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At least 1,729 records · Page 96

Hidden Killing fields, geometric symmetries and black hole mergers

Highlights: • Construction of geometric models with a variable degree of symmetry. • Formulation of Energy and Momentum Balance Laws. • Description of backreactions on spacetime geometries caused by dissipative effects. • Analytic description of accretion and/or merger processes in GR. • Exact model for the merger of two extremal Reissner–Nordström black holes. In the present work, using the recently introduced framework of local geometric deformations, special types of vector fields – so-called hidden Killing vector fields – are constructed, which solve the Killing equation not globally, but only locally, i.e. in local subregions of spacetime. Taking advantage of the fact that the vector fields coincide locally with Killing fields and therefore allow the consideration of integral laws that convert into exact physical conservation laws on local scales, balance laws in dynamical systems without global Killing symmetries are derived that mimic as closely as possible the conservation laws for energy and angular momentum of highly symmetric models. The utility of said balance laws is demonstrated by a concrete geometric example, namely a toy model for the binary merger of two extremal Reissner–Nordström black holes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Scenario storyline discovery for complex multi-actor human-natural systems

This poster was presented at the AGU Fall Meeting 2024. Abstract:Scenario analysis is a useful tool for assessing the impacts of future conditions or alternative strategies. However, the common practice of focusing on a small number of predetermined scenarios can limit our understanding of key uncertainties, and fail to represent diverse stakeholder impacts. Exploratory modeling approaches have been developed to address these issues by simulating a wide range of possible futures and system perspectives. A challenge with these approaches is that they often involve large ensemble experiments which limit interpretability and usability. We recently introduced the FRamework for Narrative Storylines and Impact Classification (FRNSIC; pronounced ``forensic''), a scenario discovery framework that helps users identify scenario storylines that capture key system dynamics and as well as important outcomes. In this poster presentation, we present training materials to support the generalizable application of the framework to other multi-actor systems with complex dynamics. Specifically, we will present a step-by-step methodological typology of tools and methods that can be used to generate and classify plausible states of the world on key metrics and consequential dynamics. The typology will also discuss potential implications of these choices and their applicability to different systems.

Colorado River↗

Transfer Trajectory Options for Servicing Sun-Earth-Moon Libration Point Missions

Future missions to the Sun-Earth Libration L1 and L2 regions will require scheduled servicing to maintain hardware and replenish consumables. While there have been statements made by various NASA programs regarding servicing of vehicles at these locations or in Cis-lunar space, a practical transfer study has not been extensively investigated in an operational fashion to determine the impacts of navigation and maneuver errors. This investigation uses dynamical systems and operational models to design transfer trajectories between the Sun-Earth Libration region (QuasiHalo orbit) and the Earth-Moon vicinity (Distant Retrograde Orbit, QuasiHalo Orbit, Halo Orbit, and Near Rectilinear Halo Orbit). We address the total delta V cost of transfers between each pair of locations using a Monte Carlo analysis.

Earth↗

Comparative Analysis of Static and Dynamic Probabilistic Risk Assessment

This study examines three different methodologies for producing loss-of-mission (LOM) and loss-of-crew (LOC) risks estimates for probabilistic risk assessments (PRA) of crewed spacecraft. The three bottom-up, component-based PRA approaches examined are a traditional static fault tree, a dynamic Monte Carlo simulation, and a fault tree hybrid that incorporates some dynamic elements. These approaches were used to model the reaction control system thruster pod of a generic crewed spacecraft and mission, and a comparative analysis of the methods is presented. The methodologies are assessed in terms of the process of modeling a system, the actionable information produced for the design team, and the overall fidelity of the quantitative risk evaluation generated. The system modeling process is compared in terms of the effort required to generate the initial model, update the model in response to design changes, and support mass-versus-risk trade studies. The results are compared by examining the top-level LOM/LOC estimates and the relative risk driver rankings at the failure mode level. The fidelity of each modeling methodology is discussed in terms of its capability to handle real-world system dynamics such as cold-sparing, changes in mission operations due to loss of redundancy, and common cause failure modes. The paper also discusses the applicability of each methodology to different phases of system development and shows that a single methodology may not be suitable for all of the many purposes of a spacecraft PRA. The fault tree hybrid approach is shown to be best suited to the needs of early assessments during conceptual design phases. As the design begins to mature, the level of detail represented in the risk model must go beyond redundancy and nominal mission operations to include dynamic, time- and state-dependent system responses as well as diverse system capabilities. This is best accomplished using the dynamic simulation approach, since these phenomena are not easily captured by static methods. Ultimately, once the design has been finalized and the goal of the PRA is to provide design validation and requirement verification, more traditional, static fault tree approaches may become as appropriate as the simulation method.

Mattenberger, Christopher J.↗

Learning physics-based reduced-order models from data using nonlinear manifolds

Here we present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The proposed approach is driven by embeddings of low-order polynomial form. A projection onto the nonlinear manifold reveals the algebraic structure of the reduced-space system that governs the problem of interest. The matrix operators of the reduced-order model are then inferred from the data using operator inference. Numerical experiments on a number of nonlinear problems demonstrate the generalizability of the methodology and the increase in accuracy that can be obtained over reduced-order modeling methods that employ a linear subspace approximation.

97 MATHEMATICS AND COMPUTING↗

Fixed interval smoothing with discrete measurements.

Smoothing equations for a linear continuous dynamic system with linear discrete measurements, derived from the discrete results of Rauch, Tung, and Striebel (1965), (R-T-S), are used to extend, through recursive updating, the previously published results of Bryson and Frazier (1963), (B-F), and yield a modified Bryson and Frazier, (M-B-F), algorithm. A comparison of the (M-B-F) and (R-T-S) algorithms leads to the conclusion that the former is to be preferred because it entails less computation, less storage, and less instability. It is felt that the presented (M-B-F) smoothing algorithm is a practical mechanization and should be of value in smoothing discretely observed dynamic linear systems.

Bierman, G. J.↗

Normal stability of slow manifolds in nearly periodic Hamiltonian systems

Kruskal [J. Math. Phys. 3, 806 (1962)] showed that each nearly periodic dynamical system admits a formal U(1) symmetry, generated by the so-called roto-rate. We prove that such systems also admit nearly invariant manifolds of each order, near which rapid oscillations are suppressed. We study the nonlinear normal stability of these slow manifolds for nearly periodic Hamiltonian systems on barely symplectic manifolds—manifolds equipped with closed, non-degenerate 2-forms that may be degenerate to leading order. In particular, we establish a sufficient condition for long-term normal stability based on second derivatives of the well-known adiabatic invariant. We use these results to investigate the problem of embedding guiding center dynamics of a magnetized charged particle as a slow manifold in a nearly periodic system. Here, we prove that one previous embedding and two new embeddings enjoy long-term normal stability and thereby strengthen the theoretical justification for these models.

97 MATHEMATICS AND COMPUTING↗

Examination of Semi-Analytical Solution Methods in the Coarse Operator of Parareal Algorithm for Power System Simulation

With continuing advances in high-performance parallel computing platforms, parallel algorithms have become powerful tools for development of faster than real-time power system dynamic simulations. In particular, it has been demonstrated in recent years that parallel-in-time (Parareal) algorithms have the potential to achieve such an ambitious goal. Here, the selection of a fast and reasonably accurate coarse operator of the Parareal algorithm is crucial for its effective utilization and performance. This paper examines semi-analytical solution (SAS) methods as the coarse operators of the Parareal algorithm and explores performance of the SAS methods to the standard numerical time integration methods. Two promising time-power series-based SAS methods were considered; Adomian decomposition method and Homotopy analysis method with a windowing approach for improving the convergence. Numerical performance case studies on 10-generator 39-bus system and 327-generator 2383-bus system were performed for these coarse operators over different disturbances, evaluating the number of Parareal iterations, computational time, and stability of convergence. All the coarse operators tested with different scenarios have converged to the same corresponding true solution (if they are convergent) and the SAS methods provide comparable computational speed, while having more stable convergence to the true solution in many cases.

97 MATHEMATICS AND COMPUTING↗

U.S. lithium resources from geothermal and extraction feasibility

As the demand for electric vehicles (EVs) increases, demand for lithium (Li) is expected to grow over the coming decade. To satisfy the demand for rechargeable batteries, it is imperative to devise solutions for sufficient Li production. Additionally, even though commercial Li currently comes from conventional saline salar brine and spodumene ore extractions, efforts to retrieve Li from geothermal brines are increasing in popularity. In this paper, we evaluate the United States’ potential to supply Li from geothermal brines using Systems Dynamics modeling. The main goals are to assess (1) the viability of US Li supply from geothermal brines and (2) the potential supply chain impact of extracting Li from this source. Results show that Li supply from geothermal brines could (1) reach around 4% to 8% of total US Li supply and (2) be economically viable.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Statistical physics and physiology: monofractal and multifractal approaches

Even under healthy, basal conditions, physiologic systems show erratic fluctuations resembling those found in dynamical systems driven away from a single equilibrium state. Do such "nonequilibrium" fluctuations simply reflect the fact that physiologic systems are being constantly perturbed by external and intrinsic noise? Or, do these fluctuations actually, contain useful, "hidden" information about the underlying nonequilibrium control mechanisms? We report some recent attempts to understand the dynamics of complex physiologic fluctuations by adapting and extending concepts and methods developed very recently in statistical physics. Specifically, we focus on interbeat interval variability as an important quantity to help elucidate possibly non-homeostatic physiologic variability because (i) the heart rate is under direct neuroautonomic control, (ii) interbeat interval variability is readily measured by noninvasive means, and (iii) analysis of these heart rate dynamics may provide important practical diagnostic and prognostic information not obtainable with current approaches. The analytic tools we discuss may be used on a wider range of physiologic signals. We first review recent progress using two analysis methods--detrended fluctuation analysis and wavelets--sufficient for quantifying monofractual structures. We then describe recent work that quantifies multifractal features of interbeat interval series, and the discovery that the multifractal structure of healthy subjects is different than that of diseased subjects.

NASA Discipline Cardiopulmonary↗

Large Deviations for Gaussian Diffusions with Delay

Dynamical systems driven by nonlinear delay SDEs with small noise can exhibit important rare events on long timescales. When there is no delay, classical large deviations theory quantifies rare events such as escapes from metastable fixed points. Near such fixed points, one can approximate nonlinear delay SDEs by linear delay SDEs. Here, we develop a fully explicit large deviations framework for (necessarily Gaussian) processes X{sub t} driven by linear delay SDEs with small diffusion coefficients. Our approach enables fast numerical computation of the action functional controlling rare events for X{sub t} and of the most likely paths transiting from X{sub 0}=p to X{sub T}=q. Via linear noise local approximations, we can then compute most likely routes of escape from metastable states for nonlinear delay SDEs. We apply our methodology to the detailed dynamics of a genetic regulatory circuit, namely the co-repressive toggle switch, which may be described by a nonlinear chemical Langevin SDE with delay.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Impact of automated battery sorting for mineral recovery from lithium-ion battery recycling in the United States

The United States has identified several lithium-ion battery materials as critical for reaching the national emission reduction targets that have been set in accordance with the 2015 Paris Agreement. However, with few natural resources available domestically, there is a rapidly growing focus on the development of a domestic recycling industry to recover these materials from end-of-life batteries. Here, we use the Lithium-Ion Battery Resources Assessment (LIBRA) system dynamics model to evaluate the impact of automated battery sorting technology in terms of the shares of cobalt and nickel that are recovered through recycling. Findings show that automated sorting has clear benefits over manual sorting methods by helping recyclers selectively process high-cobalt batteries. By maximizing cobalt recovery, recycling becomes more profitable and drives greater investment in recycling capacity, resulting in a higher share of nickel and cobalt recovered from EOL batteries over time.

25 ENERGY STORAGE↗

A Scalable, Out-of-Band Diagnostics Architecture for International Space Station Systems Support

The computational infrastructure of the International Space Station (ISS) is a dynamic system that supports multiple vehicle subsystems such as Caution and Warning, Electrical Power Systems and Command and Data Handling (C&DH), as well as scientific payloads of varying size and complexity. The dynamic nature of the ISS configuration coupled with the increased demand for payload support places a significant burden on the inherently resource constrained computational infrastructure of the ISS. Onboard system diagnostics applications are hosted on computers that are elements of the avionics network while ground-based diagnostic applications receive only a subset of available telemetry, down-linked via S-band communications. In this paper we propose a scalable, out-of-band diagnostics architecture for ISS systems support that uses a read-only connection for C&DH data acquisition, which provides a lower cost of deployment and maintenance (versus a higher criticality readwrite connection). The diagnostics processing burden is off-loaded from the avionics network to elements of the on-board LAN that have a lower overall cost of operation and increased computational capacity. A superset of diagnostic data, richer in content than the configured telemetry, is made available to Advanced Diagnostic System (ADS) clients running on wireless handheld devices, affording the crew greater mobility for troubleshooting and providing improved insight into vehicle state. The superset of diagnostic data is made available to the ground in near real-time via an out-of band downlink, providing a high level of fidelity between vehicle state and test, training and operational facilities on the ground.

Fletcher, Daryl P.↗

Bayesian inference of structured latent spaces from neural population activity with the orthogonal stochastic linear mixing model

The brain produces diverse functions, from perceiving sounds to producing arm reaches, through the collective activity of populations of many neurons. Determining if and how the features of these exogenous variables (e.g., sound frequency, reach angle) are reflected in population neural activity is important for understanding how the brain operates. Often, high-dimensional neural population activity is confined to low-dimensional latent spaces. However, many current methods fail to extract latent spaces that are clearly structured by exogenous variables. This has contributed to a debate about whether or not brains should be thought of as dynamical systems or representational systems. Here, we developed a new latent process Bayesian regression framework, the orthogonal stochastic linear mixing model (OSLMM) which introduces an orthogonality constraint amongst time-varying mixture coefficients, and provide Markov chain Monte Carlo inference procedures. We demonstrate superior performance of OSLMM on latent trajectory recovery in synthetic experiments and show superior computational efficiency and prediction performance on several real-world benchmark data sets. We primarily focus on demonstrating the utility of OSLMM in two neural data sets: μ ECoG recordings from rat auditory cortex during presentation of pure tones and multi-single unit recordings form monkey motor cortex during complex arm reaching. We show that OSLMM achieves superior or comparable predictive accuracy of neural data and decoding of external variables (e.g., reach velocity). Most importantly, in both experimental contexts, we demonstrate that OSLMM latent trajectories directly reflect features of the sounds and reaches, demonstrating that neural dynamics are structured by neural representations. Together, these results demonstrate that OSLMM will be useful for the analysis of diverse, large-scale biological time-series datasets.

59 BASIC BIOLOGICAL SCIENCES↗

Dynamic Radioisotope Power System (DRPS) Design Reference Mission (DRM) Lunar Rover

The Radioisotope Power Systems (RPS) Program tasked the Compass Team to evaluate use of Dynamic Radioisotope Power Systems (DRPS) for lunar science rovers. The object was to identify their advantages and challenges as well as to influence the technology developments with flight-type requirements. This was easily done by using the promising Volatiles Investigating Polar Exploration Rover (VIPER) solar- powered rover mission as a platform to ‘swap in’ a DRPS. The ‘pickup truck bed’ approach allowed both simplified installation and operation of the DRPS while keeping the forward lunar surface ‘blocked’ from the DRPS waste heat which could sublimate the icy surface. It was found that with the Stirling DRPS option the mass is within the planned VIPER lander capability and is very close to VIPER mass and size (the DRPS replaces large battery pack/solar arrays). The Stirling DRPS option produced ~300 Watts electrical (We) using six general purpose heat source (GPHS) bricks and eight Stirling convertors. Replacing the solar/battery power with radioisotope power allows a continuous presence (instead of 6 hours) in a permanently shadowed region (PSR) and over 18 months of operations with minimal science impact (rearward surface heating). It was also found that use of a dynamic system (instead of a thermoelectric system) reduces the heat impact on the science environment two-to-three times. The DRPS, along with a relay link (like Gateway), can provide continuous access to PSRs. The system was also found to be capable of roving for 8 hours per day with a range of over 500 km in 18 months. Preliminary cost estimates fit into a Class D mission but only assuming VIPER heritage and launch, lander, operations, nuclear specific costs [National Environmental Policy Act (NEPA), fueling, transport, Launch Services Program (LSP), etc.] and DRPS are not included.

DRPS↗

SNS: A Solution-Based Nonlinear Subspace Method for Time-Dependent Model Order Reduction

Several reduced order models have been successfully developed for nonlinear dynamical systems. To achieve a considerable speed-up, a hyper-reduction step is needed to reduce the computational complexity due to nonlinear terms. Many hyper-reduction techniques require the construction of nonlinear term basis, which introduces a computationally expensive offline phase. A novel way of constructing nonlinear term basis within the hyper-reduction process is introduced. In contrast to the traditional hyper-reduction techniques where the collection of nonlinear term snapshots is required, the SNS method avoids collecting the nonlinear term snapshots. Instead, it uses the solution snapshots that are used for building a solution basis, which enables avoiding an extra data compression of nonlinear term snapshots. As a result, the SNS method provides a more efficient offline strategy than the traditional model order reduction techniques, such as the DEIM, GNAT, and ST-GNAT methods. The SNS method is theoretically justified by the conforming subspace condition and the subspace inclusion relation. It is useful for model order reduction of large-scale nonlinear dynamical problems to reduce the offline cost. It is especially useful for ST-GNAT that has shown promising results, such as a good accuracy with a considerable online speed-up for hyperbolic problems in a recent paper by Choi and Carlberg [SIAM J. Sci. Comput., 41 (2019), pp. A26--A58], because ST-GNAT involves an expensive offline cost related to collecting nonlinear term snapshots. Error analysis for the SNS method is presented. Numerical results support that the accuracy of the solution from the SNS method is comparable to the traditional methods and a considerable speed-up (i.e., a factor of two to a hundred) is achieved in the offline phase.

97 MATHEMATICS AND COMPUTING↗