modelo que describe el trabajo realizado por la amortiguación en función de la enstrofía, es descrito en el presente documento. Este nuevo enfoque es capaz de proporcionar una correlación directa entre el desprendimiento local de vorticidad y la fuerza de amortiguación global. El análisis también incluye el estudio de los efectos de la geometría de la heave plate, y examina la sensibilidad de los coeficientes hidrodinámicos al incluir porosidad en ésta. Un diseño novedoso de una heave plate, basado en la teoría fractal, también fue analizado experimentalmente y comparado con datos experimentales obtenidos por otros autores. Para la resolución de las ecuaciones de Navier Stokes se ha usado un solver basado en el método de volúmenes finitos. El solver usa las librerías de OpenFOAM (Open source Field Operation And Manipulation), para resolver un problema multifásico e incompresible, usando la técnica VOF (volume of fluid) que permite capturar el movimiento de la superficie libre. Los resultados numéricos han sido comparados con resultados experimentales llevados a cabo en el Canal del Ensayos Hidrodinámicos (CEHINAV) de la Universidad Politécnica de Madrid y en el Canal de Experiencias Hidrodinámicas (CEHIPAR) en Madrid, al igual que con otros experimentos realizados en la Escuela de Ingeniería Mecánica de la Universidad de Western Australia. Los principales resultados se presentan a continuación: 1. Para pequeños valores de KC, los coeficientes hidrodinámicos de masa añadida y amortiguamiento incrementan su valor a medida que el disco se aproxima al fondo marino. Para los casos cuando el disco oscila cerca de la superficie libre, la dependencia de los coeficientes hidrodinámicos es más fuerte por la influencia del movimiento de la superficie libre. 2. Los casos analizados muestran la existencia de un valor crítico de KC, donde la tendencia de los coeficientes hidrodinámicos se ve alterada. Dicho valor crítico depende de la distancia al fondo marino o a la superficie libre. 3. El comportamiento físico del flujo, para valores de KC cercanos a su valor crítico ha sido estudiado mediante el análisis del campo de vorticidad. 4. Introducir porosidad al disco, reduce la masa añadida para los valores de KC estudiados, pero se ha encontrado que la porosidad incrementa el valor del coeficiente de amortiguamiento cuando se incrementa la amplitud del movimiento, logrando un máximo de damping para un disco con 10% de porosidad. 5. Los resultados numéricos y experimentales para los discos con faldón, muestran que usar este tipo de geometrías incrementa la masa añadida cuando se compara con el disco sólido, pero reduce considerablemente el coeficiente de amortiguamiento. 6. Un diseño novedoso de heave plate basado en la teoría fractal ha sido experimentalmente estudiado a diferentes calados y comparado con datos experimentales obtenidos por otro autores. Los resultados muestran un comportamiento incierto de los coeficientes y por tanto este diseño debería ser estudiado más a fondo. ABSTRACT Offshore wind energy is one of the promising resources which can reduce the fossil fuel energy consumption and cover worldwide energy demands. Offshore wind turbine concepts are based on either a fixed structure as a jacket or a floating offshore platform like a semisubmersible, spar or tension leg platform. Floating offshore wind turbines have the potential to be an important part of the energy production profile in the coming years. In order to accomplish this wind integration, these wind turbines need to be made more reliable and cost efficient to be competitive with other sources of energy. Floating offshore artifacts, such oil rings and wind turbines, may experience resonant heave motions in sea states with long peak periods. These heave resonances may increase the system downtime and cause damage on the system components and as well as on risers and mooring systems. The heave resonant response may be reduced by different means: (1) increasing the damping of the system, (2) keeping the natural heave period outside the range of the wave energy, and (3) reducing the heave excitation forces. A typical example to accomplish this reduction are “Heave Plates”. Heave plates are used in the offshore industry due to their hydrodynamic characteristics, i.e., increased added mass and damping. Conventional offshore hydrodynamic analysis considers a structure in waves, and evaluates the linear and nonlinear loads using potential theory. Viscous damping, which is expected to play a crucial role in the resonant response, is an empirical input to the analysis, and is not explicitly calculated. The present research has been mainly focused on the prediction of viscous damping and added mass of floating offshore wind turbine heave plates. In the calculations, the hydrodynamic forces have been measured in order to compute how the hydrodynamic coefficients of added mass1 and damping vary with the KC number, which characterises the amplitude of heave motion relative to the diameter of the disc. In addition, the influence on the hydrodynamic coefficients when the heave plate is oscillating close to the free surface or the seabed has been investigated. In this process, a new model describing the work done by damping in terms of the flow enstrophy, is described herein. This new approach is able to provide a direct correlation between the local vortex shedding processes and the global damping force. The analysis also includes the study of different edges geometry, and examines the sensitivity of the damping and added mass coefficients to the porosity of the plate. A novel porous heave plate based on fractal theory has also been proposed, tested experimentally and compared with experimental data obtained by other authors for plates with similar porosity. A numerical solver of Navier Stokes equations, based on the finite volume technique has been applied. It uses the open-source libraries of OpenFOAM (Open source Field Operation And Manipulation), to solve 2 incompressible, isothermal immiscible fluids using a VOF (volume of fluid) phase-fraction based interface capturing approach, with optional mesh motion and mesh topology changes including adaptive re-meshing. Numerical results have been compared with experiments conducted at Technical University of Madrid (CEHINAV) and CEHIPAR model basins in Madrid and with others performed at School of Mechanical Engineering in The University of Western Australia. A brief summary of main results are presented below: 1. At low KC numbers, a systematic increase in added mass and damping, corresponding to an increase in the seabed proximity, is observed. Specifically, for the cases when the heave plate is oscillating closer to the free surface, the dependence of the hydrodynamic coefficients is strongly influenced by the free surface. 2. As seen in experiments, a critical KC, where the linear trend of the hydrodynamic coefficients with KC is disrupted and that depends on the seabed or free surface distance, has been found. 3. The physical behavior of the flow around the critical KC has been explained through an analysis of the flow vorticity field. 4. The porosity of the heave plates reduces the added mass for the studied porosity at all KC numbers, but the porous heave plates are found to increase the damping coefficient with increasing amplitude of oscillation, achieving a maximum damping coefficient for the heave plate with 10% porosity in the entire KC range. 5. Another concept taken into account in this work has been the heave plates with flaps. Numerical and experimental results show that using discs with flaps will increase added mass when compared to the plain plate but may also significantly reduce damping. 6. A novel heave plate design based on fractal theory has tested experimentally for different submergences and compared with experimental data obtained by other authors for porous plates. Results show an unclear behavior in the coefficients and should be studied further. Future work is necessary in order to address a series of open questions focusing on 3D effects, optimization of the heave plates shapes, etc.

Analysis of distrubances in large interconnected power systems

World economies increasingly demand reliable and economical power supply and distribution. To achieve this aim the majority of power systems are becoming interconnected, with several power utilities supplying the one large network. One problem that occurs in a large interconnected power system is the regular occurrence of system disturbances which can result in the creation of intra-area oscillating modes. These modes can be regarded as the transient responses of the power system to excitation, which are generally characterised as decaying sinusoids. For a power system operating ideally these transient responses would ideally would have a “ring-down” time of 10-15 seconds. Sometimes equipment failures disturb the ideal operation of power systems and oscillating modes with ring-down times greater than 15 seconds arise. The larger settling times associated with such “poorly damped” modes cause substantial power flows between generation nodes, resulting in significant physical stresses on the power distribution system. If these modes are not just poorly damped but “negatively damped”, catastrophic failures of the system can occur. To ensure system stability and security of large power systems, the potentially dangerous oscillating modes generated from disturbances (such as equipment failure) must be quickly identified. The power utility must then apply appropriate damping control strategies. In power system monitoring there exist two facets of critical interest. The first is the estimation of modal parameters for a power system in normal, stable, operation. The second is the rapid detection of any substantial changes to this normal, stable operation (because of equipment breakdown for example). Most work to date has concentrated on the first of these two facets, i.e. on modal parameter estimation. Numerous modal parameter estimation techniques have been proposed and implemented, but all have limitations [1-13]. One of the key limitations of all existing parameter estimation methods is the fact that they require very long data records to provide accurate parameter estimates. This is a particularly significant problem after a sudden detrimental change in damping. One simply cannot afford to wait long enough to collect the large amounts of data required for existing parameter estimators. Motivated by this gap in the current body of knowledge and practice, the research reported in this thesis focuses heavily on rapid detection of changes (i.e. on the second facet mentioned above). This thesis reports on a number of new algorithms which can rapidly flag whether or not there has been a detrimental change to a stable operating system. It will be seen that the new algorithms enable sudden modal changes to be detected within quite short time frames (typically about 1 minute), using data from power systems in normal operation. The new methods reported in this thesis are summarised below. The Energy Based Detector (EBD): The rationale for this method is that the modal disturbance energy is greater for lightly damped modes than it is for heavily damped modes (because the latter decay more rapidly). Sudden changes in modal energy, then, imply sudden changes in modal damping. Because the method relies on data from power systems in normal operation, the modal disturbances are random. Accordingly, the disturbance energy is modelled as a random process (with the parameters of the model being determined from the power system under consideration). A threshold is then set based on the statistical model. The energy method is very simple to implement and is computationally efficient. It is, however, only able to determine whether or not a sudden modal deterioration has occurred; it cannot identify which mode has deteriorated. For this reason the method is particularly well suited to smaller interconnected power systems that involve only a single mode. Optimal Individual Mode Detector (OIMD): As discussed in the previous paragraph, the energy detector can only determine whether or not a change has occurred; it cannot flag which mode is responsible for the deterioration. The OIMD seeks to address this shortcoming. It uses optimal detection theory to test for sudden changes in individual modes. In practice, one can have an OIMD operating for all modes within a system, so that changes in any of the modes can be detected. Like the energy detector, the OIMD is based on a statistical model and a subsequently derived threshold test. The Kalman Innovation Detector (KID): This detector is an alternative to the OIMD. Unlike the OIMD, however, it does not explicitly monitor individual modes. Rather it relies on a key property of a Kalman filter, namely that the Kalman innovation (the difference between the estimated and observed outputs) is white as long as the Kalman filter model is valid. A Kalman filter model is set to represent a particular power system. If some event in the power system (such as equipment failure) causes a sudden change to the power system, the Kalman model will no longer be valid and the innovation will no longer be white. Furthermore, if there is a detrimental system change, the innovation spectrum will display strong peaks in the spectrum at frequency locations associated with changes. Hence the innovation spectrum can be monitored to both set-off an “alarm” when a change occurs and to identify which modal frequency has given rise to the change. The threshold for alarming is based on the simple Chi-Squared PDF for a normalised white noise spectrum [14, 15]. While the method can identify the mode which has deteriorated, it does not necessarily indicate whether there has been a frequency or damping change. The PPM discussed next can monitor frequency changes and so can provide some discrimination in this regard. The Polynomial Phase Method (PPM): In [16] the cubic phase (CP) function was introduced as a tool for revealing frequency related spectral changes. This thesis extends the cubic phase function to a generalised class of polynomial phase functions which can reveal frequency related spectral changes in power systems. A statistical analysis of the technique is performed. When applied to power system analysis, the PPM can provide knowledge of sudden shifts in frequency through both the new frequency estimate and the polynomial phase coefficient information. This knowledge can be then cross-referenced with other detection methods to provide improved detection benchmarks.

Modeling intrinsic noise and delays in chemical kinetics of coupled autoregulated oscillating cells

Delays are an important feature in temporal models of genetic regulation due to slow biochemical processes, such as transcription and translation. In this paper, we show how to model intrinsic noise effects in a delayed setting by either using a delay stochastic simulation algorithm (DSSA) or, for larger and more complex systems, a generalized Binomial τ-leap method (Bτ-DSSA). As a particular application, we apply these ideas to modeling somite segmentation in zebra fish across a number of cells in which two linked oscillatory genes (her1 and her7) are synchronized via Notch signaling between the cells.

Undamped Oscillations of Collisionless Stellar Systems: Spheres,Spheroids and Discs.

The collisionless Boltzmann equation governing self-gravitating systems such as galaxies has recently been shown to admit exact oscillating solutions with planar and spherical symmetry. The relation of the spherically symmetric solutions to the Virial theorem, as well as generalizations to non-uniform spheres, uniform spheroids and discs form the subject of this paper. These models generalize known families of static solutions. The case of the spheroid is worked out in some detail. Quasiperiodic as well as chaotic time variation of the two axes is demonstrated by studying the surface of section for the associated Hamiltonian system with two degrees of freedom. The relation to earlier work and possible implications for the general problem of collisionless relaxation in self gravitating systems are also discussed.

The Determination of the Surface Tensions of Nickel Sulfur Alloys using the Electromagnetic Oscillating Droplet Technique

An oscillating droplet method combined with electromagnetic levitation technique has been applied to determine the surface tensions of liquid nickel sulphur alloys as a function of the temperature and composition. The natural frequency of the oscillating droplet is evaluated using a Fourier analyser, and the influence of magnetic field strength on the surface tension was considered. Furthermore, the applicability of Butler's equation and subregular solution model for the surface was shown to predict the surface tension of the systems containing the surface active elements.

STOKES' SYSTEM IN A DOMAIN WITH OSCILLATING BOUNDARY: HOMOGENIZATION AND ERROR ANALYSIS OF AN INTERIOR OPTIMAL CONTROL PROBLEM

Homogenization and error analysis of an optimal interior control problem in the framework of Stokes' system, on a domain with rapidly oscillating boundary, are the subject matters of this article. We consider a three dimensional domain constituted of a parallelepiped with a large number of rectangular cylinders at the top of it. An interior control is applied in a proper subdomain of the parallelepiped, away from the oscillating volume. We consider two types of functionals, namely a functional involving the L-2-norm of the state variable and another one involving its H-1-norm. The asymptotic analysis of optimality systems for both cases, when the cross sectional area of the rectangular cylinders tends to zero, is done here. Our major contribution is to derive error estimates for the state, the co-state and the associated pressures, in appropriate functional spaces.

Nonlinear oscillations in discrete and continuous systems

The first thesis topic is a perturbation method for resonantly coupled nonlinear oscillators. By successive near-identity transformations of the original equations, one obtains new equations with simple structure that describe the long time evolution of the motion. This technique is related to two-timing in that secular terms are suppressed in the transformation equations. The method has some important advantages. Appropriate time scalings are generated naturally by the method, and don't need to be guessed as in two-timing. Furthermore, by continuing the procedure to higher order, one extends (formally) the time scale of valid approximation. Examples illustrate these claims. Using this method, we investigate resonance in conservative, non-conservative and time dependent problems. Each example is chosen to highlight a certain aspect of the method.

The second thesis topic concerns the coupling of nonlinear chemical oscillators. The first problem is the propagation of chemical waves of an oscillating reaction in a diffusive medium. Using two-timing, we derive a nonlinear equation that determines how spatial variations in the phase of the oscillations evolves in time. This result is the key to understanding the propagation of chemical waves. In particular, we use it to account for certain experimental observations on the Belusov-Zhabotinskii reaction.

Next, we analyse the interaction between a pair of coupled chemical oscillators. This time, we derive an equation for the phase shift, which measures how much the oscillators are out of phase. This result is the key to understanding M. Marek's and I. Stuchl's results on coupled reactor systems. In particular, our model accounts for synchronization and its bifurcation into rhythm splitting.

Finally, we analyse large systems of coupled chemical oscillators. Using a continuum approximation, we demonstrate mechanisms that cause auto-synchronization in such systems.