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Computational Workbench for Multibody Dynamics

PyCraft is a computer program that provides an interactive, workbenchlike computing environment for developing and testing algorithms for multibody dynamics. Examples of multibody dynamic systems amenable to analysis with the help of PyCraft include land vehicles, spacecraft, robots, and molecular models. PyCraft is based on the Spatial-Operator- Algebra (SOA) formulation for multibody dynamics. The SOA operators enable construction of simple and compact representations of complex multibody dynamical equations. Within the Py-Craft computational workbench, users can, essentially, use the high-level SOA operator notation to represent the variety of dynamical quantities and algorithms and to perform computations interactively. PyCraft provides a Python-language interface to underlying C++ code. Working with SOA concepts, a user can create and manipulate Python-level operator classes in order to implement and evaluate new dynamical quantities and algorithms. During use of PyCraft, virtually all SOA-based algorithms are available for computational experiments.

Edmonds, Karina↗

Proceedings of the 20th International Symposium on Space Flight Dynamics

Topics include: Measuring Image Navigation and Registration Performance at the 3-Sigma Level Using Platinum Quality Landmarks; Flight Dynamics Performances of the MetOp A Satellite during the First Months of Operations; Visual Navigation - SARE Mission; Determining a Method of Enabling and Disabling the Integral Torque in the SDO Science and Inertial Mode Controllers; Guaranteeing Pointing Performance of the SDO Sun-Pointing Controllers in Light of Nonlinear Effects; SDO Delta H Mode Design and Analysis; Observing Mode Attitude Controller for the Lunar Reconnaissance Orbiter; Broken-Plane Maneuver Applications for Earth to Mars Trajectories; ExoMars Mission Analysis and Design - Launch, Cruise and Arrival Analyses; Mars Reconnaissance Orbiter Aerobraking Daily Operations and Collision Avoidance; Mars Reconnaissance Orbiter Interplanetary Cruise Navigation; Motion Parameters Determination of the SC and Phobos in the Project Phobos-Grunt; GRAS NRT Precise Orbit Determination: Operational Experience; Orbit Determination of LEO Satellites for a Single Pass through a Radar: Comparison of Methods; Orbit Determination System for Low Earth Orbit Satellites; Precise Orbit Determination for ALOS; Anti-Collision Function Design and Performances of the CNES Formation Flying Experiment on the PRISMA Mission; CNES Approaching Guidance Experiment within FFIORD; Maneuver Recovery Analysis for the Magnetospheric Multiscale Mission; SIMBOL-X: A Formation Flying Mission on HEO for Exploring the Universe; Spaceborne Autonomous and Ground Based Relative Orbit Control for the TerraSAR-X/TanDEM-X Formation; First In-Orbit Experience of TerraSAR-X Flight Dynamics Operations; Automated Target Planning for FUSE Using the SOVA Algorithm; Space Technology 5 Post-Launch Ground Attitude Estimation Experience; Standardizing Navigation Data: A Status Update; and A Study into the Method of Precise Orbit Determination of a HEO Orbiter by GPS and Accelerometer.

Woodard, Mark↗

Reduced-order modeling on a near-term quantum computer

Quantum computing is an advancing area of research in which computer hardware and algorithms are developed to take advantage of quantum mechanical phenomena. In recent studies, quantum algorithms have shown promise in solving linear systems of equations as well as systems of linear ordinary differential equations (ODEs) and partial differential equations (PDEs). Reducedorder modeling (ROM) algorithms for studying fluid dynamics have shown success in identifying linear operators that can describe flowfields, where dynamic mode decomposition (DMD) is a particularly useful method in which a linear operator is identified from data. In this work, DMD is reformulated as an optimization problem to propagate the state of the linearized dynamical system on a quantum computer. This reformulation was chosen as a means of facilitating implementation on a near-term quantum computer. Quadratic unconstrained binary optimization (QUBO), a technique for optimizing quadratic polynomials in binary variables, allows for quantum annealing algorithms to be applied. A quantum circuit model (quantum approximation optimization algorithm, QAOA) is utilized to obtain predictions of the state trajectories. Results are shown for the quantum-ROM predictions for flow over a 2D cylinder at Re = 220 and flow over a NACA0009 airfoil at Re = 500 and α = 15°. The quantum-ROM predictions are found to depend on the number of bits utilized for a fixed point representation and the truncation level of the DMD model. Comparisons with DMD predictions from a classical computer algorithm are made, as well as an analysis of the computational complexity and prospects for future, more fault-tolerant quantum computers.

97 MATHEMATICS AND COMPUTING↗

Managing Data in a GIS Environment

A Geographic Information System (GIS) is a computer-based system that enables capture, modeling, manipulation, retrieval, analysis and presentation of geographically referenced data. A GIS operates in a dynamic environment of spatial and temporal information. This information is held in a database like any other information system, but performance is more of an issue for a geographic database than a traditional database due to the nature of the data. What distinguishes a GIS from other information systems is the spatial and temporal dimensions of the data and the volume of data (several gigabytes). Most traditional information systems are usually based around tables and textual reports, whereas GIS requires the use of cartographic forms and other visualization techniques. Much of the data can be represented using computer graphics, but a GIS is not a graphics database. A graphical system is concerned with the manipulation and presentation of graphical objects whereas a GIS handles geographic objects that have not only spatial dimensions but non-visual, i e., attribute and components. Furthermore, the nature of the data on which a GIS operates makes the traditional relational database approach inadequate for retrieving data and answering queries that reference spatial data. The purpose of this paper is to describe the efficiency issues behind storage and retrieval of data within a GIS database. Section 2 gives a general background on GIS, and describes the issues involved in custom vs. commercial and hybrid vs. integrated geographic information systems. Section 3 describes the efficiency issues concerning the management of data within a GIS environment. The paper ends with a summary of the main concerns of this paper.

Beltran, Maria↗

Artificial Intelligence-Driven Management of Sustainable Energy Resources: Visibility, Operation, and Control

The rapid global transition toward sustainable energy resources (SERs) is reshaping how modern power systems are observed, optimized, and controlled. While SERs have significantly advanced decarbonization, their weather dependence, variability, and inverter-dominated characteristics challenge traditional, centralized, and deterministic grid operation. At the same time, the proliferation of high-resolution data from inverters, smart meters, and sensors offers unprecedented visibility into system dynamics. Yet, it also exceeds the analytical capability of conventional model-based approaches. Artificial intelligence (AI) provides a new foundation for addressing these challenges by bridging physical laws with data-driven learning, enabling accurate state awareness, adaptive operation, and coordinated control across distributed assets. This article examines how AI transforms the management of SER-rich power systems along three critical dimensions: 1) enhancing visibility by inferring behind-the-meter (BTM) activities, assessing SER flexibility, and reconstructing system states from sparse or noisy measurements; 2) improving operation through AI-enhanced SER service provision, volt/var control (VVC), and dynamic operating envelopes (DOE) for efficiency and security; and 3) advancing control by embedding learning-based intelligence into inverter coordination, voltage and frequency regulation, and long-term dispatch. Together, these developments reveal how AI can convert the variability of SERs from an operational challenge into a source of flexibility, resilience, and intelligence, paving the way toward sustainable, adaptive, and self-optimizing power systems.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Spatial operator approach to flexible manipulator inverse and forward dynamics

This study extends to flexible multibody manipulators the recent results of the author on the use of spatially recursive filtering and smoothing techniques for robot arm dynamics. The configuration analyzed is that of a mechanical system of flexible bodies joined together by articulated joints. The inverse and forward dynamics problems are solved using the techniques of spatially recursive Kalman filtering and smoothing. The algorithms are easily developed using a set of identities associated with mass matrix factorization and inversion. The identities are easily derived using a spatial operator algebra developed by the author.

Rodriguez, G.↗

Stabilizing dynamic subsea power cables using Bi-stable nonlinear energy sinks

This study investigates vibration mitigation of dynamic subsea cables through passive bi-stable nonlinear energy sinks (B-NESs). These devices suppress vibration energy in a broadband way, and can be regarded as extensions of classical linear tuned mass dampers (TMDs) which are narrowband devices. Through the open-source MoorDyn library, we simulated the vibrations of a vertical subsea cable equipped with a set of B-NESs. Multi-objective optimization was performed to detect the B-NES parameters for optimal mitigation of the cable vibrations. Advanced signal processing verified the efficacy of the optimized B-NESs not only to rapidly absorb and locally dissipate vibration energy, but also to nonlinearly scatter vibration energy from low to high frequencies within the cable itself. This last feature is especially beneficial for vibration mitigation of the undersea cable, as at higher frequencies the cable vibrations exhibit drastically reduced amplitudes and are more effectively dissipated by inherent structural damping and hydrodynamic radiation damping. This contrasts with traditional TMDs which can mitigate vibration only at a single frequency. Furthermore, our robustness study confirms the B-NES's effectiveness under even varying environmental conditions. Overall, the B-NES's capacity for broadband vibration mitigation renders it a promising retrofit solution for improving the performance and operational safety of dynamic power cables in offshore wind farms and other marine applications.

17 WIND ENERGY↗

Solar Dynamics Observatory Guidance, Navigation, and Control System Overview

The Solar Dynamics Observatory (SDO) was designed and built at the Goddard Space Flight Center, launched from Cape Canaveral on February 11, 2010, and reached its final geosynchronous science orbit on March 16, 2010. The purpose of SDO is to observe the Sun and continuously relay data to a dedicated ground station. SDO remains Sun-pointing throughout most of its mission for the instruments to take measurements of the Sun. The SDO attitude control system (ACS) is a single-fault tolerant design. Its fully redundant attitude sensor complement includes sixteen coarse Sun sensors (CSSs), a digital Sun sensor (DSS), three two-axis inertial reference units (IRUs), and two star trackers (STs). The ACS also makes use of the four guide telescopes included as a part of one of the science instruments. Attitude actuation is performed using four reaction wheels assemblies (RWAs) and eight thrusters, with a single main engine used to provide velocity-change thrust for orbit raising. The attitude control software has five nominal control modes, three wheel-based modes and two thruster-based modes. A wheel-based Safehold running in the attitude control electronics box improves the robustness of the system as a whole. All six modes are designed on the same basic proportional-integral-derivative attitude error structure, with more robust modes setting their integral gains to zero. This paper details the final overall design of the SDO guidance, navigation, and control (GN&C) system and how it was used in practice during SDO launch, commissioning, and nominal operations. This overview will include the ACS control modes, attitude determination and sensor calibration, the high gain antenna (HGA) calibration, and jitter mitigation operation. The Solar Dynamics Observatory mission is part of the NASA Living With a Star program, which seeks to understand the changing Sun and its effects on the Solar System, life, and society. To this end, the SDO spacecraft carries three Sun-observing instruments: Helioseismic and Magnetic Imager (HMI), led by Stanford University; Atmospheric Imaging Assembly (AIA), led by Lockheed Martin Space and Astrophysics Laboratory; and Extreme Ultraviolet Variability Experiment (EVE), led by the University of Colorado. The basic mission is to observe the Sun for a very high percentage of the 5-year mission (10-year goal) with long stretches of uninterrupted observations and with constant, high-data-rate transmission to a dedicated ground station to be located in White Sands, New Mexico. These goals guided the design of the spacecraft bus that will carry and service the three-instrument payload. Overarching design goals for the bus are geosynchronous orbit, near-constant Sun observations with the ability to fly through eclipses, and constant HGA contact with the dedicated ground station. A three-axis stabilized ACS is needed both to point at the Sun accurately and to keep the roll about the Sun vector correctly positioned with respect to the solar north pole. This roll control is especially important for the magnetic field imaging of HM I. The mission requirements have several general impacts on the ACS design. Both the AIA and HMI instruments are very sensitive to the blurring caused by jitter. Each has an image stabilization system (ISS) with some ability to filter out high frequency motion, but below the bandwidth of the ISS the control system must compensate for disturbances within the ACS bandwidth or avoid exciting jitter at higher frequencies. Within the ACS bandwidth, the control requirement imposed by AIA is to place the center of the solar disk no more than 2 arc sec, 3 , from a body-defined target based on one of the GTs that accompany the instrument. This body-defined target, called the science reference boresight (SRB), was determined from the postlaunch orientation of the GTs by averaging the bounding telescope boresights for pitch to get a pitch SRB coordinate, and by averaging the bounding boresights for yaw toet the yaw SRB coordinate. The location of this SRB in the 0.5-deg field-of-view for each GT then becomes the central target for each telescope; one GT is selected for use as the ACS controlling guide telescope (CGT) at any given time. Fine Sun-pointing is effected based on this SRB for all three instruments when the Sun is within the linear range of the CGT. In addition to limiting jitter, HMI science requires averaging several observations, making the instrument sensitive to low frequency motion that induces differential motion between each observation. This requires the spacecraft attitude to be stable about the roll axis to approximately 10 arcsec over a ten-minute period. Instrument calibrations require that the spacecraft point the SRB up to 2.5 degrees in pitch and yaw away from the center of the Sun, placing the Sun outside the field-of-view of the guide telescopes. In such instances, when the GTs cannot provide the definitive target for the ACS, on-board attitude determination combined with ephemeris prediction of the Sun direction must provide the definitive target. EVE is capable of observing the Sun with less dependence on attitude control. However, the ground data processing needs for calibrations result in the most strict attitude knowledge requirements for the mission: [35,70,70] arcsec, 3 , of knowledge with respect to the center of the solar disk. In addition to driving the ACS sensor selection, the knowledge requirements, which have their effect primarily during Inertial mode calibrations, drive the accuracy requirements for the solar ephemeris. The need to achieve and maintain geosynchronous orbit (GEO) drove the need for high-efficiency propulsive systems and appropriate attitude control. The main engine provided high specific impulse for the maneuvers to attain GEO, while the smaller ACS thrusters managed the disturbance torques of the larger engine and provided the capability for much smaller adjustment burns on orbit. SDO s large solar profile means that solar radiation pressure is a large torque disturbance, and the momentum buildup from this disturbance and the GEO altitude drives the ACS to use thrusters to manage vehicle momentum. The demanding data capture budget for the mission, however, requires SDO to avoid frequent thruster maneuvers, while concerns about on-orbit jitter restrict the maximum desired wheel speeds desired from the RWAs. The plan for on-orbit wheel speed and momentum management will be discussed as well as what is now being done in operation after the jitter environment was characterized. The SDO ACS hardware complement is single-fault tolerant. Two main processors carry virtually identical copies of the command and data handling and ACS software, and two identical attitude control electronics (ACE) boxes carry Coldfire processors with contingency ACS software and other hardware interface cards; the ACE structure allows reaction wheels to be commanded by the Sun-pointing Safehold independent of the Mil Std 1553 data bus. The sixteen Adcole CSSs are grouped into primary and backup sets of eight sensors, each set providing the ability to calculate a sun vector. Each set of eight eyes provides full 4 -steradian coverage. The Adcole DSS comprises an optics head and a separate electronics box providing a 1553 data interface. The electronics box is mounted inside the Faraday cage created by the spacecraft bus module. The DSS head with its 32- deg square FOV is mounted on the instrument module with its boresight along the spacecraft X axis, nearly aligned with the Sun during observations. Adcole has designed the DSS calibration parameters so that the accuracy is 0.24 arcminutes within 10 deg of the boresight, and diminishes to 3 arcminutes as the Sun moves towards the edges of its FOV . This DSS calibration scheme provides higher accuracy attitude determination over the range of the instrument calibration maneuvers.

Morgenstern, Wendy M.↗

Measurement of hand dynamics in a microsurgery environment: Preliminary data in the design of a bimanual telemicro-operation test bed

Data describing the microsurgeon's hand dynamics was recorded and analyzed in order to provide an accurate model for the telemicrosurgery application of the Bimanual Telemicro-operation Test Bed. The model, in turn, will guide the development of algorithms for the control of robotic systems in bimanual telemicro-operation tasks. Measurements were made at the hand-tool interface and include position, acceleration and force between the tool-finger interface. Position information was captured using an orthogonal pulsed magnetic field positioning system resulting in measurements in all six degrees-of-freedom (DOF). Acceleration data at the hands was obtained using accelerometers positioned in a triaxial arrangement on the back of the hand allowing measurements in all three cartesian-coordinate axes. Force data was obtained by using miniature load cells positioned between the tool and the finger and included those forces experienced perpendicular to the tool shaft and those transferred from the tool-tissue site. Position data will provide a minimum/maximum reference frame for the robotic system's work space or envelope. Acceleration data will define the response times needed by the robotic system in order to emulate and subsequently outperform the human operator's tool movements. The force measurements will aid in designing a force-reflective, force-scaling system as well as defining the range of forces the robotic system will encounter. All analog data was acquired by a 16-channel analog-to-digital conversion system residing in a IBM PC/AT-compatible computer at the Center's laboratory. The same system was also used to analyze and present the data.

Charles, Steve↗

Assessment of flying-quality criteria for air-breathing aerospacecraft

A study of flying quality requirements for air breathing aerospacecraft gives special emphasis to the unusual operational requirements and characteristics of these aircraft, including operation at hypersonic speed. The report considers distinguishing characteristics of these vehicles, including dynamic deficiencies and their implications for control. Particular emphasis is given to the interaction of the airframe and propulsion system, and the requirements for dynamic systems integration. Past operational missions are reviewed to define tasks and maneuvers to be considered for this class of aircraft. Areas of special concern with respect to vehicle dynamics and control are identified. Experience with the space shuttle orbiter is reviewed with respect to flight control system mechanization and flight experience in approach and landing flying qualities for the National Aerospace Plane (NASP).

Mcruer, Duane T.↗

Investigation and Feasibility Assessment of TOPAZ-2 Derivations for Space Power Applications

The ability to provide continuous power at significant levels is of utmost importance for many space missions, from simple satellite operations to manned Mars missions. One of the main problems faced in delivering solar or chemical space power in the tens of kW range, is the increasingly massive nature of the power source and the costs associated with its launch, operation and maintenance. A national program had been initiated to study the feasibility of using certain advanced technologies in developing an efficient lightweight space power source. The starting point for these studies has been the Russian TOPAZ-2 space reactor system, with the ultimate goal to aid in the development of a TOPAZ-2 derivative which will be ready for flight by the year 2000. The main objective of this project has been to perform feasibility assessment and trade studies which would allow the development of an advanced space nuclear power system based on the in-core thermionic fuel element technology currently used in the Russian TOPAZ-2 reactor. Two of the important considerations in developing the concept are: (1) compliance of the current TOPAZ-2 and of any advanced designs with U.S. nuclear safety expectations, and (2) compliance of the design with the seven years lifetime requirement. The project was composed of two major phases. The initial phase of the project has concentrated on understanding the TOPAZ-2 thermionic reactor in sufficient detail to allow several follow-on tasks. The primary interest during this first phase has been given on identifying the potential of the TOPAZ-2 design for further improvements. The second phase of the project has focused on the feasibility of a TOPAZ-2 system capable of delivering 30-50 kWe. Towards the elimination of single-point failures in the load voltage regulation system an active voltage regulator has been designed to be used in conjunction with the available shunt load voltage regulator. The possible use of a dual-loop, model-based adaptive control system for load-following in the TOPAZ-2 has also been investigated. The objective of this fault-tolerant, autonomous control system is to deliver the demanded electric power at the desired voltage level, by appropriately manipulating the neutron power through the control drums. As a result, sufficient thermal power is produced to meet the required demand in the presence of dynamically changing system operating conditions and potential sensor failures. The designed controller is proposed for use in combination with the currently available shunt regulators, or as a back-up controller when other means of power system control, including some of the sensors, fail.

Parlos, Alexander G.↗

Verification Challenges of Dynamic Testing of Space Flight Hardware

The Six Degree-of-Freedom Dynamic Test System (SDTS) is a test facility at the National Aeronautics and Space Administration (NASA) Johnson Space Center in Houston, Texas for performing dynamic verification of space structures and hardware. Some examples of past and current tests include the verification of on-orbit robotic inspection systems, space vehicle assembly procedures and docking/berthing systems. The facility is able to integrate a dynamic simulation of on-orbit spacecraft mating or demating using flight-like mechanical interface hardware. A force moment sensor is utilized for input to the simulation during the contact phase, thus simulating the contact dynamics. While the verification of flight hardware presents many unique challenges, one particular area of interest is with respect to the use of external measurement systems to ensure accurate feedback of dynamic contact. There are many commercial off-the-shelf (COTS) measurement systems available on the market, and the test facility measurement systems have evolved over time to include two separate COTS systems. The first system incorporates infra-red sensing cameras, while the second system employs a laser interferometer to determine position and orientation data. The specific technical challenges with the measurement systems in a large dynamic environment include changing thermal and humidity levels, operational area and measurement volume, dynamic tracking, and data synchronization. The facility is located in an expansive high-bay area that is occasionally exposed to outside temperature when large retractable doors at each end of the building are opened. The laser interferometer system, in particular, is vulnerable to the environmental changes in the building. The operational area of the test facility itself is sizeable, ranging from seven meters wide and five meters deep to as much as seven meters high. Both facility measurement systems have desirable measurement volumes and the accuracies vary within the respective volumes. In addition, because this is a dynamic facility with a moving test bed, direct line-of-sight may not be available at all times between the measurement sensors and the tracking targets. Finally, the feedback data from the active test bed along with the two external measurement systems must be synchronized to allow for data correlation. To ensure the desired accuracy and resolution of these systems, calibration of the systems must be performed regularly. New innovations in sensor technology itself are periodically incorporated into the facility s overall measurement scheme. In addressing the challenges of the measurement systems, the facility is able to provide essential position and orientation data to verify the dynamic performance of space flight hardware.

Winnitoy, Susan↗

Intent inferencing by an intelligent operator's associate - A validation study

In the supervisory control of a complex, dynamic system, one potential form of aiding for the human operator is a computer-based operator's associate. The design philosophy of the operator's associate is that of 'amplifying' rather than automating human skills. In particular, the associate possesses understanding and control properties. Understanding allows it to infer operator intentions and thus form the basis for context-dependent advice and reminders; control properties allow the human operator to dynamically delegate individual tasks or subfunctions to the associate. This paper focuses on the design, implementation, and validation of the intent inferencing function. Two validation studies are described which empirically demonstrate the viability of the proposed approach to intent inferencing.

Jones, Patricia M.↗

Analysis of transistor and snubber turn-off dynamics in high-frequency high-voltage high-power converters

Dc to dc converters which operate reliably and efficiently at switching frequencies high enough to effect substantial reductions in the size and weight of converter energy storage elements are studied. A two winding current or voltage stepup (buck boost) dc-to-dc converter power stage submodule designed to operate in the 2.5-kW range, with an input voltage range of 110 to 180 V dc, and an output voltage of 250 V dc is emphasized. In order to assess the limitations of present day component and circuit technologies, a design goal switching frequency of 10 kHz was maintained. The converter design requirements represent a unique combination of high frequency, high voltage, and high power operation. The turn off dynamics of the primary circuit power switching transistor and its associated turn off snubber circuitry are investigated.

Wilson, P. M.↗

Robustness of continuous-time adaptive control algorithms in the presence of unmodeled dynamics

This paper examines the robustness properties of existing adaptive control algorithms to unmodeled plant high-frequency dynamics and unmeasurable output disturbances. It is demonstrated that there exist two infinite-gain operators in the nonlinear dynamic system which determines the time-evolution of output and parameter errors. The pragmatic implications of the existence of such infinite-gain operators is that: (1) sinusoidal reference inputs at specific frequencies and/or (2) sinusoidal output disturbances at any frequency (including dc), can cause the loop gain to increase without bound, thereby exciting the unmodeled high-frequency dynamics, and yielding an unstable control system. Hence, it is concluded that existing adaptive control algorithms as they are presented in the literature referenced in this paper, cannot be used with confidence in practical designs where the plant contains unmodeled dynamics because instability is likely to result. Further understanding is required to ascertain how the currently implemented adaptive systems differ from the theoretical systems studied here and how further theoretical development can improve the robustness of adaptive controllers.

Rohrs, C. E.↗

Heterogeneous Mixtures of Dictionary Functions to Approximate Subspace Invariance in Koopman Operators: Why Deep Koopman Operators Work

Abstract Koopman operators model nonlinear dynamics as a linear dynamic system acting on a nonlinear function as the state. This nonstandard state is often called a Koopman observable and is usually approximated numerically by a superposition of functions drawn from a dictionary . In a widely used algorithm, extended dynamic mode decomposition (EDMD), the dictionary functions are drawn from a fixed class of functions. Deep learning combined with EDMD has been used to learn novel dictionary functions in an algorithm called deep dynamic mode decomposition (deepDMD). The learned representation both (1) accurately models and (2) scales well with the dimension of the original nonlinear system. In this paper, we analyze the learned dictionaries from deepDMD and explore the theoretical basis for their strong performance. We explore State-Inclusive Logistic Lifting (SILL) dictionary functions to approximate Koopman observables. Error analysis of these dictionary functions show they satisfy a property of subspace approximation, which we define as uniform finite approximate closure. Typically, a Koopman dictionary’s nonlinear functions are homogeneous. In this paper, we discover that structured mixing of heterogeneous dictionary functions drawn from different classes of nonlinear functions achieve the same accuracy and dimensional scaling as the deep-learning-based deepDMD algorithm Yeung et al. ( In: 2019 American Control Conference (ACC), 2019). We specifically show this by building a heterogeneous dictionary comprised of SILL functions and conjunctive radial basis functions (RBFs). This mixed dictionary achieves similar accuracy and dimensional scaling to deepDMD with an order of magnitude reduction in parameters, while maintaining geometric interpretability. These results strengthen the viability of dictionary-based Koopman models to solving high-dimensional nonlinear learning problems.

Johnson, Charles A.↗

Further Development of the Tamped Richtmyer-Meshkov Instability Method and Application to Molybdenum Dynamic Strength Calibration and Tabulation

The high pressure and high strain rate dynamic strength of Mo is experimentally and computationally investigated in the 3–20 GPa stress, 50–600 C temperature, and 10 5 –10 6 /s strain rate regimes using a modified tamped Richtmyer-Meshkov instability (RMI) method. Modifications to the tamped RMI method include a method to determine loading states during strain, a new strength calibration function based on interface shape, and a robust uncertainty quantification method. These modifications improve fidelity of the tamped RMI method, allowing evaluation of the compensating effects of pressure hardening, strain rate hardening, strain hardening, and thermal softening. The new calibration function based on interface shape is not limited to sinusoidal corrugations and could be applied to additional interface shapes. Plate impact experiments are performed at Argonne National Laboratory’s Advanced Photon Source’s Dynamic Compression Sector operated by Washington State University (DCS), driving a planar shock front through a corrugated Mo-D 2 O or Mo-C 8 F 18 interface, forcing the corrugation to significantly deform. The extent of interfacial deformation, RMI growth, is experimentally observed using X-ray phase contrast imaging at the DCS. RMI jet lengths and jet shapes are extracted from the experimental radiographs, then used to calibrate numerical simulations performed with the Sandia National Laboratories (SNL) hydrocode CTH. Mo yield strength, Y, as a function of shock pressure, P, strain rate, $\dot{\varepsilon }$, accumulated strain, ϵ, relative volumetric compression, RD , and temperature, T , is determined for each impact experiment and presented. The calibrated Mo yield strength values range 1.2–1.8 GPa, with strength generally decreasing as the impact stress increases. This trend is likely caused by thermal softening or strain localization. The tabular yield strength versus loading condition data presented in this paper can be used to fit complex strength models.

Voorhees, T. J. [Sandia National Lab. (SNL-CA), Li↗

Resolving the Electron Plume within a Scanning Electron Microscope

Scanning electron microscopy (SEM), a century-old technique, is today a ubiquitous method of imaging the surface of nanostructures. However, most SEM detectors simply count the number of secondary electrons from a material of interest, and thereby overlook the rich material information contained within them. Here, by simple modifications to a standard SEM tool, we resolve the momentum and energy information on secondary electrons by directly imaging the electron plume generated by the electron beam of the SEM. Leveraging these spectroscopic imaging capabilities, our technique is able to image lateral electric fields across a prototypical silicon p–n junctions and to distinguish differently doped regions, even when buried beyond depths typically accessible by SEM. Intriguingly, the subsurface sensitivity of this technique reveals unexpectedly strong surface band bending within nominally passivated semiconductor structures, providing useful insights for complex layered component designs, in which interfacial dynamics dictate device operation. Further, these capabilities for noninvasive, multimodal probing of complicated electronic components are crucial in today’s electronic manufacturing but is largely inaccessible even with sophisticated techniques. These results show that seemingly simple SEM can be extended to probe complex and useful material properties.

36 MATERIALS SCIENCE↗