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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 775 records · Page 43
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Controllable Thin‐Film Approaches for Doping and Alloying Transition Metal Dichalcogenides Monolayers

Abstract Two‐dimensional (2D) transition metal dichalcogenides (TMDs) exhibit exciting properties and versatile material chemistry that are promising for device miniaturization, energy, quantum information science, and optoelectronics. Their outstanding structural stability permits the introduction of various foreign dopants that can modulate their optical and electronic properties and induce phase transitions, thereby adding new functionalities such as magnetism, ferroelectricity, and quantum states. To accelerate their technological readiness, it is essential to develop controllable synthesis and processing techniques to precisely engineer the compositions and phases of 2D TMDs. While most reviews emphasize properties and applications of doped TMDs, here, recent progress on thin‐film synthesis and processing techniques that show excellent controllability for substitutional doping of 2D TMDs are reported. These techniques are categorized into bottom–up methods that grow doped samples on substrates directly and top–down methods that use energetic sources to implant dopants into existing 2D crystals. The doped and alloyed variants from Group VI TMDs will be at the center of technical discussions, as they are expected to play essential roles in next‐generation optoelectronic applications. Theoretical backgrounds based on first principles calculations will precede the technical discussions to help the reader understand each element's likelihood of substitutional doping and the expected impact on the material properties.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Two-step deformation-induced martensitic transformation in additively manufactured High-Si stainless steel

Deformation-induced phase transformation in the additively manufactured (AM) Fe–18Cr–8Ni-5.5Si (in wt.%) alloy was analyzed using the in-situ electron backscattered diffraction (EBSD) record during uniaxial tensile testing in a scanning electron microscope (SEM). Analysis of EBSD data was focused to investigate phase transformation behavior during deformation with consideration of mechanical interactions among phases and grains in the ultrafine AM microstructure. The initial EBSD phase map illustrated that the as-built microstructure was a duplex structure consisting of major austenite (γ) and minor ferrite phases, some of which showed non-traditional orientation relationship since the rapid solidification in the AM process has produced non-equilibrium state in phase formation. In the deformed as-built AM alloy, the two-step martensitic transformation (γ→ε→α´) was identified as the main deformation-induced transformation mechanism. Martensitic transformation steps were found to be associated with glides of Shockley partial dislocations on closed packed (111) planes under the influence of atomic disturbance in the γ and ε phases, respectively. Using the closed-packed plane pole figures and unit cell orientations, their evolutions and mechanisms accompanying with the transformation were analyzed. Finally, the results indicate that one variant of ε-martensite forms from their parent γ phase, while two variants of α´ form from their parent ε phase.

36 MATERIALS SCIENCE↗
DOE OSTI2020

A structural framework for unidirectional transport by a bacterial ABC exporter

The ATP-binding cassette (ABC) transporter of mitochondria (Atm1) mediates iron homeostasis in eukaryotes, while the prokaryotic homolog from Novosphingobium aromaticivorans (NaAtm1) can export glutathione derivatives and confer protection against heavy-metal toxicity. To establish the structural framework underlying the NaAtm1 transport mechanism, we determined eight structures by X-ray crystallography and single-particle cryo-electron microscopy in distinct conformational states, stabilized by individual disulfide crosslinks and nucleotides. As NaAtm1 progresses through the transport cycle, conformational changes in transmembrane helix 6 (TM6) alter the glutathione-binding site and the associated substrate-binding cavity. Significantly, kinking of TM6 in the post-ATP hydrolysis state stabilized by MgADPVO4 eliminates this cavity, precluding uptake of glutathione derivatives. The presence of this cavity during the transition from the inward-facing to outward-facing conformational states, and its absence in the reverse direction, thereby provide an elegant and conceptually simple mechanism for enforcing the export directionality of transport by NaAtm1. One of the disulfide crosslinked NaAtm1 variants characterized in this work retains significant glutathione transport activity, suggesting that ATP hydrolysis and substrate transport by Atm1 may involve a limited set of conformational states with minimal separation of the nucleotide-binding domains in the inward-facing conformation.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

Code Coverage Status of the ARC Code PERSENT

The Argonne Reactor Code (ARC) software system supports users in their fast reactor design goals by providing neutronic, thermal-hydraulic, and structural analysis capabilities. PERSENT fulfills the role of generating reactivity coefficients for a given time point of a REBUS calculation usable in a point kinetics based safety analysis capability. PERSENT also provides a sensitivity coefficient capability on eigenvalue, reactivity worth, and several other key coefficients that are used in the follow-on safety analysis. Given a co-variance matrix, PERSENT can carry out the uncertainty quantification to indicate the amount of error in the reactivity coefficients derived from the errors in the cross section measurements. With continued improvement of computational resources, many of the geometry modeling capabilities in DIF3D that were primarily used in low order schemes are not really needed anymore. Today, the diffusion and transport capabilities of DIF3D-VARIANT are primarily used in the reactor design process with some scattered usage of DIF3D-FD and DIF3D-Nodal. PERSENT is part of the ARC code system and is built around DIF3D-VARIANT and the flux solution it provides. The purpose of the present work is to identify a set of test problems for PERSENT and assess the code coverage of PERSENT for those test problems. PERSENT treats the DIF3D executable as an external executable and thus the code coverage considerations only need to focus on the PERSENT source code and only a fraction of the connected modules in the existing ARC software library. The goal is to document what parts of the existing PERSENT code are touched by the set of test problems and which are not. Because the verification work done on PERSENT was focused on the most common uses of PERSENT for fast reactor analysis, the code coverage assessment of those capabilities is the highest priority. This will ensure that nothing is being missed by the existing verification test problems that users of PERSENT rely upon. The code coverage analysis of PERSENT was performed with the Code Coverage Tool of the Intel Fortran compiler which requires modifications to the compilation of PERSENT. The detailed coverage tables are given for each submodule of PERSENT. Most of the uncovered parts/files could be easily ignored because they are either for error message and debugging output or not needed by PERSENT today. Only a few uncovered parts of PERSENT deserve extending the verification test suite.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

Infrared triggered dwell and active cooling thermal control effects on microstructural uniformity in DED

Directed Energy Deposition (DED) offers rapid large scale fabrication, but difficulty in delivering consistent microstructures and properties hinders the use of DED fabricated components in safety or performance critical applications. Variability stems from the complex thermal cycles generated by the toolpath used to print the required geometry. Several practical methods have become established in DED to regulate overheating, such as active cooling of the baseplate structure or the use of an infrared camera to inject interlayer pauses to ensure the top layer of the component cools to a set temperature, which have been shown to affect microstructure. However, no critical assessment has been performed as to how effective these controls are in promoting microstructural uniformity in the context of complex layer timing commonly generated by non-prismatic geometries. Here we show how controls influence the thermal field, phase transformations, and dynamic annealing of a low-temperature transformation steel using infrared imaging and operando neutron diffraction. Counterintuitively, common thermal homogenization process controls can reduce microstructural uniformity because these approaches stabilize peak temperature while overlooking temperatures near the solid-state phase transformation fronts. Instead, the cyclic reheating induces spatially-variant dynamically annealed regions which can be modulated via control parameters. We show that these controls have spatially linked effects centimeters away from the active weld, which implies that microstructure control must co-optimize thermal input across many subsequent layers. In conclusion, our results demonstrate the pressing need for higher order controls that integrate predictive elements of simulation data to stabilize printed properties for future qualification of DED components.

Directed energy deposition↗
DOE OSTI2024

Acidity-Governed Rules in the Electrochemical Performance of Fluorinated Benzenes for High-Voltage Lithium Metal Batteries

Judicious selection of the optimal fluorobenzene (FB) as a nonsolvating cosolvent for lithium metal batteries (LMBs) is reported. For this work, we found the key correlation between FB structures and cycling stabilities of cells: increased fluorine substitution of FBs results in higher anodic stability but at the expense of reduced reductive stability, and FBs containing three or more fluorine atoms exhibit insufficient anodic stability in the electrolyte system comprised of fluoroethylene carbonate (FEC) and ethyl methyl carbonate (EMC). More importantly, FBs with higher acidity (lower pK a ) due to protons located between two adjacent fluorine atoms tend to be more susceptible to side reactions during cycling. Our results indicate that difluorobenzenes with no “acidic” proton (DFB2 and DFB4) have emerged as the optimal choice with the desired redox stability in high-voltage LMBs. Nuclear magnetic resonance and X-ray photoelectron spectroscopy confirmed these findings, providing guidance for selecting the most suitable FB variants as nonsolvating cosolvents for high-voltage LMBs.

25 ENERGY STORAGE↗
DOE OSTI2020

Stochastic Analysis for Long Term Capital Structures, Systems, and Components Refurbishment and Replacement

As commercial Nuclear Power Plants (NPPs) pursue extended plant operation in the form of Second License Renewal (SLR), opportunities exist for these plants to provide capital investments to ensure long-term safe and economic performance. At the current time, several utilities have announced an intention to pursue extended operation for one or more of their NPPs via SLR . The goal of this research is to develop a risk-informed approach to evaluate and prioritize plant capital investments made in preparation for, and during the period of, extended plant operations to support decisions for NPP operations. Since the capital investments are influenced by various factors, such as markets, safety and regulatory, the decision-making process of NPP operations should take into account relevant factors for balancing risks, costs and profits. The traditional method of capital budgeting is based on the priority list of candidate projects using economic measures such as benefit-investment ratio, net present value (NPV) and internal rate of return. In the literatures, the problem of capital budgeting or the variant can be represented by an appropriate knapsack problem. The knapsack approach to capital budgeting takes as input as investment, along with the cost and profit of each project. The objective of capital budgeting is to find the combination of the binary decisions for every investment such that the overall profit is as large as possible. The output is a collection of projects to be carried out, and we refer this selected collection of projects as a project portfolio. One limitation of traditional optimization models for capital budgeting is that they do not account for risk/uncertainty in profit and cost streams associated with individual projects, they do not account for risk in resource availability in future years [1,2,3]. Projects can incur cost over-runs, especially when projects are large, performed infrequently, and when there is risk regarding technical viability, external contractors, and/or suppliers of requisite parts and materials. Occasionally, projects are performed ahead of schedule and with cost savings. Planned budgets for capital improvements can be cut and key personnel may be lost. Or, there may be surprise windfalls in budgets for maintenance activities due to decreased costs for “unplanned” maintenance. In these cases, how should we resolve capital budgeting when we have risk forecasts for costs, profits and budgets? One approach we proposed in this summary is to re-solve the optimization models based on assumed statistical distributions of given parameters. If these distributions were not available, a two-stage stochastic optimization approach can be used to provide priority lists to decision-makers to support better risk-informed decisions [4, 5]. In this summary, we will only focus on the first approach.

42 ENGINEERING↗
DOE OSTI2022

A systematic exploration of boceprevir-based main protease inhibitors as SARS-CoV-2 antivirals

Boceprevir is an HCV NSP3 inhibitor that was explored as a repurposed drug for COVID-19. It inhibits the SARS-CoV-2 main protease (M Pro ) and contains an α-ketoamide warhead, a P1 β-cyclobutylalanyl moiety, a P2 dimethylcyclopropylproline, a P3 tert-butylglycine, and a P4 N-terminal tert-butylcarbamide. By introducing modifications at all four positions, we synthesized 20 boceprevir-based M Pro inhibitors including PF-07321332 and characterized their M Pro inhibition potency in test tubes (in vitro) and 293T cells (in cellulo). Crystal structures of M Pro bound with 10 inhibitors and cytotoxicity and antiviral potency of 4 inhibitors were characterized as well. Replacing the P1 site with a β-(S-2-oxopyrrolidin-3-yl)-alanyl (Opal) residue and the warhead with an aldehyde leads to high in vitro potency. The original moieties at P2, P3 and the P4 N-terminal cap positions in boceprevir are better than other tested chemical moieties for high in vitro potency. In crystal structures, all inhibitors form a covalent adduct with the M Pro active site cysteine. Here, the P1 Opal residue, P2 dimethylcyclopropylproline and P4 N-terminal tert-butylcarbamide make strong hydrophobic interactions with M Pro , explaining high in vitro potency of inhibitors that contain these moieties. A unique observation was made with an inhibitor that contains a P4 N-terminal isovaleramide. In its M Pro complex structure, the P4 N-terminal isovaleramide is tucked deep in a small pocket of M Pro that originally recognizes a P4 alanine side chain in a substrate. Although all inhibitors show high in vitro potency, they have drastically different in cellulo potency to inhibit ectopically expressed M Pro in human 293T cells. In general, inhibitors with a P4 N-terminal carbamide or amide have low in cellulo potency. This trend is reversed when the P4 N-terminal cap is changed to a carbamate. The installation of a P3 O-tert-butyl-threonine improves in cellulo potency. Three molecules that contain a P4 N-terminal carbamate were advanced to cytotoxicity tests on 293T cells and antiviral potency tests on three SARS-CoV-2 variants. They all have relatively low cytotoxicity and high antiviral potency with EC 50 values around 1 μM. A control compound with a nitrile warhead and a P4 N-terminal amide has undetectable antiviral potency. Based on all observations, we conclude that a P4 N-terminal carbamate in a boceprevir derivative is key for high antiviral potency against SARS-CoV-2.

60 APPLIED LIFE SCIENCES↗
NASA NTRS2019

TPSAS-NF1676L-32920-DND

In June 2019, a full-scale crash test of a Fokker F28 Fellowship aircraft will be conducted at NASA Langley Research Center?s Landing and Impact Research (LandIR) Facility. The F28 is a high-performance twin-turbo fan narrow-body aircraft with seating in a 3+2 configuration. The MK4000 variant, used in this test, is capable of carrying up to 85 passengers on medium range routes. The F28 was first type certified by the Federal Aviation Administration (FAA) in 1969 and now the majority of the F28 fleet has retired from service in the United States. In 2016, the FAA and NASA Langley Research Center (LaRC) signed an interagency agreement for conducting a research program to obtain test data that will support the development of airframe level crash requirements for transport category airplanes [1]. The objectives of the full-scale crash test can be divided into six categories: (1) To compare and contrast responses in identical aircraft undergoing vertical only to combined vertical and horizontal loading conditions, (2) To examine the effects of horizontal loading on aircraft structure during a crash event, (3) To generate data for the use in calibration of computer modelling efforts, (4) To generate data from onboard Anthropomorphic Test Devices (ATDs) for the evaluation of injury, (5) To obtain data from experimental seats, and (6) To obtain data from new and novel ATD designs including Warrior Injury Assessment MANikin (WIAMan) [2], Test device for Human Occupant Response (THOR), and other newly developed child ATDs. The focus of this presentation will be to document finite element model development of the full-scale F28 aircraft and to present preliminary test-analysis predictions. NASA obtained the full-scale F28 aircraft, plus three fuselage sections and two sets of wings with funding through the NASA Aviation Safety Program in 1998. In addition to the hardware, NASA purchased a full NASTRAN model of the airframe that had been developed by the Dutch manufacturer, Fokker. Beginning in 2016, the NASTRAN model was converted to LS-DYNA? [4, 5] format and modified by combining parts, adding missing parts of internal structure, and including ballast for loading weights, etc. It contains: 89,223 nodes; 24,065 beam elements; 55,404 shell elements; 29,044 solid elements; 740 parts; 80 material definitions; and, 46 Constrained Nodal Rigid Bodies (CNRBs). The aircraft model will be executed in LSDYNA to simulate the test article impact onto a 2-ft.-high bed of soil under combined velocity conditions of 70-ft/s forward and 30-ft/s vertical velocity. Pre-test simulation predictions will be generated and correlated with test data.

Karen E Jackson↗
NASA NTRS2018

FUELEAP Model-Based System Safety Analysis

NASA researchers, in a partnership with Boeing, are investigating a fuel-cell powered variant of the X-57 “Maxwell” Mod-II electric propulsion aircraft, which is itself derived from a stock Tecnam P2006T. The “Fostering Ultra-Efficient Low-Emitting Aviation Power” (FUELEAP) project will replace the X-57 power subsystem with a hybrid Solid-Oxide Fuel Cell (SOFC) system to increase the potential range of the electric-propulsion aircraft while dramatically improving efficiency and emissions over stock internal-combustion engines. Our FUELEAP safety analysis faces two primary challenges. First, the Part 23 certificated Tecnam P2006T is undergoing significant modifications to host the hybrid electric-propulsion system, and the challenge is to assure that the safety inherent in the stock aircraft (and subsequently in X-57 Mod-II) is not compromised by changes in avionics, aircraft structural loading, weight and balance, or other considerations. Secondly, because the SOFC power system has little (if any) relevant in-service precedent, our challenge is to assure that we identify and mitigate all reasonably plausible hazards introduced by unique FUELEAP equipage. We are investigating and utilizing Model-Based Safety Analysis (MBSA) methods to help us address these FUELEAP safety challenges. We captured aircraft-level system hazard conditions using instances of a SysML hazard block via aircraft-level Functional Hazard Analysis (FHA). Then, using SysML models of the FUELEAP architecture, we related the hazard conditions to initiating system events and possible mitigations, such as design architecture modifications or operational constraints. We are continuing to define our approach to MBSA by developing a component-by-component inventory of local failure modes and tracing their possible contribution to hazard conditions. Finally, we are applying an argument-based approach to FUELEAP assurance. Through a FUELEAP “safety case,” we are providing an explicit argument for FUELEAP safety by associating assurance evidence with overarching safety claims through a structured argument.

Woodham, Kurt P.↗
DOE OSTI2023

Optimal design of chemoepitaxial guideposts for the directed self-assembly of block copolymer systems using an inexact Newton algorithm

Directed self-assembly (DSA) of block copolymers (BCPs) is one of the most promising developments in the cost-effective production of nanoscale devices. The process makes use of the natural tendency for BCP melts to form nanoscale structures upon phase separation. The phase separation can be directed through the use of chemically patterned substrates to promote the formation of morphologies that are essential to the production of semiconductor devices. Moreover, the design of substrate pattern can be formulated as an optimization problem for which we seek optimal substrate designs that effectively produce given target morphologies. In this paper, we adopt a phase field model given by a nonlocal Cahn–Hilliard partial differential equation (PDE) based on the minimization of the Ohta–Kawasaki free energy, and present an efficient PDE-constrained optimization framework for the optimal design problem. The design variables are the locations of circular- or strip-shaped guiding posts that are used to model the substrate chemical pattern. To solve the ensuing optimization problem, we propose a variant of an inexact Newton conjugate gradient algorithm tailored to this problem. Additionally, we demonstrate the effectiveness of our computational strategy on numerical examples that span a range of target morphologies. Owing to our second-order optimizer and fast state solver, the numerical results demonstrate five orders of magnitude reduction in computational cost over previous work. The efficiency of our framework and the fast convergence of our optimization algorithm enable us to rapidly solve the optimal design problem in not only two, but also three spatial dimensions.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2014

Assessment of Shape Memory Alloys - From Atoms To Actuators - Via In Situ Neutron Diffraction

As shape memory alloys (SMAs) become an established actuator technology, it is important to identify the fundamental mechanisms responsible for their performance by understanding microstructure performance relationships from processing to final form. Yet, microstructural examination of SMAs at stress and temperature is often a challenge since structural changes occur with stress and temperature and microstructures cannot be preserved through quenching or after stress removal, as would be the case for conventional materials. One solution to this dilemma is in situ neutron diffraction, which has been applied to the investigation of SMAs and has offered a unique approach to reveal the fundamental micromechanics and microstructural aspects of bulk SMAs in a non-destructive setting. Through this technique, it is possible to directly correlate the micromechanical responses (e.g., internal residual stresses, lattice strains), microstructural evolutions (e.g., texture, defects) and phase transformation properties (e.g., phase fractions, kinetics) to the macroscopic actuator behavior. In this work, in situ neutron diffraction was systematically employed to evaluate the deformation and transformation behavior of SMAs under typical actuator conditions. Austenite and martensite phases, yield behavior, variant selection and transformation temperatures were characterized for a polycrystalline NiTi (49.9 at. Ni). As the alloy transforms under thermomechanical loading, the measured textures and lattice plane-level variations were directly related to the cyclic actuation-strain characteristics and the dimensional instability (strain ratcheting) commonly observed in this alloy. The effect of training on the shape memory characteristics of the alloy and the development of two-way shape memory effect (TWSME) were also assessed. The final conversion from a material to a useful actuator, typically termed shape setting, was also investigated in situ during constrained heatingcooling and subsequent shape recovery experiments. Neutron diffraction techniques are also being applied to the investigation of novel high temperature SMAs with the objective of designing alloys with better stability, higher transition temperatures and ultimately superior durability.

Shape Memory Alloys↗
DOE OSTI2023

Exploring novel HIV ‐1 reverse transcriptase inhibitors with drug‐resistant mutants: A double mutant surprise

Abstract HIV‐1 reverse transcriptase (RT) remains a key target for HIV drug development. As successful management of the disease requires lifelong treatment, the emergence of resistance mutations is inevitable, making development of new RT inhibitors, which remain effective against resistant variants crucial. To this end, previous computationally guided drug design efforts have resulted in catechol diether compounds, which inhibit wildtype RT with picomolar affinities and appear to be promising preclinical candidates. To confirm that these compounds remain potent against Y181C, a widespread mutation conferring resistance to first generation inhibitors, they were screened against the HIV‐1 N119 clinical isolate, reported as a Y181C single mutant. In comparison to a molecular clone with the same mutation, N119 appears less susceptible to inhibition by our preclinical candidate compounds. A more detailed sequencing effort determined that N119 was misidentified and carries V106A in combination with Y181C. While both indolizine and naphthalene substituted catechol diethers are potent against the classical Y181C single mutant, the addition of V106A confers more resistance against the indolizine derivatives than the naphthalene derivatives. Crystal structures presented in this study highlight key features of the naphthyl group, which allow these compounds to remain potent in the double mutant, including stronger interactions with F227 and less reliance on V106 for stabilization of the ethoxy‐uracil ring, which makes critical hydrogen bonds with other residues in the binding pocket.

Biochemistry & Molecular Biology↗
DOE OSTI2021

Comparing different density-matrix expansions for long-range pion exchange

Empirical energy density functionals (EDFs) are generally successful in describing nuclear properties across the table of nuclides. But their limitations motivate using the density-matrix expansion (DME) to embed long-range pion interactions into a Skyrme functional. Recent results on the impact of the pion were both encouraging and puzzling, necessitating a careful re-examination of the DME implementation. In this study, we take the first steps, focusing on two-body scalar terms in the DME. Exchange energies with long-range one-pion contributions are well approximated by all DME implementations considered, with preference for variants that do not truncate at two derivatives in every EDF term. The use of the DME for chiral pion contributions is therefore supported by this investigation. For scalar-isovector energies it is important to treat neutrons and protons separately. The results are found to apply under broad conditions, although self-consistency is not yet tested.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Spectroscopic factors in dripline nuclei

Single-nucleon knockout reaction studies of the proton-dripline nuclei 9 C and 13 O suggest an appreciable suppression of spectroscopic factors. In this work, we calculate the one-neutron and one-proton spectroscopic factors for the mirror pair 9 C – 9 Li and 13 O using two variants of the continuum shell model: the complex-energy Gamow shell model and the real-energy shell model embedded in the continuum. Furthermore, our results indicate that the continuum effects strongly suppress the spectroscopic factors of well-bound orbits in the dripline systems but have less impact on the spectroscopic factors of weakly bound states.

6 ≤ A ≤ 19↗
DOE OSTI2021

Colossal Density-Driven Resistance Response in the Negative Charge Transfer Insulator MnS 2

A reversible density driven insulator to metal to insulator transition in high-spin MnS 2 is experimentally observed, leading with a colossal electrical resistance drop of $10^8$ Omega by 12 GPa. Density functional theory simulations reveal the metallization to be unexpectedly driven by previously unoccupied $S_{2}^{-2}$ $\sigma^{*}_{3p}$ antibonding states crossing the Fermi level. This is a unique variant of the charge transfer insulator to metal transition for negative charge transfer insulators having anions with an unsaturated valence. By 36 GPa the emergence of the low-spin insulating arsenopyrite ($P2_1/c$) is confirmed, and the bulk metallicity is broken with the system returning to an insulative electronic state.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
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↗