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NASA NTRS2004

Rapid Structured Volume Grid Smoothing and Adaption Technique

A rapid, structured volume grid smoothing and adaption technique, based on signal processing methods, was developed and applied to the Shuttle Orbiter at hypervelocity flight conditions in support of the Columbia Accident Investigation. Because of the fast pace of the investigation, computational aerothermodynamicists, applying hypersonic viscous flow solving computational fluid dynamic (CFD) codes, refined and enhanced a grid for an undamaged baseline vehicle to assess a variety of damage scenarios. Of the many methods available to modify a structured grid, most are time-consuming and require significant user interaction. By casting the grid data into different coordinate systems, specifically two computational coordinates with arclength as the third coordinate, signal processing methods are used for filtering the data [Taubin, CG v/29 1995]. Using a reverse transformation, the processed data are used to smooth the Cartesian coordinates of the structured grids. By coupling the signal processing method with existing grid operations within the Volume Grid Manipulator tool, problems related to grid smoothing are solved efficiently and with minimal user interaction. Examples of these smoothing operations are illustrated for reduction in grid stretching and volume grid adaptation. In each of these examples, other techniques existed at the time of the Columbia accident, but the incorporation of signal processing techniques reduced the time to perform the corrections by nearly 60%. This reduction in time to perform the corrections therefore enabled the assessment of approximately twice the number of damage scenarios than previously possible during the allocated investigation time.

Alter, Stephen J.↗

NASA NTRS2006

Rapid Structured Volume Grid Smoothing and Adaption Technique

A rapid, structured volume grid smoothing and adaption technique, based on signal processing methods, was developed and applied to the Shuttle Orbiter at hypervelocity flight conditions in support of the Columbia Accident Investigation. Because of the fast pace of the investigation, computational aerothermodynamicists, applying hypersonic viscous flow solving computational fluid dynamic (CFD) codes, refined and enhanced a grid for an undamaged baseline vehicle to assess a variety of damage scenarios. Of the many methods available to modify a structured grid, most are time-consuming and require significant user interaction. By casting the grid data into different coordinate systems, specifically two computational coordinates with arclength as the third coordinate, signal processing methods are used for filtering the data [Taubin, CG v/29 1995]. Using a reverse transformation, the processed data are used to smooth the Cartesian coordinates of the structured grids. By coupling the signal processing method with existing grid operations within the Volume Grid Manipulator tool, problems related to grid smoothing are solved efficiently and with minimal user interaction. Examples of these smoothing operations are illustrated for reductions in grid stretching and volume grid adaptation. In each of these examples, other techniques existed at the time of the Columbia accident, but the incorporation of signal processing techniques reduced the time to perform the corrections by nearly 60%. This reduction in time to perform the corrections therefore enabled the assessment of approximately twice the number of damage scenarios than previously possible during the allocated investigation time.

Alter, Stephen J.↗

NASA NTRS2011

Grid-Tied Photovoltaic Power System

A grid-tied photovoltaic (PV) power system is connected directly to the utility distribution grid. Facility power can be obtained from the utility system as normal. The PV system is synchronized with the utility system to provide power for the facility, and excess power is provided to the utility. Operating costs of a PV power system are low compared to conventional power technologies. This method can displace the highest-cost electricity during times of peak demand in most climatic regions, and thus reduce grid loading. Net metering is often used, in which independent power producers such as PV power systems are connected to the utility grid via the customers main service panels and meters. When the PV power system is generating more power than required at that location, the excess power is provided to the utility grid. The customer pays the net of the power purchased when the on-site power demand is greater than the onsite power production, and the excess power is returned to the utility grid. Power generated by the PV system reduces utility demand, and the surplus power aids the community. Modern PV panels are readily available, reliable, efficient, and economical, with a life expectancy of at least 25 years. Modern electronics have been the enabling technology behind grid-tied power systems, making them safe, reliable, efficient, and economical with a life expectancy equal to the modern PV panels. The grid-tied PV power system was successfully designed and developed, and this served to validate the basic principles developed, and the theoretical work that was performed. Grid-tied PV power systems are reliable, maintenance- free, long-life power systems, and are of significant value to NASA and the community. Of particular value are the analytical tools and capabilities that have been successfully developed. Performance predictions can be made confidently for grid-tied PV systems of various scales. The work was done under the NASA Hybrid Power Management (HPM) Program, which is the integration of diverse power devices in an optimal configuration for space and terrestrial applications.

Eichenberg, Dennis J.↗

NASA NTRS2013

Aeroacoustic Simulation of Nose Landing Gear on Adaptive Unstructured Grids With FUN3D

Numerical simulations have been performed for a partially-dressed, cavity-closed nose landing gear configuration that was tested in NASA Langley s closed-wall Basic Aerodynamic Research Tunnel (BART) and in the University of Florida's open-jet acoustic facility known as the UFAFF. The unstructured-grid flow solver FUN3D, developed at NASA Langley Research center, is used to compute the unsteady flow field for this configuration. Starting with a coarse grid, a series of successively finer grids were generated using the adaptive gridding methodology available in the FUN3D code. A hybrid Reynolds-averaged Navier-Stokes/large eddy simulation (RANS/LES) turbulence model is used for these computations. Time-averaged and instantaneous solutions obtained on these grids are compared with the measured data. In general, the correlation with the experimental data improves with grid refinement. A similar trend is observed for sound pressure levels obtained by using these CFD solutions as input to a FfowcsWilliams-Hawkings noise propagation code to compute the farfield noise levels. In general, the numerical solutions obtained on adapted grids compare well with the hand-tuned enriched fine grid solutions and experimental data. In addition, the grid adaption strategy discussed here simplifies the grid generation process, and results in improved computational efficiency of CFD simulations.

Vatsa, Veer N.↗

NASA NTRS2017

Aeroacoustic Simulations of a Nose Landing Gear with FUN3D: A Grid Refinement Study

A systematic grid refinement study is presented for numerical simulations of a partially-dressed, cavity-closed (PDCC) nose landing gear configuration that was tested in the University of Florida's open-jet acoustic facility known as the UFAFF. The unstructured-grid flow solver FUN3D is used to compute the unsteady flow field for this configuration. Mixed-element grids generated using the Pointwise (Registered Trademark) grid generation software are used for numerical simulations. Particular care is taken to ensure quality cells and proper resolution in critical areas of interest in an effort to minimize errors introduced by numerical artifacts. A set of grids was generated in this manner to create a family of uniformly refined grids. The finest grid was then modified to coarsen the wall-normal spacing to create a grid suitable for the wall-function implementation in FUN3D code. A hybrid Reynolds-averaged Navier-Stokes/large eddy simulation (RANS/LES) turbulence modeling approach is used for these simulations. Time-averaged and instantaneous solutions obtained on these grids are compared with the measured data. These CFD solutions are used as input to a FfowcsWilliams-Hawkings (FW-H) noise propagation code to compute the farfield noise levels. The agreement of the computed results with the experimental data improves as the grid is refined.

Vatsa, Veer N.↗

NASA NTRS2019

Verification of Unstructured Grid Adaptation Components

Adaptive unstructured grid techniques have made limited impact on production analysis workflows where the control of discretization error is critical to obtaining reliable simulation results. Recent progress has matured a number of independent implementations of flow solvers, error estimation methods, and anisotropic grid adaptation mechanics. Known differences and previously unknown differences in grid adaptation components and their integrated processes are identified here for study. Unstructured grid adaptation tools are verified using analytic functions and the Code Comparison Principle. Three analytic functions with different smoothness properties are adapted to show the impact of smoothness on implementation differences. A scalar advection-diffusion problem with an analytic solution that models a boundary layer is adapted to test individual grid adaptation components. Laminar flow over a delta wing and turbulent flow over an ONERA M6 wing are verified with multiple, independent grid adaptation procedures to show consistent convergence to fine-grid forces and a moment. The scalar problems illustrate known differences in a grid adaptation component implementation and a previously unknown interaction between components. The wing adaptation cases in the current study document a clear improvement to existing grid adaptation procedures. The stage is set for the infusion of verified grid adaptation into production fluid flow simulations.

Park, Michael A.↗

NASA NTRS2021

Grid-Stretching Capability for the GEOS-Chem 13.0.0 Atmospheric Chemistry Model

Modeling atmospheric chemistry at fine resolution globally is computationally expensive; the capability to focus on specific geographic regions using a multi scale grid is desirable. Here, we develop, validate, and demonstrate stretched grids in the GEOS-Chem atmospheric chemistry model in its high-performance implementation (GCHP). These multiscale grids are specified at runtime by four parameters that offer users nimble control of the region that is refined and the resolution of the refinement. We validate the stretched-grid simulation versus global cubed-sphere simulations. We demonstrate the operation and flexibility of stretched-grid simulations with two case studies that compare simulated tropospheric NO2column densities from stretched-grid and cubed-sphere simulations to retrieved column densities from the TROPOspheric Monitoring Instrument (TROPOMI). The first case study uses a stretched grid with a broad refinement covering the contiguous US to produces imulated columns that perform similarly to a C180 (∼50 km) cubed-sphere simulation at less than one-ninth the computational expense. The second case study experiments with a large stretch-factor for a global stretched-grid simulation with a highly localized refinement with∼10 km resolution for California. We find that the refinement improves spatial agreement with TROPOMI columns compared to a C90 cubed-sphere simulation of comparable computational demands. Overall we find that stretched grids in GEOS-Chem are a practical tool for fine resolution regional- or continental-scale simulations of atmospheric chemistry. Stretched grids are available in GEOS-Chem version 13.0.0

GEOS-Chem↗

DOE OSTI2025

Harnessing distributed GPU computing for generalizable graph convolutional networks in power grid reliability assessments

Although machine learning (ML) has emerged as a powerful tool for rapidly assessing grid contingencies, prior studies have largely considered a static grid topology in their analyses. This limits their application, since they need to be re-trained for every new topology. Here, this paper explores the development of generalizable graph convolutional network (GCN) models by pre-training them across a range of grid topologies and contingency types. We found that a GCN model with auto-regressive moving average (ARMA) layers with a line graph representation of the grid offered the best predictive performance in predicting voltage magnitudes (VM) and voltage angles (VA). We introduced the concept of phantom nodes to consider disparate grid topologies with a varying number of nodes and lines. For pre-training the GCN ARMA model across a variety of topologies, distributed graphics processing unit (GPU) computing afforded us significant training scalability. The predictive performance of this model on grid topologies that were part of the training data is substantially better than the direct current (DC) approximation. Although direct application of the pre-trained model to topologies that are not part of the grid is not particularly satisfactory, fine-tuning with small amounts of data from a specific topology of interest significantly improves predictive performance. In general, this paper highlights the feasibility of training large-scale GNN models to assess the reliability of power grids by considering a wide variety of grid topologies and contingency types. With the advent of foundational models in ML and the exponential increase in GPU computing clusters, generalizable ML models will significantly enhance how utilities manage power systems and make decisions in real-time or near-real-time.

24 - POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

Future grid mix impacts on whole-building life cycle assessment

Building construction and operation are a significant contribution to global greenhouse gas emissions, so understanding and mitigating emissions is crucial for reliable and realistic emissions accounting. Whole-building Life Cycle Assessment (WBLCA) is an emissions accounting method that considers lifetime environmental impacts of a building during its construction, operation, and eventual end-of-life. When performing WBLCAs, emission calculations from the building's operation over the entire building lifespan are typically based on today's energy grid mixes. This method does not consider changes or advancements in the clean energy proportion within the grid mix and can over or under-inflate results, skewing the ratio of embodied vs. operational environmental impacts. While a variety of prediction tools estimate what future grid emissions might be, predictions can vary widely. To predict the clean energy ratio within future grid mixes and the potential impact these changes might have on WBLCA, annual data from several existing U.S. grid models was averaged and probabilistic modeling was used to extend the usable projections of shorter forecasts. Results show that clean energy sources will likely continue to increase over time, although the rate of growth varies by model. On average, by 2085, the clean energy penetration of the grid is projected to reach ~81% and renewable energy is projected to reach ~71%, although no widespread consensus is reached. To understand how the future grid mix impacts lifetime building emissions within a WBLCA context, the team analyzed two 2021 IECC-compliant all-electric residential buildings: one built from traditional materials and construction processes and the other built with carbon sequestering materials and modular assembly, with a portion of energy generated on site. The results indicate that a moderate estimate of future electricity grid mixes shows a reduction of yearly operational emissions for traditional residential buildings of 55% between 2025 and 2085, and a corresponding reduction of 48% of total emissions over a 60 year building lifespan. This study offers a nuanced approach to account for the variability of future grid mix models and provides an average trend-line based on a robust collection of scenarios.

Life Cycle Assessment (LCA)↗

DOE OSTI2024

U.S. Department of Energy-National Lab Equity Summit: Grid Planning and Operations (Workshop Report)

This report summarizes the U.S. DOE and national laboratories equity summit that was held on February 5, 2024, and focused on grid planning and operations. The objectives of the summit were to connect DOE and lab researchers working on grid-related equity issues, share information on current and planned grid-related equity projects and initiatives, and inspire and educate participants by hearing from our panelists about solutions and challenges to integrating equity in grid planning and operations. The summit included two panels of industry leaders. The first was a state and community perspectives panel that included representatives from a state public utility commission (Oregon Public Utility Commission), a state energy office (Washington Department of Commerce), a state utility consumer advocate (Connecticut Consumer Counsel), and industry consultants (Elevated Engagement and ArkSpring Consulting). Panelists shared successes they have seen, critical challenges related to equity and grid planning and operations, and other considerations. The second panel addressed utility perspectives and included representatives from two utilities (Commonwealth Edison and Tacoma Power), the National Rural Electric Cooperative (NRECA), and a former utility employee and legal consultant. Panelists discussed the role of the utility concerning equity, the most significant technical and data modeling needs and opportunities, and the role the labs could help advance equity in grid planning and operations. There was also a session on partner organization presentations. Argonne National Laboratory made a short presentation on the Grid Modernization Laboratory Consortium (GMLC) project they are leading on equity-informed power system planning. NARUC, NASEO, and the Clean Energy States Alliance, as partners of the GMLC project also shared updates on relevant activities and resources. During the summit, there were two rounds of lightning presentations by national labs and DOE highlighting research that addresses equity and grid planning and operations (Tables 5 and 6 and slides in the Appendix). The goal of the lightning rounds was to share information between participants to encourage collaboration and leverage ongoing research at labs and DOE. The summit included two interactive exercises where summit participants shared their perspectives on relevant equity projects and initiatives (Table 2), key challenges regarding equity and grid planning and operations (Table 3), and promising innovations or progress (Table 4). At the end of the session, participants were asked to share essential insights from the event (Table 7) and an action they plan to take as a result of the event. Participants agreed that the event was useful in helping them share and learn from each other. The project team plans to use the information from the summit as a starting point to help inform future research and technical assistance. In 2026, another Equity Summit will be held (virtually or in person) as part of the same project to help raise awareness and disseminate research and resources completed during the project's duration.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2026

Demonstrating the data center as a flexible grid asset using a C-HIL setup

Increasing data center demand is outpacing grid infrastructure development. Artificial intelligence workloads and hyperscale cloud growth are creating unprecedented demand for power, while traditional grid expansion faces multiyear development timelines. Verrus is developing an innovative datacenter solution for this challenge, data centers that act as active grid-supportive assets rather than passive loads. Our approach integrates a novel grid-aware power flow management system with battery energy storage systems(BESS) into a microgrid-controlled, medium-voltage power distribution architecture that delivers critical capabilities, such as: * Fast response to grid disturbances such over/ under voltage or over/ under frequency * Demand flexibility that can service requests from the utility within 10 s * Uninterrupted transition to islanded operation during grid outages * Continuous uptime assurance for compute loads while maintaining all customer service level agreements. Through Verrus' strategic partnership with the National Renewable Energy Laboratory (NREL), these capabilities were validated using NREL's Advanced Research on Integrated Energy Systems (ARIES) virtual emulation environment to model a 70-MW grid-interactive data center. This paper outlines the design, methodology, and results of this emulated deployment, demonstrating that data centers can provide both critical load resilience and ancillary grid support without compromising uptime requirements. Specifically, we present a digital real time simulation of a 70 MW data center integrated with a physical microgrid controller, and demonstrate the data center response in the event of a grid voltage and frequency event, utility demand response request and utility outage.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2022

Using a Grid-Forming Inverter to Stabilize a Low-Inertia Power System - Maui Hawaiian Island

As power systems around the world integrate greater amounts of wind and solar photovoltaic power, periods of very high instantaneous power shares of inverters, the primary interfacing technology for these generation sources, are complicating system stability and control. The contemporary, primary mode of inverter operation, grid-following, which explicitly assumes the presence of a local, stable voltage waveform, yields operational inadequacy at high instantaneous power shares potentially leading to instability due to the low-inertia conditions, as well as the correlated reduced voltage forming capacity on the respective system. Parallel connected grid-forming inverters, which directly regulate the local voltage, are a solution that is expected to bolster system stability and mitigate the shortcomings of the grid-following technology. In this paper, grid-following and two types of grid-forming inverter control, the traditional linear droop and the recently introduced nonlinear exponential droop (Droop-e), are simulated on a low-inertia, H = 0.48s, high inverter-based resource scenario, 97%, with a validated electromagentic transient domain model of the Hawaiian island of Maui power system. The benefit of a single grid-forming device over its grid-following counterpart is significant, both in terms frequency deviation and voltage stability. Further, the superiority of the Droop-e and the associated secondary power sharing control over both grid-following and linear droop grid-forming technologies is displayed, with improved nadir and rate of change of frequency over the linear droop control.

droop control↗

DOE OSTI2023

Developing a Disaster-Ready Power Grid Agent Through Geophysically-Informed Fault Event Scenarios

Management of the nation’s power grid over the coming decades will need to factor multiple climate-driven threats to the power system that can be stressful or even detrimental to its operations. During disasters, grid operators suffer from cognitive overload where the electric grid is severely impacted by the weather, yet grid operators have limited awareness of these factors. Meanwhile, the electric grid is facing an explosion of data coming from a variety of sources which can enable the operator to evaluate the risks and develop mitigation strategies against hazardous events. In this work, we processed heterogeneous environmental and power grid data to learn and model grid behavior caused by extreme weather events. In this study, we focused on two weather-driven hazards, hurricanes and wildfires, which were analysed for the electric grid of Texas. We the used this data to train a Reinforcement Learning (RL) agent by analysing and predicting future behaviour of the grid during those hazard events. All these parts are incorporated in one framework to have a geophysically informed power simulators that can be used to train RL agents.

electic grid, reinforcement learning, climate adap↗

DOE OSTI2025

Utility-Scale Operational Consequences for Solar Grid Services

This report delves into the critical aspects of grid services provided by solar inverter-based resources (IBRs), with an emphasis on the evolving landscape of microgrids, virtual power plants (VPPs), aggregators, and distributed energy resource management systems (DERMS). As the energy sector undergoes a transformative shift towards more decentralized and resilient grid architectures, understanding the multifaceted risks associated with these technologies becomes paramount. The report categorizes these risks into organizational, technical, and procedural domains, providing a thorough risk assessment framework that stakeholders can utilize to anticipate and mitigate potential issues. In addressing the increasing complexity of grid interconnections, the report highlights the importance of Cyber-Informed Engineering (CIE). By embedding engineering controls and cybersecurity measures into the early stages of system design, this approach aims to fortify grid infrastructure against emerging cyber threats. The analysis includes an exploration of best practices and strategies for integrating CIE principles to enhance grid security and resilience. To provide practical insights, the report conducts a detailed consequence analysis of various grid services and cyber mitigations that can be applied through the interconnection process. This analysis evaluates the potential impacts of different failure modes and vulnerabilities, offering a clear understanding of the consequences that could arise from disruptions within the energy grid. The findings are further enriched by a series of case studies that illustrate real-world scenarios and lessons learned from past incidents. Through this comprehensive examination of grid services and their criticality, the report aims to prepare industry professionals with the knowledge and tools necessary to navigate the complexities of modern energy systems. By providing a comprehensive approach that includes risk assessment, cybersecurity, and consequence analysis, solar stakeholders can more effectively guarantee the reliability, efficiency, and security of the energy grid.

14 SOLAR ENERGY↗

DOE OSTI2021

Resilient Information Architecture Platform for Smart Grid (RIAPS)

A number of emerging trends will substantially alter the operation and control of the electric grid over the next several decades. These trends include ensuring resiliency under severe weather events, increasing integration of renewable electricity generation, supporting changing electricity demand patterns, and the improving cost effectiveness of distributed energy resources. To address these challenges, the future “Smart Grid” management will need to transition from centralized to coordinated distributed control paradigm. Reliable operation of the Smart Grid depends on distributed intelligence realized through software applications that run on distributed computing devices attached to the power system to collect data and collaboratively manage resources. However, much of the existing software for Smart Grid-enabled devices is either proprietary or developed with custom solutions, which limits interoperability among the heterogeneous devices and hinders the ability to manage system-level reliability, security, and resiliency requirements. Additionally, this approach makes Smart Grid applications hard to maintain, evolve, verify, and replace; resulting in high development and deployment costs. Further development of the Smart Grid requires a reusable software base-layer to move from hard-coded functionality to a plug-and-play architecture capable of managing system-level objectives and constraints in addition to providing consistent common services across heterogeneous devices and applications. Vanderbilt University, in collaboration with North Carolina State University and Washington State University has developed a foundation ‘software platform’ for developing and deploying robust, reliable, effective and secure software applications for the Smart Grid. The Resilient Information Architecture Platform for the Smart Grid (RIAPS) provides core services for building effective and powerful smart grid applications. It offers unique services for real-time data dissemination, fault tolerance, and coordination across apps distributed over the network.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2024

GLIMPSE of Future Power Grid Models

Power grid is one of the critical national infrastructures with social, economics, and national security impacts. Particularly, power distribution systems represent part of the infrastructure between power distribution substations and customers such as residential, commercial, and industrial. To address various grid modernization challenges, state-of-the-art algorithms and methodologies have been developed to deploy, operate, and expand a secure and resilient power grid. At the same time, there is a need to develop capabilities to assist power grid stakeholders to quickly get insight into the design and structure of the grid. Data visualization is a key approach to comprehend and understand complex systems such as the power grid. We present GLIMPSE Grid Layout Interface for Model Preview and System Exploration), a graph-based semantic-aware application to visualize and update distribution power grid models. The GLIMPSE can be used with standard IEEE models to search and highlight power grid objects such as generators, loads, overhead lines, etc. Additionally, it supports updating attributes and model export to integrate with GridLAB-D simulations.

Cybersecurity, power grid, visualization↗

DOE OSTI2020

Rapid generation of optimal generalized Monkhorst-Pack grids

In this report computational modeling of the properties of crystalline materials has become an increasingly important aspect of materials research, consuming hundreds of millions of CPU-hours at scientific computing centers around the world each year, if not more. A routine operation in such calculations is the evaluation of integrals over the Brillouin zone. We have previously demonstrated that performing such integrals using generalized Monkhorst-Pack k-point grids can roughly double the speed of these calculations relative to the widely-used traditional Monkhorst-Pack grids. However the generation of optimal generalized Monkhorst-Pack grids is not implemented in most software packages due to the computational cost and difficulty of identifying the best grids. To address this problem, we present new algorithms that allow rapid generation of optimal generalized Monkhorst-Pack grids on the fly. We demonstrate that the grids generated by these algorithms are on average significantly more efficient than those generated using existing algorithms across a range of grid densities. For grids that correspond to a real-space supercell with at least 50 Å between lattice points, which is sufficient to converge density functional theory calculations within 1 meV/atom for nearly all materials, our algorithm finds optimized grids in an average of 0.19 s on a single processing core. To facilitate the widespread adoption of this approach, we present new open-source tools including a library designed for integration with third-party software packages.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Are grid cells used for navigation? On local metrics, subjective spaces, and black holes

The symmetric, lattice-like spatial pattern of grid-cell activity is thought to provide a neuronal global metric for space. This view is compatible with grid cells recorded in empty boxes but inconsistent with data from more naturalistic settings. Here, we review evidence arguing against the global-metric notion, including the distortion and disintegration of the grid pattern in complex and three-dimensional environments. We argue that deviations from lattice symmetry are key for understanding grid-cell function. We propose three possible functions for grid cells, which treat real-world grid distortions as a feature rather than a bug. First, grid cells may constitute a local metric for proximal space rather than a global metric for all space. Second, grid cells could form a metric for subjective action-relevant space rather than physical space. Third, distortions may represent salient locations. Finally, we discuss mechanisms that can underlie these functions. These ideas may transform our thinking about grid cells.

59 BASIC BIOLOGICAL SCIENCES↗