Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “simulation testbed”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 451 records · Page 25
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Performance-driven optimization of urban open space configuration in the cold-winter and hot-summer region of China

Urbanization has led to changes in urban morphology and climate, while urban open space has become an important ecological factor for evaluating the performance of urban development. This study presents an optimization approach using computational performance simulation. With a genetic algorithm using the Grasshopper tool, this study analyzed the layout and configuration of urban open space and its impact on the urban micro-climate under summer and winter conditions. The outdoor mean Universal Thermal Climate Index (UTCI) was applied as the performance indicator for evaluating the quality of the urban micro-climate. Two cases—one testbed and one real urban block in Nanjing, China -- were used to validate the computer-aided simulation process. The optimization results in the testbed showed UTCI values varied from 36.5 to 37.3 °C in summer and from -4.9 to -1.9 °C in winter. In the case of the real urban block, optimization results show, for summer, although the average UTCI value increased by 0.6 °C, the average air velocity increased by 0.2 m/s; while in winter, the average UTCI value increased by 1.7 °C and the average air velocity decreased by 0.2 m/s. These results demonstrate that the proposed computer-aided optimization process can improve the thermal comfort conditions of open space in urban blocks. Finally, this study discusses strategies and guidelines for the layout design of urban open space to improve urban environment comfort.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
NASA NTRS2016

Link Adaptation for Mitigating Earth-To-Space Propagation Effects on the NASA SCaN Testbed

In Earth-to-Space communications, well-known propagation effects such as path loss and atmospheric loss can lead to fluctuations in the strength of the communications link between a satellite and its ground station. Additionally, the typically unconsidered effect of shadowing due to the geometry of the satellite and its solar panels can also lead to link degradation. As a result of these anticipated channel impairments, NASA's communication links have been traditionally designed to handle the worst-case impact of these effects through high link margins and static, lower rate, modulation formats. The work presented in this paper aims to relax these constraints by providing an improved trade-off between data rate and link margin through utilizing link adaptation. More specifically, this work provides a simulation study on the propagation effects impacting NASA's SCaN Testbed flight software-defined radio (SDR) as well as proposes a link adaptation algorithm that varies the modulation format of a communications link as its signal-to-noise ratio fluctuates. Ultimately, the models developed in this work will be utilized to conduct real-time flight experiments on-board the NASA SCaN Testbed.

software defined radio↗
DOE OSTI2021

CPS Testbed Architectures for WAMPAC using Industrial Substation and Control Center Platforms and Attack-Defense Evaluation

Advanced persistent threats and cyberattacks can impact wide-area monitoring, protection, and control (WAMPAC) system operation. Many cyber-physical system (CPS) testbeds have been developed for attack-defense experimentation and attack-resiliency tools evaluation for WAMPAC, but they are limited to a simulation-and-emulation based environment. This paper presents a quasi-realistic CPS attack-defense testbed-based framework for WAMPAC applications using the industrial substation and control center platforms such as eTerra integrated with the hardware-in-the-loop CPS smart grid testbed available at Iowa State University. The proposed framework includes various combinations of industry-grade substation and control center platforms, communication topologies, real-time digital simulators, and a novel cyber-physical distributed intrusion-and-anomaly detection system (D-IADS) for WAMPAC applications. The D-IADS includes a master at the control center and geographically distributed sensor devices at each substation. Each D-IADS sensor deployed at a substation or control center network monitors ingress and egress traffic, detect intrusions, and dispatch alerts to the D-IADS master. The D-IADS master centrally monitors and analyze the alerts and controls D-IADS sensors. We considered an EMP60 synthetic CPS grid as a case study to demonstrate the framework and proposed D-IADS for WAMPAC applications against cyberattack vectors such as Man-in-the-Middle DNP3 attack, denial-of-service, and data-integrity attacks.

24 POWER TRANSMISSION AND DISTRIBUTION↗
NASA NTRS1988

NASA telerobot testbed development and core technology demonstration

In 1985, NASA initiated a major program of technology development and demonstration for robotics applications to space servicing, assembly, repair, and remote exploration. A ground-based telerobot testbed at the Jet Propulsion Laboratory has been the focal point within this program. Designed to prove technology concepts for supervised automation of increasingly unstructured and complex tasks, the testbed has reached an initial stage of integration. Several significant testbed experiments have been performed, including visual tracking and grapple of a satellite, dual-arm spatial coordination and manipulator control, force-reflecting teleoperations, and simulated task planning for a satellite servicing scenario. The current NASA plans for continuing testbed development and demonstration are also described.

Schenker, Paul S.↗
NASA NTRS1990

A testbed for the evaluation of computer aids for enroute flight path planning

A simulator study of the five airline flight crews engaged in various enroute planning activities has been conducted. Based on a cognitive task analysis of this data, a flight planning workstation has been developed on a Mac II controlling three color monitors. This workstation is being used to study design concepts to support the flight planning activities of dispatchers and flight crews in part-task simulators.

Smith, Philip J.↗
DOE OSTI2022

Hybrid quantum-classical algorithms for approximate graph coloring

We show how to apply the recursive quantum approximate optimization algorithm (RQAOA) to MAX- k -CUT, the problem of finding an approximate k -vertex coloring of a graph. We compare this proposal to the best known classical and hybrid classical-quantum algorithms. First, we show that the standard (non-recursive) QAOA fails to solve this optimization problem for most regular bipartite graphs at any constant level p : the approximation ratio achieved by QAOA is hardly better than assigning colors to vertices at random. Second, we construct an efficient classical simulation algorithm which simulates level- 1 QAOA and level- 1 RQAOA for arbitrary graphs. In particular, these hybrid algorithms give rise to efficient classical algorithms, and no benefit arising from the use of quantum mechanics is to be expected. Nevertheless, they provide a suitable testbed for assessing the potential benefit of hybrid algorithm: We use the simulation algorithm to perform large-scale simulation of level- 1 QAOA and RQAOA with up to 300 qutrits applied to ensembles of randomly generated 3 -colorable constant-degree graphs. We find that level- 1 RQAOA is surprisingly competitive: for the ensembles considered, its approximation ratios are often higher than those achieved by the best known generic classical algorithm based on rounding an SDP relaxation. This suggests the intriguing possibility that higher-level RQAOA may be a potentially useful algorithm for NISQ devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2018

The East River, Colorado, Watershed: A Mountainous Community Testbed for Improving Predictive Understanding of Multiscale Hydrological–Biogeochemical Dynamics

Core Ideas Development of a 300‐km 2 mountainous headwater testbed began in 2016 in the East River. The testbed can be used to explore how watershed changes impact downgradient water availability and quality. System‐of‐system, scale‐adaptive approaches can potentially improve watershed dynamics simulation. We have new approaches to monitor and simulate water partitioning and system responses. The East River watershed has been developed as a “community” testbed. Extreme weather, fires, and land use and climate change are significantly reshaping interactions within watersheds throughout the world. Although hydrological–biogeochemical interactions within watersheds can impact many services valued by society, uncertainty associated with predicting hydrology‐driven biogeochemical watershed dynamics remains high. With an aim to reduce this uncertainty, an approximately 300‐km 2 mountainous headwater observatory has been developed at the East River, CO, watershed of the Upper Colorado River Basin. The site is being used as a testbed for the Department of Energy supported Watershed Function Project and collaborative efforts. Building on insights gained from research at the “sister” Rifle, CO, site, coordinated studies are underway at the East River site to gain a predictive understanding of how the mountainous watershed retains and releases water, nutrients, carbon, and metals. In particular, the project is exploring how early snowmelt, drought, and other disturbances influence hydrological–biogeochemical watershed dynamics at seasonal to decadal timescales. A system‐of‐systems perspective and a scale‐adaptive simulation approach, involving the combined use of archetypal watershed subsystem “intensive sites” are being tested at the site to inform aggregated watershed predictions of downgradient exports. Complementing intensive site hydrological, geochemical, geophysical, microbiological, geological, and vegetation datasets are long‐term, distributed measurement stations and specialized experimental and observational campaigns. Several recent research advances provide insights about the intensive sites as well as aggregated watershed behavior. The East River “community testbed” is currently hosting scientists from more than 30 institutions to advance mountainous watershed methods and understanding.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Field Experiments and Model Validation: The EGS Collab Project

Implementing enhanced geothermal systems (EGS) will require improvements in understanding stimulation of crystalline rock to create appropriate flow pathways, and the ability to effectively simulate both the stimulation and the flow and transport processes in the resulting fracture network. The US Department of Energy (DOE) is addressing these and other challenges at multiple scales. The EGS Collab project, addressed here, is performing tests and modeling at the 10 m scale. The FORGE project is performing tests at the full reservoir scale. The EGS Collab team created an underground testbed at the Sanford Underground Research Facility (SURF) in Lead, South Dakota, at a depth of approximately 1.5 km to examine hydraulic fracturing (Experiment 1). We are currently building a second testbed at SURF at a depth of about 1.25 km aimed at investigating shear stimulation (Experiment 2). In Experiment 1, we drilled eight boreholes in a well-characterized phyllite and installed geophysical sensors in six of them to create a well-instrumented testbed to allow careful monitoring of stimulation events and flow tests. Numerical simulation was used to answer key experimental design questions, to forecast fracture propagation trajectories and extents, and to analyze and evaluate results both in near-real-time and in detailed process studies. Stimulations performed in this testbed allowed quantification of processes occurring during stimulation and the examination of dynamic flow occurrences. Long-term ambient temperature and chilled water flow tests were performed in addition to many tracer tests to examine system behavior. Our second testbed, targeted at shear stimulation, is currently being built at the SURF Facility at a depth of about 1.25 km in amphibolite under a different set of stress and fracture conditions than Experiment 1.

artificial intelligence↗
NASA NTRS2012

Modular, Rapid Propellant Loading System/Cryogenic Testbed

The Cryogenic Test Laboratory (CTL) at Kennedy Space Center (KSC) has designed, fabricated, and installed a modular, rapid propellant-loading system to simulate rapid loading of a launch-vehicle composite or standard cryogenic tank. The system will also function as a cryogenic testbed for testing and validating cryogenic innovations and ground support equipment (GSE) components. The modular skid-mounted system is capable of flow rates of liquid nitrogen from 1 to 900 gpm (approx equals 3.8 to 3,400 L/min), of pressures from ambient to 225 psig (approx equals 1.5 MPa), and of temperatures to -320 F (approx equals -195 C). The system can be easily validated to flow liquid oxygen at a different location, and could be easily scaled to any particular vehicle interface requirements

Hatfield, Walter, Sr.↗
NASA NTRS2017

Narrowband Rejection of Reaction Wheel and Environmental Disturbances for the WFIRST OMC Testbed

The Wide Field Infrared Survey Telescope (WFIRST) is a NASA observatory with two scientific instruments. The first is the Wide Field Instrument (WFI) designed to perform wide field imaging and surveys of the near infrared (NIR) sky. The second is a coronagraph (CGI) that will enable astronomers to detect and measure properties of planets in other solar systems. The coronagraph requires 0.5 milli-arcsecond (mas) RMS pointing per axis of the line of sight (LOS) to achieve a contrast of 1x10-9. This paper discusses the approach used for achieving this level of pointing performance on the occulting mask coronagraph (OMC) testbed at JPL. This testbed uses a low-order wavefront sensing (LOWFS) camera and fast steering mirror (FSM) to suppress injected LOS jitter and environmental LOS jitter. The injected jitter includes representative broadband spacecraft attitude control system (ACS) LOS motion and tonal LOS jitter caused by the reaction wheel assemblies (RWA). The environmental jitter includes thermal LOS variations and harmonics of the line noise. The LOWFS camera uses high flux from the obscured science target to achieve high rate measurements of the LOS. These measurements are augmented with fictitious RWA tachometer information and an estimate of the line noise frequency. A LOS servo using a combination of feedback and feedforward control is used in the testbed to compensate for all of the disturbance sources and to mitigate jitter caused by in-band camera noise. The feedforward uses a novel robust least mean squares (RLMS) filter algorithm to reject the RWA and line frequency tones. High fidelity models of the sensors, disturbances and actuator are presented in this paper. These models were developed as part of a simulation of the LOS control system. Performance results from the hardware testbed at the Jet Propulsion Laboratory (JPL) are discussed in this paper.

Shields, Joel↗
NASA NTRS2017

Precision Projector Laboratory: Detector Characterization with an Astronomical Emulation Testbed

As astronomical observations benefit from improved sensitivity, the effectiveness of scientific programs is becoming limited by systematics that often originate in poorly understood image sensor behavior. Traditional, bottom-up detector characterization methods provide one way to model underlying detector physics, and generate ever more faithful numerical simulations, but this approach is vulnerable to preconceptions and over-simplification. The alternative top-down approach is laboratory emulation, which enables observation, calibration, and analysis scenarios to be tested without relying on a complete understanding of the underlying physics. This complements detector characterization and simulation efforts by testing their validity. We describe a laboratory facility and experimental testbed that supports the emulation of a wide range of mission concepts such as gravitational weak lensing measurements by WFIRST and high precision spectrophotometry of transiting exoplanets by JWST. An Offner relay projects readily customizable "scenes" (e.g. stars, galaxies, spectra) with very low optical aberration over the full area of a typical optical or near infrared image sensor. f/8 and slower focal ratios may be selected, spanning those of most proposed space missions and approximating the point spread function (PSF) size of seeing limited ground based surveys. Diffraction limited PSFs are projected over a wide field of view and wavelength range to deliver highly predictable image patterns down to sub-pixel scales with stable intensity and fine motion control. The testbed enables realistic validation of detector performance on science-like images, which aids mission design and survey strategy, as well as targeted investigations of various detector effects.

Seshadri, Suresh↗
DOE OSTI2025

Evaluation of E3SM Simulated Aerosols and Aerosol‐Cloud Interactions Across GCM and Convection‐Permitting Scales

This paper introduces an Earth system modeling testbed for predicting aerosols and aerosol‐cloud interactions (ACIs) at convection‐permitting scales. Using the Energy Exascale Earth System Model (E3SM) version 2 with a four‐mode Modal Aerosol Module, we conduct simulations at 3.25 km resolution on a regionally refined mesh (RRM) across four regions with distinct aerosol and cloud regimes. Results are compared with the standard 100 km E3SM configuration and evaluated against satellite, aircraft, and ground‐based observations. We find that increasing model resolution improves heavy precipitation simulation but amplifies positive bias in light drizzle at coarse resolution. These resolution‐induced changes affect cloud and aerosol properties to varying degrees across regions. Generally, cloud cover and liquid water path (LWP) show better agreement with satellite retrievals at 3.25 km, though surface‐based comparisons suggest otherwise. Aerosol composition remains poorly represented at both resolutions. The RRM increases Aitken mode aerosol number concentrations via enhanced new particle formation. However, accumulation mode aerosols are decreased at higher resolution as aerosol removals become more efficient. This partially contributes to fewer cloud condensation nuclei (CCN) and lower cloud droplet number concentrations (N d ), which produces larger model biases in some scenarios. These findings suggest that solely increasing horizontal resolution to kilometer scales is insufficient to broadly improve aerosol and cloud predictions without concurrent advancements in physical and chemical process representations. Nonetheless, the RRM moderately improves key ACI relationships such as CCN‐N d correlation, reflecting enhanced aerosol activation representation. The LWP‐N d relationship is also better captured by RRM, suggesting a better characterization of LWP adjustment.

Huang, Meng [Pacific Northwest National Laboratory↗
NASA NTRSDate not supplied

Emulated Spacecraft Communication Testbed for Evaluating Cognitive Networking Technology

The ability to emulate the full space protocol stack is an essential aspect required to evaluate and mature cognitive communication capabilities. The interaction between the physical layer and network layers is key to developing network optimizations for a dynamic and complex environment. We present a laboratory testbed for the evaluation of cognitive radio and networking techniques applied to space communications. The testbed is a high fidelity, flight-like hardware testbed consisting of software-defined radios, channel emulators, modems, and orbital analysis and scheduling software. The testbed uses RF links with signal quality, propagation delay, and Doppler effects driven by orbital mechanics simulations of emulated spacecraft. Our framework enables control of link bidirectionality, data rates, and interference sources. In addition to hardware radio nodes, the testbed can incorporate virtualized emulated nodes for larger and more challenging network scenarios. Our approach to a cognitive communication system uses delay tolerant networking (DTN) to mitigate the challenges of the space environment. While many DTN networks use only preplanned schedules, our system uses User-Initiated Service (UIS) to dynamically schedule service providers. Software-defined radio allows the system to adapt to a variety of service providers. Integration of DTN, UIS, and software-defined radio technologies provides a framework for the implementation of a cognitive communication system. This paper describes the testbed capabilities, network emulation approach, component integration, and initial end-to-end testing results.

cognitive radio↗
DOE OSTI2020

Application of an Embedded Fracture and Borehole Modeling Approach to the Understanding of EGS Collab Experiment 1

EGS Collab is a series of meso-scale experiments and associated numerical simulation activities being funded by the United States Department of Energy, Geothermal Technologies Office (GTO) to investigate enhanced geothermal system processes under in-situ stress and slightly elevated temperature conditions. This project is designed to provide scientists and engineers with immediate access to impermeable rock at scales larger than possible in the laboratory, but generally smaller than those for commercial production. Immediate access to rock is provided via the existing drifts of the former Homestake Gold Mine, now operated as the Sanford Underground Research Facility in Lead, South Dakota. The objectives of the EGS Collab project are to develop well controlled fracture networks between injector and producer boreholes using normal and shear stimulation for permeability enhancement. The first experimental site was located off the West Access drift on the 4850 Level (4850 feet below ground surface) in phyllite of the Precambrian Poorman formation, and involved the creation of a fracture network comprising a combination of hydraulic and natural fractures. A second experimental site is now being considered near the battery alcove on the 4100 Level in amphibolite and rhyolite of the Yates Unit. Data generated during these experiments will be compared against predictions of a suite of computer codes specifically designed to solve problems involving coupled thermal, hydrological, geomechanical, and geochemical processes. Comparisons between experimental and numerical simulation results will provide code developers with direction for improvements and verification of process models, build confidence in the suite of available numerical tools, and ultimately identify critical future development needs for the geothermal modeling community. Moreover, conducting thorough comparisons of models, modelling approaches, measurement approaches and measured data, via the EGS Collab project, will serve to identify techniques that are most likely to succeed at the Frontier Observatory for Research in Geothermal Energy (FORGE), the GTO’s flagship EGS research effort. Experiment 1 has comprised a series of successful tests, including a long-term chilled-water circulation test, but the testbed has two atypical EGS elements. Active ventilation in the adjacent drift over a 50-year period cooled the testbed rock mass and hydraulic fracturing intersected monitoring boreholes making them conduits for fluid flow. Numerical simulations executed in support of the design of the EGS Collab Experiment 1, computed a radial temperature distribution and stress gradient orthogonal to the drift axis, resulting in the forecast of an oblong hydraulic fracture geometry, extended in the direction of the drift from the stimulation borehole. This paper describes the numerical simulation of long-term chilled-water circulation test with an embedded fracture and borehole modeling approach. The principal objective of the simulation work is show agreement between experimental observations in terms of production fluid temperatures, monitoring borehole temperatures, injection and production pressures, and tracer recoveries using a single conceptual model for the fracture network, using characterization and monitoring data generally available for EGS. A secondary objective is to improve the numerical simulation result comparisons with additional data available from the broader monitoring equipment within the testbed versus deeper, hotter, and more remote EGS. One complicating factor for comparisons between the numerical simulation results and experimental observations, is the Joule-Thomson heating associated with large pressure drops across the fracture network.

numerical simulation, embedded fractures and boreh↗
NASA NTRS2014

NASA Tech Briefs, February 2014

Topics include: JWST Integrated Simulation and Test (JIST) Core; Software for Non-Contact Measurement of an Individual's Heart Rate Using a Common Camera; Rapid Infrared Pixel Grating Response Testbed; Temperature Measurement and Stabilization in a Birefringent Whispering Gallery Resonator; JWST IV and V Simulation and Test (JIST) Solid State Recorder (SSR) Simulator; Development of a Precision Thermal Doubler for Deep Space; Improving Friction Stir Welds Using Laser Peening; Methodology of Evaluating Margins of Safety in Critical Brazed Joints; Interactive Inventory Monitoring; Sensor for Spatial Detection of Single-Event Effects in Semiconductor-Based Electronics; Reworked CCGA-624 Interconnect Package Reliability for Extreme Thermal Environments; Current-Controlled Output Driver for Directly Coupled Loads; Bulk Metallic Glasses and Matrix Composites as Spacecraft Shielding; Touch Temperature Coating for Electrical Equipment on Spacecraft; Li-Ion Electrolytes Containing Flame-Retardant Additives; Autonomous Robotic Manipulation (ARM); CARVE Log; Platform Perspective Toolkit; Convex Hull-Based Plume and Anomaly Detection; Pre-Filtration of GOSAT Data Using Only Level 1 Data and an Intelligent Filter to Remove Low Clouds; Affordability Comparison Tool - ACT; "Ascent - Commemorating Shuttle" for iPad; Cassini Mission App; Light-Weight Workflow Engine: A Server for Executing Generic Workflows; Model for System Engineering of the CheMin Instrument; Timeline Central Concepts; Parallel Particle Filter Toolkit; Particle Filter Simulation and Analysis Enabling Non-Traditional Navigation; Quasi-Terminator Orbits for Mapping Small Primitive Bodies; The Subgrid-Scale Scalar Variance Under Supercritical Pressure Conditions; Sliding Gait for ATHLETE Mobility; and Automated Generation of Adaptive Filter Using a Genetic Algorithm and Cyclic Rule Reduction.

Source record↗
DOE OSTI2020

Learning to Predict Crystal Plasticity at the Nanoscale: Deep Residual Networks and Size Effects in Uniaxial Compression Discrete Dislocation Simulations

The density and configurational changes of crystal dislocations during plastic deformation influence the mechanical properties of materials. These influences have become clearest in nanoscale experiments, in terms of strength, hardness and work hardening size effects in small volumes. The mechanical characterization of a model crystal may be cast as an inverse problem of deducing the defect population characteristics (density, correlations) in small volumes from the mechanical behavior. In this work, we demonstrate how a deep residual network can be used to deduce the dislocation characteristics of a sample of interest using only its surface strain profiles at small deformations, and then statistically predict the mechanical response of size-affected samples at larger deformations. As a testbed of our approach, we utilize high-throughput discrete dislocation simulations for systems of widths that range from nano- to micro- meters. We show that the proposed deep learning model significantly outperforms a traditional machine learning model, as well as accurately produces statistical predictions of the size effects in samples of various widths. By visualizing the filters in convolutional layers and saliency maps, we find that the proposed model is able to learn the significant features of sample strain profiles.

36 MATERIALS SCIENCE↗
NASA NTRS2018

Experimental Evaluation of BLI Propulsion: The Boundary Layer Ingesting Inlet/Distortion-Tolerant Fan Solution

NASA has successfully developed a new testbed configuration for experimentally evaluating embedded boundary layer ingesting aircraft propulsors in its 8'x6' Supersonic Wind Tunnel. This testbed meets the challenges of providing the necessary freestream flow Mach conditions and desired range and distribution of boundary layer thickness for embedded aircraft propulsion systems. The testbed consists of a 48ft long raised wind tunnel floor aircraft surface simulator and a boundary layer regulation system to produce propulsion-local aircraft aerodynamic flow fields. This durable special test equipment is designed to be installed in the wind tunnel's transonic test section and is capable of evaluating a wide range of subcritical and supercritical airframe-propulsion integration configurations for subsonic cruise aircraft. The wind tunnel and testbed are well suited for meeting the test requirements of these propulsors in the most cost efficient way and has been aerodynamically calibrated and proven through tests of a first-of-its-kind boundary layer ingesting propulsor.

Arend, David J.↗
DOE OSTI2021

Clock model interpolation and symmetry breaking in O(2) models

The $q$-state clock model is a classical spin model that corresponds to the Ising model when $q=2$ and to the $XY$ model when $q\to\infty$. The integer-$q$ clock model has been studied extensively and has been shown to have a single phase transition when $q=2$,$3$,$4$ and two phase transitions when $q>4$.We define an extended $q$-state clock model that reduces to the ordinary $q$-state clock model when $q$ is an integer and otherwise is a continuous interpolation of the clock model to noninteger $q$. We investigate this class of clock models in 2D using Monte Carlo (MC) and tensor renormalization group (TRG) methods, and we find that the model with noninteger $q$ has a crossover and a second-order phase transition. We also define an extended-$O(2)$ model (with a parameter $\gamma$) that reduces to the $XY$ model when $\gamma=0$ and to the extended $q$-state clock model when $\gamma\to\infty$, and we begin to outline the phase diagram of this model. These models with noninteger $q$ serve as a testbed to study symmetry breaking in situations corresponding to quantum simulators where experimental parameters can be tuned continuously.

Hostetler, Leon↗