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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Integrating Concentrating Solar Power Technologies into the Hybrid Optimization and Performance Platform (HOPP)

As the world increases renewable energy deployment, there is an increasing interest in hybridizing various generation and storage technologies to maximize net benefit to the developer and/or off-taker. A particularly interesting combination of renewable technologies is concentrating solar power (CSP) with thermal energy storage (TES), photovoltaics (PV), and electrochemical battery energy storage (BESS). Due to the system complexity of CSP technology, it is difficult to evaluate the technological and financial performance of a CSP-PV hybrid system without detailed modeling of annual operations. To address this challenge, we have developed a modeling framework for evaluating the performance and financial viability of CSP systems hybridized with PV and battery technologies. This modeling effort incorporates CSP tower and trough systems into an existing modeling tool recently developed by NREL referred to as the Hybrid Optimization and Performance Platform (HOPP). This report outlines the modeling methodology as well as preliminary results from example case studies conducted using the model. The methodology describes: (i) the integration of CSP tower and troughs into HOPP using python interfaces to access System Advisor Model (SAM) underlining technology models, (ii) the mathematical formulation of the mixed integer linear program dispatch optimization model which optimizes operations of storage asset to either maximize system revenue or minimize operating cost while load following, (iii) the design analysis methods implemented within HOPP, and (iv) simulation clustering for the purposes of reducing computational expense. We exercise the model using a case study of a future scenario where we assume (i) CSP and PV technologies achieve the 2030 cost targets provided by the Solar Energy Technologies Office (SETO), (ii) battery costs reduce to the 2030 mid cost projection presented by NREL. Lastly, (iii) electricity prices for southern California in 2030 are provided by NREL's Cambium database, and (iv) a capacity payment of $150/kW-yr based on the system capacity factor during the to 100 net-load hours.

14 SOLAR ENERGY↗
DOE OSTI2014

Nucleon-nucleon interaction: A typical/concise review

Nearly a recent century of work is divided to Nucleon-Nucleon (NN ) interaction issue. We review some overall perspectives of NN interaction with a brief discussion about deuteron, general structure and symmetries of NN Lagrangian as well as equations of motion and solutions. Meanwhile, the main NN interaction models, as frameworks to build NN potentials, are reviewed concisely. We try to include and study almost all well-known potentials in a similar way, discuss more on various commonly used plain forms for two-nucleon interaction with an emphasis on the phenomenological and meson-exchange potentials as well as the constituent-quark potentials and new ones based on chiral effective field theory and working in coordinate-space mostly. The potentials are constructed in a way that fit NN scattering data, phase shifts, and are also compared in this way usually. An extra goal of this study is to start comparing various potentials forms in a unified manner. So, we also comment on the advantages and disadvantages of the models and potentials partly with reference to some relevant works and probable future studies.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Prototype-Wise Sensitivity Analysis of Urban Building Energy Simulation Surrogate Modeling Accuracy

Urban Building Energy Modeling (UBEM) is an important reference for urban energy-related policymaking. Because of the significant impact of urban microclimates on the energy simulation, UBEM requires simulations of many microclimate-prototype pairs. Surrogate modeling is commonly used to reduce the cost of simulation computations. In UBEM surrogate modeling, it is important to determine the percentage of microclimates related to a prototype used for generating surrogate model training data. This study analyzes the prototype-wise variations and sensitivities of surrogate model estimation accuracy to the microclimate sampling ratios. The results of the study can help determine the number of simulations used for generating surrogate modeling data, avoid redundant simulations, and reduce the computational cost for UBEM surrogate modeling and its time.

Pan, Xiyu↗
DOE OSTI2017

A Tutorial on Control-Oriented Modeling and Control of Wind Farms

Wind turbines are often sited together in wind farms as it is economically advantageous. However, the wake inevitably created by every turbine will lead to a time-varying interaction between the individual turbines. Common practice in industry has been to control turbines individually and ignore this interaction while optimizing the power and loads of the individual turbines. However, turbines that are in a wake experience reduced wind speed and increased turbulence, leading to a reduced energy extraction and increased dynamic mechanical loads on the turbine, respectively. Neglecting the dynamic interaction between turbines in control will therefore lead to suboptimal behaviour of the total wind farm. Therefore, wind farm control has been receiving an increasing amount of attention over the past years, with the focus on increasing the total power production and reducing the dynamic loading on the turbines. In this paper, wind farm control-oriented modeling and control concepts are explained. In addition, recent developments and literature are discussed and categorized. This paper can serve as a source of background information and provides many references regarding control-oriented modeling and control of wind farms.

17 WIND ENERGY↗
DOE OSTI2012

Organ doses for reference pediatric and adolescent patients undergoing computed tomography estimated by Monte Carlo simulation

Purpose: To establish an organ dose database for pediatric and adolescent reference individuals undergoing computed tomography (CT) examinations by using Monte Carlo simulation. The data will permit rapid estimates of organ and effective doses for patients of different age, gender, examination type, and CT scanner model. Methods: The Monte Carlo simulation model of a Siemens Sensation 16 CT scanner previously published was employed as a base CT scanner model. A set of absorbed doses for 33 organs/tissues normalized to the product of 100 mAs and CTDI{sub vol} (mGy/100 mAs mGy) was established by coupling the CT scanner model with age-dependent reference pediatric hybrid phantoms. A series of single axial scans from the top of head to the feet of the phantoms was performed at a slice thickness of 10 mm, and at tube potentials of 80, 100, and 120 kVp. Using the established CTDI{sub vol}- and 100 mAs-normalized dose matrix, organ doses for different pediatric phantoms undergoing head, chest, abdomen-pelvis, and chest-abdomen-pelvis (CAP) scans with the Siemens Sensation 16 scanner were estimated and analyzed. The results were then compared with the values obtained from three independent published methods: CT-Expo software, organ dose for abdominal CT scan derived empirically from patient abdominal circumference, and effective dose per dose-length product (DLP). Results: Organ and effective doses were calculated and normalized to 100 mAs and CTDI{sub vol} for different CT examinations. At the same technical setting, dose to the organs, which were entirely included in the CT beam coverage, were higher by from 40 to 80% for newborn phantoms compared to those of 15-year phantoms. An increase of tube potential from 80 to 120 kVp resulted in 2.5-2.9-fold greater brain dose for head scans. The results from this study were compared with three different published studies and/or techniques. First, organ doses were compared to those given by CT-Expo which revealed dose differences up to several-fold when organs were partially included in the scan coverage. Second, selected organ doses from our calculations agreed to within 20% of values derived from empirical formulae based upon measured patient abdominal circumference. Third, the existing DLP-to-effective dose conversion coefficients tended to be smaller than values given in the present study for all examinations except head scans. Conclusions: A comprehensive organ/effective dose database was established to readily calculate doses for given patients undergoing different CT examinations. The comparisons of our results with the existing studies highlight that use of hybrid phantoms with realistic anatomy is important to improve the accuracy of CT organ dosimetry. The comprehensive pediatric dose data developed here are the first organ-specific pediatric CT scan database based on the realistic pediatric hybrid phantoms which are compliant with the reference data from the International Commission on Radiological Protection (ICRP). The organ dose database is being coupled with an adult organ dose database recently published as part of the development of a user-friendly computer program enabling rapid estimates of organ and effective dose doses for patients of any age, gender, examination types, and CT scanner model.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2024

Large language model evaluation for high–performance computing software development

We apply AI-assisted large language model (LLM) capabilities of GPT-3 targeting high-performance computing (HPC) kernels for (i) code generation, and (ii) auto-parallelization of serial code in C ++, Fortran, Python and Julia. Our scope includes the following fundamental numerical kernels: AXPY, GEMV, GEMM, SpMV, Jacobi Stencil, and CG, and language/programming models: (1) C++ (e.g., OpenMP [including offload], OpenACC, Kokkos, SyCL, CUDA, and HIP), (2) Fortran (e.g., OpenMP [including offload] and OpenACC), (3) Python (e.g., numpy, Numba, cuPy, and pyCUDA), and (4) Julia (e.g., Threads, CUDA.jl, AMDGPU.jl, and KernelAbstractions.jl). Kernel implementations are generated using GitHub Copilot capabilities powered by the GPT-based OpenAI Codex available in Visual Studio Code given simple + + prompt variants. To quantify and compare the generated results, we propose a proficiency metric around the initial 10 suggestions given for each prompt. For auto-parallelization, we use ChatGPT interactively giving simple prompts as in a dialogue with another human including simple “prompt engineering” follow ups. Results suggest that correct outputs for C++ correlate with the adoption and maturity of programming models. For example, OpenMP and CUDA score really high, whereas HIP is still lacking. We found that prompts from either a targeted language such as Fortran or the more general-purpose Python can benefit from adding language keywords, while Julia prompts perform acceptably well for its Threads and CUDA.jl programming models. Finally, we expect to provide an initial quantifiable point of reference for code generation in each programming model using a state-of-the-art LLM. Overall, understanding the convergence of LLMs, AI, and HPC is crucial due to its rapidly evolving nature and how it is redefining human-computer interactions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

An analytic and complete equation of state for condensed phase materials

Analytic equations of state (EOS) are intended to reproduce theoretical and experimental data in a single phase portion of the thermodynamic space. We devise a complete and thermodynamically consistent model with four distinct features: (1) a reference isotherm that remains thermodynamically stable, (2) a flexible specific heat model based on a fourth-order rational polynomial, (3) a Grüneisen parameter that depends on specific volume and temperature, and (4) pressure and internal energy functions that can be inverted analytically in temperature. The model aims to improve the accuracy of existing equations of state while remaining computationally efficient. To demonstrate its features, we include calibrations for single-crystal pentaerythritol tetranitrate (PETN), liquid nitromethane (NM), and hexagonal close-packed beryllium (Be) metal. The parameter optimization uses the specific heat capacity, Grüneisen parameter, and static compression curves obtained from density functional theory for the crystalline solids and molecular dynamics simulations for liquid NM. We also present a velocity autocorrelation function that yields accurate phonon densities of states for the EOS calibration from the molecular dynamics trajectories. Each of the three calibrations is constrained to enforce the ambient state from experimental measurements and validated against experimental Hugoniot data from multiple sources. We also include one-dimensional hydrodynamic simulations of the isentropic compression experiments for beryllium conducted at the Z facility.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

Fragmentation Prediction for a Brittle Ceramic: An Integrated Two-Scale Model Approach

A new implementation of a multi-scale fragmentation model is introduced that combines existing independent macro and micro-scale models into a single material model within the Library of Advanced Materials for Engineering (LAME) that can be used directly by the finite element structural mechanics code SIERRA/SM, developed at Sandia National Laboratories. The implementation not only joins existing independent fragmentation models into a single framework, but also enables further development by virtue of being integrated into SIERRA/SM. Integration with a finite element structural mechanics code for a true two-way coupling of the fragmentation models that were previously independent. Hereafter, the prior implementation will be referred to as the sequentially applied fragmentation model. In contrast, the newly developed model will be called the integrated two-scale model. The sequentially applied fragmentation model consists of two independent models applied sequentially to account for the macro-scale and microscale fragmentation. The macro-scale fragmentation behavior is calculated using an elastic gradient damage explicit material model developed to model fracture in brittle materials. The micro-scale fragmentation model is an implementation of the 1D cohesive-zone model developed by Zhou, et al. The micro-scale model is implemented by post-processing the macro-scale data that provides initial conditions for the 1D analysis. The micro-scale model is necessary to predict the resulting fragment size distribution at length scales inaccessible to the finite element based macro-scale model. The full range of fragmentation behavior is then predicted by combining the results from the two independent models. The sequentially applied fragmentation model was used to predict the fragments that result from impact loading of a brittle material, which in that case was a ceramic cylinder of commercial UO{sub 2} nuclear fuel. Understanding the fragmentation behavior of such materials is important for evaluating the risk of airborne particulate release under impact loading scenarios. This work will verify the implementation of the integrated two-scale model using the same experiment modeled by the existing sequentially applied model. The purpose of this manuscript is to introduce the new integrated two-scale fragmentation model and validate the implementation against the existing sequentially applied model for a specific case of impact loading of a brittle material. This validation case will not fully utilize the benefits of having the model integrated into the finite element code as a material model. Rather, this study will demonstrate consistency between the two fragmentation models to ensure that the success of the sequentially applied model will be duplicated by the integrated two-scale approach. Once validated, further development of the model can be made by utilizing the integration into the finite element code to create a fully two-way coupled fragmentation model that will be extended to include higher fidelity models.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

A benchmark dataset for Hydrogen Combustion

The generation of reference data for deep learning models is challenging for reactive systems, and more so for combustion reactions due to the extreme conditions that create radical species and alternative spin states during the combustion process. Here, we extend intrinsic reaction coordinate (IRC) calculations with ab initio MD simulations and normal mode displacement calculations to more extensively cover the potential energy surface for 19 reaction channels for hydrogen combustion. A total of ~290,000 potential energies and ~1,270,000 nuclear force vectors are evaluated with a high quality range-separated hybrid density functional, ωB97X-V, to construct the reference data set, including transition state ensembles, for the deep learning models to study hydrogen combustion reaction.

08 HYDROGEN↗
DOE OSTI2017

Hamiltonian methods of modeling and control of AC microgrids with spinning machines and inverters

This study presents a novel approach to the modeling and control of AC microgrids that contain spinning machines, power electronic inverters and energy storage devices. The inverters in the system can adjust their frequencies and power angles very quickly, so the modeling focuses on establishing a common reference frequency and angle in the microgrid based on the spinning machines. From this dynamic model, nonlinear Hamiltonian surface shaping and power flow control method is applied and shown to stabilize. From this approach the energy flow in the system is used to show the energy storage device requirements and limitations for the system. This paper first describes the model for a single bus AC microgrid with a Hamiltonian control, then extends this model and control to a more general class of multiple bus AC microgrids. Finally, simulation results demonstrate the efficacy of the approach in stabilizing and optimization of the microgrid.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Bayesian model mixing with multireference energy density functional

Reliably predicting nuclear properties across the entire chart of isotopes is important for applications ranging from nuclear astrophysics to superheavy science to nuclear technology. To this day, however, all the theoretical models that can scale at the level of the chart of isotopes remain semiphenomenological. Because they are fitted locally, their predictive power can vary significantly; different versions of the same theory provide different predictions. Bayesian model mixing takes advantage of such imperfect models to build a local mixture of a set of models to make improved predictions. Earlier attempts to use Bayesian model mixing for mass table calculations relied on models treated at single-reference energy density functional level, which fail to capture some of the correlations caused by configuration mixing or the restoration of broken symmetries. In this study we have applied Bayesian model mixing techniques within a multireference energy density functional (MR-EDF) framework. We considered predictions of two-particle separation energies from particle number projection or angular momentum projection with four different energy density functionals—a total of eight different MR-EDF models. We used a hierarchical Bayesian stacking framework with a Dirichlet prior distribution over weights together with an inverse log-ratio transform to enable positive correlations between different models. We found that Bayesian model mixing provides significantly improved predictions compared to the participating models. Published by the American Physical Society 2025

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Safeguards Considerations for Coated Particle Fuel Fabrication Facilities

This study aims to identify where existing fuel fabrication safeguards are limited in application to coated particle fuel fabrication facilities; perform a review of techniques that may be appropriate to address these limitations; and identify where further study is required. The purpose is to ensure the necessary technology and safeguards developments are established to facilitate safeguards-by-design for coated particle fuel fabrication facilities, analogous to the research and development (R&D) efforts in the advanced reactor space, including those requiring coated particle fuels and progress to higher technology readiness levels. Finally, this study will also help meet high priority objectives set forth by the IAEA in establishing safeguards R&D precedence and measurement/procedural standards at emerging fuel fabrication facilities. To achieve these objectives, the report is formatted to (1) distill relevant background information on fuel fabrication of oxide and coated particle fuels; (2) provide an overview of the fuel fabrication techniques for a reference oxide fuel fabrication facility and two selected TRISO fuel fabrication facilities; (3) develop facility models of safeguards approaches for the reference facility and the two TRISO facilities; and (4) identify any observed technology needs or gaps from this analysis.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2014

Design of Experiments, Model Calibration and Data Assimilation

This presentation provides an overview of emulation, calibration and experiment design for computer experiments. Emulation refers to building a statistical surrogate from a carefully selected and limited set of model runs to predict unsampled outputs. The standard kriging approach to emulation of complex computer models is presented. Calibration refers to the process of probabilistically constraining uncertain physics/engineering model inputs to be consistent with observed experimental data. An initial probability distribution for these parameters is updated using the experimental information. Markov chain Monte Carlo (MCMC) algorithms are often used to sample the calibrated parameter distribution. Several MCMC algorithms commonly employed in practice are presented, along with a popular diagnostic for evaluating chain behavior. Space-filling approaches to experiment design for selecting model runs to build effective emulators are discussed, including Latin Hypercube Design and extensions based on orthogonal array skeleton designs and imposed symmetry requirements. Optimization criteria that further enforce space-filling, possibly in projections of the input space, are mentioned. Designs to screen for important input variations are summarized and used for variable selection in a nuclear fuels performance application. This is followed by illustration of sequential experiment design strategies for optimization, global prediction, and rare event inference.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2016

Thermal Safety Analyses for the Production of Plutonium-238 at the High Flux Isotope Reactor

There has been a considerable effort over the previous few years to demonstrate and optimize the production of plutonium-238 ( 238 Pu) at the High Flux Isotope Reactor (HFIR). This effort has involved resources from multiple divisions and facilities at the Oak Ridge National Laboratory (ORNL) to demonstrate the fabrication, irradiation, and chemical processing of targets containing neptunium-237 ( 237 Np) dioxide (NpO 2 )/aluminum (Al) cermet pellets. A critical preliminary step to irradiation at the HFIR is to demonstrate the safety of the target under irradiation via documented experiment safety analyses. The steady-state thermal safety analyses of the target are simulated in a finite element model with the COMSOL Multiphysics code that determines, among other crucial parameters, the limiting maximum temperature in the target. Safety analysis efforts for this model discussed in the present report include: (1) initial modeling of single and reduced-length pellet capsules in order to generate an experimental knowledge base that incorporate initial non-linear contact heat transfer and fission gas equations, (2) modeling efforts for prototypical designs of partially loaded and fully loaded targets using limited available knowledge of fabrication and irradiation characteristics, and (3) the most recent and comprehensive modeling effort of a fully coupled thermo-mechanical approach over the entire fully loaded target domain incorporating burn-up dependent irradiation behavior and measured target and pellet properties, hereafter referred to as the production model. These models are used to conservatively determine several important steady-state parameters including target stresses and temperatures, the limiting condition of which is the maximum temperature with respect to the melting point. The single pellet model results provide a basis for the safety of the irradiations, followed by parametric analyses in the initial prototypical designs that were necessary due to the limiting fabrication and irradiation data available. The calculated parameters in the final production target model are the most accurate and comprehensive, while still conservative. Over 210 permutations in irradiation time and position were evaluated, and are supported by the most recent inputs and highest fidelity methodology. The results of these analyses show that the models presented in this report provide a robust and reliable basis for previous, current and future experiment safety analyses. In addition, they reveal an evolving knowledge of the steady-state behavior of the NpO 2 /Al pellets under irradiation for a variety of target encapsulations and potential conditions.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Data for Bistline, et al. (2025) "Policy Implications of Net-Zero Emissions: A Multi-Model Analysis of United States Emissions and Energy System Impacts"

These files contain input assumptions, results, and figures associated with the Bistline, et al. (2025) article "Policy Implications of Net-Zero Emissions: A Multi-Model Analysis of United States Emissions and Energy System Impacts" in Energy and Climate Change as part of the Energy Modeling Forum 37 study. Please refer to the original paper for details.

climate policy↗
DOE OSTI2024

Near-global summer circulation response to the spring surface temperature anomaly in Tibetan Plateau –– the GEWEX/LS4P first phase experiment

Subseasonal to seasonal (S2S) prediction of droughts and floods is one of the major challenges of weather and climate prediction. Recent studies suggest that the springtime land surface temperature/subsurface temperature (LST/SUBT) over the Tibetan Plateau (TP) can be a new source of S2S predictability. The project “Impact of Initialized Land Surface Temperature and Snowpack on Subseasonal to Seasonal Prediction (LS4P)” was initiated to study the impact of springtime LST/SUBT anomalies over high mountain areas on summertime precipitation predictions. The present work explores the simulated global scale response of the atmospheric circulation to the springtime TP land surface cooling by 16 current state-of-the-art Earth System Models (ESMs) participating in the LS4P Phase I (LS4P-I) experiment. The LS4P-I results show, for the first time, that springtime TP surface anomalies can modulate a persistent quasi-barotropic Tibetan Plateau-Rocky Mountain Circumglobal (TRC) wave train from the TP via the northeast Asia and Bering Strait to the western part of the North America, along with the springtime westerly jet from TP across the whole North Pacific basin. The TRC wave train modulated by the TP thermal anomaly play a critical role on the early summer surface air temperature and precipitation anomalies in the regions along the wave train, especially over the northwest North America and the southern Great Plains. The participant models that fail in capturing the TRC wave train greatly under-predict climate anomalies in reference to observations and the successful models. These results suggest that the TP LST/SUBT anomaly via the TRC wave train is the first order source of the S2S variability in the regions mentioned. Furthermore, the TP surface temperature anomaly can influence the Southern Hemispheric circulation by generating cross-equator wave trains. However, the simulated propagation pathways from the TP into the Southern Hemisphere show large inter-model differences. More dynamical understanding of the TRC wave train as well as its cross-equator propagation into the Southern Hemisphere will be explored in the newly launched LS4P phase II experiment.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2013

A multi-objective programming model for assessment the GHG emissions in MSW management

Highlights: • The multi-objective multi-period optimization model. • The solution approach for the generation of the Pareto front with mathematical programming. • The very detailed description of the model (decision variables, parameters, equations). • The use of IPCC 2006 guidelines for landfill emissions (first order decay model) in the mathematical programming formulation. - Abstract: In this study a multi-objective mathematical programming model is developed for taking into account GHG emissions for Municipal Solid Waste (MSW) management. Mathematical programming models are often used for structure, design and operational optimization of various systems (energy, supply chain, processes, etc.). The last twenty years they are used all the more often in Municipal Solid Waste (MSW) management in order to provide optimal solutions with the cost objective being the usual driver of the optimization. In our work we consider the GHG emissions as an additional criterion, aiming at a multi-objective approach. The Pareto front (Cost vs. GHG emissions) of the system is generated using an appropriate multi-objective method. This information is essential to the decision maker because he can explore the trade-offs in the Pareto curve and select his most preferred among the Pareto optimal solutions. In the present work a detailed multi-objective, multi-period mathematical programming model is developed in order to describe the waste management problem. Apart from the bi-objective approach, the major innovations of the model are (1) the detailed modeling considering 34 materials and 42 technologies, (2) the detailed calculation of the energy content of the various streams based on the detailed material balances, and (3) the incorporation of the IPCC guidelines for the CH{sub 4} generated in the landfills (first order decay model). The equations of the model are described in full detail. Finally, the whole approach is illustrated with a case study referring to the application of the model in a Greek region.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2021

From hard spheres to hard-core spins

A system of hard spheres exhibits physics that is controlled only by their density. This comes about because the interaction energy is either infinite or zero, so all allowed configurations have exactly the same energy. The low-density phase is liquid, while the high-density phase is crystalline, an example of “order by disorder” as it is driven purely by entropic considerations. Here we study a family of hard spin models, which we call hard-core spin models, where we replace the translational degrees of freedom of hard spheres with the orientational degrees of freedom of lattice spins. Their hard-core interaction serves analogously to divide configurations of the many spin system into allowed and disallowed sectors. We present detailed results on the square lattice in d = 2 for a set of models with $\mathbb{Z}_n$ symmetry, which generalize Potts models, and their U(1) limits, for ferromagnetic and antiferromagnetic senses of the interaction, which we refer to as exclusion and inclusion models. As the exclusion and inclusion angles are varied, we find a Kosterlitz-Thouless phase transition between a disordered phase and an ordered phase with quasi-long-ranged order, which is the form order by disorder takes in these systems. These results follow from a set of height representations, an ergodic cluster algorithm, and transfer matrix calculations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗