Control of Unstable Ship Motions Using Anti-Rolling Tanks: Erosion of Safe Basins

2010 ◽  
Author(s):  
Marcelo A. S. Neves ◽  
Claudio A. Rodri´guez ◽  
Jorge A. Merino ◽  
Jerver E. M. Vivanco ◽  
Jose´ C. Villago´mez Rosales ◽  
...  
Keyword(s):  
Quantitative Assessment ◽  
Initial Conditions ◽  
Dynamical Behavior ◽  
Design Procedure ◽  
Ship Motions ◽  
Numerical Techniques ◽  
Liquid Motion ◽  
Critical Amplitude ◽  
Parametric Rolling ◽  
Limits Of Stability

The objective of the paper is to apply modern numerical techniques of nonlinear dynamics to the problem of control of the roll motion employing U-shaped anti rolling tanks (ART). Parametric rolling in head seas is the focus of the paper. A transom stern small vessel, well known for her tendency to develop strong parametric excitation is investigated. Nonlinear equations are employed to describe the liquid motion inside the tank, the forces and moments generated by the tank on the ship and the coupled ship motions (heave, roll and pitch). These are numerically solved for different initial conditions. An analysis of the dynamical behavior of the vessel with stabilization is presented in the form of numerical limits of stability, safe basins, integrity curves and integrity surfaces. Finally, curves of critical amplitude for different wave tunings are computed. A design procedure for quantitative assessment of the level of parametric rolling mitigation by means of ART’s is discussed.

Nonlinear Coupling of Unstable Ship Motions in Head Seas: Bifurcation Analysis and Erosion of Safe Basin

2009 ◽  
Author(s):  
Marcelo A. S. Neves ◽  
Jerver E. M. Vivanco ◽  
Claudio A. Rodri´guez
Keyword(s):  
Bifurcation Analysis ◽  
Wave Amplitude ◽  
Coupled System ◽  
Ship Motions ◽  
Nonlinear Coupling ◽  
Bifurcation Diagrams ◽  
Parametric Rolling ◽  
Limits Of Stability ◽  
Dynamical Characteristics ◽  
Safe Basin

Parametric rolling in head seas may lead to large roll angles in few cycles with substantial coupling of this mode with heave and pitch. The present paper investigates in depth the essential dynamical characteristics governing the complex coupling of the three modes at the first region of instability of the limits of stability. Bifurcation diagrams and Poincare´ mappings are employed to investigate the appearance of intermittence, multistability and chaos associated with increased values of wave amplitude. Erosion of the safe basin of the coupled system for some sea conditions is also addressed.

Behavior of a Self-Sustained Electromechanical Transducer and Routes to Chaos

2005 ◽  
Vol 128 (3) ◽  
pp. 282-293 ◽  
Author(s):  
J. C. Chedjou ◽  
K. Kyamakya ◽  
I. Moussa ◽  
H.-P. Kuchenbecker ◽  
W. Mathis
Keyword(s):  
Electronic Circuit ◽  
Initial Conditions ◽  
Dynamical Behavior ◽  
Period Doubling ◽  
Electromechanical System ◽  
Phase Portraits ◽  
Coupling Coefficients ◽  
Oscillatory Solutions ◽  
Electromechanical Transducer ◽  
Design Engineers

This paper studies the dynamics of a self-sustained electromechanical transducer. The stability of fixed points in the linear response is examined. Their local bifurcations are investigated and different types of bifurcation likely to occur are found. Conditions for the occurrence of Hopf bifurcations are derived. Harmonic oscillatory solutions are obtained in both nonresonant and resonant cases. Their stability is analyzed in the resonant case. Various bifurcation diagrams associated to the largest one-dimensional (1-D) numerical Lyapunov exponent are obtained, and it is found that chaos can appear suddenly, through period doubling, period adding, or torus breakdown. The extreme sensitivity of the electromechanical system to both initial conditions and tiny variations of the coupling coefficients is also outlined. The experimental study of̱the electromechanical system is carried out. An appropriate electronic circuit (analog simulator) is proposed for the investigation of the dynamical behavior of the electromechanical system. Correspondences are established between the coefficients of the electromechanical system model and the components of the electronic circuit. Harmonic oscillatory solutions and phase portraits are obtained experimentally. One of the most important contributions of this work is to provide a set of reliable analytical expressions (formulas) describing the electromechanical system behavior. These formulas are of great importance for design engineers as they can be used to predict the states of the electromechanical systems and respectively to avoid their destruction. The reliability of the analytical formulas is demonstrated by the very good agreement with the results obtained by both the numeric and the experimental analysis.

A Quasi-three-dimensional Finite-volume Shallow Water Model for Green Water on Deck

2013 ◽  
Vol 57 (03) ◽  
pp. 125-140
Author(s):  
Daniel A. Liut ◽  
Kenneth M. Weems ◽  
Tin-Guen Yen
Keyword(s):  
Shallow Water ◽  
Finite Volume ◽  
Time Domain ◽  
Degrees Of Freedom ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Green Water ◽  
Water Model ◽  
Ship Motions ◽  
Shallow Water Model

A quasi-three-dimensional hydrodynamic model is presented to simulate shallow water phenomena. The method is based on a finite-volume approach designed to solve shallow water equations in the time domain. The nonlinearities of the governing equations are considered. The methodology can be used to compute green water effects on a variety of platforms with six-degrees-of-freedom motions. Different boundary and initial conditions can be applied for multiple types of moving platforms, like a ship's deck, tanks, etc. Comparisons with experimental data are discussed. The shallow water model has been integrated with the Large Amplitude Motions Program to compute the effects of green water flow over decks within a time-domain simulation of ship motions in waves. Results associated to this implementation are presented.

Fanno Design of Blow-Off Lines in Heavy Duty Gas Turbine

2013 ◽  
Author(s):  
Marco Cioffi ◽  
Enrico Puppo ◽  
Andrea Silingardi
Keyword(s):  
Gas Turbines ◽  
Gas Flow ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Design Procedure ◽  
Flow Equation ◽  
Heavy Duty ◽  
Cross Sectional ◽  
Pipe Length ◽  
Choked Flow

In typical heavy duty gas turbines the multistage axial compressor is provided with anti-surge pipelines equipped with on-off valves (blow-off lines), to avoid dangerous flow instabilities during start-ups and shut-downs. Blow-off lines show some very peculiar phenomena and somewhat challenging fluid dynamics, which require a deeper regard. In this paper the blow-off lines in axial gas turbines are analyzed by adopting an adiabatic quasi-unidimensional model of the gas flow through a pipe with a constant cross-sectional area and involving geometrical singularities (Fanno flow). The determination of the Fanno limit, on the basis of the flow equation and the second principle of thermodynamics, shows the existence of a critical pipe length which is a function of the pipe parameters and the initial conditions: for a length greater than this maximum one, the model requires a mass-flow reduction. In addition, in the presence of a regulating valve, so-called multi-choked flow can arise. The semi-analytical model has been implemented and the results have been compared with a three-dimensional CFD analysis and cross-checked with available field data, showing a good agreement. The Fanno model has been applied for the analysis of some of the actual machines in the Ansaldo Energia fleet under different working conditions. The Fanno tool will be part of the design procedure of new machines. In addition it will define related experimental activities.

scholarly journals Predicting Collapse of Complex Ecological Systems: Quantifying the Stability-Complexity Continuum

2019 ◽  
Author(s):  
Susanne Pettersson ◽  
Van M. Savage ◽  
Martin Nilsson Jacobi
Keyword(s):  
Single Species ◽  
Ecological Systems ◽  
Ecological Research ◽  
Stability Criteria ◽  
Numerical Techniques ◽  
Intermediate Regime ◽  
Limits Of Stability ◽  
Species Abundances ◽  
The Stability ◽  
Degree Of Instability

Dynamical shifts between the extremes of stability and collapse are hallmarks of ecological systems. These shifts are limited by and change with biodiversity, complexity, and the topology and hierarchy of interactions. Most ecological research has focused on identifying conditions for a system to shift from stability to any degree of instability—species abundances do not return to exact same values after perturbation. Real ecosystems likely have a continuum of shifting between stability and collapse that depends on the specifics of how the interactions are structured, as well as the type and degree of disturbance due to environmental change. Here we map boundaries for the extremes of strict stability and collapse. In between these boundaries, we find an intermediate regime that consists of single-species extinctions, which we call the Extinction Continuum. We also develop a metric that locates the position of the system within the Extinction Continuum—thus quantifying proximity to stability or collapse—in terms of ecologically measurable quantities such as growth rates and interaction strengths. Furthermore, we provide analytical and numerical techniques for estimating our new metric. We show that our metric does an excellent job of capturing the system behaviour in comparison with other existing methods—such as May’s stability criteria or critical slowdown. Our metric should thus enable deeper insights about how to classify real systems in terms of their overall dynamics and their limits of stability and collapse.

scholarly journals Numerical daemons of hydrological models are summoned by extreme precipitation

2021 ◽  
Author(s):  
Peter T. La Follette ◽  
Adriaan J. Teuling ◽  
Nans Addor ◽  
Martyn Clark ◽  
Koen Jansen ◽  
...  
Keyword(s):  
Numerical Methods ◽  
Extreme Precipitation ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Computational Cost ◽  
Numerical Error ◽  
Hydrological Models ◽  
Multiple Model ◽  
Numerical Techniques ◽  
Modeling Framework

Abstract. Hydrological models are usually systems of nonlinear differential equations for which no analytical solutions exist and thus rely on approximate numerical solutions. While some studies have investigated the relationship between numerical method choice and model error, the extent to which extreme precipitation like that observed during hurricanes Harvey and Katrina impacts numerical error of hydrological models is still unknown. This knowledge is relevant in light of climate change, where many regions will likely experience more intense precipitation events. In this experiment, a large number of hydrographs is generated with the modular modeling framework FUSE, using eight numerical techniques across a variety of forcing datasets. Multiple model structures, parameter sets, and initial conditions are incorporated for generality. The computational expense and numerical error associated with each hydrograph were recorded. It was found that numerical error (root mean square error) usually increases with precipitation intensity and decreases with event duration. Some numerical methods constrain errors much more effectively than others, sometimes by many orders of magnitude. Of the tested numerical methods, a second-order adaptive explicit method is found to be the most efficient because it has both low numerical error and low computational cost. A basic literature review indicates that many popular modeling codes use numerical techniques that were suggested by this experiment to be sub-optimal. We conclude that relatively large numerical errors might be common in current models, and because these will likely become larger as the climate changes, we advocate for the use of low cost, low error numerical methods.

scholarly journals Bifurcation and global dynamical behavior of the f(T) theory

2014 ◽  
Vol 29 (07) ◽  
pp. 1450033 ◽  
Author(s):  
Chao-Jun Feng ◽  
Xin-Zhou Li ◽  
Li-Yan Liu
Keyword(s):  
Dynamical System ◽  
Critical Points ◽  
Initial Conditions ◽  
Dynamical Behavior ◽  
Nonlinear Effects ◽  
Local Analysis ◽  
Local Method ◽  
Initial Values ◽  
Bifurcation Phenomenon

Usually, in order to investigate the evolution of a theory, one may find the critical points of the system and then perform perturbations around these critical points to see whether they are stable or not. This local method is very useful when the initial values of the dynamical variables are not far away from the critical points. Essentially, the nonlinear effects are totally neglected in such kind of approach. Therefore, one cannot tell whether the dynamical system will evolute to the stable critical points or not when the initial values of the variables do not close enough to these critical points. Furthermore, when there are two or more stable critical points in the system, local analysis cannot provide the information on which the system will finally evolute to. In this paper, we have further developed the nullcline method to study the bifurcation phenomenon and global dynamical behavior of the f(T) theory. We overcome the shortcoming of local analysis. And, it is very clear to see the evolution of the system under any initial conditions.

Dynamical Analysis and Circuit Simulation of a New Fractional-Order Hyperchaotic System and Its Discretization

2016 ◽  
Vol 26 (13) ◽  
pp. 1650222 ◽  
Author(s):  
A. M. A. El-Sayed ◽  
A. Elsonbaty ◽  
A. A. Elsadany ◽  
A. E. Matouk
Keyword(s):  
Fractional Order ◽  
Initial Conditions ◽  
Circuit Simulation ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Phase Portraits ◽  
Control Technique ◽  
Order System ◽  
Qualitative Behavior ◽  
Hyperchaotic System

This paper presents an analytical framework to investigate the dynamical behavior of a new fractional-order hyperchaotic circuit system. A sufficient condition for existence, uniqueness and continuous dependence on initial conditions of the solution of the proposed system is derived. The local stability of all the system’s equilibrium points are discussed using fractional Routh–Hurwitz test. Then the analytical conditions for the existence of a pitchfork bifurcation in this system with fractional-order parameter less than 1/3 are provided. Conditions for the existence of Hopf bifurcation in this system are also investigated. The dynamics of discretized form of our fractional-order hyperchaotic system are explored. Chaos control is also achieved in discretized system using delay feedback control technique. The numerical simulation are presented to confirm our theoretical analysis via phase portraits, bifurcation diagrams and Lyapunov exponents. A text encryption algorithm is presented based on the proposed fractional-order system. The results show that the new system exhibits a rich variety of dynamical behaviors such as limit cycles, chaos and transient phenomena where fractional-order derivative represents a key parameter in determining system qualitative behavior.

scholarly journals Predicting collapse of complex ecological systems: quantifying the stability–complexity continuum

2020 ◽  
Vol 17 (166) ◽  
pp. 20190391 ◽  
Author(s):  
Susanne Pettersson ◽  
Van M. Savage ◽  
Martin Nilsson Jacobi
Keyword(s):  
Single Species ◽  
Ecological Systems ◽  
Ecological Research ◽  
Stability Criteria ◽  
Numerical Techniques ◽  
Intermediate Regime ◽  
Limits Of Stability ◽  
Species Abundances ◽  
The Stability ◽  
Degree Of Instability

Dynamical shifts between the extremes of stability and collapse are hallmarks of ecological systems. These shifts are limited by and change with biodiversity, complexity, and the topology and hierarchy of interactions. Most ecological research has focused on identifying conditions for a system to shift from stability to any degree of instability—species abundances do not return to exact same values after perturbation. Real ecosystems likely have a continuum of shifting between stability and collapse that depends on the specifics of how the interactions are structured, as well as the type and degree of disturbance due to environmental change. Here we map boundaries for the extremes of strict stability and collapse. In between these boundaries, we find an intermediate regime that consists of single-species extinctions, which we call the extinction continuum. We also develop a metric that locates the position of the system within the extinction continuum—thus quantifying proximity to stability or collapse—in terms of ecologically measurable quantities such as growth rates and interaction strengths. Furthermore, we provide analytical and numerical techniques for estimating our new metric. We show that our metric does an excellent job of capturing the system's behaviour in comparison with other existing methods—such as May’s stability criteria or critical slowdown. Our metric should thus enable deeper insights about how to classify real systems in terms of their overall dynamics and their limits of stability and collapse.

scholarly journals Dynamical contribution of mean potential vorticity pseudo-observations derived from MetOp/GOME2 ozone data into short-range weather forecast during high precipitation events

2015 ◽  
Vol 4 (2) ◽  
pp. 206
Author(s):  
Siham Sbii ◽  
Mimoun Zazoui ◽  
Noureddine Semane
Keyword(s):  
Potential Vorticity ◽  
Short Range ◽  
Initial Conditions ◽  
Weather Prediction ◽  
Dynamical Behavior ◽  
Heavy Precipitation ◽  
Limited Area ◽  
Total Column Ozone ◽  
Ozone Data ◽  
Precipitation Events

<p>Satellites are uniquely capable of providing uniform data coverage globally. Motivated by such capability, this study builds on a previously described methodology that generates numerical weather prediction initial conditions from satellite total column ozone data. The methodology is based on two principal steps. Firstly, the studied linear regression between vertical (100hPa-500hPa) Mean Potential Vorticity (MPV) and MetOp/GOME2 total ozone data (O3) generates MPV pseudo-observations. Secondly, the 3D variational (3D-Var) assimilation method is designed to take into account MPV pseudo-observations in addition to conventional observations.</p><p>After a successful assimilation of MPV pseudo-observations using a 3D-Var approach within the Moroccan version of the ALADIN limited-area model, the present study aims to assess the dynamical behavior of the short-range forecast at upper levels during heavy precipitation events (HPEs). It is found that MPV assimilation offers the possibility to internally monitor the model upper-level dynamics in addition to the use of Water Vapor Satellite images.</p>

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