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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 235 records · Page 13

Pulse-by-pulse transient thermal deformation in crystal optics under high-repetition-rate FEL

Time-domain modeling of the thermal deformation of crystal optics can help define acceptable operational ranges across the pulse-energy repetition-rate phase space. In this paper, we have studied the transient thermal deformation of a water-cooled diamond crystal for a cavity-based X-ray free-electron laser (CBXFEL), either an X-ray free-electron laser oscillator (XFELO) or a regenerative amplifier X-ray free-electron laser (RAFEL), by numerical simulations including finite-element analysis and advanced data processing. Pulse-by-pulse transient thermal deformation of a 50 µm-thick diamond crystal has been performed with X-ray pulse repetition rates between 50 kHz and 1 MHz. Results for temperature and thermal deformation have been compared with the results of transient analysis using a continuous wave (CW) power loading. Temperature and thermal deformation results from pulse-by-pulse transient analysis vary with time about the results for the CW case for the same average power. The variation amplitude increases with pulse energy and decreases with repetition rate. When the repetition rate increases to infinity, both temperature and thermal deformation converge to the results for the CW case. Two critical time scales for the operation of crystal optics in a CBXFEL are (1) first-turn time, i.e. the time for the XFEL pulse to complete the first turn around the cavity so that the crystal sees the recirculated XFEL pulse, and (2) period-end time, i.e. the time that the next electron bunch arrives for the amplification, so that the crystal outcouples the amplified FEL power. For the same average power, simulation results show that the crystal thermal deformation seen by the XFEL beam decreases with repetition rate at the first-turn time of a 300 m-long cavity and increases with repetition rate at the period-end time. For the wavefront preservation requirement of the crystal optics, a pulse-energy versus repetition-rate phase space has been established. The upper bounds of the pulse energy at both first-turn and period-end times decreases with repetition rate, especially at the period-end time. The upper bound of the thermal deformation of the crystal at the period-end time for any repetition frequency can be estimated from the CW case. For a water-cooled diamond crystal of dimension 5 mm × 5 mm × 0.05 mm, the time to reach a quasi steady-state is about 50 ms for temperature and 50 µs for thermal deformation.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Cost Projections for Utility-Scale Battery Storage: 2025 Update

In this work we describe the development of cost and performance projections for utility-scale lithium-ion battery systems, with a focus on 4-hour duration systems. The projections are developed from an analysis of recent publications that include utility-scale storage costs. The suite of publications demonstrates wide variation in projected cost reductions for battery storage over time. We present the suite of projected cost reductions collected from the literature as well as the low, mid, and high cost projections developed in this work. Storage cost projections are $\$$152/kWh, $\$$247/kWh, and $\$$349/kWh in 2035 and $\$$111/kWh, $\$$184/kWh, and $\$$333/kWh in 2050 for the low, mid, and high cases respectively. Battery variable operations and maintenance costs, lifetimes, and efficiencies are also discussed, with recommended values selected based on the publications surveyed.

25 ENERGY STORAGE↗

Evaluating Thermostats' Deadbands Using HVAC Hardware-In-the-Loop Experiment for Advanced Control Strategies

Smart thermostats have gained significant popularity due to their potential for optimizing energy consumption and enhanced user control while ensuring occupants' comfort. The deadband, also referred to as temperature differential, is defined as the temperature difference between the desired setpoint and upper threshold or lower threshold for the HVAC equipment to turn on. It is a key factor influencing energy efficiency and user satisfaction. This paper presents a comparative analysis of the deadbands of five different smart thermostats, tested with a heat pump, aiming to identify variations in their deadband settings and implications for energy management. The experimental study was conducted using a HVAC hardware-in-theloop (HIL) system that integrates smart thermostats with physical HVAC equipment in a simulated house environment. The study explores the trade-offs between energy efficiency and occupant comfort and highlights how different thermostats participating in demand response event cycle differently based on their deadband settings. The findings offer valuable insights into how selecting the right thermostat or configuring smart thermostat with appropriate deadband settings can be leveraged to enhance demand response capabilities, shift loads effectively and improve operational flexibility in HVAC systems.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Evaluating Thermostats' Deadbands Using HVAC Hardware-In-the-Loop Experiment for Advanced Control Strategies: Preprint

Smart thermostats have gained significant popularity due to their potential for optimizing energy consumption and enhanced user control while ensuring occupants' comfort. The deadband, also referred to as temperature differential, is defined as the temperature difference between the desired setpoint and upper threshold or lower threshold for the HVAC equipment to turn on. It is a key factor influencing energy efficiency and user satisfaction. This paper presents a comparative analysis of the deadbands of five different smart thermostats, tested with a heat pump, aiming to identify variations in their deadband settings and implications for energy management. The experimental study was conducted using a HVAC hardware-in-theloop (HIL) system that integrates smart thermostats with physical HVAC equipment in a simulated house environment. The study explores the trade-offs between energy efficiency and occupant comfort and highlights how different thermostats participating in demand response event cycle differently based on their deadband settings. The findings offer valuable insights into how selecting the right thermostat or configuring smart thermostat with appropriate deadband settings can be leveraged to enhance demand response capabilities, shift loads effectively and improve operational flexibility in HVAC systems.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Evaluating Thermostats’ Deadbands Using HVAC Hardware-In-the-Loop Experiment for Advanced Control Strategies

Thermostats play a crucial role in energy consumption, user control, and occupant comfort by serving as the interface between the heating, ventilation, and air conditioning (HVAC) system and the building's occupants. The deadband, also referred to as temperature differential, is defined as the temperature difference between the desired setpoint and upper threshold or lower threshold for the HVAC equipment to turn on or off. It is a key factor influencing energy efficiency and user satisfaction. This paper presents a comparative analysis of the deadbands of five different thermostats, tested with a residential heat pump, aiming to identify variations in their deadband settings and implications for energy usage and management. The experimental study was conducted using a HVAC hardware-in-the-loop (HIL) system that allows thermostats to be connected with physical HVAC equipment, driven by conditions in a simulated residential building. The study explores the trade-offs between energy efficiency and occupant comfort and highlights how different thermostats cycle differently based on their deadband settings. The findings offer valuable insights into how thermostat deadband affects comfort and energy use, as well as the cycling frequency of a heat pump.

Ramaraj, Sugirdhalakshmi [National Renewable Energ↗

Probing the Mechanism of Selective Phosphate Adsorption from Wastewater Using Aqueous and Synchrotron X-ray Characterization

Ion exchange shows promise for recovering phosphate from wastewater as value-added products, but requires high phosphate selectivity to compete with conventional treatment. Hybrid anion exchange (HAIX) resins, which contain non-selective basic functional groups and selective iron oxide nanoparticles (FeOnp), can effectively remove phosphate from wastewater. However, knowledge gaps remain regarding the mechanisms of phosphate selectivity and influence of competing ions, hindering needed efforts to model adsorption dynamics and design scalable adsorption processes for varying wastewaters. To address these gaps, we integrated aqueous-phase adsorption analysis with solid-phase, synchrotron-based X-ray characterization; this integration facilitated elucidation of the distribution and speciation of iron, phosphate, and competing anions on HAIX resins. We compared a quaternary ammonium-functionalized HAIX resin (SBA) to a tertiary amine version (WBA) to determine the role of functional groups. X-ray radiography revealed differences in FeOnp speciation (goethite vs. ferrihydrite) and distribution (peripheral vs. homogeneous) between the resins, resulting in varied phosphate affinity and intraparticle diffusion resistance. Using micro-X-ray fluorescence (μ-XRF) and micro-X-ray absorption near-edge structure (μ-XANES) spectroscopy, we identified differences in where and how phosphate binds across resin types and wastewaters. Across wastewater compositions, FeOnp sites in WBA contribute more to phosphate adsorption than in SBA, possibly due to variations in Fe distribution and speciation. Phosphate adsorption densities calculated from quantitative μ-XRF maps matched those from aqueous analysis, demonstrating the effectiveness of this integrated approach. Altogether, results demonstrate the use of synchrotron-based X-ray characterization for investigating adsorption mechanisms and advance HAIX as a phosphate recovery technology from complex wastewaters.

Nutrient recovery↗

In‐situ Analysis of Paste Properties in Resonant Acoustic Mixers for Quality Monitoring

Formulation control is key to achieving consistent target properties of energetic materials, as feedstock variations and slight deviations in the ratios of different ingredients can have major effects on final product properties, particularly in dense pastes with high particle loading >65 vol.%. In large‐scale operations, it is imperative to either correct or remove batches of material that perform outside baseline property specifications as early as possible to avoid unnecessary processing of suboptimal material. Quality monitoring is the practice of measuring material properties during processing using process analytical technologies as opposed to only testing the properties of the final product; it is a key principle in the quality‐by‐design frameworks used for designing formulations and manufacturing processes. Herein, a process analytical technology method for correlating material properties of dense pastes directly after mixing in a Resonant Acoustic Mixer to motor data is developed and used to detect differences in the particle content of dense paste formulations. This method was also capable of detecting variations in powder feedstock properties, such as particle packing efficiency, and is sensitive enough to detect changes of 2 wt.% in the total solids content of the formulation. The techniques presented herein show excellent promise for use as a process analytical technology capable of quantifying formulation effects on material movement modes during resonant acoustic mixing.

Materials science↗

Density Functional Theory Study of Iron–Oxygen Divacancies in Magnetite (Fe 3 O 4 ) and Hematite (Fe 2 O 3 )

Density functional theory (DFT) calculations are employed to investigate the formation energies, charge redistribution, and binding energies of iron–oxygen divacancies in magnetite (Fe 3 O 4 ) and hematite (Fe 2 O 3 ). For magnetite, we focus on the low-temperature phase to explore variations with local environments. Building on previous DFT calculations of the variations in formation energies for oxygen vacancies with local charge and spin order in magnetite, we extend this analysis to include octahedral iron vacancies before analyzing the iron–oxygen divacancies. We also assessed the relative stability of iron–oxygen divacancies by comparing their formation energies with those of individual vacancies. Our findings reveal a significant energetic driving force for the formation of divacancy clusters, particularly in magnetite, where divacancies in the +1 charge state exhibit formation energies comparable to those of neutral iron vacancies under oxidizing conditions. In hematite, the results indicate a strong tendency for oxygen vacancies to bind to iron vacancies. These results highlight the significance of iron–oxygen vacancy complexes in the transport properties of iron oxides, with particular relevance to diffusion mechanisms under irradiation conditions.

36 MATERIALS SCIENCE↗

Nanocluster Rearrangement Forms a Family of Ordered Cerium–Titanium Bimetallic Metal–Organic Frameworks with Three Different Nodes, Nanocavities, and Thermal Stabilities

Metal–organic frameworks (MOFs) provide a versatile platform for incorporating multiple metal ions within a single crystalline framework, yet achieving spatial and stoichiometric order in heterometallic nodes remains a synthetic challenge. Building on our previously reported, highly thermally stable Ce/Ti bimetallic MOF NU-3000, we identified and isolated two additional crystalline phases, NU-2998 and NU-2999, that arise from the same Ce/Ti nanocluster precursor under modified solvothermal conditions. Systematic variation of reaction temperature, time, solvent ratio, and modulator concentration directs the assembly of these distinct frameworks. Structural analysis and comprehensive characterization studies reveal that these MOFs each feature an unreported nodal geometry with nanocavities of different sizes. NU-2998 even adopts an unreported topology, denoted nui , that features an elongated pore spanning 4 nm. Together, these findings establish a synthesis route that starts with a nanocluster and ends with a set of bimetallic MOFs, offering a glimpse into the pathway-dependent assembly of multimetallic porous materials. Finally, we evaluated the thermal stability of each additional analogue and compared them to NU-3000, providing further insight into material stability. NU-3000 maintained the highest thermal stability and was evaluated as a catalyst for CO oxidation at elevated temperatures.

bimetallic MOFs↗

Solvent selection for a biomass-to-bioproduct pipeline through integrated reductive catalytic fractionation and microbial funneling

The growing significance of lignin-first biorefineries, which focus on upgrading the aromatics resulting from lignin depolymerization, presents opportunities for bioproduct synthesis using microbial strains capable of funneling a diverse array of phenolics into a single commodity chemical. In this study, we evaluated a biomass-to-bioproduct pipeline involving the reductive catalytic fractionation (RCF) of poplar biomass followed by biological funneling with a Novosphingobium aromaticivorans strain that produces 2-pyrone-4,6-dicarboxylic acid (PDC), a potential bioplastic precursor. Considering the impact of solvent on RCF reactor operating pressure, and the potential inhibitory effects of solvent on downstream microbial funneling, we performed an analysis of six pure solvents, namely methanol, ethanol, isopropanol, isobutanol, 1,4-dioxane and ethylene glycol, and different variations of their aqueous mixtures comprising 5 to 50 vol% water. For each pure solvent and solvent/water system, we measured phenolic monomer yields in the RCF process and PDC yields from the phenolic monomers. We then developed correlation models that relate phenolic monomer yields from RCF-derived samples to Hansen solubility parameters to determine solvent descriptors that contribute to high yields. Furthermore, we developed an integrated biorefinery system to estimate the minimum selling price (MSP) of PDC and the associated carbon footprint to identify solvent systems with better costs and sustainability metrics. These analyses resulted in the 50 vol% methanol/water system being identified as optimal because it reduces RCF reactor pressure and is compatible with microbial funneling with N. aromaticivorans. This solvent system produced 63 g PDC per kg biomass (264 g PDC per kg lignin) from 85 g phenolic monomers per kg biomass at a reduced reactor pressure of 48 bar (reduced by 26% compared to our previous poplar-to-PDC pipeline). The MSP for this system is $\$$13.98 per kg of purified PDC (carbon footprint of 1.47 kg CO 2 e per kg), which is about 24% lower than a previously described poplar-to-PDC pipeline and 46% lower than a lignin-to-PDC pipeline that used pure methanol as the solvent. The results from this study illustrate improvements that can be made in lignocellulosic biorefineries that are compatible with the hybrid chemical and biological processes needed to gain value from lignin.

Sripada, Sarada [Great Lakes Bioenergy Research Ce↗

Microstructural stability and mechanical properties of the as-cast and heat-treated newly developed TiNbCrTa refractory complex concentrated alloy

In this study, a TiNbCrTa refractory complex concentrated alloy (RCCA) was prepared using vacuum arc remelting. The microstructural evolution and mechanical properties of both as-cast and heat-treated RCCA samples were analyzed. Heat treatment (HT) was performed at 800–1200 °C for 1 h in a vacuum-sealed environment. These samples exhibited a formation of Cr 2 Nb and Cr 2 Ti Laves phases. A variation in elemental distribution was observed, with interdendritic (ID) regions showing higher fractions of Ti and Cr, while the dendritic regions had a greater concentration of Ta and Nb. Micro-segregation at the IDs was confirmed through energy dispersive x-ray spectroscopy mapping, which inferred the formation of Cr- and Ti-rich phases during HT at 800–1200 °C. High-temperature HT at 1200 °C for 1 h led to the evolution of the hcp omega phase. Prolonged HT at 1200 °C for 96 h resulted in the evolution of a Cr-rich Laves phase (Cr 2 Ta), which was homogeneously distributed within the microstructure, indicating an unstable microstructure. Furthermore, despite prolonged HT, a variation in the elemental distribution persisted due to the presence of dendritic and ID regions. Electron backscattered diffraction analysis revealed the presence of bcc and hcp phases in the dendritic and ID regions, respectively, of the as-cast and HTed samples. The as-cast samples demonstrated a high compressive strength of approximately 2 GPa. Micro-hardness values increased with the HT temperature up to 1000 °C. Further increases under HT conditions did not significantly reduce the microhardness value, whereas prolonged HT at 1200 °C led to an increase in the microhardness value. Overall, the newly developed TiNbCrTa RCCA exhibited high-strength behavior even after the phase transformation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Analyzing the Effects of Atmospheric Turbulent Fluctuations on the Wake Structure of Wind Turbines and Their Blade Vibrational Dynamics

In recent trends, a rising demand for renewable energy has driven wind turbines to larger proportions, where lighter blade designs are often adopted to reduce the costs associated with logistics and production. This causes modern utility-scale wind turbine blades to be inherently more flexible, and their amplified aeroelastic sensitivity results in complex multi-physics reactions to variant atmospheric conditions, including dynamic patterns of aerodynamic loading at the rotor and vortex structure evolutions within the wake. In this paper, we analyze the influence of inflow variance for wind turbines with large, flexible rotors through simulations of the National Rotor Testbed (NRT) turbine, located at Sandia National Labs’ Scaled Wind Farm Technology (SWiFT) facility in Lubbock, Texas. The Common Ordinary Differential Equation Framework (CODEF) modeling suite is used to simulate wind turbine aeroelastic oscillatory behavior and wind farm vortex wake interactions for a range of flexible NRT blade variations, operating in differing conditions of variant atmospheric flow. CODEF solutions of turbine operation in Steady-In-The-Average (SITA) wind conditions are compared to SITA wind conditions featuring a controlled gust-like pulse overimposed, to isolate the effects of typical wind fluctuations. Finally, simulations of realistic time-varying wind conditions from SWiFT meteorological tower measurements are compared to the solutions of SITA wind conditions. These increasingly complex atmospheric inflow variations are tested to show the differing effects evoked by various patterns of spatiotemporal atmospheric flow fluctuations. An analysis is presented for solutions of wind turbine aeroelastic response and vortex wake evolution, to elucidate the consequences of variant inflow, which pertain to wind turbine dynamics at an individual and farm-collective scale. The comparisons of simulated farm flow for SITA and measured fluctuating wind conditions show that certain regions of the wake contain up to a 12% difference in normalized axial velocity, due to the introduction of wind fluctuations. The findings of this study prove valuable for practical applications in wind farm control and optimization strategies, with particular significance for modern utility-scale wind power plants operating in variant atmospheric conditions.

Farrell, Alayna (ORCID:000000023555720X)↗

Core Physics Characteristics of Extended Enrichment and High Burnup Boiling Water Reactor Fuel

This paper presents the highlights of boiling water reactor (BWR) core physics studies performed at Oak Ridge National Laboratory as part of a series of studies conducted to compare low-enriched uranium (LEU) with LEU+ fuel. The studies analyzed isotopic fuel content, lattice parameters (Phase 1), and core physics (Phase 2) to identify challenges in operation, storage, and transportation for BWRs and pressurized water reactors (PWRs). Because of a lack of publicly available lattice and core designs for modern BWR fuel assemblies and reactor cores, several optimized lattice designs were generated, and different core loading strategies were investigated. Twelve optimized lattice designs with 235 U enrichments ranging from 1.6% to 9% and gadolinia loadings ranging from 3 to 8 wt% were used to model axial enrichment and geometry variations in fuel assemblies for core designs. Each core shares a common set of approximations in design and analysis to allow for consistent comparisons between LEU and LEU+ fuel. The objective is to highlight anticipated changes in core behavior with respect to the reference LEU core. The results of this study show that the differences in LEU and LEU+ core reactor physics characteristics are less significant than the differences in lattice physics characteristics reported in the Phase 1 studies.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Chemoproteogenomic stratification of the missense variant cysteinome

Abstract Cancer genomes are rife with genetic variants; one key outcome of this variation is widespread gain-of-cysteine mutations. These acquired cysteines can be both driver mutations and sites targeted by precision therapies. However, despite their ubiquity, nearly all acquired cysteines remain unidentified via chemoproteomics; identification is a critical step to enable functional analysis, including assessment of potential druggability and susceptibility to oxidation. Here, we pair cysteine chemoproteomics—a technique that enables proteome-wide pinpointing of functional, redox sensitive, and potentially druggable residues—with genomics to reveal the hidden landscape of cysteine genetic variation. Our chemoproteogenomics platform integrates chemoproteomic, whole exome, and RNA-seq data, with a customized two-stage false discovery rate (FDR) error controlled proteomic search, which is further enhanced with a user-friendly FragPipe interface. Chemoproteogenomics analysis reveals that cysteine acquisition is a ubiquitous feature of both healthy and cancer genomes that is further elevated in the context of decreased DNA repair. Reference cysteines proximal to missense variants are also found to be pervasive, supporting heretofore untapped opportunities for variant-specific chemical probe development campaigns. As chemoproteogenomics is further distinguished by sample-matched combinatorial variant databases and is compatible with redox proteomics and small molecule screening, we expect widespread utility in guiding proteoform-specific biology and therapeutic discovery.

Desai, Heta (ORCID:0000000343621707)↗

Lithium inventory tracking as a non-destructive battery evaluation and monitoring method

Tracking the active lithium (Li) inventory in an electrode shows the true state of a Li battery, akin to a fuel gauge for an engine. However, non-destructive Li inventory tracking is currently unavailable. Here, in this work, we used the theoretical capacity of a transition metal oxide to convert capacity into a Li inventory analysis. The Li inventory in electrodes was tracked reliably to show how battery formulations and test methods affect performance. Contrary to capacity, Li inventory tracking reveals stoichiometric variations near the electrode–electrolyte interface. Verifiable results rationalized differences in measurements, clarifying and reducing interferences from cell formulations and experimental manipulations. By tracing four variables from formation to end-of-life, we characterize electrode and cell performance with a thermodynamic framework. Accurate rationalization of subtle differences in Li inventory utilization promises precise battery engineering, evaluation, failure analysis and risk mitigation. The method could be applicable from cell design optimization and fabrication to battery management, improving battery performance and reliability.

25 ENERGY STORAGE↗

Stacked reverberation mapping of high-redshift quasars in DESI. I. Feasibility analysis

The broad-line region of quasars has long been probed by reverberation mapping techniques that measure time lags between continuum and broad emission-line variations. Stacked reverberation mapping has been proposed as a less observationally expensive alternative to traditional methods. This ensemble approach also reduces biases from small-number statistics. The Dark Energy Spectroscopic Instrument (DESI) is conducting the most extensive spectroscopic survey of quasars to date. We create mock light curves emulating expected DESI quasar observations at redshifts $1.48\lt z\lt 5.2$ and luminosities $44.68 \le \log \lambda L_{1350 \mathring{\rm A}{}} / \mathrm{erg\, s^{-1}} \le 45.99$ to test stacked reverberation mapping feasibility using sparse spectroscopic data paired with well-sampled photometric data. The pipeline, using the lag estimation code JAVELIN (Just Another Vehicle for Estimating Lags In Nuclei), successfully recovers the simulated C IV lags within 1σ of the true values using spectroscopic light curves composed of only a few spectral epochs (2–10) with irregular cadences. We investigate how observational factors, including C IV flux error magnitude, number of stacked quasars, and spectral epoch count, affect performance. This work motivates a pathway for future stacked reverberation mapping projects with large-scale spectroscopic surveys of quasars having $\ge 2$ spectroscopic observations. Our results suggest an economical alternative for constraining and extending the radius–luminosity relation to higher redshifts and luminosities. Subsequently, this relation can be employed more reliably in single-epoch black hole mass measurements and quasar cosmology in these distant regimes.

quasars: general, quasars: supermassive black hole↗

Discovering Innovations in Stress Tolerance through Comparative Gene Regulatory Network Analysis and Cell-Type Specific Expression Maps (Final Technical Report with Cover Page)

Through this grant, we developed a comparative framework to elucidate the mechanisms behind variations in environmental stress responses among a diverse group of species within the Brassicaceae family. Our focus was on the differences in physiological and transcriptomic responses to abscisic acid (ABA), a hormone associated with water stress. We examined the differential growth responses of four Brassicaceae species, finding that most exhibited reduced root growth correlated with smaller meristem size. In contrast, Schrenkiella parvula showed accelerated growth due to increased root cell elongation. We employed RNA sequencing to analyze the transcriptional responses to ABA across these species, and innovative bioinformatics techniques were used to pinpoint biological pathways with significant divergence. Additionally, we utilized DAP-seq to map the gene regulatory networks associated with ABAresponsive transcription factors, revealing that variations in the regulation of growth hormone biosynthesis play a critical role in the distinct ABA effects on root growth among the species. This research sets a new standard for comparative physiology by integrating comparative genomics and transcriptomics to uncover pathway divergences.

59 BASIC BIOLOGICAL SCIENCES↗

A Type II Hamiltonian Variational Principle and Adjoint Systems for Lie Groups

We present a novel Type II variational principle on the cotangent bundle of a Lie group which enforces Type II boundary conditions, i.e., fixed initial position and final momentum. In general, such Type II variational principles are only globally defined on vector spaces or locally defined on general manifolds; however, by left translation, we are able to define this variational principle globally on cotangent bundles of Lie groups. Type II boundary conditions are particularly important for adjoint sensitivity analysis, which is our motivating application. As such, we additionally discuss adjoint systems on Lie groups, their properties, and how they can be used to solve optimization problems subject to dynamics on Lie groups.

97 MATHEMATICS AND COMPUTING↗