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NASA NTRS2003

Effects of Two-Pulse Sequencing on Characteristics of Elementary Propellants for Ablative Laser Propulsion

This work continues on previous investigations of elementary propellants for Ablative Laser Propulsion (ALP). This paper details the experimental methods used for alignment of a non-colinear temporal pulse splitting apparatus. Spatial coincidence of the separate pulses is established, the pulses are delayed, and first data is reported on this pulse spacing effect on time-of-fight (TOF) measurements. This includes ion velocity and number density measurements, and this data is compared to results from a previous work. Also, first data on the experimental determination of the time required for the laser-induced plasma to become purely reflective to incident pulses is presented.

Thompson, M. Shane↗

NASA NTRS2000

A Tool for Automatic Data Distribution for CFD Applications on Structured Grids

Development of HPF versions of NPB and ARC3D has shown that HPF provides an efficient, concise way to express parallelism and to organize data traffic. The use of HPF, as noted in the papers, requires an intimate knowledge of the applications and a detailed analysis of data affinity, data movement, and data granularity. To simplify and accelerate the task of developing HPF versions of existing CFD applications we have designed and implemented ADAPT (Automatic Data Alignment and Placement Tool). ADAPT analyzes a CFD application working on a single structured grid and generates HPF TEMPLATE, (RE)DISTRIBUTION, ALIGNMENT, and INDEPENDENT directives. The directives can be generated on the nest level, subroutine level, application level, or on the application interface level. ADAPT annotates an existing CFD FORTRAN application, performing computations on single or multiple grids. On each grid the application is considered as a sequence of operators, each applied to a set of variables defined in a particular grid domain. ADAPT automatically detects implicit operators (i.e., having data dependences) and explicit operators (without data dependences). For parallelization of an explicit operator ADAPT creates a template for the operator domain, aligns arrays used in the operator with the template, distributes the template, and declares the loops over the distributed dimensions as INDEPENDENT. For parallelization of an implicit operator, the distribution of the operator's domain should be consistent with the operator's dependences. Any dependence between sections distributed on different processors would preclude parallelization if the compiler does not have an ability to pipeline computations. If a data distribution is "orthogonal" to the dependences of an implicit operator, then the loop which implements the operator can be declared as INDEPENDENT. ADAPT starts with an analysis of array index expressions of the loop nests. For each pair of arrays referenced in an assignment statement, it generates an arc in the alignment graph and annotates it with an affinity relation. The template, alignment, and distribution directives for a particular loop nest are then derived from a transitive closure of the affinity relation. A compromise of data distributions in different nests and subroutines is achieved by merging annotated alignment graphs for adjacent nests/stibroutine calls in the nest/call graph of the application in the process called distribution lifting. ADAPT has been implemented as a C++ program running in conjunction with a parallelization tool called CAPTools. ADAPT uses the parse tree, interprocedural analysis and application database generated by CAPTools. It also uses the Directed Graph class, initially implemented in p2d2 (parallel debugger oi distributed programs), and some other classes supporting symbolic computations. ADAPT uses data distribution techniques described. ADAPT was tested with ARC3D and the FT benchmark and has demonstrated a code performance within a factor of 1.5 of handwritten versions.

Frumkin, Michael↗

NASA NTRS2007

CEV Trajectory Design Considerations for Lunar Missions

The Crew Exploration Vehicle (CEV) translational maneuver Delta-V budget must support both the successful completion of a nominal lunar mission and an "anytime" emergency crew return with the potential for much more demanding orbital maneuvers. This translational Delta-V budget accounts for Earth-based LEO rendezvous with the lunar surface access module (LSAM)/Earth departure stage (EDS) stack, orbit maintenance during the lunar surface stay, an on-orbit plane change to align the CEV orbit for an in-plane LSAM ascent, and the Moon-to-Earth trans-Earth injection (TEI) maneuver sequence as well as post-TEI TCMs. Additionally, the CEV will have to execute TEI maneuver sequences while observing Earth atmospheric entry interface objectives for lunar high-latitude to equatorial sortie missions as well as near-polar sortie and long duration missions. The combination of these objectives places a premium on appropriately designed trajectories both to and from the Moon to accurately size the translational V and associated propellant mass in the CEV reference configuration and to demonstrate the feasibility of anytime Earth return for all lunar missions. This report examines the design of the primary CEV translational maneuvers (or maneuver sequences) including associated mission design philosophy, associated assumptions, and methodology for lunar sortie missions with up to a 7-day surface stay and with global lunar landing site access as well as for long duration (outpost) missions with up to a 210-day surface stay at or near the polar regions. The analyses presented in this report supports the Constellation Program and CEV project requirement for nominal and anytime abort (early return) by providing for minimum wedge angles, lunar orbit maintenance maneuvers, phasing orbit inclination changes, and lunar departure maneuvers for a CEV supporting an LSAM launch and subsequent CEV TEI to Earth return, anytime during the lunar surface stay.

Condon, Gerald L.↗

DOE OSTI2022

Structure of the Core Postfusion Porcine Endogenous Retrovirus Fusion Protein

Retroviral elements from endogenous retroviruses have functions in mammalian physiology. The best-known examples are the envelope proteins that function in placenta development and immune suppression. Porcine endogenous retroviruses (PERVs) are an understudied class of endogenous retroviruses that infect cultured human cells, raising concern regarding porcine xenografts. The PERV envelope glycoprotein has also been proposed as a possible swine syncytin with a role in placental development. Despite the growing interest in PERVs, their envelope glycoproteins remain poorly characterized. Here, we successfully determined the postfusion crystal structure of the PERV core fusion ectodomain. The PERV fusion protein structure reveals a conserved class I viral fusion protein six-helix bundle. Biophysical experiments demonstrated that the thermodynamic stability of the PERV fusion protein secondary structure was the same at physiological and acidic pHs. A conserved surface analysis highlights the high degree of sequence conservation among retroviral fusogens in the chain reversal region that facilitates the large-scale conformational change required for membrane fusion. Further structural alignment of class I viral fusogens revealed a phylogenetic clustering that shows evolution into various lineages that correlate with virus mechanisms of cell entry. Our work indicates that structural dendrograms can be used to qualitatively infer insights into the fusion mechanisms of newly discovered class I viral fusogen structures.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS1988

Geology and geochemistry of the Middle Proterozoic Eastern Ghat mobile belt and its comparison with the lower crust of the Southern Peninsular shield

Two prominent rock suites constitute the lithology of the Eastern Ghat mobile belt: (1) the khondalite suite - the metapelites, and (2) the charnockite suite. Later intrusives include ultramafic sequences, anorthosites and granitic gneisses. The chief structural element in the rocks of the Eastern Ghats is a planar fabric (gneissosity), defined by the alignment of platy minerals like flattened quartz, garnet, sillimanite, graphite, etc. The parallelism between the foliation and the lithological layering is related to isoclinal folding. The major structural trend (axial plane foliation trend) observed in the belt is NE-SW. Five major tectonic events have been delineated in the belt. A boundary fault along the western margin of the Eastern Ghats, bordering the low grade terrain has been substantiated by recent gravity and the deep seismic sounding studies. Field evidence shows that the pyroxene granulites (basic granulites) post-date the khondalite suite, but are older than the charnockites as well as the granitic gneisses. Polyphase metamorphism, probably correlatable with different periods of deformation is recorded. The field relations in the Eastern Ghats point to the intense deformation of the terrain, apparently both before, during and after metamorphism.

Rao, M. V. Subba↗

NASA NTRS1999

Automatic Data Distribution for CFD Applications on Structured Grids

Development of HPF versions of NPB and ARC3D showed that HPF has potential to be a high level language for parallelization of CFD applications. The use of HPF requires an intimate knowledge of the applications and a detailed analysis of data affinity, data movement and data granularity. Since HPF hides data movement from the user even with this knowledge it is easy to overlook pieces of the code causing low performance of the application. In order to simplify and accelerate the task of developing HPF versions of existing CFD applications we have designed and partially implemented ADAPT (Automatic Data Distribution and Placement Tool). The ADAPT analyzes a CFD application working on a single structured grid and generates HPF TEMPLATE, (RE)DISTRIBUTION, ALIGNMENT and INDEPENDENT directives. The directives can be generated on the nest level, subroutine level, application level or inter application level. ADAPT is designed to annotate existing CFD FORTRAN application performing computations on single or multiple grids. On each grid the application can considered as a sequence of operators each applied to a set of variables defined in a particular grid domain. The operators can be classified as implicit, having data dependences, and explicit, without data dependences. In order to parallelize an explicit operator it is sufficient to create a template for the domain of the operator, align arrays used in the operator with the template, distribute the template, and declare the loops over the distributed dimensions as INDEPENDENT. In order to parallelize an implicit operator, the distribution of the operator's domain should be consistent with the operator's dependences. Any dependence between sections distributed on different processors would preclude parallelization if compiler does not have an ability to pipeline computations. If a data distribution is "orthogonal" to the dependences of an implicit operator then the loop which implements the operator can be declared as INDEPENDENT.

Frumkin, Michael↗

DOE OSTI2023

SCALE depletion capabilities for molten salt reactors and other liquid-fueled systems

Nuclear reactor systems that use fuel dissolved in a liquid have the potential for enhanced safety characteristics, improved fuel-cycle outcomes, and more efficient isotope-production configurations. In these reactor systems, the fueled liquid may simultaneously undergo irradiation, physical and chemical removal processes, and fueling. The modeling and simulation of this transmutation and decay with material additions and removals is an ongoing research area. An accurate simulation tool is critical to the reactor and fuel-cycle design, reactor deployment, and source-term characterization for these advanced reactor systems. The work described herein involved implementing, testing, and applying the capability to perform reactor physics simulations within the Oak Ridge National Laboratory-developed SCALE suite for nuclear systems analyses and design, leveraging much of its pedigree in quality-assurance and reactor-analysis capabilities. The functionalities to simulate irradiation with material feeds and removals had been added in ORIGEN, and the TRITON reactor physics sequence was extended to calculate the total removed material and track external nonirradiated mixtures to estimate separate processing or waste streams. Results from these capabilities align with analytical expectations obtained from ORIGEN for simplified test cases and with expectations for a molten salt reactor application. This implementation, available with the SCALE 6.3 release, provides for a more efficient and accurate material accountability methodology, allowing for the characterization, design, and analysis of the complete isotopic material inventory of advanced liquid-fueled systems for a variety of applications.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2020

Identifying DQ-Domain Admittance Models of a 2.3-MVA Commercial Grid-Following Inverter Via Frequency-Domain and Time-Domain Data

Here, we present two methods to identify the admittance of a 2.3-MVA commercial grid-following inverter through frequency-domain data and time-domain data. In addition to the well-known harmonic injection method to obtain the admittance at frequency points followed by vector fitting, we adopt a step response-based method where the step response data of the converter are collected and their s-domain expressions are obtained. In turn, the s-domain admittance model of the converter is found. The two methods can be used for cross validation. Step responses and frequency-domain responses obtained from the two methods are compared. Results show that the time- domain data-based method leads to an admittance comparable with that from the frequency-domain measurement in the range less than 60 Hz. In addition, two insights are obtained from the frequency-domain admittance measurements. First, when the dq- frame is aligned to the point of common coupling (PCC) voltage, the per unit DQ-domain admittance directly reflects operating conditions. Second, existence of negative-sequence control can be detected via sequence-domain admittances.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2026

Nanocrystal Geometry Governs Phase Transformation Pathways in Palladium Hydride

Pathways and structural dynamics of phase transformations impact performance of materials in energy and information storage technologies. Palladium hydride (PdH x ) nanocrystals are an ideal model system for studying solute-induced phase transformations, where elastic energy from lattice mismatch between α-PdH x and β-PdH x phases is often considered a key to determining the transformation pathways. α/β-PdH x interfacial elastic energy is affected by the confined geometry of a nanocrystal. However, how nanocrystal geometry influences phase transformation pathways is largely unknown. Using in situ liquid phase transmission electron microscopy, we directly visualize hydrogenation in Pd nanocrystals with two geometries, a nanocube and a hexagonal nanoplate. Both follow similar sequences of an initially curved nucleus, interface flattening, and reverse-stage nucleation; however, their evolving α/β-PdH x interfaces exhibit geometry-dependent crystallographic alignments. In nanocubes, {100}-aligned configurations conform to static elastic energy ordering, representing a pathway that maintains a local mechanical equilibrium, whereas nanoplates display both {110}- and {211}-aligned interfaces. Theoretical simulations show that geometry determines the accessibility of alternative phase transformation pathways as the system is driven far from equilibrium during hydrogenation. In conclusion, these findings identify geometry as a fundamental parameter for directing phase transformation pathways, offering design principles for accessing atypical configurations and improving properties of intercalation-based devices.

Lee, Daewon [Lawrence Berkeley National Laboratory↗

NASA NTRS1989

Chip Advancer For GPS Receiver

Instrument errors made negligible. For each integration interval, both delay and rate of change of delay initialized to small fraction of chip - for example, to order of 10 to the negative 7th power - thereby making feedback control and extraction of delay highly accurate and flexible. With appropriate selection of sampling rate relative to chip rate, commensurability errors reduced to extremely small levels. In Global Positioning System (GPS) receiver, pseudorandom code sequence generated by simple digital logic incorporating effects of time, delay, and rate of change of delay. Flexibility in starting time and sum interval very useful in aligning correlation interval with beginnings and endings of data bits.

Meehan, Thomas K.↗

NASA NTRS1993

Generating local addresses and communication sets for data-parallel programs

Generating local addresses and communication sets is an important issue in distributed-memory implementations of data-parallel languages such as High Performance Fortran. We show that for an array A affinely aligned to a template that is distributed across p processors with a cyclic(k) distribution, and a computation involving the regular section A, the local memory access sequence for any processor is characterized by a finite state machine of at most k states. We present fast algorithms for computing the essential information about these state machines, and extend the framework to handle multidimensional arrays. We also show how to generate communication sets using the state machine approach. Performance results show that this solution requires very little runtime overhead and acceptable preprocessing time.

Chatterjee, Siddhartha↗

NASA NTRS2011

Telemetry-Based Ranging

A telemetry-based ranging scheme was developed in which the downlink ranging signal is eliminated, and the range is computed directly from the downlink telemetry signal. This is the first Deep Space Network (DSN) ranging technology that does not require the spacecraft to transmit a separate ranging signal. By contrast, the evolutionary ranging techniques used over the years by NASA missions, including sequential ranging (transmission of a sequence of sinusoids) and PN-ranging (transmission of a pseudo-noise sequence) whether regenerative (spacecraft acquires, then regenerates and retransmits a noise-free ranging signal) or transparent (spacecraft feeds the noisy demodulated uplink ranging signal into the downlink phase modulator) relied on spacecraft power and bandwidth to transmit an explicit ranging signal. The state of the art in ranging is described in an emerging CCSDS (Consultative Committee for Space Data Systems) standard, in which a pseudo-noise (PN) sequence is transmitted from the ground to the spacecraft, acquired onboard, and the PN sequence is coherently retransmitted back to the ground, where a delay measurement is made between the uplink and downlink signals. In this work, the telemetry signal is aligned with the uplink PN code epoch. The ground station computes the delay between the uplink signal transmission and the received downlink telemetry. Such a computation is feasible because symbol synchronizability is already an integral part of the telemetry design. Under existing technology, the telemetry signal cannot be used for ranging because its arrival-time information is not coherent with any Earth reference signal. By introducing this coherence, and performing joint telemetry detection and arrival-time estimation on the ground, a high-rate telemetry signal can provide all the precision necessary for spacecraft ranging.

Hamkins, Jon↗

NASA NTRS2013

Modeling Delamination in Postbuckled Composite Structures Under Static and Fatigue Loads

The ability of the Abaqus progressive Virtual Crack Closure Technique (VCCT) to model delamination in composite structures was investigated for static, postbuckling, and fatigue loads. Preliminary evaluations were performed using simple Double Cantilever Beam (DCB) and Mixed-Mode Bending (MMB) specimens. The nodal release sequences that describe the propagation of the delamination front were investigated. The effect of using a sudden or a gradual nodal release was evaluated by considering meshes aligned with the crack front as well as misaligned meshes. Fatigue simulations were then performed using the Direct Cyclic Fatigue (DCF) algorithm. It was found that in specimens such as the DCB, which are characterized by a nearly linear response and a pure fracture mode, the algorithm correctly predicts the Paris Law rate of propagation. However, the Abaqus DCF algorithm does not consider different fatigue propagation laws in different fracture modes. Finally, skin/stiffener debonding was studied in an aircraft fuselage subcomponent in which debonding occurs deep into post-buckling deformation. VCCT was shown to be a robust tool for estimating the onset propagation. However, difficulties were found with the ability of the current implementation of the Abaqus progressive VCCT to predict delamination propagation within structures subjected to postbuckling deformations or fatigue loads.

Bisagni, Chiara↗

DOE OSTI2023

Rapid identification of enteric bacteria from whole genome sequences using average nucleotide identity metrics

Identification of enteric bacteria species by whole genome sequence (WGS) analysis requires a rapid and an easily standardized approach. We leveraged the principles of average nucleotide identity using MUMmer (ANIm) software, which calculates the percent bases aligned between two bacterial genomes and their corresponding ANI values, to set threshold values for determining species consistent with the conventional identification methods of known species. The performance of species identification was evaluated using two datasets: the Reference Genome Dataset v2 (RGDv2), consisting of 43 enteric genome assemblies representing 32 species, and the Test Genome Dataset (TGDv1), comprising 454 genome assemblies which is designed to represent all species needed to query for identification, as well as rare and closely related species. The RGDv2 contains six Campylobacter spp., three Escherichia/Shigella spp., one Grimontia hollisae, six Listeria spp., one Photobacterium damselae, two Salmonella spp., and thirteen Vibrio spp., while the TGDv1 contains 454 enteric bacterial genomes representing 42 different species. The analysis showed that, when a standard minimum of 70% genome bases alignment existed, the ANI threshold values determined for these species were ≥95 for Escherichia/Shigella and Vibrio species, ≥93% for Salmonella species, and ≥92% for Campylobacter and Listeria species. Using these metrics, the RGDv2 accurately classified all validation strains in TGDv1 at the species level, which is consistent with the classification based on previous gold standard methods.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS1982

Reverse draping of magnetic field lines in the boundary layer

An unexpected orientation of field lines has been found by ISEE satellite measurements of the earth magnetosphere boundary layer, perhaps indicating a reverse draping. Three-dimensional plasma flow measurements by ISEE 1 and 2 show the tailward flow in the boundary layer to have an equatorward component which suggests high-latitude plasma entry. Simultaneous magnetic field measurements with the two satellites during a boundary crossing sequence yielded data on the boundary layer electric currents and the boundary layer interface with plasma sheet and magnetosheath. The currents are found to be largely field-aligned, with intensities in the 0.03-0.06 microampere/sq m range.

Hones, E. W., Jr.↗

DOE OSTI2023

The Dark Energy Survey Year 3 and eBOSS: constraining galaxy intrinsic alignments across luminosity and colour space

ABSTRACT We present direct constraints on galaxy intrinsic alignments (IAs) using the Dark Energy Survey Year 3 (DES Y3), the Extended Baryon Oscillation Spectroscopic Survey (eBOSS), and its precursor, the Baryon Oscillation Spectroscopic Survey (BOSS). Our measurements incorporate photometric red sequence (redMaGiC) galaxies from DES with median redshift z ∼ 0.2–1.0, luminous red galaxies from eBOSS at z ∼ 0.8, and also an SDSS-III BOSS CMASS sample at z ∼ 0.5. We measure two-point IA correlations, which we fit using a model that includes lensing, magnification, and photometric redshift error. Fitting on scales 6 Mpc h−1 < rp < 70 Mpc h−1, we make a detection of IAs in each sample, at 5σ–22σ (assuming a simple one-parameter model for IAs). Using these red samples, we measure the IA–luminosity relation. Our results are statistically consistent with previous results, but offer a significant improvement in constraining power, particularly at low luminosity. With this improved precision, we see detectable dependence on colour between broadly defined red samples. It is likely that a more sophisticated approach than a binary red/blue split, which jointly considers colour and luminosity dependence in the IA signal, will be needed in future. We also compare the various signal components at the best-fitting point in parameter space for each sample, and find that magnification and lensing contribute $\sim 2\!-\!18~{{\ \rm per\ cent}}$ of the total signal. As precision continues to improve, it will certainly be necessary to account for these effects in future direct IA measurements. Finally, we make equivalent measurements on a sample of emission-line galaxies from eBOSS at z ∼ 0.8. We constrain the non-linear alignment amplitude to be $A_1=0.07^{+0.32}_{-0.42}$ (|A1| < 0.78 at 95 per cent CL).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS2025

Provider of Services for Urban Air Mobility (PSU) Prototype Simulation (X5) Final Report

Urban Air Mobility (UAM) is a new air transportation service concept to carry passengers or cargo in metropolitan areas, leveraged by innovative aircraft and air traffic automation technologies. NASA has conducted a series of simulations, called the X-series simulation, to evaluate the UAM concept of operations and support the development of airspace procedures and services for UAM operations. The simulation called “X5” was conducted in 2023 to test a Provider of Services for UAM (PSU) prototype developed by NASA for UAM flight planning, strategic conflict management support, and data exchange between UAM operators. In this simulation, two strategic conflict management capabilities, Demand-Capacity Balancing and Sequencing and Scheduling, were further investigated. This document describes the UAM system architecture modeled, the X5 simulation environment to be executed (e.g., traffic scenario and UAM airspace construct), and the strategic conflict management processes developed and evaluated in this study. Then, the simulation results are provided using several system performance metrics, such as the number of operations planned and activated, demand-capacity imbalances detected and resolved, and pre-departure delays. Based on these metrics, the test findings and lessons learned from this simulation are discussed. NASA developed a PSU prototype as part of a reference implementation of UAM system architecture and evolved strategic conflict management capabilities for UAM operations from the previous collaborative simulations with industry partners. Below is the summary of the achievements: - Aligned NASA’s UAM reference architecture with the FAA’s UAM ConOps notional architecture - Extended UAM airspace management capabilities to include 1) Demand-Capacity Balancing (DCB) to ensure operators coordinate planned usage of shared vertiports, and 2) Sequencing and Scheduling (S&S) at UAM corridor entry and exit points to help facilitate an orderly flow of traffic - Defined the PSU information exchange APIs and requirements towards informing industry standards - Developed and tested a NASA PSU prototype as reference implementation to validate the requirements and APIs - Developed a prototype service connecting NASA’s PSU and the FAA system for testing future PSU-ATM interface requirements - Tested NASA-developed assumptions for UAM operations such as airspace design, procedures, vehicle performance, and strategic conflict management methods to inform future Cooperative Operating Practices (COPs) development with industry - Evaluated system performance metrics such as number of simultaneous operations and ground delays that can help define system-level requirements. The simulation results showed that the UAM traffic demand could be managed to minimize the needs of tactical separation provision with ground delays assigned by DCB and S&S. These accomplishments and the lessons learned from the PSU Prototype X5 simulation activities will be valuable inputs for the Air Mobility Pathfinders (AMP) project, which is NASA’s new project to create and evaluate a reference architecture for safe, secure, and scalable UAM operations.

Simulation↗

DOE OSTI2025

Superspin renormalization and slow relaxation in random spin systems

We develop an excited-state real-space renormalization group (RSRG-X) formalism to describe the dynamics of conserved densities in randomly interacting spin-12 systems. Our formalism is suitable for systems with U(1) and Z2 symmetries, and we apply it to chains of randomly positioned spins with dipolar XX+YY interactions, as arise in Rydberg quantum simulators and other platforms. The formalism generates a sequence of effective Hamiltonians that provide approximate descriptions for dynamics on successively smaller energy scales. These effective Hamiltonians involve “superspins”: two-level collective degrees of freedom constructed from (anti)aligned microscopic spins. Conserved densities can then be understood as relaxing via coherent collective spin flips. For the well-studied simpler case of randomly interacting nearest-neighbor XX+YY chains, the superspins reduce to single spins. Our formalism also leads to a numerical method capable of simulating the dynamics up to an otherwise inaccessible combination of large system size and late time. Focusing on disorder-averaged infinite-temperature autocorrelation functions, in particular the spin survival probability Sp¯(t), we demonstrate quantitative agreement between our algorithm and exact diagonalization (ED) at low but nonzero frequencies. Such agreement holds for chains with nearest-neighbor, next-nearest-neighbor, and long-range dipolar interactions. Our results indicate decay of Sp¯(t) slower than any power law and feature no significant deviation from the ∼1/ln2(t) asymptote expected from the infinite-randomness fixed-point of the nearest-neighbor model. We also apply the RSRG-X formalism to two-dimensional long-range systems of moderate size and find slow late-time decay of Sp¯(t).

Zhao, Yi J↗