The Bifurcation Interpreter: A Step Towards the Automatic Analysis of Dynamical Systems

The Bifurcation Interpreter is a computer program that autonomously explores the steady-state orbits of one-parameter families of periodically- driven oscillators. To report its findings, the Interpreter generates schematic diagrams and English text descriptions similar to those appearing in the science and engineering research literature. Given a system of equations as input, the Interpreter uses symbolic algebra to automatically generate numerical procedures that simulate the system. The Interpreter incorporates knowledge about dynamical systems theory, which it uses to guide the simulations, to interpret the results, and to minimize the effects of numerical error.

Prediction of limit cycle oscillations under uncertainty using a Harmonic Balance method

The Harmonic Balance method is an attractive solution for computing periodic responses and can be an alternative to time domain methods, at a reduced computational cost. The current paper investigates using a Harmonic Balance method for simulating limit cycle oscillations under uncertainty. The Harmonic Balance method is used in conjunction with a non-intrusive polynomial-chaos approach to propagate variability and is validated against Monte Carlo analysis. Results show the potential of the approach for a range of nonlinear dynamical systems, including a full wing configuration exhibiting supercritical and subcritical bifurcations, at a fraction of the cost of performing time domain simulations.

The prediction of Northern Hemisphere tropical cyclone extended life cycles by the ECMWF Ensemble and Deterministic Prediction Systems. Part I: tropical cyclone stage

This study has explored the prediction errors of tropical cyclones (TCs) in the European Centre for Medium-Range Weather Forecasts (ECMWF) Ensemble Prediction System (EPS) for the Northern Hemisphere summer period for five recent years. Results for the EPS are contrasted with those for the higher-resolution deterministic forecasts. Various metrics of location and intensity errors are considered and contrasted for verification based on IBTrACS and the numerical weather prediction (NWP) analysis (NWPa). Motivated by the aim of exploring extended TC life cycles, location and intensity measures are introduced based on lower-tropospheric vorticity, which is contrasted with traditional verification metrics. Results show that location errors are almost identical when verified against IBTrACS or the NWPa. However, intensity in the form of the mean sea level pressure (MSLP) minima and 10-m wind speed maxima is significantly underpredicted relative to IBTrACS. Using the NWPa for verification results in much better consistency between the different intensity error metrics and indicates that the lower-tropospheric vorticity provides a good indication of vortex strength, with error results showing similar relationships to those based on MSLP and 10-m wind speeds for the different forecast types. The interannual variation in forecast errors are discussed in relation to changes in the forecast and NWPa system and variations in forecast errors between different ocean basins are discussed in terms of the propagation characteristics of the TCs.

Limit sets and the Poincare-Bendixson Theorem in impulsive semidynamical systems

We consider semidynamical systems with impulse effects at variable times and we discuss some properties of the limit sets of orbits of these systems such as invariancy, compactness and connectedness. As a consequence we obtain a version of the Poincare-Bendixson Theorem for impulsive semidynamical systems. (C) 2008 Elsevier Inc. All rights reserved.

Cold-atom systems and the scaling limit

With perspective to applications of cold-atom systems, some aspects of few-body physics at very low energies will be reviewed. By exploring the possibilities of varying the two-body interaction via the Feshbach resonance mechanism, some recent results are reported for condensed systems in optical lattices.

On the existence of infinite heteroclinic cycles in polynomial systems and its dynamic consequences

In this work we consider the dynamic consequences of the existence of infinite heteroclinic cycle in planar polynomial vector fields, which is a trajectory connecting two saddle points at infinity. It is stated that, although the saddles which form the cycle belong to infinity, for certain types of nonautonomous perturbations the perturbed system may present a complex dynamic behavior of the solutions in a finite part of the phase plane, due to the existence of tangencies and transversal intersections of their stable and unstable manifolds. This phenomenon might be called the chaos arising from infinity. The global study at infinity is made via the Poincare Compactification and the argument used to prove the statement is the Birkhoff-Smale Theorem. (c) 2004 WILEY-NCH Verlag GmbH & Co. KGaA, Weinheim.

Scaling limit of virtual states of triatomic systems

Natural scales determine the physics of quantum few-body systems with short-range interactions. Thus, the scaling limit is found when the ratio between the scattering length and the interaction range tends to infinity, while the ratio between the physical scales are kept fixed. From the formal point of view, the relation of the scaling limit and the renormalization aspects of a few-body model with a zero-range interaction, through the derivation of subtracted three-body T-matrix equations that are renormalization-group invariant.

Tjon Lines and Scaling Limit in Four-Body Systems

The fixed-slope correlation between tetramer and trimer binding energies, observed by Tjon in the context of nuclear physics, is mainly a manifestation of the dominance of the two-nucleon force in the nuclear potential, which makes the four-body scale on the order of the three-body one. In a more general four-boson case, the correlation between tetramer and trimer binding energies has a non-fixed slope, which expresses the dependence on the new scale. The associated scaling function generates a family of Tjon lines. This conclusion relies on a recent study with weakly-bound four identical bosons, within a renormalized zero-range Faddeev-Yakubovsky formalism. © 2012 Springer-Verlag.

Generic bifurcation of refracted systems

In this article we discuss some qualitative and geometric aspects of non-smooth dynamical systems theory. Our goal is to study the diagram bifurcation of typical singularities that occur generically in one parameter families of certain piecewise smooth vector fields named Refracted Systems. Such systems has a codimension-one submanifold as its discontinuity set. © 2012 Elsevier Ltd.

Hero's journey in bifurcation diagram

The hero's journey is a narrative structure identified by several authors in comparative studies on folklore and mythology. This storytelling template presents the stages of inner metamorphosis undergone by the protagonist after being called to an adventure. In a simplified version, this journey is divided into three acts separated by two crucial moments. Here we propose a discrete-time dynamical system for representing the protagonist's evolution. The suffering along the journey is taken as the control parameter of this system. The bifurcation diagram exhibits stationary, periodic and chaotic behaviors. In this diagram, there are transition from fixed point to chaos and transition from limit cycle to fixed point. We found that the values of the control parameter corresponding to these two transitions are in quantitative agreement with the two critical moments of the three-act hero's journey identified in 10 movies appearing in the list of the 200 worldwide highest-grossing films. (C) 2011 Elsevier B.V. All rights reserved.

Design of alternative energy storage systems for hybrid vehicles based on statistical processing of driving cycles information

Hybrid vehicles represent the future for automakers, since they allow to improve the fuel economy and to reduce the pollutant emissions. A key component of the hybrid powertrain is the Energy Storage System, that determines the ability of the vehicle to store and reuse energy. Though electrified Energy Storage Systems (ESS), based on batteries and ultracapacitors, are a proven technology, Alternative Energy Storage Systems (AESS), based on mechanical, hydraulic and pneumatic devices, are gaining interest because they give the possibility of realizing low-cost mild-hybrid vehicles. Currently, most literature of design methodologies focuses on electric ESS, which are not suitable for AESS design. In this contest, The Ohio State University has developed an Alternative Energy Storage System design methodology. This work focuses on the development of driving cycle analysis methodology that is a key component of Alternative Energy Storage System design procedure. The proposed methodology is based on a statistical approach to analyzing driving schedules that represent the vehicle typical use. Driving data are broken up into power events sequence, namely traction and braking events, and for each of them, energy-related and dynamic metrics are calculated. By means of a clustering process and statistical synthesis methods, statistically-relevant metrics are determined. These metrics define cycle representative braking events. By using these events as inputs for the Alternative Energy Storage System design methodology, different system designs are obtained. Each of them is characterized by attributes, namely system volume and weight. In the last part the work, the designs are evaluated in simulation by introducing and calculating a metric related to the energy conversion efficiency. Finally, the designs are compared accounting for attributes and efficiency values. In order to automate the driving data extraction and synthesis process, a specific script Matlab based has been developed. Results show that the driving cycle analysis methodology, based on the statistical approach, allows to extract and synthesize cycle representative data. The designs based on cycle statistically-relevant metrics are properly sized and have satisfying efficiency values with respect to the expectations. An exception is the design based on the cycle worst-case scenario, corresponding to same approach adopted by the conventional electric ESS design methodologies. In this case, a heavy system with poor efficiency is produced. The proposed new methodology seems to be a valid and consistent support for Alternative Energy Storage System design.

Neutronics analyses for fast spectrum nuclear systems and scenario studies for advanced nuclear fuel cycles

The present PhD thesis summarizes the three-years study about the neutronic investigation of a new concept nuclear reactor aiming at the optimization and the sustainable management of nuclear fuel in a possible European scenario. A new generation nuclear reactor for the nuclear reinassance is indeed desired by the actual industrialized world, both for the solution of the energetic question arising from the continuously growing energy demand together with the corresponding reduction of oil availability, and the environment question for a sustainable energy source free from Long Lived Radioisotopes and therefore geological repositories. Among the Generation IV candidate typologies, the Lead Fast Reactor concept has been pursued, being the one top rated in sustainability. The European Lead-cooled SYstem (ELSY) has been at first investigated. The neutronic analysis of the ELSY core has been performed via deterministic analysis by means of the ERANOS code, in order to retrieve a stable configuration for the overall design of the reactor. Further analyses have been carried out by means of the Monte Carlo general purpose transport code MCNP, in order to check the former one and to define an exact model of the system. An innovative system of absorbers has been conceptualized and designed for both the reactivity compensation and regulation of the core due to cycle swing, as well as for safety in order to guarantee the cold shutdown of the system in case of accident. Aiming at the sustainability of nuclear energy, the steady-state nuclear equilibrium has been investigated and generalized into the definition of the ``extended'' equilibrium state. According to this, the Adiabatic Reactor Theory has been developed, together with a New Paradigm for Nuclear Power: in order to design a reactor that does not exchange with the environment anything valuable (thus the term ``adiabatic''), in the sense of both Plutonium and Minor Actinides, it is required indeed to revert the logical design scheme of nuclear cores, starting from the definition of the equilibrium composition of the fuel and submitting to the latter the whole core design. The New Paradigm has been applied then to the core design of an Adiabatic Lead Fast Reactor complying with the ELSY overall system layout. A complete core characterization has been done in order to asses criticality and power flattening; a preliminary evaluation of the main safety parameters has been also done to verify the viability of the system. Burn up calculations have been then performed in order to investigate the operating cycle for the Adiabatic Lead Fast Reactor; the fuel performances have been therefore extracted and inserted in a more general analysis for an European scenario. The present nuclear reactors fleet has been modeled and its evolution simulated by means of the COSI code in order to investigate the materials fluxes to be managed in the European region. Different plausible scenarios have been identified to forecast the evolution of the European nuclear energy production, including the one involving the introduction of Adiabatic Lead Fast Reactors, and compared to better analyze the advantages introduced by the adoption of new concept reactors. At last, since both ELSY and the ALFR represent new concept systems based upon innovative solutions, the neutronic design of a demonstrator reactor has been carried out: such a system is intended to prove the viability of technology to be implemented in the First-of-a-Kind industrial power plant, with the aim at attesting the general strategy to use, to the largest extent. It was chosen then to base the DEMO design upon a compromise between demonstration of developed technology and testing of emerging technology in order to significantly subserve the purpose of reducing uncertainties about construction and licensing, both validating ELSY/ALFR main features and performances, and to qualify numerical codes and tools.