Perturbation theory for the analysis of instability in nonlinear feedback systems.
Instability and periodic solutions in nonlinear feedback systems obtained using perturbation theory of Hale and Cesari
PERTURBATION THEORY↗
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Water Recovery System Design to Accommodate Dormant Periods for Manned Missions
Future manned missions beyond lower Earth orbit may include intermittent periods of extended dormancy. Under the NASA Advanced Exploration System (AES) project, NASA personnel evaluated the viability of the ISS Water Recovery System (WRS) to support such a mission. The mission requirement includes the capability for life support systems to support crew activity, followed by a dormant period of up to one year, and subsequently for the life support systems to come back online for additional crewed missions. Dormancy could be a critical issue due to concerns with microbial growth or chemical degradation that might prevent water systems from operating properly when the crewed mission began. As such, it is critical that the water systems be designed to accommodate this dormant period. This paper details the results of this evaluation, which include identification of dormancy issues, results of testing performed to assess microbial stability of pretreated urine during dormancy periods, and concepts for updating to the WRS architecture and operational concepts that will enable the ISS WRS to support the dormancy requirement.
Tabb, David↗
Doubly-periodic orbits in the Sun-Earth-Moon system
A series of periodic orbits in the Earth-Moon circular restricted problem of three bodies was found which is ideally suited for exploring the Earth's geomagnetic tail. The mean apsidal motion of the basic highly elliptical Earth orbit was maintained at about one degree per day by a sequence of lunar swingbys, keeping the apogees in the anti-Sun direction. The orbits were periodic in reference frames rotating at both lunar and solar rates. Apogee distances were alternately raised and lowered by the lunar swingby maneuvers. Several categories of these Sun-synchronous double lunar swingby orbits were identified. The strength and flexibility of this trajectory concept was demonstrated with real world simulations.
Farohar, R.↗
Cascaded systems and methods for controlling energy use during a demand limiting period
A cascaded control system is configured to control power consumption of a building during a demand limiting period. The cascaded control system includes an energy use setpoint generator and a feedback controller. The energy use setpoint generator is configured to use energy pricing data and measurements of a variable condition within the building to generate an energy use setpoint during the demand limiting period. The feedback controller is configured to use a difference between the energy use setpoint and a measured energy use to generate a control signal for building equipment that operate to affect the variable condition within the building during the demand limiting period.
Wenzel, Michael J.↗
Asymptotically almost periodic solutions of a nonlinear Volterra system
Nonlinear Volterra integral equation system solution using almost periodic forced oscillations
Miller, R. K.↗
On the nonlinear stability of the unsteady, viscous flow of an incompressible fluid in a curved pipe
The stability of the flow of an incompressible, viscous fluid through a pipe of circular cross-section curved about a central axis is investigated in a weakly nonlinear regime. A sinusoidal pressure gradient with zero mean is imposed, acting along the pipe. A WKBJ perturbation solution is constructed, taking into account the need for an inner solution in the vicinity of the outer bend, which is obtained by identifying the saddle point of the Taylor number in the complex plane of the cross-sectional angle co-ordinate. The equation governing the nonlinear evolution of the leading order vortex amplitude is thus determined. The stability analysis of this flow to periodic disturbances leads to a partial differential system dependent on three variables, and since the differential operators in this system are periodic in time, Floquet theory may be applied to reduce this system to a coupled infinite system of ordinary differential equations, together with homogeneous uncoupled boundary conditions. The eigenvalues of this system are calculated numerically to predict a critical Taylor number consistent with the analysis of Papageorgiou. A discussion of how nonlinear effects alter the linear stability analysis is also given, and the nature of the instability determined.
Shortis, Trudi A.↗
System III variations in apparent distance of Io plasma torus from Jupiter
System III variations in apparent distance of the Io plasma torus from Jupiter are examined on the basis of data obtained from UVS scans across Jupiter's satellite system. The displacement of the dawn and dusk ansae are found to be unexpectedly complex. The displacements are unequal and both ansae are in motion with the motion of the approaching ansa being the lesser of the two. The radial motions, as measured from either the center of Jupiter or the offset-tilted dipole, are of unequal magnitude and have the System III periodicity. It is concluded that the cross-tail electric field that causes these torus motions is concentrated on the dusk ansa, varied with the System III period, and shows magnetic-anomaly phase control. It is found that the dawn-dust asymmetry in brightness is not explained simply by the cross-tail electric field. It is concluded that there is a heating mechanism that causes the dusk side of the Io plasma torus to be brighter than the dawn side.
Dessler, A. J.↗
Annual survey of spaceflight safety systems - 10th supplement /Survey period: July 1979-June 1980/
The survey summarizes 15 papers whose topics represent significant safety developments reported between July 1979 and June 1980 in connection with spaceflight. The majority of the papers address the Space Shuttle mission (control-system software modification; abort procedures; Vandenberg AFB launch operations; assembly and repair of the Orbiter's Thermal Protection System; flight hardware). One paper describes a procedure aiding Space Transportation System (STS) payload organizations in complying with safety requirements established by NASA. Spacecraft cabin environments, collision avoidance in near-earth space, and intercept and rendezvous charts are other topics of discussion. The survey also includes two papers outlining the European and Chinese approaches to astronaut selection and training.
Brown, N. E.↗
Tunable fragile topology in Floquet systems
We extend the notion of fragile topology to periodically driven systems. Here we demonstrate driving-induced fragile topology in two different models, namely, the Floquet honeycomb model and the Floquet π-flux square-lattice model. In both cases, we discover a rich phase diagram that includes Floquet fragile topological phases protected by crystalline rotation or mirror symmetries, Floquet Chern insulators, and trivial atomic phases, with distinct boundary features. Remarkably, the transitions between different phases can be feasibly achieved by simply tuning the driving amplitudes, which is a unique feature of driving-enabled topological phenomena. Moreover, corner-localized fractional charges are identified as a “smoking-gun” signal of fragile topology in our systems. Our work paves the way for studying and realizing fragile topology in Floquet systems.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Interuser Interference Analysis for Direct-Sequence Spread-Spectrum Systems Part I: Partial-Period Cross-Correlation
This presentation discusses an analysis approach to evaluate the interuser interference for Direct-Sequence Spread-Spectrum (DSSS) Systems for Space Network (SN) Users. Part I of this analysis shows that the correlation property of pseudo noise (PN) sequences is the critical factor which determines the interuser interference performance of the DSSS system. For non-standard DSSS systems in which PN sequence s period is much larger than one data symbol duration, it is the partial-period cross-correlation that determines the system performance. This study reveals through an example that a well-designed PN sequence set (e.g. Gold Sequence, in which the cross-correlation for a whole-period is well controlled) may have non-controlled partial-period cross-correlation which could cause severe interuser interference for a DSSS system. Since the analytical derivation of performance metric (bit error rate or signal-to-noise ratio) based on partial-period cross-correlation is prohibitive, the performance degradation due to partial-period cross-correlation will be evaluated using simulation in Part II of this analysis in the future.
Ni, Jianjun (David)↗
Stability of certain periodic solutions of a forced system with hysteresis
Many physical systems exhibit the phenomenon of nonlinear hysteresis when the amplitude of oscillation exceeds some small limit. It was shown that under certain conditions there are periodic motions of such a system with small forcing which are near the largest periodic motion of the corresponding unforced system. Conditions for the stability of these periodic motions are derived.
Drew, J. H.↗
Annual survey of spaceflight safety systems: 11th supplement. Survey period - July 1980-June 1981
Reports in the field of space flight safety applicable to current and future operational space activities which appeared between July 1980 and June 1981 are surveyed. Subjects in the area of flight rescue and safety during launch, on-orbit, reentry and landing phases include the major activities and findings of the first Shuttle test flight, a slidewire system for emergency egress from the Space Shuttle on the launch pad, and the testing of the Spacelab engineering model. In the area of human capabilities and crew roles, attention is given to reports of repairs to the Salyut 6 space station made by a Soyuz crew, and an assessment of weightlessness effects on space worker health and safety. Safety requirements for STS payloads including pressure vessels, and the Orbiter window system and for spacecraft testing are also presented, along with those for a television system to aid in monitoring astronaut extravehicular activities. For the operation of large space structures, reports include EVA equipment for satellite servicing and the safety aspects of connectors used in construction. Finally, attention is given to safety-related criteria in a study of Shuttle interactions with the proposed Space Operations Center.
Brown, N. E.↗
Transfer of training on manual control systems differing in short period frequency and damping characteristics
Each of four groups of 16 subjects was trained on one of four compensatory tracking tasks that differed with regard to short period natural frequency and damping characteristics. After completion of the training sessions, the members of each group either transferred to a task on which they had not been trained or continued with their original task. Analysis of the training data indicated that relative task difficulty was largely determined by system damping which, however, had little effect on the amount of transfer during the transfer trials. The effect of system frequency was essentially reversed, and a marked interaction between training and transfer frequencies was observed in the transfer data. Similar results were obtained both with relative error scores and transinformation scores. Positive transfer was exhibited by most of the groups when they transferred to tasks on which they had not been trained.
Lincoln, R. S.↗
Coarse-graining Hamiltonian systems using WSINDy
Abstract Weak form equation learning and surrogate modeling has proven to be computationally efficient and robust to measurement noise in a wide range of applications including ODE, PDE, and SDE discovery, as well as in coarse-graining applications, such as homogenization and mean-field descriptions of interacting particle systems. In this work we extend this coarse-graining capability to the setting of Hamiltonian dynamics which possess approximate symmetries associated with timescale separation. A smooth $$\varepsilon$$ ε -dependent Hamiltonian vector field $$X_\varepsilon$$ X ε possesses an approximate symmetry if the limiting vector field $$X_0=\lim _{\varepsilon \rightarrow 0}X_\varepsilon$$ X 0 = lim ε → 0 X ε possesses an exact symmetry. Such approximate symmetries often lead to the existence of a Hamiltonian system of reduced dimension that may be used to efficiently capture the dynamics of the symmetry-invariant dependent variables. Deriving such reduced systems, or approximating them numerically, is an ongoing challenge. We demonstrate that WSINDy can successfully identify this reduced Hamiltonian system in the presence of large perturbations imparted in the $$\varepsilon >0$$ ε > 0 regime, while remaining robust to extrinsic noise. This is significant in part due to the nontrivial means by which such systems are derived analytically. WSINDy naturally preserves the Hamiltonian structure by restricting to a trial basis of Hamiltonian vector fields. The methodology is computationally efficient, often requiring only a single trajectory to learn the global reduced Hamiltonian, and avoiding forward solves in the learning process. In this way, we argue that weak-form equation learning is particularly well-suited for Hamiltonian coarse-graining. Using nearly-periodic Hamiltonian systems as a prototypical class of systems with approximate symmetries, we show that WSINDy robustly identifies the correct leading-order system, with dimension reduced by at least two, upon observation of the relevant degrees of freedom. While our main contribution is computational, we also provide a contribution to the literature on averaging theory by proving that first-order averaging at the level of vector fields preserves Hamiltonian structure in nearly-periodic Hamiltonian systems. This provides theoretical justification for our approach as WSINDy’s computations occur at the level of Hamiltonian vector fields. We illustrate the efficacy of our proposed method using physically relevant examples, including coupled oscillator dynamics, the Hénon–Heiles system for stellar motion within a galaxy, and the dynamics of charged particles.
97 MATHEMATICS AND COMPUTING↗
Computer program offers new method for constructing periodic orbits in nonlinear dynamical systems
Computer program uses an iterative method to construct precisely periodic orbits which dynamically approximate solutions that converge to precise dynamical solutions in the limit of the sequence. The method used is a modification of the generalized Newton-Raphson algorithm used in analyzing two point boundary problems.
Bennett, A. G.↗
Data system interprobability
Software was developed and tested which allows an end-user to build a book data object in an interactive fashion. The electronic book model was developed for the Library front-end of the DAVID (Distributed Access View Integrated Database) system. It is a complex data object which is capable of holding data of different types and formats. After the task, the plan was to assess the Book model and investigate the possibility of it serving as a knowledge base for a expert system front-end to the DAVID system. For the rest of the fellowship period, data system interoperability was examined. Specifically, a plan was prepared titled Implementations of the Land Analysis System (LAS) to Meet UNEP/GRID Requirements. This plan is aimed at reaching the goal of building one virtual global change information system which will link existing and future data systems allowing earth and space scientists to learn about, locate, access, and correlate data of interest regardless of its physical location. The plan proposed the construction of a master directory (MD) for the European data systems that is equivalent in structure to NASA's MD. The MD is to contain brief, high-level information about existing Earth and space science data sets sufficient for a user to know where data of interest reside and how to go about getting additional information. The plan also outlined the tasks that would be involved to electronically connect the MD system to the various discipline data systems (e.g., LAS) in order to achieve general interroperabilty, that is, the abilty to perform cross-systems searches and exchange of and access to distributed information.
Wakim, Nagi T.↗
Assimilating All-Sky Microwave Radiance Data to Improve NASA GEOS Forecasts and Analysis
The NASA Global Modeling and Assimilation Office (GMAO) has been pursuing efforts to utilize all-sky (clear+cloudy+precipitating) MW radiance data and has developed a system to assimilate all-sky GPM Microwave Imager (GMI) radiance data in the Goddard Earth Observing System (GEOS) during the last PMM funding period. The system provides additional constraints on the analysis process near the storm regions and adjusts the geophysical parameters such as precipitation, cloud, moisture, surface pressure, and wind by combining information from GMI radiance measurements and model forecasts in an optimal manner. The system proved that assimilating the GMI all-sky radiance data improve the GEOS atmospheric analyses and forecasts. This all-sky data framework has been included in the GEOS Forward Processing (FP) system since July 11, 2018 and assimilates all-sky GMI data in real-time for GEOS global analysis and forecast production at the GMAO. We are currently extending this all-sky GMI radiance data assimilation system to assimilate more all-sky MW radiance data from other sensors such as the Microwave Humidity Sounder (MHS), the Advanced Technology Microwave Sounder (ATMS), the Special Sensor Microwave Imager/Sounder (SSMIS), Advanced Microwave Scanning Radiometer 2 (AMSR2), and the Sounder for Atmospheric Profiling of Humidity in the Intertropics by Radiometery (SAPHIR) onboard the GPM constellation spacecrafts. Preliminary results from this extended all-sky system show increased benefit from cloud- and precipitation-affected MW radiances with much larger spatial and temporal coverages compared to the all-sky system assimilating GMI alone and improved GEOS forecast skills especially for lower tropospheric humidity fields.
Kim, Min-Jeong↗
Periodic intensity variations in sulfur emissions from the Io plasma torus
In November and December 1988, we acquired 157 spectra of (S II) lambda 6731 emissions from the Io plasma torus with a Fabry-Perot interferometer at the McMath-Pierce Solar Telescope facility on Kitt Peak. A major goal of this experiment was to extend our earlier studies of intensity variations in the plasma torus. Our earlier analysis (F. L. Roesler, F. Scherb, and R. J. Oliversen, 1984, of (S III) lambda 9531 emission spectra acquired in April 1982 had shown that the intensity of torus emissions varied periodically with a period of 10.20 +/- 0.06 hr (1-sigma uncertainty level), slightly longer than Jupiter's System 3 rotational period of 9.925 hr. We present here an reanalysis of our 1982 data revealing, in addition to the 10.20-hr period, a clear secondary periodicity at 9.95 +/- 0.906 hr. By constrast, we show that our new (S II) lambda 6731 data have a single period of 10.14 +/- 0.03 hr. which is neither the System 3 period nor the proposed 'System 4' period of 10.224 hr.
Woodward, R. Carey, Jr.↗