Control of integrable Hamiltonian systems and degenerate bifurcations

In this dissertation, we study the control of near-integrable systems. A near-integrable system is one whose phase space has a similar structure to an integrable system during short time periods and for some parameter regime. We begin by studying the control of integrable Hamiltonian systems. The controller targets an exact solution to the integrable system using dissipative and conservative terms. We find that a Takens-Bogdanov bifurcation occurs in the limit of no dissipative control. The presence of a Takens-Bogdanov bifurcation implies that the control is highly susceptible to noise. We illustrate our results using a two- and four-dimensional integrable systems generated by low order truncations of solutions to the nonlinear Schrodinger equation (NLS). We then extend our results to a near-integrable system related to the NLS; the Ginzburg-Landau equation. We attempt to control the Ginzburg-Landau equation to a plane wave solution of the NLS. We show that for a certain parameter regime; a Takens-Bogdanov bifurcation occurs in the limit of no dissipative control. Through this example, we show that solutions of integrable systems can be viable control targets for related near-integrable systems

Discriminating chaotic and stochastic dynamics through the permutation spectrum test

In this paper, we propose a new heuristic symbolic tool for unveiling chaotic and stochastic dynamics: the permutation spectrum test. Several numerical examples allow us to confirm the usefulness of the introduced methodology. Indeed, we show that it is robust in situations in which other techniques fail (intermittent chaos, hyperchaotic dynamics, stochastic linear and nonlinear correlated dynamics, and deterministic non-chaotic noise-driven dynamics). We illustrate the applicability and reliability of this pragmatic method by examining real complex time series from diverse scientific fields. Taking into account that the proposed test has the advantages of being conceptually simple and computationally fast, we think that it can be of practical utility as an alternative test for determinism. The importance of distinguishing between periodic, chaotic, and stochastic dynamics from time series analysis is well-recognized for understanding the mechanisms that govern the regarded complex systems. In this work, we have introduced a conceptually simple and computationally fast symbolic visual test for discriminating chaotic and stochastic dynamics, called the permutation spectrum test. Because the symbolization is made by implementing the Bandt and Pompe methodology, all the advantages associated with this natural encoding (simplicity, extremely fast calculation, robustness, and invariance with respect to monotonous transformations) are inherited by the permutation spectrum test. We have shown that this pragmatic approach is robust in situations in which other tests fail. We have also confirmed its practical utility by examining several experimental and natural time series.Centro de Investigaciones Óptica

Discriminating chaotic and stochastic dynamics through the permutation spectrum test

In this paper, we propose a new heuristic symbolic tool for unveiling chaotic and stochastic dynamics: the permutation spectrum test. Several numerical examples allow us to confirm the usefulness of the introduced methodology. Indeed, we show that it is robust in situations in which other techniques fail (intermittent chaos, hyperchaotic dynamics, stochastic linear and nonlinear correlated dynamics, and deterministic non-chaotic noise-driven dynamics). We illustrate the applicability and reliability of this pragmatic method by examining real complex time series from diverse scientific fields. Taking into account that the proposed test has the advantages of being conceptually simple and computationally fast, we think that it can be of practical utility as an alternative test for determinism. The importance of distinguishing between periodic, chaotic, and stochastic dynamics from time series analysis is well-recognized for understanding the mechanisms that govern the regarded complex systems. In this work, we have introduced a conceptually simple and computationally fast symbolic visual test for discriminating chaotic and stochastic dynamics, called the permutation spectrum test. Because the symbolization is made by implementing the Bandt and Pompe methodology, all the advantages associated with this natural encoding (simplicity, extremely fast calculation, robustness, and invariance with respect to monotonous transformations) are inherited by the permutation spectrum test. We have shown that this pragmatic approach is robust in situations in which other tests fail. We have also confirmed its practical utility by examining several experimental and natural time series.Fil: Kulp, C. W.. Lycoming College; Estados UnidosFil: Zunino, Luciano José. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico La Plata. Centro de Investigaciones Opticas (i); Argentina. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas; Argentina. Universidad Nacional de La Plata. Facultad de Ingenieria; Argentin

Composition and Analysis of Music Using Mathematica

In this paper we demonstrate how to create and analyze musical compositions using Mathematica. In §1, we begin by demonstrating how to create a musical composition for an orchestra based on the butterfly curve using traditional means. In §2, we then show how a computer generated piece based on any curve can be composed using Mathematica. Finally, in §3, we show how Mathematica can be used to analyze musical compositions using the methods from nonlinear time series analysis

The results of the in-flight attitude sensor calibration for the Arthur Holly Compton Gamma Ray Observatory

The Arthur Holly Compton Gamma Ray Observatory (GRO) was launched by the shuttle Atlantis in April 1991. This paper presents the results of the attitude sensor calibration that was performed during the early mission. The GSFC Flight Dynamics Facility (FDF) performed an alignment calibration of the two fixed-head star trackers (FHST's) and two fine Sun sensors (FSS's) on board Compton GRO. The results show a 27-arcsecond shift between the bore sights of the FHST's with respect to prelaunch measurements. The alignments of the two FSS's shifted by 0.20 and 0.05 degree. During the same time period, the Compton GRO science teams performed an alignment calibration of the science instruments with respect to the attitude reported by the on board computer (OBC). In order to preserve these science alignments, FDF adjusted the overall alignments of the FHST's and FSS's, obtained by the FDF calibration, such that when up linked to the OBC, the shift in the OBC-determined attitude is minimized. FDF also calibrated the inertial reference unit (IRU), which consists of three dual-axis gyroscopes. The observed gyro bias matched the bias that was solved for by the OBC. This bias drifted during the first 6 days after release. The results of the FDF calibration of scale factor and alignment shifts showed changes that were of the same order as their uncertainties

Control of Integrable Hamiltonian Systems and Degenerate Bifurcations

We discuss control of low-dimensional systems which, when uncontrolled, are integrable in the Hamiltonian sense. The controller targets an exact solution of the system in a region where the uncontrolled dynamics has invariant tori. Both dissipative and conservative controllers are considered. We show that the shear flow structure of the undriven system causes a Takens-Bogdanov birfurcation to occur when control is applied. This implies extreme noise sensitivity. We then consider an example of these results using the driven nonlinear Schrodinger equation.Comment: 25 pages, 11 figures, resubmitted to Physical Review E March 2004 (originally submitted June 2003), added content and reference

International Space Station United States Orbital Segment Oxygen Generation System On-Orbit Operational Experience

The International Space Station (ISS) United States Orbital Segment (USOS) Oxygen Generation System (OGS) was originally intended to be installed in ISS Node 3. The OGS rack delivery was accelerated, and it was launched to ISS in July of 2006 and installed in the US Laboratory Module. Various modification kits were installed to provide its interfaces, and the OGS was first activated in July of 2007 for 15 hours, In October of 2007 it was again activated for 76 hours with varied production rates and day/night cycling. Operational time in each instance was limited by the quantity of feedwater in a Payload Water Reservoir (PWR) bag. Feedwater will be provided by PWR bag until the USOS Water Recovery System (WRS) is delivered to SS in fall of 2008. This paper will discuss operating experience and characteristics of the OGS, as well as operational issues and their resolution

Electrochemical Deposition and Characterization of Fe₃O₄ Films Produced by the Reduction of Fe(III)-triethanolamine

In this paper, we demonstrate that films of magnetite, Fe3O4, can be deposited by the electrochemical reduction of a Fe(III)-triethanolamine complex in aqueous alkaline solution. the films were deposited with a columnar microstructure and a [100] preferred orientation on stainless steel substrates. In-plane electrical transport and magnetoresistance measurements were performed on the films after they were stripped off onto glass substrates. the resistance of the films was dependent on the oxygen partial pressure. We attribute the increase in resistance in O2 and the decrease in resistance in Ar to the oxidation and reduction of grain boundaries. the decrease in resistance in an Ar atmosphere exhibited first-order kinetics, with an activation energy of 0.2 eV. the temperature dependence of the resistance showed a linear dependence of log(R) versus T-1/2, consistent with tunneling across resistive grain boundaries. a room-temperature magnetoresistance of -6.5% was observed at a magnetic field of 9 T

Search for Intrinsic Excitations in 152Sm

The 685 keV excitation energy of the first excited 0+ state in 152Sm makes it an attractive candidate to explore expected two-phonon excitations at low energy. Multiple-step Coulomb excitation and inelastic neutron scattering studies of 152Sm are used to probe the E2 collectivity of excited 0+ states in this "soft" nucleus and the results are compared with model predictions. No candidates for two-phonon K=0+ quadrupole vibrational states are found. A 2+, K=2 state with strong E2 decay to the first excited K=0+ band and a probable 3+ band member are established.Comment: 4 pages, 6 figures, accepted for publication as a Rapid Communication in Physical Review