NONLINEAR TIME SERIES/SYSTEM ANALYSIS (STATE-SPACE, DYNAMICS, INTERVENTION, RESILIENCE, KALMAN)

A discussion of nonlinear dynamics, demonstrated by the familiar automobile, is followed by the development of a systematic method of analysis of a possibly nonlinear time series using difference equations in the general state-space format. This format allows recursive state-dependent parameter estimation after each observation thereby revealing the dynamics inherent in the system in combination with random external perturbations.^ The one-step ahead prediction errors at each time period, transformed to have constant variance, and the estimated parametric sequences provide the information to (1) formally test whether time series observations y(,t) are some linear function of random errors (ELEM)(,s), for some t and s, or whether the series would more appropriately be described by a nonlinear model such as bilinear, exponential, threshold, etc., (2) formally test whether a statistically significant change has occurred in structure/level either historically or as it occurs, (3) forecast nonlinear system with a new and innovative (but very old numerical) technique utilizing rational functions to extrapolate individual parameters as smooth functions of time which are then combined to obtain the forecast of y and (4) suggest a measure of resilience, i.e. how much perturbation a structure/level can tolerate, whether internal or external to the system, and remain statistically unchanged. Although similar to one-step control, this provides a less rigid way to think about changes affecting social systems.^ Applications consisting of the analysis of some familiar and some simulated series demonstrate the procedure. Empirical results suggest that this state-space or modified augmented Kalman filter may provide interesting ways to identify particular kinds of nonlinearities as they occur in structural change via the state trajectory.^ A computational flow-chart detailing computations and software input and output is provided in the body of the text. IBM Advanced BASIC program listings to accomplish most of the analysis are provided in the appendix. ^

Simulation model for the study of overhead rail current collector systems dynamics, focused on the design of a new conductor rail

Overhead rigid conductor arrangements for current collection for railway traction have some advantages compared to other, more conventional, energy supply systems. They are simple, robust and easily maintained, not to mention their flexibility as to the required height for installation, which makes them particularly suitable for use in subway infrastructures. Nevertheless, due to the increasing speeds of new vehicles running on modern subway lines, a more efficient design is required for this kind of system. In this paper, the authors present a dynamic analysis of overhead conductor rail systems focused on the design of a new conductor profile with a dynamic behaviour superior to that of the system currently in use. This means that either an increase in running speed can be attained, which at present does not exceed 110 km/h, or an increase in the distance between the rigid catenary supports with the ensuing saving in installation costs. This study has been carried out using simulation techniques. The ANSYS programme has been used for the finite element modelling and the SIMPACK programme for the elastic multibody systems analysis.

The use of non-reflecting boundary conditions in soil dynamics

In this paper some aspects of the use of non-reflecting boundaries in dynamic problems, analyzed in time domain, are considered. Current trends for treating the above mentioned problems are summarized with a particular emphasis on the use of numerical techniques, such as Boundary Element Method (BEM) or mixed and hybrid formulations, Finite Element Method (FEM) plus BEM. As an alternative to these methods, an easy time domain boundary condition, obtained from the well known consistent transmitting boundary developed by Waas for frequency domain analysis, can be applied to represent the reactions of the unbounded soil on the interest zone. The behaviour of this proposed boundary condition is studied when waves of different frequency to the one used for its obtention are acting on the physical edge of the model. As an application example,an analysis is made of the soil-structure interaction of a rigid strip foundation on a horizontal non-linear elastic layer on bed rock. The results obtained suggest the need of time domain solutions for this type of problem

On the application of meshfree methods to the nonlinear dynamics of multibody systems

Esta tesis propone una completa formulación termo-mecánica para la simulación no-lineal de mecanismos flexibles basada en métodos libres de malla. El enfoque se basa en tres pilares principales: la formulación de Lagrangiano total para medios continuos, la discretización de Bubnov-Galerkin, y las funciones de forma libres de malla. Los métodos sin malla se caracterizan por la definición de un conjunto de funciones de forma en dominios solapados, junto con una malla de integración de las ecuaciones discretas de balance. Dos tipos de funciones de forma se han seleccionado como representación de las familias interpolantes (Funciones de Base Radial) y aproximantes (Mínimos Cuadrados Móviles). Su formulación se ha adaptado haciendo sus parámetros compatibles, y su ausencia de conectividad predefinida se ha aprovechado para interconectar múltiples dominios de manera automática, permitiendo el uso de mallas de fondo no conformes. Se propone una formulación generalizada de restricciones, juntas y contactos, válida para sólidos rígidos y flexibles, siendo estos últimos discretizados mediante elementos finitos (MEF) o libres de malla. La mayor ventaja de este enfoque reside en que independiza completamente el dominio con respecto de las uniones y acciones externas a cada sólido, permitiendo su definición incluso fuera del contorno. Al mismo tiempo, también se minimiza el número de ecuaciones de restricción necesarias para la definición de uniones realistas. Las diversas validaciones, ejemplos y comparaciones detalladas muestran como el enfoque propuesto es genérico y extensible a un gran número de sistemas. En concreto, las comparaciones con el MEF indican una importante reducción del error para igual número de nodos, tanto en simulaciones mecánicas, como térmicas y termo-mecánicas acopladas. A igualdad de error, la eficiencia numérica de los métodos libres de malla es mayor que la del MEF cuanto más grosera es la discretización. Finalmente, la formulación se aplica a un problema de diseño real sobre el mantenimiento de estructuras masivas en el interior de un reactor de fusión, demostrando su viabilidad en análisis de problemas reales, y a su vez mostrando su potencial para su uso en simulación en tiempo real de sistemas no-lineales. A new complete formulation is proposed for the simulation of nonlinear dynamic of multibody systems with thermo-mechanical behaviour. The approach is founded in three main pillars: total Lagrangian formulation, Bubnov-Galerkin discretization, and meshfree shape functions. Meshfree methods are characterized by the definition of a set of shape functions in overlapping domains, and a background grid for integration of the Galerkin discrete equations. Two different types of shape functions have been chosen as representatives of interpolation (Radial Basis Functions), and approximation (Moving Least Squares) families. Their formulation has been adapted to use compatible parameters, and their lack of predefined connectivity is used to interconnect different domains seamlessly, allowing the use of non-conforming meshes. A generalized formulation for constraints, joints, and contacts is proposed, which is valid for rigid and flexible solids, being the later discretized using either finite elements (FEM) or meshfree methods. The greatest advantage of this approach is that makes the domain completely independent of the external links and actions, allowing to even define them outside of the boundary. At the same time, the number of constraint equations needed for defining realistic joints is minimized. Validation, examples, and benchmarks are provided for the proposed formulation, demonstrating that the approach is generic and extensible to further problems. Comparisons with FEM show a much lower error for the same number of nodes, both for mechanical and thermal analyses. The numerical efficiency is also better when coarse discretizations are used. A final demonstration to a real problem for handling massive structures inside of a fusion reactor is presented. It demonstrates that the application of meshfree methods is feasible and can provide an advantage towards the definition of nonlinear real-time simulation models.

Nonlinear dynamics of a satellite with deployable solar panel arrays

The multibody dynamics of a satellite in circular orbit, modeled as a central body with two hinge-connected deployable solar panel arrays, is investigated. Typically, the solar panel arrays are deployed in orbit using preloaded torsional springs at the hinges in a near symmetrical accordion manner, to minimize the shock loads at the hinges. There are five degrees of freedom of the interconnected rigid bodies, composed of coupled attitude motions (pitch, yaw and roll) of the central body plus relative rotations of the solar panel arrays. The dynamical equations of motion of the satellite system are derived using Kane's equations. These are then used to investigate the dynamic behavior of the system during solar panel deployment via the 7-8th-order Runge-Kutta integration algorithms and results are compared with approximate analytical solutions. Chaotic attitude motions of the completely deployed satellite in circular orbit under the influence of the gravity-gradient torques are subsequently investigated analytically using Melnikov's method and confirmed via numerical integration. The Hamiltonian equations in terms of Deprit's variables are used to facilitate the analysis. (C) 2003 Published by Elsevier Ltd.

Degeneracy of velocity constraints in rigid body systems

The equations governing the dynamics of rigid body systems with velocity constraints are singular at degenerate configurations in the constraint distribution. In this report, we describe the causes of singularities in the constraint distribution of interconnected rigid body systems with smooth configuration manifolds. A convention of defining primary velocity constraints in terms of orthogonal complements of one-dimensional subspaces is introduced. Using this convention, linear maps are defined and used to describe the space of allowable velocities of a rigid body. Through the definition of these maps, we present a condition for non-degeneracy of velocity constraints in terms of the one dimensional subspaces defining the primary velocity constraints. A method for defining the constraint subspace and distribution in terms of linear maps is presented. Using these maps, the constraint distribution is shown to be singular at configuration where there is an increase in its dimension.

Dynamics of galaxies in the cluster environment: a resonant origin for the ISP?

The internal dynamics of elliptical galaxies in clusters depends on many factors, including the environment in which the galaxy is located. In addition to the strong encounters with the other galaxies, we can also consider the gravitational interaction with the ubiquitous Cluster Tidal Field (CTF). As recognized in many studies, one possible way in which CTF affects the dynamics of galaxies inside the cluster is related to the fact that they may start oscillating as “rigid bodies” around their equilibrium positions in the field, with the periods of these oscillations curiously similar to those of stellar orbits in the outer parts of galaxies. Resonances between the two motions are hence expected and this phenomenon could significantly contribute to the formation of the Intracluster Stellar Population (ISP), whose presence is abundantly confirmed by observations. In this thesis work, we propose to study the motion of an elliptical galaxy, modelled as a rigid body, in the CTF, especially when its center of mass traces a quasi-circular orbit in the cluster gravitational potential. This case extends and generalizes the previous models and findings, proceeding towards a much more realistic description of galaxy motion. In addition to this, the presence of a further oscillation, namely that of the entire galaxy along its orbit, will possibly increase the probability of having resonances and, consequently, the rate of ISP production nearly to observed values. Thus, after reviewing the dynamics of a rigid body in a generic force field, we will assess some physically relevant studies and report their main results, discussing their implications with respect to our problem. We will conclude our discussion focusing on the more realistic scenario of an elliptical galaxy whose center of mass moves on a quasi-circular orbit in a spherically symmetric potential. The derivation of the fundamental equations of motion will serve as the basis for future modelling and discussions.

Comparison Of Postoperative Stability Of Three Rigid Internal Fixation Techniques After Sagittal Split Ramus Osteotomy For Mandibular Advancement.

The aim of this investigation was to compare the skeletal stability of three different rigid fixation methods after mandibular advancement. Fifty-five class II malocclusion patients treated with the use of bilateral sagittal split ramus osteotomy and mandibular advancement were selected for this retrospective study. Group 1 (n = 17) had miniplates with monocortical screws, Group 2 (n = 16) had bicortical screws and Group 3 (n = 22) had the osteotomy fixed by means of the hybrid technique. Cephalograms were taken preoperatively, 1 week within the postoperative care period, and 6 months after the orthognathic surgery. Linear and angular changes of the cephalometric landmarks of the chin region were measured at each period, and the changes at each cephalometric landmark were determined for the time gaps. Postoperative changes in the mandibular shape were analyzed to determine the stability of fixation methods. There was minimum difference in the relapse of the mandibular advancement among the three groups. Statistical analysis showed no significant difference in postoperative stability. However, a positive correlation between the amount of advancement and the amount of postoperative relapse was demonstrated by the linear multiple regression test (p < 0.05). It can be concluded that all techniques can be used to obtain stable postoperative results in mandibular advancement after 6 months.

Mechanical Properties And Fracture Dynamics Of Silicene Membranes.

As graphene has become one of the most important materials, there is renewed interest in other similar structures. One example is silicene, the silicon analogue of graphene. It shares some of the remarkable graphene properties, such as the Dirac cone, but presents some distinct ones, such as a pronounced structural buckling. We have investigated, through density functional based tight-binding (DFTB), as well as reactive molecular dynamics (using ReaxFF), the mechanical properties of suspended single-layer silicene. We calculated the elastic constants, analyzed the fracture patterns and edge reconstructions. We also addressed the stress distributions, unbuckling mechanisms and the fracture dependence on the temperature. We analysed the differences due to distinct edge morphologies, namely zigzag and armchair.

Site Specific Spin Dynamics In Bafe2as2: Tuning The Ground State By Orbital Differentiation.

The role of orbital differentiation on the emergence of superconductivity in the Fe-based superconductors remains an open question to the scientific community. In this investigation, we employ a suitable microscopic spin probe technique, namely Electron Spin Resonance (ESR), to investigate this issue on selected chemically substituted BaFe2As2 single crystals. As the spin-density wave (SDW) phase is suppressed, we observe a clear increase of the Fe 3d bands anisotropy along with their localization at the FeAs plane. Such an increase of the planar orbital content is interestingly independent of the chemical substitution responsible for suppressing the SDW phase. As a consequence, the magnetic fluctuations in combination with this particular symmetry of the Fe 3d bands are propitious ingredients for the emergence of superconductivity in this class of materials.

[between The Country And The Laboratory: The Dynamics Of The Production Of Knowledge At The Menopause Outpatients Clinic At Caism, Unicamp.]

This study investigates the practices involved in the production of knowledge about menopause at Caism, Unicamp, a reference center for public policies for women's health. Gynecological appointments and psychological support meetings were observed, and women and doctors were interviewed in order to identify what discourse circulates there and how different actors are brought in to ensure that the knowledge produced attains credibility and travels beyond the boundaries of the teaching hospital to become universal. The analysis is based on localized studies aligned with social studies of science and technology.

[between The Country And The Laboratory: The Dynamics Of The Production Of Knowledge At The Menopause Outpatients Clinic At Caism, Unicamp].

This study investigates the practices involved in the production of knowledge about menopause at Caism, Unicamp, a reference center for public policies for women's health. Gynecological appointments and psychological support meetings were observed, and women and doctors were interviewed in order to identify what discourse circulates there and how different actors are brought in to ensure that the knowledge produced attains credibility and travels beyond the boundaries of the teaching hospital to become universal. The analysis is based on localized studies aligned with social studies of science and technology.

Na "periferia" da quadra : educação fisica, cultura e sociabilidade na escola

Universidade Estadual de Campinas . Faculdade de Educação Física

Population dynamics: seasonal variation of phytoplankton functional groups in brazilian reservoirs (Billings and Guarapiranga, São Paulo)

Phytoplankton may function as a "sensor" of changes in aquatic environment and responds rapidly to such changes. In freshwaters, coexistence of species that have similar ecological requirements and show the same environmental requirements frequently occurs; such species groups are named functional groups. The use of phytoplankton functional groups to evaluate these changes has proven to be very useful and effective. Thus, the aim of this study was to evaluate the occurrence of functional groups of phytoplankton in two reservoirs (Billings and Guarapiranga) that supply water to millions of people in São Paulo city Metropolitan Area, southeastern Brazil. Surface water samples were collected monthly and physical, chemical and biological (quantitative and qualitative analyses of the phytoplankton) were performed. The highest biovolume (mm³.L-1) of the descriptor species and functional groups were represented respectively by Anabaena circinalis Rabenh. (H1), Microcystis aeruginosa (Kützing) Kützing (L M/M) and Mougeotia sp. (T) in the Guarapiranga reservoir and Cylindrospermopsis raciborskii (Wolosz.) Seen. and Subba Raju (S N), Microcystis aeruginosa and M. panniformis Komárek et al. (L M/M), Planktothrix agardhii (Gom.) Anagn. and Komárek and P. cf. clathrata (Skuja) Anagn. and Komárek (S1) in the Billings reservoir. The environmental factors that most influenced the phytoplankton dynamics were water temperature, euphotic zone, turbidity, conductivity, pH, dissolved oxygen, nitrate and total phosphorous.

An Eulerian Immersed Boundary Method for flow simulations over stationary and moving rigid bodies

The fluid flow over bodies with complex geometry has been the subject of research of many scientists and widely explored experimentally and numerically. The present study proposes an Eulerian Immersed Boundary Method for flows simulations over stationary or moving rigid bodies. The proposed method allows the use of Cartesians Meshes. Here, two-dimensional simulations of fluid flow over stationary and oscillating circular cylinders were used for verification and validation. Four different cases were explored: the flow over a stationary cylinder, the flow over a cylinder oscillating in the flow direction, the flow over a cylinder oscillating in the normal flow direction, and a cylinder with angular oscillation. The time integration was carried out by a classical 4th order Runge-Kutta scheme, with a time step of the same order of distance between two consecutive points in x direction. High-order compact finite difference schemes were used to calculate spatial derivatives. The drag and lift coefficients, the lock-in phenomenon and vorticity contour plots were used for the verification and validation of the proposed method. The extension of the current method allowing the study of a body with different geometry and three-dimensional simulations is straightforward. The results obtained show a good agreement with both numerical and experimental results, encouraging the use of the proposed method.