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

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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Nuclear Materials Packaging, Transportation, and Systems Analysis Group Software Quality Assurance Plan: ANSYS Mechanical Finite Element Analysis Software Version 2023R1

ANSYS Inc. develops and markets engineering simulation software and services used in the aerospace, automotive, manufacturing, electronics, biomedical, energy, defense, and many other industries. ANSYS is dedicated to engineering simulation and is the world’s leading software provider. ANSYS was founded in 1970 and is headquartered in Canonsburg, Pennsylvania. ANSYS provides an engineering analysis tool combining structural, thermal, computational fluid dynamics, acoustic, and electromagnetic simulation capabilities. ANSYS has two main programs, which use the same solvers: (1) Mechanical APDL (ANSYS Design Parametric Language), a Fortran-based coding platform, and (2) ANSYS Workbench, which uses a graphical user interface to aid in finite element analysis implementation. This plan covers both APDL and Workbench. The ANSYS computer program is a large-scale, multipurpose finite element program that can be used to solve several classes of engineering analyses. The analysis capabilities of ANSYS include the ability to solve static and dynamic structural analyses, steady-state and transient heat transfer problems, mode-frequency and buckling eigenvalue problems, static or time-varying magnetic analyses, and various types of field and coupled-field applications. The program contains many special features that allow nonlinearities or secondary effects such as plasticity, large strain, hyperelasticity, creep, swelling, large deflections, contact, stress stiffening, temperature dependency, material anisotropy, and radiation to be included in the solution. As ANSYS has been developed, other special capabilities such as substructuring, submodeling, random vibration, kinetostatics, kinetodynamics, free convection fluid analysis, acoustics, magnetics, piezoelectrics, coupled-field analysis, and design optimization have been added to the program. These capabilities contribute further to making ANSYS a multipurpose analysis tool for varied engineering disciplines. The ANSYS program has been in commercial use for over 50 years and has been used extensively in the aerospace, automotive, construction, electronic, energy services, manufacturing, nuclear, plastics, oil, and steel industries. Additionally, many consulting firms and hundreds of universities have used ANSYS for analysis, research, and educational purposes. ANSYS is recognized worldwide as one of the most widely used and capable programs of its type. Ansys design analysis software is the first created within a quality system with ISO 9001 certification, the internationally accepted quality standard. Product development, testing, maintenance and support processes also meet the United States Nuclear Regulatory Commission's quality requirements, as they have for nearly four decades. The Quality Assurance Service Agreement is suitable for the customers working in the nuclear industry who need to meet specific federal regulations including 10CRF50 Appendix B and provisions of 10CFR21. ANSYS has retained its original International Organization for Standardization (ISO) 9001 accreditation certificate since1995-05-04, It’s current certificate is valid until 2027-05-29.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Wear of Wave Energy Converters Mooring Lines Belts

Using a belt as a replacement for a rope on a rotary power take-offs (PTOs) system has become more common for wave energy converters, improving cyclic bend over sheave performance with a smaller bending thickness for belts. However, the service life predictions of PTOs are a major concern in design, because belt performance under harsh underwater environments is largely less studied. Here, in this work, the effect of fleet and twist angles on wear life is being investigated both experimentally and numerically. Two three-dimensional equivalent static finite element models are constructed to evaluate the complex stress state of polyurethane-steel belts around steel drums. The first is to capture the response of the experimental investigation performed on the wear life, and the second to predict the wear life of an existing functional PTO. The results show a significant effect for fleet and twist angles on stress concentrations and estimated service life.

16 TIDAL AND WAVE POWER↗
DOE OSTI2026

Symposium MT02: Statistical Mechanics-Based Computational Tools for the Study of Phase Transformation in Complex Materials (Final Report)

Symposium MT02 brought together a diverse and interdisciplinary community of scientists specializing in Statistical Mechanics-based computational modeling to investigate phase transformations in materials exhibiting complex disordered structures. As the demand for materials with extreme performance metrics grows—from aerospace components to next-generation optical fibers—the ability to predict microstructural evolution under non-equilibrium conditions has become paramount. The primary goal of this symposium was to identify, evaluate, and discuss advanced computational tools capable of designing precise manufacturing conditions to tailor material properties efficiently. By fostering a dialogue between computational theorists and experimentalists, the symposium sought to establish new protocols for predicting how processing history—such as cooling rates or strain paths—dictates the final microstructure.

36 MATERIALS SCIENCE↗
DOE OSTI2021

3D Mechanical Analysis of a Compact Nb 3 Sn IR Quadrupole for EIC

Abstract-The Electron Ion Collider (EIC) will require large aperture quadrupole magnets for the Hadron beam in the insertion region. Key requirements include high field, compact size, and tight control of the fringe fields. A 120 mm aperture, 308.4 mm outer diameter actively shielded Nb 3 Sn quadrupole model is under development to support these goals. This work is being carried out by a collaboration of BNL, JLAB and LBNL. A compact shell-based structure preloaded with a bladder and key system was developed for this project. In this paper, the effect of the compact structure on the mechanical behavior was investigated. In particular, the impact of the assembly tolerances and coil size variations on the actual coil stresses and bladder pressures was computed and compared with results from larger bladder and key structures developed for the LHC IR. The longitudinal preload is provided by stainless steel rods. Differently from other bladder and key magnets, the rods are first preloaded axially before coil axial load is applied. This new design aims to increase the overall stiffness of the system and reduce the longitudinal coil displacement during powering. Based on the results of a 3D mechanical analysis, the preliminary preload targets for the EIC quadrupole assembly will be reviewed and discussed.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

A High-Speed Rotational Diamond Anvil Cell for In Situ Analysis of Hierarchical Microstructural Evolution of Metallic Alloys during Extreme Shear Deformation

High speed shear deformation is ubiquitous in engineering applications, ranging from material processing methods such as friction stir processing/extrusion and in tribological contacts. However, analyzing the microstructural evolution of materials while they are undergoing high speed shear deformation have been a long-standing challenge. This led to predominant reliance on ex situ microscopy before and after shear deformation. But ex situ microscopy lacks the ability to analyze dynamic and transient hierarchical microstructural evolution mechanisms that could occur during shear deformation of materials. Therefore, to better understand the dynamic mechanisms of mass and energy transfer in materials under shear deformation, we developed a first of its kind high-speed rotational diamond anvil cell (HS-RDAC) for synchrotron-based in situ high-energy x-ray diffraction (XRD). We studied the time resolved lattice strain evolution, XRD peak broadening and changes in spatial variation of shear deformation induced alloying in pure metal and metal alloy sheets and powder mixture using the HS-RDAC. These in situ results were combined with detailed ex situ microstructural characterization before and after the shear deformation using transmission electron microscopy and atom probe tomography, which revealed the different stages of evolution of a shear deformation induced hierarchical nanostructure. Multiscale computational simulations including computational fluid dynamics, crystal plasticity, molecular dynamic simulation and density functional theory uncovered the mechanisms behind morphological changes, evolution of defect structures and changes in driving force for shear deformation induced intermixing. In conclusion, this in situ HS-RDAC capability, in combination with ex situ microstructural characterization and computational simulations, can provide new insights into the hierarchical microstructural evolution pathway during shear deformation.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Electric-field-induced crossover of polarization reversal mechanisms in Al 1–x Sc x N ferroelectrics

Scandium-doped aluminum nitride, Al 1–x Sc x N, represents a new class of displacive ferroelectric materials with high polarization and sharp hysteresis along with high-temperature resilience, facile synthesizability and compatibility with standard CMOS fabrication techniques. The fundamental physics behind the transformation of unswitchable piezoelectric AlN into switchable Al–Sc–N ferroelectrics depends upon important atomic properties such as local structure, dopant distributions and the presence of competing mechanism of polarization switching in the presence of an applied electric-field that have not been understood. We computationally synthesize Al 1–x Sc x N to quantify the inhomogeneity of Sc distribution and phase segregation, and characterize its crystal and electronic structure as a function of Sc-doping. Nudged elastic band calculations of the potential energy surface and quantum molecular dynamics simulations of direct electric-field-driven ferroelectric switching reveal a crossover between two polarization reversal mechanisms—inhomogeneous nucleation-and-growth mechanism originating near Sc-rich regions in the limit of low applied fields and nucleation-limited-switching in the high-field regime. Finally, understanding polarization reversal pathways for these two mechanisms as well as the role of local Sc concentration on activation barriers provides design rules to identify other combinations of dopant elements, such as Zr, Mg etc. to synthesize superior AlN-based ferroelectric materials.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2025

Toward engineering lattice structures with the material point method (MPM)

This study examines the potential of two variants of the material point method—the generalized interpolation material point (GIMP) and dual domain material point (DDMP) methods—in developing a robust computational framework for engineering lattice structures under different loading conditions. The study begins with assessing the ability of the two methods in predicting elastic buckling phenomena using column geometries with and without initial geometric imperfections. The results indicate that both methods effectively capture buckling phenomena when initial geometric imperfections are introduced. After this verification step, we create several models of tetrahedral lattice structures with varying strut diameter and orientation and subject them to quasi-static loading. We then validate the numerical results using laboratory test results. The results show that, while both methods accurately predict load–displacement curves in the pre-buckling regime, their predictive capabilities diminish in the post-buckling regime. Through visual comparison between the numerical and experimental deformed shapes, it appears that the discrepancies between model and experimental results are attributed to initial geometric imperfections in the lattices that occurred during 3D printing. We then establish a second set of lattice models where different types of initial geometric imperfections are considered. The results from these models show that imperfections have a negligible influence in the pre-buckling regime but affect the behavior considerably in the post-buckling regime. As a final step in this work, we subject the lattice models to impact loading and employ hypothetical soft and stiff materials. These results show that the lattice stiffness, which depends on material stiffness, strut diameter, and orientation, significantly influences the ability of a lattice structure to resist impact. In particular, we find that a stiffer lattice (i.e., one made with a stiff material and thicker struts) is capable of absorbing more energy than a softer one during impact. Although material nonlinearities, inelasticity, and detailed contact formulations are not considered in this study, the findings obtained herein lay the groundwork for engineering lattice structures under extreme loading conditions through a simulation-driven framework based on particle-based methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Electronic structure theory with molecular point group symmetries on quantum annealers

Quantum computation has the potential to revolutionize quantum chemistry through major speedups in computation times and an exponential reduction in computational resources. Here, we combine the symmetry-adapted Jordan–Wigner encoding based on the full Boolean symmetry group $\mathbb{Z}$$^{k}_{2}$ with our new implementation of the Xia–Bian–Kais (XBK) method for improving the efficiency of electronic structure theory calculations on quantum annealers, particularly by reducing the number of qubits needed to achieve the same accuracy. By providing a more extensive symmetry-adapted encoding (SAE) than previous work, we are able to simulate molecules larger than those previously reported that have been studied using methods developed for quantum annealers and without using an active space. We calculated the potential energy surfaces of H 2 , LiH, He 2 , H 2 O, O 2 , N 2 , Li 2 , F 2 , CO, BH 3 , NH 3 , and CH 4 , with the largest molecule in the STO-6G basis set requiring 16 qubits with our SAE, and compared them with full configuration interaction results. The application of SAE to the XBK method provides an exponential reduction in the size of the Hilbert space and scales well with the size of the problem. It does not introduce significant additional errors for even or large values of a key variational parameter that determines the number of ancilla qubits used in the XBK method’s Hamiltonian embedding, or for certain molecules such as He 2 and H 2 O. Here, we provide an explanation for this behavior and a recommendation on the usage of our method. In addition, we briefly discuss the potential of extracting electronic excited states from our method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Institute for Catalysis in Energy Processes (ICEP) (Final Report)

The Institute for Catalysis in Energy Processes (ICEP) was a multi-PI program located at the Northwestern University Center for Catalysis and Surface Science from 2006-2024. Over several renewal cycles and several organizing themes, ICEP addressed fundamental questions in catalysis science. In turn, the scientific questions addressed were directly relevant to the efficient use of the nation’s resources to produce fuels and commodity chemicals, harness alternate energy sources for chemical reactions such as light or electricity, reduce emissions and waste, and minimize the impact of our use of plastics. Selective oxidation, (oxidative) dehydrogenation, deNOx, CO 2 reduction, hydrogen release, polymer decomposition / depolymerization, and many other reactions of intense interest to the US Department of Energy were studied in the center. Major ICEP strengths were in catalyst synthesis, in measurements that elucidated catalyst properties, in reaction mechanisms and kinetics, and in predictive theory and modeling. ICEP researchers were often the inventors or developers of materials and methods that were brought to bear on the Institute’s catalytic systems. Key characterization tools advanced through this project included resonance Raman and related techniques, sum frequency generation, and X-ray standing wave spectroscopy. Center members relied extensively on computational tools such as density functional theory and microkinetic modeling to fully investigate catalyst structures and catalytic mechanisms. ICEP researchers were early developers of atomic layer deposition (ALD) for catalyst synthesis and were early pioneers of metal organic frameworks for catalysis. ICEP innovations are found in areas of intense research such as single-atom catalysts, catalytic deconstruction of plastics, and catalytic MOFs, to name a few. Research areas initiated by ICEP indirectly led to DOE EFRCs, startup companies, and other achievements. Over its 18 years of existence, ICEP involved two different PIs (Stair and Notestein) and 24 senior investigators across several academic disciplines at Northwestern University. There were tight collaborations with Argonne National Laboratory, including specialized equipment and experiments permanently located there. The center supported ~400 person-years of effort by graduate students and postdocs, either directly through DOE support or indirectly by leveraging independent support provided to the trainees, e.g. through the NSF GRFP or internal fellowships. The project resulted in 328 manuscripts and numerous conference presentations.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Computational Fluid Dynamics Modeling to Simulate a Combined Reforming Process for Syngas and Hydrogen Production

An Oxygen Transport Membrane (OTM) combined reforming technology for producing syngas and hydrogen integrates the advantages of multiple processes—steam methane reforming (SMR), autothermal reforming (ATR), an air separation unit (ASU)—into a single integrated technology. The OTM consists of a primary reforming tube, in which desulfurized natural gas is partially reformed by steam at high pressure in the presence of a metal catalyst. This process is followed in series by a ceramic OTM with a secondary reformer, in which residual methane reforms and O 2 - ions react with a portion of the CO and H 2 fuel to provide the heat to support both primary and secondary reforming. Although the OTM combined reformer technology for syngas and H 2 production has been substantially developed in the last decade, several challenges that affect the overall production efficiency and reliability are yet to be fully understood, addressed, and resolved. Therefore, developing Computational Fluid Dynamics (CFD) models that incorporate fluid dynamics, mass transport, kinetics, heat transport, and structural mechanics is critical to understanding and minimizing the probability of tube failures during the startup and operation. In this report, an exhaustive literature review was performed to survey the current state of technology for producing syngas and H 2 using either conventional or renewable energy sources. The feedstocks reviewed include natural gas and coal for the conventional technologies, whereas biomass, solar, wind, and nuclear energy for the renewable technologies. The existing industry-grade COMSOL multiphysics models of OTM were upgraded for the latest software release. In addition, they were improved to help achieve grid and solver independence and were successfully ported on the ORNL high-performance computing clusters to speed up their run times. A 42% reduction in the simulation run time was achieved. A new higher-fidelity CFD model of an OTM tube was developed in the StarCCM+ simulation platform. This new model was designed to simulate various physics using first principles, e.g., turbulent flow, heat transfer, and chemical reactions while avoiding unnecessary simplifications. The resulting predictions were qualitatively assessed and provided useful insights into the multiphysics complexity of an OTM tube.

08 HYDROGEN↗
DOE OSTI2020

Non-destructive simulation of node defects in additively manufactured lattice structures

Additive Manufacturing (AM), commonly referred to as 3D printing, offers the ability to not only fabricate geometrically complex lattice structures but parts in which lattice topologies in-fill volumes bounded by complex surface geometries. However, current AM processes produce defects on the strut and node elements which make up the lattice structure. This creates an inherent difference between the as-designed and as-fabricated geometries, which negatively affects predictions (via numerical simulation) of the lattice’s mechanical performance. Although experimental and numerical analysis of an AM lattice’s bulk structure, unit cell and struts have been performed, there exists almost no research data on the mechanical response of the individual as-manufactured lattice node elements. Here we propose a methodology that, for the first time, allows non-destructive quantification of the mechanical response of node elements within an as-manufactured lattice structure. A custom-developed tool is used to extract and classify each individual node geometry from micro-computed tomography scans of an AM fabricated lattice. Voxel-based finite element meshes are generated for numerical simulation and the mechanical response distribution is compared to that of the idealised computer-aided design model. The method demonstrates compatibility with Uncertainty Quantification methods that provide opportunities for efficient prediction of a population of nodal responses from sampled data. Overall, the non-destructive and automated nature of the node extraction and response evaluation is promising for its application in qualification and certification of additively manufactured lattice structures.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Tuning Catalytic Reactivity via Wetting Control through Oxygen Vacancies: Ru Clusters on Anatase TiO 2 and CeO 2 Supports

The shape of supported metal particles regulates their catalytic reactivity and is determined by the degree of wetting between the metal particle and the support surface. Flattened particles that wet support surfaces were reported in various catalytic systems, particularly in the subnanometer size regime. Such consequential metal–support wetting phenomena are poorly understood, and methods to study them on powder catalysts under realistic conditions are lacking. Here, we investigate the size-dependent wetting behaviors of Ru particles on two reducible-oxide supports, anatase TiO 2 (TiO 2 -A) and CeO 2 , under reducing catalytic conditions. X-ray absorption spectroscopy (XAS), low-energy ion scattering (LEIS), and density functional theory (DFT) are combined to determine the shape of Ru particles. Ru particles remain three-dimensional without wetting the TiO 2 -A support within the coverage range studied (0.06–0.98 Ru nm –2 ). In contrast, at low coverages (<0.25 Ru nm –2 ), Ru wets the CeO 2 support to form flat, disordered structures. The higher wettability of CeO 2 than TiO 2 -A is attributed to oxygen vacancies in the near-surface region. The shape difference between small Ru particles or clusters on the two supports leads to drastically contrasting catalytic reactivities in polyolefin hydrogenolysis, despite similar diameters. As a result, this work highlights the implications of metal–support wetting, or cluster shape, on catalytic behaviors of small metal clusters, while establishing the foundation for future systematic studies of such a phenomenon in realistic systems, by delivering a multitechnique methodology and revealing governing fundamental principles.

42 ENGINEERING↗
DOE OSTI2025

Single Crystals of Vanadium Oxides as a Lens for Understanding Structural and Electronic Phase Transformations, Ion Transport, Chemo-Mechanical Coupling, and Electrothermal Neuronal Emulation

Vanadium oxides cystallize in a diverse array of structures and compositions arising from the redox versatility of vanadium, variable covalency of V−O bonds, and myriad coordination geometries. Their open frameworks present abundant interstitial sites that enable insertion of guest-ions. In such compounds, V3d electron and spin localization and disorder couple strongly to structural preferences. The rich structural diversity manifests as a “rugged” free energy landscape with multiple interconvertible polymorphs. Such a landscape sets up structural, electronic, and magnetic transitions that underpin the promise of these materials as ion-insertion battery electrodes; compact primitives for brain-inspired computing, and heterogeneous catalysts. Here, we examine the structural and compositional diversity, electronic instabilities, defect dynamics, structure transformations, mechanical properties, and surface structure of vanadium oxides using single crystals as a distinctive lens. Single crystals enable the measurement of structure−function correlations without the ensemble and orientational averaging inevitable in polycrystalline materials. Their well-defined surfaces further enable examination of facet-dependent reactivity toward molecular adsorbates, ion fluxes, and lattice (mis)matched solids. We provide a comprehensive account of vanadium-oxide single-crystal studies, from delineation of common structural motifs to single-crystal growth techniques, topochemical modification strategies, mechanisms underpinning electronic instabilities, and implementation as electrothermal neurons and battery electrode materials.

Ponis, John [Texas A&M University, College Station↗
DOE OSTI2021

Reviewing computational studies of defect formation and behaviors in carbon fiber structural units

Solid-state carbon materials, such as graphite and graphene, are at the forefront of materials research because of their unique electronic, vibrational, and mechanical properties, leading to a broad range of potential and realized applications. One key application is their role as basic structural units of carbon fiber (CF), a lightweight alternative to steel. In CF, a delicate relationship exists between ultimate material strength and the atomic-scale density of defects contained at the inter- and intra-subunit levels. Computational studies provide insight into the stability of various types of defects that can form in these systems and connect with experimental observables such as bandgap and spectroscopic measurements. Therefore, the literature contains many computational studies that focus on changes induced by defects, including vacancies and Dienes transformations (Stone-Wales and Thrower defects). However, wide-ranging methods and cell sizes have been used, and property-specific information is often lacking. Furthermore, this review summarizes key literature findings, paying particular attention to changes in the electronic, vibrational, and mechanical properties induced by defects in graphitic materials relevant to CF.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Failure of molecular dynamics to provide appropriate structures for quantum mechanical description of the aqueous chloride ion charge-transfer-to-solvent ultraviolet spectrum

The lowest band in the charge-transfer-to-solvent ultraviolet absorption spectrum of aqueous chloride ion is studied by experiment and computation. Interestingly, the experiments indicate that at concentrations up to at least 0.25 M, where calculations indicate ion pairing to be significant, there is no notable effect of ionic strength on the spectrum. The experimental spectra are fitted to aid comparison with computations. Classical molecular dynamic simulations are carried out on dilute aqueous Cl - , Na + , and NaCl, producing radial distribution functions in reasonable agreement with experiment and, for NaCl, clear evidence of ion pairing. Clusters are extracted from the simulations for quantum mechanical excited state calculations. Accurate ab initio coupled-cluster benchmark calculations on a small number of representative clusters are carried out and used to identify and validate an efficient protocol based on time-dependent density functional theory. The latter is used to carry out quantum mechanical calculations on thousands of clusters. The resulting computed spectrum is in excellent agreement with experiment for the peak position, with little influence from ion pairing, but is in qualitative disagreement on the width, being only about half as wide. It is concluded that simulation by classical molecular dynamics fails to provide an adequate variety of structures to explain the experimental CTTS spectrum of aqueous Cl - .

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Physics-informed machine learning exploration of Na storage mechanisms in disordered carbon

Sodium-ion batteries are a cost-effective, sustainable alternative to lithium-ion systems for large-scale energy storage. However, optimizing sodium storage in carbon-based anodes with microstructural complexity and atomic disorder remains a major challenge. The intrinsic inhomogeneity of these materials produces diverse local environments, making it difficult for conventional methods to predict and control ion dynamics. Hard carbon (HC) anodes, composed of ranges of ordered-to-disordered graphitic and amorphous nanodomains, offer tunable ion storage and rate capacity, yet rationale design remains a challenge due to poorly understood correlation between local atomic feature and ion transport mechanism. Here, to address this challenge, we introduce a data-driven framework that integrates validated machine-learned interatomic potentials, large-scale molecular dynamics simulations, and machine learning to elucidate sodium transport mechanisms as a function of carbon and sodium loading densities. By computing per-ion structural descriptors and applying unsupervised learning, we identify distinct diffusion modes governed by microscopic features. Supervised analysis and correlation mapping then establish quantitative links between these transport regimes and processing variables such as bulk carbon density and sodium content. This physics-informed approach establishes quantitative structure–transport relationships and offers actionable design principles for engineering high-performance HC anodes.

Data-driven framework↗
DOE OSTI2022

Algebraic Theory of Patterns as Generalized Symmetries

We generalize the exact predictive regularity of symmetry groups to give an algebraic theory of patterns, building from a core principle of future equivalence. For topological patterns in fully-discrete one-dimensional systems, future equivalence uniquely specifies a minimal semiautomaton. We demonstrate how the latter and its semigroup algebra generalizes translation symmetry to partial and hidden symmetries. This generalization is not as straightforward as previously considered. Here, though, we clarify the underlying challenges. A stochastic form of future equivalence, known as predictive equivalence, captures distinct statistical patterns supported on topological patterns. Finally, we show how local versions of future equivalence can be used to capture patterns in spacetime. As common when moving to higher dimensions, there is not a unique local approach, and we detail two local representations that capture different aspects of spacetime patterns. A previously developed local spacetime variant of future equivalence captures patterns as generalized symmetries in higher dimensions, but we show that this representation is not a faithful generator of its spacetime patterns. This motivates us to introduce a local representation that is a faithful generator, but we demonstrate that it no longer captures generalized spacetime symmetries. Taken altogether, building on future equivalence, the theory defines and quantifies patterns present in a wide range of classical field theories.

97 MATHEMATICS AND COMPUTING↗