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At least 649 records · Page 36

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NASA NTRS2012

Community Coordinated Modeling Center: Addressing Needs of Operational Space Weather Forecasting

Models are key elements of space weather forecasting. The Community Coordinated Modeling Center (CCMC, http://ccmc.gsfc.nasa.gov) hosts a broad range of state-of-the-art space weather models and enables access to complex models through an unmatched automated web-based runs-on-request system. Model output comparisons with observational data carried out by a large number of CCMC users open an unprecedented mechanism for extensive model testing and broad community feedback on model performance. The CCMC also evaluates model's prediction ability as an unbiased broker and supports operational model selections. The CCMC is organizing and leading a series of community-wide projects aiming to evaluate the current state of space weather modeling, to address challenges of model-data comparisons, and to define metrics for various user s needs and requirements. Many of CCMC models are continuously running in real-time. Over the years the CCMC acquired the unique experience in developing and maintaining real-time systems. CCMC staff expertise and trusted relations with model owners enable to keep up to date with rapid advances in model development. The information gleaned from the real-time calculations is tailored to specific mission needs. Model forecasts combined with data streams from NASA and other missions are integrated into an innovative configurable data analysis and dissemination system (http://iswa.gsfc.nasa.gov) that is accessible world-wide. The talk will review the latest progress and discuss opportunities for addressing operational space weather needs in innovative and collaborative ways.

Kuznetsova, M.↗

NASA NTRS2015

Mineralogy of Interplanetary Dust Particles from the Comet Giacobini-Zinner Dust Stream Collections

The Draconoid meteor shower, originating from comet 21P/Giacobini-Zinner, is a low-velocity Earth-crossing dust stream that had a peak anticipated flux on Oct. 8, 2012. In response to this prediction, NASA performed dedicated stratospheric dust collections to target interplanetary dust particles (IDPs) from this comet stream on Oct 15-17, 2012 [3]. Twelve dust particles from this targeted collection were allocated to our coordinated analysis team for studies of noble gas (Univ. Minnesota, Minnesota State Univ.), SXRF and Fe-XANES (SSL Berkeley) and mineralogy/isotopes (JSC). Here we report a mineralogical study of 3 IDPs from the Draconoid collection..

Nakamura-Messenger, K.↗

NASA NTRS2017

Development of a High-Fidelity Simulation Environment for Shadow-Mode Assessments of Air Traffic Concepts

This paper describes the Shadow-Mode Assessment Using Realistic Technologies for the National Airspace System (SMART-NAS) Test Bed. The SMART-NAS Test Bed is an air traffic simulation platform being developed by the National Aeronautics and Space Administration (NASA). The SMART-NAS Test Bed's core purpose is to conduct high-fidelity, real-time, human-in-the-loop and automation-in-the-loop simulations of current and proposed future air traffic concepts for the United States' Next Generation Air Transportation System called NextGen. The setup, configuration, coordination, and execution of realtime, human-in-the-loop air traffic management simulations are complex, tedious, time intensive, and expensive. The SMART-NAS Test Bed framework is an alternative to the current approach and will provide services throughout the simulation workflow pipeline to help alleviate these shortcomings. The principle concepts to be simulated include advanced gate-to-gate, trajectory-based operations, widespread integration of novel aircraft such as unmanned vehicles, and real-time safety assurance technologies to enable autonomous operations. To make this possible, SNTB will utilize Web-based technologies, cloud resources, and real-time, scalable, communication middleware. This paper describes the SMART-NAS Test Bed's vision, purpose, its concept of use, and the potential benefits, key capabilities, high-level requirements, architecture, software design, and usage.

human-in-the-loop↗

NASA NTRSDate not supplied

Real-time Hardware-in-the-Loop Evaluation of a Partially Turboelectric Propulsion Control Design

In support of aviation fuel burn and emission reduction goals, NASA is pursuing high-payoff research investments that promise to transform aviation. This includes investments in Electrified Aircraft Propulsion (EAP). Multiple technology challenges must be addressed to unlock the full potential of EAP. This includes addressing challenges related to propulsion controls, which will be vital for ensuring efficient coordinated operation of EAP subsystems. This paper presents results from real-time hardware-in-the-loop testing of a control design for a single aisle partially-turboelectric aircraft propulsion concept conducted at the NASA Electric Aircraft Testbed (NEAT) facility. The control system under test is designed for a propulsion concept consisting of two wing-mounted turbofan engines that produce thrust and generate electrical power to drive a boundary layer ingesting tailfan propulsor via an electrical motor. An integrated control strategy is applied to ensure coordinated operation of the turbofan and tailfan subsystems during steady-state and transient operation throughout the flight envelope. The NEAT test of this integrated control design consists of a partially hardware-in-the-loop, partially simulated configuration. A subscale representation of the electrical system design is implemented in hardware and mechanically coupled to electric machines that emulate turbomachinery and propulsor shaft dynamics. The hardware configuration is then operated under the control of a real-time computer application that runs a simulation of the propulsion system and the developed control logic. The NEAT facility test campaign includes a series of experiments that subject the control design to throttle transients conducted throughout the flight envelope and full-flight mission profiles. Testing under simulated performance degradation is also conducted to evaluate control design robustness. This includes constant and abrupt changes in degradation levels. Results from the hardware-in-the-loop test are presented and shown to be in good agreement with pre-test simulation predictions demonstrating the efficacy of the integrated control design approach.

Electrified Aircraft Propulsion↗

NASA NTRSDate not supplied

Real-time Hardware-in-the-Loop Evaluation of a Partially Turboelectric Propulsion Control Design

Electrified Aircraft Propulsion↗

NASA NTRS2023

Real-Time Hardware-in-the-Loop Evaluation of A Partially Turboelectric Propulsion Control Design

In support of aviation fuel burn and emission reduction goals, NASA is pursuing high-payoff research investments that promise to transform aviation. This includes investments in Electrified Aircraft Propulsion (EAP). Multiple technology challenges must be addressed to unlock the full potential of EAP. This includes addressing challenges related to propulsion controls, which will be vital for ensuring efficient coordinated operation of EAP subsystems. This paper presents results from real-time hardware-in-theloop (HIL) testing of a control design for a single aisle partially-turboelectric aircraft propulsion concept conducted at the NASA Electric Aircraft Testbed (NEAT) facility. The control system under test is designed for a propulsion concept consisting of two wing-mounted turbofan engines that produce thrust and generate electrical power to drive a boundary layer ingesting tailfan propulsor via an electrical motor. An integrated control strategy is applied to ensure coordinated operation of the turbofan and tailfan subsystems during steady-state and transient operation throughout the flight envelope. The NEAT test of this integrated control design consists of a partially HIL, partially simulated configuration. A subscale representation of the electrical system design is implemented in hardware and mechanically coupled to electric machines that emulate turbomachinery and propulsor shaft dynamics. The hardware configuration is then operated under the control of a real-time computer application that runs a simulation of the propulsion system and the developed control logic. The NEAT facility test campaign includes a series of experiments that subject the control design to throttle transients conducted throughout the flight envelope and full-flight mission profiles. Testing under simulated performance degradation is also conducted to evaluate control design robustness. This includes constant and abrupt changes in degradation levels. Results from the HIL test are presented and shown to be in good agreement with pretest simulation predictions demonstrating the efficacy of the integrated control design approach.

Electrified Aircraft Propulsion↗

DOE OSTI2020

DC Fast Charging Infrastructure for Electrified Road Trips

To assess DC fast charging station network required for electrified road trips by 2030 in California, a new charging infrastructure simulation tool/model, EVI-Pro (Electric Vehicle Infrastructure Projection) RoadTrip, has been developed. In contrast to the existing EVI-Pro model that is primarily for short-distance travels, EVI-Pro RoadTrip is exclusively focused on road trips (long-distance travels, 100 or miles per day per vehicle). Also, the charging paradigm or strategy is different. EVI-Pro RoadTrip is built upon waypoint charging, in which vehicles are forced to stop to charge or replenish the on-board batteries, along the routes between origins and destinations. On the other hand, EVI-Pro is based on destination charging, in which charging is conducted when vehicles are parked in destinations (e.g., work, home). EVI-Pro RoadTrip takes coordinate-level origin and destination data for road trips (intra-state as well as domestic or international out-of-state) and estimates energy consumption and charging needs along the routes between origins and destinations on a minute-by-minute resolution. Based on charging demands for electrified road trips across the state, the optimal locations of charging stations are determined accounting for preferred land use types (e.g., commercial areas) and station service area (e.g., 5 or less miles). Based on station-by-station charging load profiles, the required number of plugs/connectors is estimated for each station and entire state. By comparing hosting capacity of the electric grid (circuit-level) and the charging load output from EVI-Pro RoadTrip, capacity deficit is also evaluated.

ADVANCED PROPULSION SYSTEMS,ENERGY STORAGE↗

DOE OSTI2020

Steady-State Analysis of Microgrid Distributed Control Under Denial of Service Attacks

Distributed control is an effective method to coordinate multiple components in a microgrid. It usually has mandatory requirements for communication graph topology; changing the topology unexpectedly could disrupt the operation of a distributed controller. A denial of service (DoS) attack blocks communication channels to cause variations in communication graph. Unforeseen topology changes render a controller to receive incomplete system information. Control decisions made based on incorrect information can lead to significantly reduced grid supporting capability. As a result, the vital power balance between generation and load may be challenged. Determining power balance requires steady-state power flow analysis; however, the cyber-induced steady-state analysis is not well studied in the literature. Here, in this article, we show that a cyber–physical microgrid with unknown DoS attacks has augmented uncertain power flow equations, whose special structure creates new computational issue to determining power balance. To deal with the issue, we develop a novel cyber-induced microgrid model: the cyber–physical system is transformed into a pure physical model, where the disruption effects of DoS in the cyber layer are shown to be equivalent to the variations of the physical model parameters. With the transformed system, we develop a sufficient condition to ascertain the system power balance under unknown DoS attacks. In addition, practical insights for resilient distributed control design are shown as well.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2020

Room‐Temperature Phosphorescent Platinum(II) Alkynyls with Microsecond Lifetimes Bearing a Strong‐Field Pincer Ligand

Abstract The use of organometallic triplet emitters in organic light emitting diodes (OLEDs) is motivated by the premise of efficient intersystem crossing leading to unit internal quantum efficiencies. However, since most devices are based on solid‐state components, an inherent limitation to square‐planar platinum(II) phosphors is their tendency toward aggregation‐based quenching. Here, a new class of emissive, four‐coordinate Pt II species based on the bisimidazolyl carbazolide (BIMCA) ligand is introduced, which displays highly efficient, long‐lived solid‐state phosphorescence at room temperature. A set of four BIMCAPt phenyl acetylides were synthesized that emit in the green ( λ max =507–540 nm) with >60 % quantum yield and millisecond lifetimes. The structures of the resulting species reveal a non‐planar structure imposed by steric clashes between BIMCA and the iodo or alkynyl co‐ligand. Ground‐state and photophysical characterization are presented. Density functional theory calculations indicate that the BIMCA ligand dominates the frontier orbitals along with the first Franck–Condon singlet and triplet excited states.

Liska, Tadeas↗

DOE OSTI2025

Analysis of Bis(trifluoromethylsulfonyl)imide Interactions with Metal Cations Through a Chemical Informatics Approach

Nominally weakly coordinating anions are useful for modulating the solubility and chemical properties of metal complexes, but identification and analysis of the systematics of the interactions of anions with cationic metal complexes has not received the attention it deserves. Here, a chemical informatics approach is demonstrated for identifying and quantitatively analyzing the ways that the bis(trifluoromethylsulfonyl)imide anion (TFSI) can interact with metal-containing species. An open access computer program (PyCIFTer) was developed to facilitate large-scale structural analysis of TFSI-containing species by utilization of experimental atomic coordinate data from single-crystal X-ray diffraction (XRD) studies obtained from the Cambridge Structural Database (CSD). PyCIFTer establishes a three-dimensional vector space from the raw atomic coordinates, generating acyclic, undirected graphs that are used to rapidly analyze the structural properties (bond lengths and angles) of TFSI in individual structures in sequential/batch fashion. The structures are sorted by PyCIFTer into groups based on pre-set and chemically sensible criteria, affording a comprehensive and systematic view of TFSI structural chemistry. This approach avoids tedious one-at-a-time interrogation of structures, a prospect unreasonable in this case, and many others of contemporary chemical relevance; there were over 1500 structures in the CSD containing TFSI as of November 2024. The results demonstrate that TFSI only rarely binds to cations in the solid state, favoring the formation of species in which TFSI is found in cations’ outer coordination spheres. The prospect of applying PyCIFTer to other moieties is also discussed. PyCIFTer is also schematically compared to the commercial CSD Python application programming interface (API). Taken together, this work demonstrates the usefulness of modular workflows for sequential/batch analysis of structural data from XRD, an approach that appears poised to accelerate the translation of legacy structural results into new chemical insights and hypotheses.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1974

Investigations on classification categories for wetlands of Chesapeake Bay using remotely sensed data

The use of remote sensors to determine the characteristics of the wetlands of the Chesapeake Bay and surrounding areas is discussed. The objectives of the program are stated as follows: (1) to use data and remote sensing techniques developed from studies of Rhode River, West River, and South River salt marshes to develop a wetland classification scheme useful in other regions of the Chesapeake Bay and to evaluate the classification system with respect to vegetation types, marsh physiography, man-induced perturbation, and salinity; and (2) to develop a program using remote sensing techniques, for the extension of the classification to Chesapeake Bay salt marshes and to coordinate this program with the goals of the Chesapeake Research Consortium and the states of Maryland and Virginia. Maps of the Chesapeake Bay areas are developed from aerial photographs to display the wetland structure and vegetation.

Williamson, F. S. L.↗

DOE OSTI2026

Polyoxometalate-Assisted Crystallization: A General Strategy Enabling Structural Characterization of Molecular Radium Complexes

A fundamental understanding of radium (Ra) coordination chemistry has been hindered by the scarcity and radiological hazards of 226 Ra, leaving the structural characterization of molecular Ra complexes almost entirely unexplored. Here, we introduce a polyoxometalate (POM)-assisted crystallization strategy that enables single-crystal X-ray diffraction analysis of Ra–chelator complexes from microgram-scale samples. Employing the plenary Keggin anion [SiW 12 O 40 ] 4– , we isolated and structurally characterized Ra 2+ complexes of 18-crown-6 and the bis-picolinate macrocycle macropa, together with their Sr 2+ and Ba 2+ analogues. The resulting structures reveal systematic, size-dependent trends in coordination number and metal-donor distances across the alkaline earth series and provide the first direct experimental measurements of Ra–N and Ra–OCOO bond distances. Together, these results establish POM-assisted crystallization as a robust approach for obtaining solid-state structural information on Ra 2+ complexes of organic chelators, opening new opportunities to advance the coordination chemistry needed to fully realize radium’s potential in isotope production and targeted radiotherapy. More broadly, this approach expands the experimental toolkit available for studying scarce, highly radioactive elements accessible only in microgram quantities.

Anions↗

DOE OSTI2026

Explainable machine learning reveals that local structural motifs encode the thermodynamic state across the CuZr metallic glass-forming range

Metallic glasses derive their properties from the statistics of local atomic motifs rather than from long-range order, yet a quantitative, chemistry-specific link between motif populations and the underlying glassy state has remained elusive. In this work we combine large-scale molecular dynamics, Voronoi tessellation, deep neural networks, and SHapley Additive exPlanations (SHAP) to identify which local structural motifs define the glassy state of Cu—Zr metallic glasses. A dataset of 17,180 atomistic configurations spanning ten compositions (Cu 20 Zr 80 –Cu 80 Zr 20 ) and four quench rates (10 9 –10 12 K/s) is used to train a feed-forward neural network that regresses temperature across the 50–2000 K liquid–supercooled–glass range, achieving a mean absolute error of 19.89 K and R 2 = 0.9974, confirming that the local structural state is faithfully encoded in motif-level structure. SHAP analysis then reveals that a tightly coupled near-icosahedral family of motifs (coordination numbers (CN) 11–13, including the full icosahedron 001200 and its single-atom-perturbation sibling 10930) collectively encodes the thermodynamic state of the system across the full glass-forming range. The CN = 11–13 ordered members carry negative SHAP values at high populations, tracking the most deeply-quenched configurations, while 10930 shows the reversed signature consistent with its role as a soft-spot host whose population shrinks as the icosahedral network deepens. The analysis demonstrates that explainable machine learning can isolate the minimal motif vocabulary defining the glassy state and recovers the near-icosahedral building blocks previously identified by data-driven analyses of Cu—Zr. The approach provides a general, chemistry-specific route for characterizing the structural state of disordered materials.

36 MATERIALS SCIENCE↗

DOE OSTI2025

A Novel Protection Scheme for Unbalanced Faults in Inverter Dominated Networks: A Computationally Efficient Algorithm for Entry-Level Relays

Microgrids are now a common practice in distribution systems to increase resilience and reliability. However, microgrid protection remains a critical challenge, considering its requirement to operate in both grid connected and islanded, and the variability in fault characteristics under each mode of operation. This paper presents unbalanced power (S unb ) based fault detection algorithm, which considers local voltage and current unbalances to determine faults in the system. S unb is a computationally efficient fault detection algorithm that is suitable for implementation in the programmable logic of entry level protective relays. In addition, the difference in current and voltage unbalance (D n ) is used to determine the fault type. The proposed method demonstrates high sensitivity and selectivity for line-to-ground (LG), line-to-line (LL), and double line-to-ground (LLG) faults, representing the most common faults in distribution systems. It also allows relay coordination with upstream and downstream protection devices in both island and grid connected operation, while preserving grading margins. The same pickup and time multiplier settings of a particular relay for both modes of operation eliminates the need for adaptive settings, which rely on communication networks. Validation was performed with a hardware-in-the-loop (HIL) setup using Typhoon HIL real time simulator interfaced with three entry-level, SEL 751 relays. Results confirmed the algorithm’s ability to discriminate fault conditions, and determine the fault type under both operating modes, maintain fast detection times, and ensure proper protection coordination.

fault classification↗

DOE OSTI2025

Alkaline Earth-Based Ternary Chalcogenide Nanocrystals: Cadmium- and Lead-Free Optical Materials

As some of the most abundant elements on the Earth’s crust, alkaline earths bear great potential in Cd- and Pb-free catalytic, energy conversion, and light-emitting devices. Further, because large electropositive alkaline earths (Ae) can adopt high coordination numbers, they offer structural complexity beyond the tetrahedral (c-Si, II–VI, III–V) or octahedral (IV–VI) atomic sites that─with the notable exception of halide perovskites─are ubiquitous among nanocrystalline semiconductors. Here, in this work, we present a general route to photoluminescent 6–125 nm nanocrystals of ternary AeIn 2 Ch 4 semiconductors (Ae = Sr, Ba; Ch = S, Se) featuring eight- (Ae) as well as four-coordinate (In and Ch) atomic sites. Powder X-ray diffraction, electron microscopy, optical absorption, photoluminescence, and solid-state (ss)NMR spectroscopies attest to the ternary composition and phase purity of the nanocrystals. Continuous shape measures pinpoint the degree of distortion of individual crystallographic sites from ideal coordination polyhedra, allowing us to identify two very distinct types of Se coordination environments. Based on their higher order, pseudo-3-fold rotational symmetry, we assign 77 Se ssNMR peaks with negligible chemical shift anisotropy (CSA) to pyramidalized Se sites with vacant-trigonal bipyramid-like geometries and those with larger CSA to lower symmetry Se sites with seesaw-distorted geometries. Calculations help to better understand the electronic band structure of these materials. The nanocrystals are stable at room temperature in open air for several weeks, and some compositions up to 1000 °C under Ar, making them strong candidates for practical applications.

alkaline earth↗

DOE OSTI2020

State Charlton & MRCSP 1 Characterization Well Report

The Midwest Regional Carbon Sequestration Partnership (MRCSP) was founded in 2003 as part of the U.S. Department of Energy’s (DOE’s) Regional Carbon Sequestration Partnership initiative. Since its founding, MRCSP has made significant strides toward making CCUS a viable option for states in the region. The public/private consortium, funded through the DOE Regional Carbon Sequestration Initiative, brings together nearly 40 industry partners and 10 states. Battelle, as the project lead, oversees research, development and operations and coordinates activities among the partners. The incremental, phased approach has built a valuable knowledge base for the industry and paved the way for commercial-scale adoption of CCUS technologies. From 2008 to 2020, MRCSP Phase III focused on the development of large-scale injection projects. This report is part of a series of reports prepared under the Midwestern Regional Carbon Sequestration Partnership (MRCSP) Phase III (Development Phase). These reports summarize and detail the findings of the work conducted under the Phase III project. This report describes the efforts to drill and complete a well in the St. Peter sandstone for characterization and evaluation of storage potential in norther Michigan. However, as presented in this report, the well was not drilled and completed up to the intended target intervals due to drilling related difficulties. While the drilling issues were being resolved, the new Class VI injection well regulations were finalized by the US EPA. MRCSP efforts focused on evaluating CO 2 storage and containment using site characterization, modeling, and monitoring in conjunction with the ongoing CO 2 -EOR operations in the same area. This report describes work associated with the initial test well, the State Chester and MRCSP Well No. 1, drilled to a depth of about 7,968 feet TVD, and subsequently plugged and designated as temporarily abandoned. A high-level overview of data collected and analyzed is provided for shallower units.

01 COAL, LIGNITE, AND PEAT↗

NASA NTRS2011

Project Management Using Modern Guidance, Navigation and Control Theory

Implementing guidance, navigation, and control (GN&C) theory principles and applying them to the human element of project management and control is not a new concept. As both the literature on the subject and the real-world applications are neither readily available nor comprehensive with regard to how such principles might be applied, this paper has been written to educate the project manager on the "laws of physics" of his or her project (not to teach a GN&C engineer how to become a project manager) and to provide an intuitive, mathematical explanation as to the control and behavior of projects. This paper will also address how the fundamental principles of modern GN&C were applied to the National Aeronautics and Space Administration's (NASA) Constellation Program (CxP) space suit project, ensuring the project was managed within cost, schedule, and budget. A project that is akin to a physical system can be modeled and managed using the same over arching principles of GN&C that would be used if that project were a complex vehicle, a complex system(s), or complex software with time-varying processes (at times nonlinear) containing multiple data inputs of varying accuracy and a range of operating points. The classic GN&C theory approach could thus be applied to small, well-defined projects; yet when working with larger, multiyear projects necessitating multiple organizational structures, numerous external influences, and a multitude of diverse resources, modern GN&C principles are required to model and manage the project. The fundamental principles of a GN&C system incorporate these basic concepts: State, Behavior, Feedback Control, Navigation, Guidance and Planning Logic systems. The State of a system defines the aspects of the system that can change over time; e.g., position, velocity, acceleration, coordinate-based attitude, and temperature, etc. The Behavior of the system focuses more on what changes are possible within the system; this is denoted in the state of the system. The behavior of a system, as captured in the system modeling, when properly done will aid in accurately predicting future system performance. The Feedback Control system understands the state and behavior of the system and uses feedback to adjust control inputs into the system. The feedback, which is the right arm of the Control system, allows change to be affected in the overall system; it therefore is important to not only correctly identify the system feedback inputs, but also the system response to the feedback inputs. The Navigation system takes multiple data inputs and based on a priori knowledge of the inputs, develops a statistically based weighting of the inputs and measurements to determine the system's state. Guidance and Planning Logic of the system, complete with an understanding of where the system is (provided by the Navigation system), will in turn determine where the system needs to be and how to get it there. With any system/project, it is critical that the objective of the system/project be clearly defined -- not only to plan but to measure performance and to aid in guiding the system or the project. The system principles discussed above, which can be and have been applied to the current CxP space suit development project, can also be mapped to real-world constituents, thus allowing project managers to apply systems theories that are well defined in engineering and mathematics to a discipline (i.e., Project Management) that historically has been based in personal experience and intuition. This mapping of GN&C theory to Project Management will, in turn, permit a direct, methodical approach to Project Management, planning and control providing a tool to help predict (and guide) performance and an understanding of the project constraints, how the project can be controlled, and the impacts to external influences and inputs. This approach, to a project manager, flows down to the three bottom-line variables of cost, schedule, and scope ando the needed control of these three variables to successfully perform and complete a project.

Hill, Terry R.↗

NASA NTRS1976

Rigid rotators

The two-particle, steady-state Schroedinger equation is transformed to center of mass and internuclear distance vector coordinates, leading to the free particle wave equation for the kinetic energy motion of the molecule and a decoupled wave equation for a single particle of reduced mass moving in a spherical potential field. The latter describes the vibrational and rotational energy modes of the diatomic molecule. For fixed internuclear distance, this becomes the equation of rigid rotator motion. The classical partition function for the rotator is derived and compared with the quantum expression. Molecular symmetry effects are developed from the generalized Pauli principle that the steady-state wave function of any system of fundamental particles must be antisymmetric. Nuclear spin and spin quantum functions are introduced and ortho- and para-states of rotators, along with their degeneracies, are defined. Effects of nuclear spin on entropy are deduced. Next, rigid polyatomic rotators are considered and the partition function for this case is derived. The patterns of rotational energy levels for nonlinear molecules are discussed for the spherical symmetric top, for the prolate symmetric top, for the oblate symmetric top, and for the asymmetric top. Finally, the equilibrium energy and specific heat of rigid rotators are derived.

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