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At least 307 records · Page 17

Shifting the closed-loop spectrum in the optimal linear quadratic regulator problem for hereditary systems

In the optimal linear quadratic regulator problem for finite dimensional systems, the method known as an alpha-shift can be used to produce a closed-loop system whose spectrum lies to the left of some specified vertical line; that is, a closed-loop system with a prescribed degree of stability. This paper treats the extension of the alpha-shift to hereditary systems. As infinite dimensions, the shift can be accomplished by adding alpha times the identity to the open-loop semigroup generator and then solving an optimal regulator problem. However, this approach does not work with a new approximation scheme for hereditary control problems recently developed by Kappel and Salamon. Since this scheme is among the best to date for the numerical solution of the linear regulator problem for hereditary systems, an alternative method for shifting the closed-loop spectrum is needed. An alpha-shift technique that can be used with the Kappel-Salamon approximation scheme is developed. Both the continuous-time and discrete-time problems are considered. A numerical example which demonstrates the feasibility of the method is included.

Gibson, J. S.↗

Numerical algorithms for computations of feedback laws arising in control of flexible systems

Several continuous models will be examined, which describe flexible structures with boundary or point control/observation. Issues related to the computation of feedback laws are examined (particularly stabilizing feedbacks) with sensors and actuators located either on the boundary or at specific point locations of the structure. One of the main difficulties is due to the great sensitivity of the system (hyperbolic systems with unbounded control actions), with respect to perturbations caused either by uncertainty of the model or by the errors introduced in implementing numerical algorithms. Thus, special care must be taken in the choice of the appropriate numerical schemes which eventually lead to implementable finite dimensional solutions. Finite dimensional algorithms are constructed on a basis of a priority analysis of the properties of the original, continuous (infinite diversional) systems with the following criteria in mind: (1) convergence and stability of the algorithms and (2) robustness (reasonable insensitivity with respect to the unknown parameters of the systems). Examples with mixed finite element methods and spectral methods are provided.

Lasiecka, Irena↗

Computation of Transonic Flows Using Potential Methods

The proposed paper will describe the state of the art associated with numerical solution of the full or exact velocity potential equation for solving transonic, external-aerodynamic flows. The presentation will begin with a review of the literature emphasizing research activities of the past decade. Next, the various forms of the full or exact velocity potential equation, the equation's corresponding mathematical characteristics, and the derivation assumptions will be presented and described in detail. Impact of the derivation assumptions on simulation accuracy, especially with respect to shock wave capture, will be presented and discussed relative to the more complete Euler or Navier-Stokes formulations. The technical presentation will continue with a description of recently developed full potential numerical approach characteristics. This description will include governing equation nondimensionalization, physical-to-computational-domain mapping procedures, a limited description of grid generation requirements, the spatial discretization scheme, numerical implementation of boundary conditions, and the iteration scheme. The next portion of the presentation will present and discuss numerical results for several two- and three-dimensional aerodynamic applications. Included in the results section will be a discussion and demonstration of a typical grid refinement analysis for determining spatial convergence of the numerical solution and level of solution accuracy. Computer timings for a variety of full potential applications will be compared and contrasted with similar results for the Euler equation formulation. Finally. the presentation will end with concluding remarks and recommendations for future work.

Hoist, Terry L.↗

Plasma expansion characteristics of ionized clouds in the ionosphere - Macroscopic formulation

A macroscopic plasma expansion model, based on a numerical solution of the type-dependent nonlinear coupled continuity and momentum equations for background O(+) ions and several released ion species, was used to examine plasma expansion characteristics of ionized clouds in the ionosphere. Information is obtained on Ba(+), Li(+), and Ba(+) - Li(+) clouds; different cloud sizes (Gaussian half widths of 0.1, 0.5, and 1 km); cloud/background ion density ratios covering two orders of magnitude; electron/ion temperature ratios of 1, 5, and 10; and several cloud-background relative velocities along B (0, 1, 2, 4, 6, and 8 km/sec). The macroscopic expansion features obtained were found to be in general agreement with those obtained from the small-scale numerical simulations.

Schunk, R. W.↗

Using XR for Improving Scientific Discovery With Numerical Weather Models

Earth science (ES) digital twins will help us understand the complex interactions and interrelationships that make up our Earth system and the impacts of earth science phenomena on it. Our work addresses two underdeveloped areas in current ES digital twin work: improving the understanding and interaction with ES model outputs by using Virtual and Mixed Reality (XR) tools and improving the non-intuitive mapping of continuous ES natural phenomena to gridded reference frames in current numerical models. Traditionally, scientists working on ES view and analyze the results of calculated or measured observables with static 1-dimensional (1D), 2D or 3D plots displayed on flat computer screens or paper. Using such limited mediums, it can be very difficult to identify, track and understand the evolution of key features due to poor viewing angles and the nature of flat computer screens. In addition, numerical models, such as the NASA Goddard Earth Observing System (GEOS) ES model, are almost exclusively formulated, visualized and analyzed in an Eulerian reference frame with fixed grid points in space and time. However, ES phenomena such as convective clouds, hurricanes and wildfire smoke plumes are visualized and analyzed in a Lagrangian reference frame: therefore it is often difficult and unnatural to understand these phenomena in relation to each other, visualized either in an Eulerian or Lagrangian context. In 3D visualizations, data generally takes one of three forms: gridded (e.g., voxelized) data, where space is divided into regions; point clouds, where data is represented as a set of points; and meshes, where objects are rendered as surfaces composed of small polygons (usually triangles). A gridded, Eulerian reference frame has been the default representation for the 2D visual analysis of atmospheric data in part because the numerical methods used to generate atmospheric model data in the first place use a gridded approach, with equations defining the relationships between the physical variables in each of a grid's cells across successive timesteps. In our work, we are particularly interested in data from GEOS. Another reason why gridded representations tend to be used for visualizing data from such models is because trajectories are difficult to interpret from representations on 2D surfaces, due to line-of-sight ambiguity. Instead of a fixed grid from GEOS, we embed a trajectory model to simulate particles' movement throughout a GEOS run. We then ingest these particle trajectories as animated point clouds with a NASA open source XR toolkit, the Mixed Reality Exploration Toolkit (MRET), and merge GEOS data with ES phenomena data onto one combined visualization that the user can intuitively interact with. Efficient rendering of arbitrarily large point clouds is an ongoing challenge being addressed by the computer science community, with the GPU-based optimizations and efficient GPU memory utilization a common theme of recent advances, especially for XR, where sustained high frame rate is mandatory to save the user from suffering due to simulation sickness. In this work, we describe and evaluate our progress in choosing and implementing appropriate methods for rendering arbitrarily large point clouds within MRET for XR. While tracking the XR headset enables the immersion of a user within a 3D scene of a data visualization, tracking of XR handheld controllers or user’s hands enables us to implement intuitive user interactions with the visualized datasets. Conventional tools require a user working with an ES visualization to conduct many interactions to commit their intended selections or manipulations with a visualized dataset; for example to specify a set of points in 3D space. Doing so in a 2D flat screen interface has traditionally required specifying a set of points in three distinct 2D coordinate systems (XY, XZ, and YZ), which is cumbersome. In other scientific domains, it has been shown that specifying or selecting a location or volume in XR using handheld controllers or tracked hands allows for greater speed and accuracy. We anticipate the same will hold true for atmospheric data, and we will share initial results of measuring the utility of such an interface. Notably, as the data being visualized is generated by GEOS as a prediction based on initial conditions, an intended application of our tool is to serve as part of an iterative feedback loop. Through XR, a scientist will review and manipulate a GEOS model run, modifying the conditions as needed to do subsequent runs of GEOS. Thereby, XR-based improvements to speed and accuracy of 3D tagging of points minimizes the effort required by both the scientist and the computer cluster conducting the necessary calculations.

Thomas Grubb↗

Synthesis of offset dual reflector antennas transforming a given feed illumination pattern into a specified aperture distribution

The problem of transforming a given primary feed pattern into a desired aperture field distribution through two reflections by an offset dual reflector system is investigated using the concepts of geometrical optics. A numerically rigorous solution for the reflector surfaces is developed which realizes an exact aperture phase distribution and an aperture amplitude distribution that is accurate to within an arbitrarily small numerical tolerance. However, this procedure does not always yield a smooth solution, i.e., the reflector surfaces thus realized may not be continuous or their slopes may vary too rapidly. In the event of nonexistence of a numerically rigorous smooth solution, an approximate solution that enforces the smoothness of the reflector surfaces can be obtained. In the approximate solution, only the requirement for the aperture amplitude distribution is relaxed, and the condition on the aperture phase distribution is continued to be satisfied exactly.

Mittra, R.↗

High order interpolation of magnetic fields with vector potential reconstruction for particle simulations

We propose a method for interpolating divergence-free continuous magnetic fields via vector potential reconstruction using Hermite interpolation, which ensures high-order continuity for applications requiring adaptive, high-order ordinary differential equation (ODE) integrators, such as the Dormand-Prince method. The method provides C(m) continuity and achieves high-order accuracy, making it particularly suited for particle trajectory integration and Poincaré section analysis under optimal integration order and timestep adjustments. Through numerical experiments, we demonstrate that the Hermite interpolation method preserves volume and continuity, which are critical for conserving toroidal canonical momentum and magnetic moment in guiding center simulations, especially over long-term trajectory integration. Furthermore, we analyze the impact of insufficient derivative continuity on Runge-Kutta schemes and show how it degrades accuracy at low error tolerances, introducing discontinuity-induced truncation errors. Lastly, we demonstrate performant Poincaré section analysis in two relevant settings of field data collocated from finite element meshes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Staffing the ISS Control Centers: Lessons Learned from Long-Duration Human Space Flight

The International Space Station (ISS) has been in operation with a permanent human presence in space for over five years, and plans for continued operations stretch ten years into the future. Ground control and support operations are, likewise, a 15-year enterprise. This long-term, 24-hour per day, 7 day per week support has presented numerous challenges in the areas of ground crew training, initial and continued certification, and console staffing. The Mission Control Center in Houston, Texas and the Payload Operations Center in Huntsville, Alabama have both tackled these challenges, with similar, yet distinct, approaches. This paper describes the evolution of the staffing and training policies of both control centers in a chronological progression. The relative merits and shortcomings of the various policies employed are discussed and a summary of "lessons learned" is presented. Finally, recommendations are made as best practices for future long-term space missions.

Olsen, Carrie D.↗

A combined algorithm for minimum time slewing of flexible spacecraft

The use of Pontryagin's Maximum Principle for the large-angle slewing of large flexible structures usually results in the so-called two-point boundary-value problem (TPBVP), in which many requirements (e.g., minimum time, small flexible amplitude, and limited control powers, etc.) must be satisfied simultaneously. The successful solution of this problem depends largely on the use of an efficient numerical computational algorithm. There are many candidate algorithms available for his problem (e.g., quasilinearization, gradient, and shooting, etc.). In this paper, a proposed algorithm, which combines the quasilinearization method with a time shortening technique and a shooting method, is applied to the minimum-time, three-dimensional, and large-angle maneuver of flexible spacecraft, particularly the orbiting Spacecraft Control Laboratory Experiment (SCOLE) configuration. Theoretically, the nonlinear TPBVP can be solved only through the shooting method to find the 'exact' switching times for the bang-bang controls. However, computationally, a suitable guess for the missing initial costates is crucial because the convergence range of the unknown initial costates is usually narrow, especially for systems with high dimensions and when a multi-bang-bang control strategy is needed. On the other hand, the problems of near minimum time attitude maneuver of general rigid spacecraft and fast slewing of flexible spacecraft have been examined by the authors through a numerical approach based on the quasilinearization algorithm with a time shortening technique. Computational results have demonstrated its broad convergence range and insensitivity to initial costate choices. Consequently, a combined approach is naturally suggested here to solve the minimum time slewing problem. That is, in the computational process, the quasilinearization method is used first to obtain a near minimum time solution. Then, the acquired converged initial costates from the quasilinearization approach are transformed (tailored) to and used as the initial costate guess for starting the shooting method. Finally, the shooting method takes over the remaining calculations until the minimum-time solution converges. The nonlinear equations of motion of the SCOLE are formulated by using Lagrange's equations, with the mast modeled as a continuous beam subject to three-dimensional deformations. The numerical results will be presented and some related computational issues will also be discussed.

Bainum, P. M.↗

Numerical simulation of backward step and jet exhaust flows

Preparatory to a continuing study of efficient, high resolution flow structure capture on patched mesh systems, turbulent flowfield solutions for a tactical missile base flow problem are computed on two first level composite grids of differing topologies. One mesh is of the wraparound character and the other is a step mesh on the Cartesian topology. A simplified Baldwin-Lomax algebraic eddy viscosity model is applied in the wake region. Results for the two meshes are compared with each other and with other computations reported in the literature. The totality of results suggest both mesh topology and resolution are important factors in the accuracy of predictive results as well as turbulence modeling. Related to interests in high altitude laminar flows bluff bodies such as the AOTV, the paper also presents results from a solution from laminar flow over a backward facing step and makes comparison with the available classical experiment of Chapman, et al.

Lombard, C. K.↗

Numerical simulation of the non-Newtonian mixing layer

This work is a continuing effort to advance our understanding of the effects of polymer additives on the structures of the mixing layer. In anticipation of full nonlinear simulations of the non-Newtonian mixing layer, we examined in a first stage the linear stability of the non-Newtonian mixing layer. The results of this study show that, for a fluid described by the Oldroyd-B model, viscoelasticity reduces the instability of the inviscid mixing layer in a special limit where the ratio (We/Re) is of order 1 where We is the Weissenberg number, a measure of the elasticity of the flow, and Re is the Reynolds number. In the present study, we pursue this project with numerical simulations of the non-Newtonian mixing layer. Our primary objective is to determine the effects of viscoelasticity on the roll-up structure. We also examine the origin of the numerical instabilities usually encountered in the simulations of non-Newtonian fluids.

Azaiez, Jalel↗

Improvement of method for experimental determination of flutter speed by parameter identification

The method investigated in the current research work is based on the identification of the equations of motion during test flights, followed by the solution of these identified equations to numerically compute the flutter dynamic pressure. The current research work is aimed at overcoming two main difficulties which arise when: (1) A continuous system is truncated into a system with a finite number of degrees of freedom. (2) The desired range of frequencies is wide; in the latter case, numerical difficulties occur that can only partly be overcome by giving relatively more weight to the high frequency modes. Results pertaining to the above first point will be presented under section entitled 'Truncation Effects', and results pertaining to the above second point will be presented under section entitled 'Frequency Range Effects'. The numerical example used herein consists of a continuous simply supported beam. It is further assumed that the object of the identification procedure is to identify the beam's first seven modes.

Nissim, E.↗

Hierarchical Statistical 3D ' Atomistic' Simulation of Decanano MOSFETs: Drift-Diffusion, Hydrodynamic and Quantum Mechanical Approaches

When MOSFETs are scaled to deep submicron dimensions the discreteness and randomness of the dopant charges in the channel region introduces significant fluctuations in the device characteristics. This effect, predicted 20 year ago, has been confirmed experimentally and in simulation studies. The impact of the fluctuations on the functionality, yield, and reliability of the corresponding systems shifts the paradigm of the numerical device simulation. It becomes insufficient to simulate only one device representing one macroscopical design in a continuous charge approximation. An ensemble of macroscopically identical but microscopically different devices has to be characterized by simulation of statistically significant samples. The aims of the numerical simulations shift from predicting the characteristics of a single device with continuous doping towards estimating the mean values and the standard deviations of basic design parameters such as threshold voltage, subthreshold slope, transconductance, drive current, etc. for the whole ensemble of 'atomistically' different devices in the system. It has to be pointed out that even the mean values obtained from 'atomistic' simulations are not identical to the values obtained from continuous doping simulations. In this paper we present a hierarchical approach to the 'atomistic' simulation of aggressively scaled decanano MOSFETs. A full scale 3D drift-diffusion'atomostic' simulation approach is first described and used for verification of the more economical, but also more restricted, options. To reduce the processor time and memory requirements at high drain voltage we have developed a self-consistent option based on a thin slab solution of the current continuity equation only in the channel region. This is coupled to the Poisson's equation solution in the whole simulation domain in the Gummel iteration cycles. The accuracy of this approach is investigated in comparison with the full self-consistent solution. At low drain voltage only single solution of the nonlinear Poisson equation is sufficient to extract the current with satisfactory accuracy. A pilot version of a hydrodynamic 'atomistic' simulator has been developed in order to study the effect of the nonequilibrium, non local transport in decanano MOSFETs on the random dopant induced current fluctuations. For the first time we have also applied the density gradient approach in 3D to investigate the effect of the quantum confinement on the threshold voltage fluctuations. The developed 'atomistic' simulation techniques have been applied to study various fluctuation resistant MOSFET architectures including epitaxial and delta doped devices.

Asenov, Asen↗

Exact quantization and analytic continuation

In this paper we give a streamlined derivation of the exact quantization condition (EQC) on the quantum periods of the Schrödinger problem in one dimension with a general polynomial potential, based on Wronskian relations. We further generalize the EQC to potentials with a regular singularity, describing spherical symmetric quantum mechanical systems in a given angular momentum sector. We show that the thermodynamic Bethe ansatz (TBA) equations that govern the quantum periods undergo nontrivial monodromies as the angular momentum is analytically continued between integer values in the complex plane. The TBA equations together with the EQC are checked numerically against Hamiltonian truncation at real angular momenta and couplings, and are used to explore the analytic continuation of the spectrum on the complex angular momentum plane in examples.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Automatic speech recognition predicts contemporaneous earthquake fault displacement

Abstract Significant progress has been made in probing the state of an earthquake fault by applying machine learning to continuous seismic waveforms. The breakthroughs were originally obtained from laboratory shear experiments and numerical simulations of fault shear, then successfully extended to slow-slipping faults. Here we apply the Wav2Vec-2.0 self-supervised framework for automatic speech recognition to continuous seismic signals emanating from a sequence of moderate magnitude earthquakes during the 2018 caldera collapse at the Kīlauea volcano on the island of Hawai’i. We pre-train the Wav2Vec-2.0 model using caldera seismic waveforms and augment the model architecture to predict contemporaneous surface displacement during the caldera collapse sequence, a proxy for fault displacement. We find the model displacement predictions to be excellent. The model is adapted for near-future prediction information and found hints of prediction capability, but the results are not robust. The results demonstrate that earthquake faults emit seismic signatures in a similar manner to laboratory and numerical simulation faults, and artificial intelligence models developed for encoding audio of speech may have important applications in studying active fault zones.

58 GEOSCIENCES↗

FOREWORD: Satellite Remote Sensing Beyond 2015

Satellite remote sensing has progressed tremendously since the first Landsat was launched on June 23, 1972. Since the 1970s, satellite remote sensing and associated airborne and in situ measurements have resulted in vital and indispensable observations for understanding our planet through time. These observations have also led to dramatic improvements in numerical simulation models of the coupled atmosphere-land-ocean systems at increasing accuracies and predictive capability. The same observations document the Earth's climate and are driving the consensus that Homo sapiens is changing our climate through greenhouse gas emissions. These accomplishments are the combined work of many scientists from many countries and a dedicated cadre of engineers who build the instruments and satellites that collect Earth observation data from satellites, all working toward the goal of improving our understanding of the Earth. This edition of the Remote Sensing Handbook (Vol. I, II, and III) is a compendium of information for many research areas of our Planet that have contributed to our substantial progress since the 1970s. Remote sensing community is now using multiple sources of satellite and in situ data to advance our studies, what ever they might be. In the following paragraphs, I will illustrate how valuable and pivotal role satellite remote sensing has played in climate system study over last five decades, The Chapters in the Remote Sensing Handbook (Vol. I, II, and III) provides many other specific studies on land, water, and other applications using EO data of last five decades, The Landsat system of Earth-observing satellites has led the way in pioneering sustained observations of our planet. From 1972 to the present, at least one and sometimes two Landsat satellites have been in operation. Starting with the launch of the first NOAA-NASA Polar Orbiting Environmental Satellites NOAA-6 in 1978, improved imaging of land, clouds, and oceans and atmospheric soundings of temperature were accomplished. The NOAA system of polar-orbiting meteorological satellites has continued uninterrupted since that time, providing vital observations for numerical weather prediction. These same satellites are also responsible for the remarkable records of sea surface temperature and land vegetation index from the Advanced Very High Resolution Radiometers (AVHRR) that now span more than 33 years, although no one anticipated these valuable climate records from this instrument before the launch of NOAA-7 in 1981. The success of data from the AVHRR led to the design of the MODIS instruments on NASA's Earth Observing System of satellite platforms that improved substantially upon the AVHRR. The first of the EOS platforms, Terra, was launched in 2000 and the second of these platforms, Aqua, was launched in 2002.

Tucker, Compton J.↗

A general non-Fourier Stefan problem formulation that accounts for memory effects

The Stefan problem is the classical model of a melting phase change. In heterogeneous systems, such phase changes can exhibit non-Fourier (anomalous) behaviors, where the advance of the melt interface does not follow the expected time scaling. These situations can be modeled by replacing the derivatives, in the governing partial differential equations, with fractional order derivatives. In particular, replacing the time derivatives leads to non-Fourier models that account for memory effects in the system. In this work, by using appropriate time convolution integrals, a general thermodynamic balance statement for melting phase problems, explicitly accounting for memory effects, is developed. From this balance, a general model formulation applicable to problems involving melting over a temperature range (i.e., a mushy region) is derived. A key component in this model is the representation of memory effects through the use of fractional derivative based constitutive models of the enthalpy and heat flux. Further, on shrinking the mushy region to a single isotherm, a general sharp interface melting model is obtained. Here, in contrast to the classic Stefan problem, the fractional derivatives induce a natural regularization, such that the constitutive models for enthalpy and heat flux are continuous at the melt interface; a result confirmed through numerical simulation. To further support the theoretical findings, a physical example of a non-Fourier Stefan problem is presented. Overall the development and results in this paper underscore the importance of explicitly relating the development of fractional calculus models to the appropriate thermodynamic balance statements.

42 ENGINEERING↗

Model predictive control for voltage restoration in microgrids using temporal logic specifications

Power system operation will encounter numerous voltage variabilities as the proliferation of renewable energy continues. Real-time monitoring and communication technologies can potentially improve voltage stability by enabling the rapid detection of voltage deviations and the implementation of corrective actions. These corrective actions will only be effective in restoring stability if they are chosen in a timely and scalable manner. This paper considers the problem of power systems’ load voltage control in order to simultaneously address both magnitude and time voltage specifications. In order to comply with grid codes and avoid unnecessary relay protection actions, a model predictive control (MPC)-based control strategy employing temporal logic specifications (TLSs) is proposed. The TLSs strategy is introduced as a formalism to control the voltage variation at a critical load bus against operational bounds over time. The control objective is to schedule optimal control input signals from the available supportive energy storage systems, which provide reactive power injections, leading to satisfying the specified finite-time restoration described by the TLSs with minimal control efforts. The simulation results display that the TLSs strategy for power systems’ voltage control synthesis is extremely significant.

24 POWER TRANSMISSION AND DISTRIBUTION↗