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At least 1,063 records · Page 59
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Surface Energies of LaMnO 3 High-Index Surfaces Obtained from Density-Functional Theory

Here, the first six cubic LaMnO 3 high-index surfaces, (210), (211), (221), (310), (311), and (320), are examined for the first time. The unrelaxed and relaxed surface energies of the surfaces are computed as a function of surface model thickness using unrelaxed and relaxed surface models, respectively. The (210), (320), (211), and (221) surfaces are found to be more stable than the low-index (011) and (111) surfaces. Helping to explain this result, the surface terminations of the (210), (320), (211), or (221) surface are seen to exhibit a rotational relaxation of the MnO 6 or oxygen octahedra extending from the surface into the bulk. By contrast, the relaxed surface energies of the (310) and (311) surfaces are concluded to be difficult to determine due to a structural transformation or phase change in the surface models of the surfaces away from cubic LaMnO 3 . The finding of a phase change is important. It indicates that a phase change in the surface models of a surface for another material could occur if the surface is relatively open and a different phase of the material is stable at low temperature. When modeling such a surface, two steps are suggested to be taken.

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

Data-based filtered dissipation rate modelling for multi-modal turbulent combustion: evaluating a priori model generalizability

Manifold-based models offer a computationally efficient alternative to directly transporting the thermochemical state in computational simulations of turbulent reacting flows, projecting the high-dimensional thermochemical state-space onto a low-dimensional manifold. Recent efforts have yielded a manifold-based model applicable to multi-modal combustion, enabling reconstruction of the thermochemical state from solutions to two-dimensional manifold equations in mixture fraction and generalized progress variable that are parameterised by three scalar dissipation rates. In coarse-grained simulations such as Large Eddy Simulation (LES), closure of the multi-modal manifold equations and subfilter variances/covariance requires closure of three filtered scalar dissipation rates. Here, the present work adopts a data-based approach, providing closure for the three filtered scalar dissipation rates via deep neural networks (DNNs). High-fidelity datasets corresponding to an autoigniting n-dodecane jet flame and a bluff body swirl-stabilized confined lifted spray flame of two aviation fuels (Jet-A and C1) with different ignition propensities are leveraged to generate training data that spans a diverse range of thermodynamic conditions and combustion modes, including low- and high-temperature ignition regimes in addition to premixed and nonpremixed behaviour. A final DNN model is trained to enforce inherent physical constraints by learning nonlinear functional transformations of the three filtered scalar dissipation rates. The generalizability of this constrained DNN model is demonstrated a priori via conditional statistics evaluated on the lifted spray flame with C1–a configuration that had not been included in the training data. Excellent DNN agreement with conditional DNS statistics is observed, and integrated gradients are computed to identify the most sensitive input variables. The similarity of the marginal PDFs of the most informative input variables and outputs across configurations are quantified via the Wasserstein metric, demonstrating that data-based models may successfully generalize to unseen parametric conditions so long as the most informative input variables share similar distributions across training and testing datasets.

Data-based modelling↗
DOE OSTI2021

The predictive skill of convolutional neural networks models for disease forecasting

In this paper we investigate the utility of one-dimensional convolutional neural network (CNN) models in epidemiological forecasting. Deep learning models, in particular variants of recurrent neural networks (RNNs) have been studied for ILI (Influenza-Like Illness) forecasting, and have achieved a higher forecasting skill compared to conventional models such as ARIMA. In this study, we adapt two neural networks that employ one-dimensional temporal convolutional layers as a primary building block—temporal convolutional networks and simple neural attentive meta-learners—for epidemiological forecasting. We then test them with influenza data from the US collected over 2010-2019. We find that epidemiological forecasting with CNNs is feasible, and their forecasting skill is comparable to, and at times, superior to, plain RNNs. Thus CNNs and RNNs bring the power of nonlinear transformations to purely data-driven epidemiological models, a capability that heretofore has been limited to more elaborate mechanistic/compartmental disease models.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS2000

Simian virus 40, poliovirus vaccines, and human cancer: research progress versus media and public interests

From 1955 through early 1963, millions of people were inadvertently exposed to simian virus 40 (SV40) as a contaminant of poliovirus vaccines; the virus had been present in the monkey kidney cultures used to prepare the vaccines and had escaped detection. SV40 was discovered in 1960 and subsequently eliminated from poliovirus vaccines. This article reviews current knowledge about SV40 and considers public responses to reports in the media. SV40 is a potent tumour virus with broad tissue tropism that induces tumours in rodents and transforms cultured cells from many species. It is also an important laboratory model for basic studies of molecular processes in eukaryotic cells and mechanisms of neoplastic transformation. SV40 neutralizing antibodies have been detected in individuals not exposed to contaminated poliovirus vaccines. There have been many reports of detection of SV40 DNA in human tumours, especially mesotheliomas, brain tumours and osteosarcomas; and DNA sequence analyses have ruled out the possibility that the viral DNA in tumours was due to laboratory contamination or that the virus had been misidentified. However, additional studies are necessary to prove that SV40 is the cause of certain human cancers. A recently published review article evaluated the status of the field and received much media attention. The public response emphasized that there is great interest in the possibility of health risks today from vaccinations received in the past.

Review, Tutorial↗
DOE OSTI2023

Uncertainty-aware molecular dynamics from Bayesian active learning for phase transformations and thermal transport in SiC

Abstract Machine learning interatomic force fields are promising for combining high computational efficiency and accuracy in modeling quantum interactions and simulating atomistic dynamics. Active learning methods have been recently developed to train force fields efficiently and automatically. Among them, Bayesian active learning utilizes principled uncertainty quantification to make data acquisition decisions. In this work, we present a general Bayesian active learning workflow, where the force field is constructed from a sparse Gaussian process regression model based on atomic cluster expansion descriptors. To circumvent the high computational cost of the sparse Gaussian process uncertainty calculation, we formulate a high-performance approximate mapping of the uncertainty and demonstrate a speedup of several orders of magnitude. We demonstrate the autonomous active learning workflow by training a Bayesian force field model for silicon carbide (SiC) polymorphs in only a few days of computer time and show that pressure-induced phase transformations are accurately captured. The resulting model exhibits close agreement with both ab initio calculations and experimental measurements, and outperforms existing empirical models on vibrational and thermal properties. The active learning workflow readily generalizes to a wide range of material systems and accelerates their computational understanding.

36 MATERIALS SCIENCE↗
NASA NTRS1974

Mathematical crew motion disturbance models for spacecraft control system design

Several techniques for modeling the disturbances to a spacecraft's attitude caused by moving crew members are presented. These disturbances can be the largest moments acting on a manned spacecraft, and knowledge of their effect is important in the sizing, design, and analysis/simulation of spacecraft attitude control systems. The modeling techniques are identified as two principal types: deterministic and stochastic. Three techniques of each type are presented. The deterministic models include point-mass motion derivatives and a discussion on dynamic models of moving crew members. The stochastic techniques are highlighted by a Fourier transform method and the representation of long-term crew disturbance activities as outputs from appropriately designed filters. A z-transform technique is developed to obtain a difference-equation form of stochastic models for use on digital computers. An appendix derives spacecraft equations of motion which can be used with many of the models discussed.

Conway, B. A.↗
DOE OSTI2025

Neutrino Flavor Transformation in Neutron Star Mergers

Here, we present the first numerical relativity simulations including neutrino flavor transformations that could result from flavor instabilities, quantum many-body effects, or potential beyond standard model physics in neutron star mergers. We find that neutrino flavor transformations impact the composition and structure of the remnant, potentially leaving an imprint on the postmerger gravitational-wave signal. They also have a significant impact on the composition and nucleosynthesis yields of the ejecta.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1975

Investigation to develop a multistage forest sampling inventory system using ERTS-1 imagery

The author has identified the following significant results. The annotation system produced a RMSE of about 200 m ground distance in the MSS data system with the control data used. All the analytical MSS interpretation models tried were highly significant. However, the gains in forest sampling efficiency that can be achieved by using the models vary from zero to over 50 percent depending on the area to which they are applied and the sampling method used. Among the sampling methods tried, regression sampling yielded substantial and the most consistent gains. The single most significant variable in the interpretation model was the difference between bands 5 and 7. The contrast variable, computed by the Hadamard transform was significant but did not contribute much to the interpretation model. Forest areas containing very large timber volumes because of large tree sizes were not separable from areas of similar crown cover but containing smaller trees using ERTS image interpretation only. All correlations between space derived timber volume predictions and estimates obtained from aerial and ground sampling were relatively low but significant and stable. There was a much stronger relationship between variables derived from MSS and U2 data than between U2 and ground data.

Langley, P. G.↗
NASA NTRS1985

Adiabatic thermal models for planetary bodies

In a number of recent experiments it was found that the logarithmic derivative with respect to volume of the adiabatic temperature increase with pressure P to be an approximately constant quantity n. It was found that n decreases slightly with temperature, to be virtually unaffected by increasing pressure and to take values between 4 and 8 for a wide variety of materials. It is shown that these findings can be substantiated from thermodynamic arguments, finite strain theory, atomic potential theory and experimental data on the thermal expansion coefficient and the bulk modulus B. It will be shown that n is independent of pressure if it is exactly equal to dB/dP + 1. For these materials d log gamma/d log v = -1, where gamma is the thermodynamic Gruneisenparameter. It will increase with P during an isothermal transformation if n dB/dP + 1 and decrease of n dB/dP + 1. For most materials n is close to dB/dP and the changes will be slight if pressures do not become too extreme. During an adiabatic transformation n is virtually constant. Adiabatic thermal models for planetary bodies were calculated and are presented.

Spohn, T.↗
DOE OSTI2025

Analyzing and Exploring Training Recipes for Large-Scale Transformer-Based Weather Prediction

Abstract The rapid rise of deep learning (DL) in numerical weather prediction (NWP) has led to a proliferation of models which forecast atmospheric variables with comparable or superior skill than traditional physics-based NWP. However, among these leading DL models, there is a wide variance in both the training settings and architecture used. Further, the lack of thorough ablation studies makes it hard to discern which components are most critical to success. In this work, we show that it is possible to attain high forecast skill even with relatively off-the-shelf architectures, simple training procedures, and moderate compute budgets. Specifically, we train a minimally modified Swin Transformer V2 (SwinV2) on ERA5 data and find that it attains superior skill in terms of mean-square errors of deterministic forecasts when compared against the European Centre for Medium-Range Weather Forecasts’ Integrated Forecasting System (IFS). Almost all DL–NWP systems share a core set of hyperparameters and design decisions. To aid and expedite future DL–NWP research, we present an in-depth, systematic exploration of different loss functions, model sizes and depths, patch sizes, and multistep training objectives. We also examine the model performance with metrics beyond the typical accuracy (ACC) and RMSE and investigate how the performance scales with model size. Through our open-source code, scoring pipelines, and models, we share our findings on key aspects of the training pipeline. These ablations reduce the necessity for expensive hyperparameter tuning and lower the barrier to entry for future DL–NWP research. Significance Statement This study investigates the potential of using large-scale transformer-based models for weather prediction, showing that it is possible to achieve high forecast accuracy with simpler, off-the-shelf architectures. By training a minimally modified SwinV2 transformer on ERA5 data, we show that the model achieves competitive forecast skill in terms of mean-square error for key variables, outperforming the European Centre for Medium-Range Weather Forecasts’ Integrated Forecasting System (IFS) at all lead times. Our findings suggest that effective training strategies, such as multistep fine-tuning and channel-weighted losses, significantly enhance the model’s performance. However, we also highlight that these improvements come with trade-offs in other areas, such as ensemble spread and high-frequency spatial detail. This work highlights the promise of deep learning in improving weather forecasts, which could lead to better preparedness and response to weather events, ultimately benefiting society by providing more reliable weather predictions.

Willard, Jared D. [Lawrence Berkeley National Labo↗
NASA NTRS1991

Ionosphere-exosphere coupling through charge exchange and momentum transfer in hydrogen-proton collisions

The implications of a traditional assumption of exospheric physics, that collisions of hydrogen atoms and protons preferentially result in charge exchange with negligible momentum transfer are examined. Initially adopted as a necessary convenience to accommodate limited computer resources in exosphere model calculations, this approximation results in a direct transformation of the proton velocity distribution into a hot component of neutral hydrogen. With expanding computational facilities, the need for the approximation has passed. As the first step toward its replacement with a realistic, quantum mechanical model of the H - H(+) collision process, differential and cumulative cross sections were calculated for quantum elastic scattering of indistinguishable nuclei for a fine grid of encounter energies and scattering angles. These data are used to study the nature of ionosphere-exosphere coupling through H - H(+) collisions, and to demonstrate that the distribution of velocities of scattered H produced in the traditional exospheric charge exchange approximation, as well as that arising from an alternative, fluid dynamic approach, leads to unacceptable abundances of coronal atoms in long-term, highly elliptic trajectories.

Hodges, R. R., Jr.↗
NASA NTRS2024

Spacecraft Modeling, Attitude Determination, and Control: Quaternion-Based Approach

Spacecraft attitude determination and control is an important part of a spacecraft to achieve its designed mission. As of today, many spacecrafts have been successfully launched, and most of them have performed well as they were designed. Many research papers have been published to address the attitude determination and control design problems. Several text books are available for students to learn the technology and for engineers to use as references. The most popular spacecraft models for attitude determination algorithms and control design methods are the Euler angle models and the quaternion models . The Euler angle models have been proved very efficient as the linearized models are controllable, and all standard linear control system design methods are directly applicable. The drawbacks related to the Euler angle methods are (a) the designs based on linearized models may not globally stabilize the original nonlinear spacecraft, i.e., the design may not work when the attitude of the spacecraft is far away from the point where the linearization is performed; (b) the models depend on the rotational sequences, this can be error prone if several teams work on the same project and they use different rotational sequences; (c) for any rotational sequence, there is a singular point where the model is not applicable; and (d) since most attitude determination methods use quaternion to represent the spacecraft attitude, there is a need to transform quaternion into Euler angles. On the other hand, for quaternion models, people have found controllers that can globally stabilize nonlinear spacecraft systems; the models do not depend on rotational sequences and they have no singular point; and the quaternion is provided by attitude determination system and ready to use. The main problem with the quaternion model based control system design is that the linearized quaternion model is not controllable. Therefore, most published design methods heavily rely on Lyapunov functions for the nonlinear spacecraft system. But there is no systematic way to obtain a desired Lyapunov functions. Moreover, the Lyapunov function based designs focus on the closed-loop system stability but pay little attention to the closed-loop system performance. In a series of papers, the author proposed some reduced quaternion models which lead to some controllable linearized spacecraft models. Therefore, all standard linear system theory can be directly applied to analyze and design the spacecraft control systems. We showed that, in some cases, the designed control system is not only optimal for the linearized system, but also globally stabilize the original nonlinear system . Clearly, the reduced quaternion models do not depend on rotational sequences. Due to the special structure of the linearized spacecraft model, some most important design methods, such as LQR design and robust pole assignment design are very simple, enjoy the analytical solutions for some problems, have direct connection to the performance measures, such as settling time, rising time , and percentage of overshoot . All these features are attractive for high quality control system designs. The idea mentioned above is then extended to more spacecraft control problems using specific actuators such as magnetic torque bars and control momentum gyroscopes. These types of actuators may not provide exactly desired torques. Most existing methods use different conversions to get approximate solutions, meaning that these actuators may generate a torque close to but not equal to the desired one. Using the reduced quaternion models that incorporate the actuators into the system model, the control inputs are not torques but the operational parameters. The main benefit of this idea is that the control actions are not approximate but accurate. As all actuators have their operational limit, design with input constraints are also considered in this book by using recently developed interior-point optimization techniques. This book grows up from my research on the spacecraft attitude determination and control design methods in more than a decade which is focused on using reduced quaternion models because of their merits stated above. The book provides all necessary background materials on orbital dynamics, rotations and quaternion, frequently used reference frames, transformations between reference frames, space environment and disturbance torques, ephemeris astronomical vector calculations and measurement instruments, spacecraft control actuators and their models, so that the readers will get a global picture and can apply all these information into the spacecraft system modeling, attitude determination, and spacecraft control system designs, which is the main purpose of this book. This book is different from existing books in that we focus on quaternion based spacecraft control system designs and we consider only attitude control system design related problems, from spacecraft modeling, to attitude determination and estimation, to control system design method selection, to control algorithm development, and to the simulation of the control system designs. Moreover, this book addresses different attitude control tasks in the spacecraft life cycle, including spacecraft maneuver, orbit raising, attitude control, and rendezvous. Finally, this book emphasizes the state space design methods rather than the classical frequency design methods.

Attitude determination and control↗
NASA NTRS1993

Application of fast Fourier transforms to the direct solution of a class of two-dimensional separable elliptic equations on the sphere

An efficient, direct, second-order solver for the discrete solution of a class of two-dimensional separable elliptic equations on the sphere (which generally arise in implicit and semi-implicit atmospheric models) is presented. The method involves a Fourier transformation in longitude and a direct solution of the resulting coupled second-order finite-difference equations in latitude. The solver is made efficient by vectorizing over longitudinal wave-number and by using a vectorized fast Fourier transform routine. It is evaluated using a prescribed solution method and compared with a multigrid solver and the standard direct solver from FISHPAK.

Moorthi, Shrinivas↗
DOE OSTI2023

Modeling the co-assembly of binary nanoparticles

Abstract In this work, we present a binary assembly model that can predict the co-assembly structure and spatial frequency spectra of monodispersed nanoparticles with two different particle sizes. The approach relies on an iterative algorithm based on geometric constraints, which can simulate the assembly patterns of particles with two distinct diameters, size distributions, and at various mixture ratios on a planar surface. The two-dimensional spatial-frequency spectra of the modeled assembles can be analyzed using fast Fourier transform analysis to examine their frequency content. The simulated co-assembly structures and spectra are compared with assembled nanoparticles fabricated using transfer coating method are in qualitative agreement with the experimental results. The co-assembly model can also be used to predict the peak spatial frequency and the full-width at half-maximum bandwidth, which can lead to the design of the structure spectra by selection of different monodispersed particles. This work can find applications in fabrication of non-periodic nanostructures for functional surfaces, light extraction structures, and broadband nanophotonics.

Mohanty, Saurav (ORCID:0009000302592855)↗
NASA NTRSDate not supplied

Enhancing Air Traffic Control Planning with Automatic Speech Recognition

The decisions made during the Federal Aviation Administration Air Traffic Control System Command Center's planning teleconferences hold significant sway over the National Airspace System. Held every two hours, these teleconferences convene air traffic managers and stakeholders from across the nation to discuss airspace conditions, weather, and constraints, leading to the formulation and adjustment of traffic management initiatives. Given the critical nature of these decisions, the need for accurate and efficient record-keeping is paramount. In recent years, the application of automatic speech recognition has gained popularity across diverse industries, including aviation. While traditional applications focus on transcribing air traffic control communication, this paper explores a unique application of automatic speech recognition by converting the audio from planning teleconferences into text transcriptions. This innovative approach addresses key challenges in the field, presenting potential benefits for quality assurance, real-time participation, and downstream natural language processing tasks. A notable breakthrough in the machine learning community, namely the transformer neural network architecture, forms the backbone of the proposed solution in this paper. The transformer architecture's role in this research represents a paradigm shift in the efficiency of automatic speech recognition models. By reducing the amount of in-domain training data required, this architecture allows for the fine-tuning of such models like Whisper, originally pretrained on vast English speech datasets. The adaptability of the transformer architecture proves invaluable in capturing the nuances of aviation terminology and specific language used in planning teleconferences. Leveraging the Whisper model as a baseline, our research details the fine-tuning and validation using a dataset comprising 20 hours of meticulously transcribed planning teleconferences. Notably, the baseline pretrained Whisper model exhibited a word error rate of 18.77%. Through the fine-tuning process, the model achieved a substantial improvement, demonstrating an impressive performance with a reduced word error rate of 6.82%. This substantial decrease in WER not only highlights the effectiveness of the transformer architecture but also emphasizes the practical advancements achieved through the application of automatic speech recognition in this specific domain. The utilization of automatic speech recognition in planning teleconferences in this work introduces several novelties. Firstly, the creation of text transcriptions offers a valuable tool for quality assurance and facilitates the efficient review of teleconferences. This is an important aspect of the proposed solution, given the time-sensitive and high-stakes nature of decisions made during these meetings. Furthermore, text-searchable transcriptions provide a streamlined approach for locating and validating critical information, potentially saving hours of manual effort in searching through audio recordings. Moreover, our research identifies a key use case for external facilities and stakeholders. In situations where attendance at the planning teleconference is not feasible, having access to text transcriptions in real-time or shortly after the teleconference ends, proves to be a time-saving and informative resource. This feature enhances collaboration and ensures that stakeholders can stay abreast of important discussions and decisions even in their absence. Despite the efficiency gains facilitated by the transformer architecture in automatic speech recognition technology, it is essential to acknowledge the human factors in data creation. Subject matter experts play a crucial role in accurately transcribing planning teleconferences due to the specificity and complexity of the information discussed. The research dataset, consisting of 20 hours of transcribed planning teleconferences, forms the foundation for fine-tuning and validating the Whisper model. The achieved word error rate of 6.82% demonstrates promising advancements, particularly in recognizing essential aviation terminology within the teleconferences. In conclusion, this paper presents a comprehensive exploration of the application of automatic speech recognition in Air Traffic Control System Command Center planning teleconferences, leveraging the transformer architecture for enhanced efficiency. The novel contributions lie in the improved accessibility of decision-making records, real-time participation opportunities for external stakeholders, and the potential for downstream natural language processing advancements. As the aviation industry continues to evolve, the integration of automatic speech recognition technologies holds the promise of revolutionizing decision-making processes and contributing to the overall safety and efficiency of air traffic management.

ATM↗
DOE OSTI2026

TRACE Input Modernization

This work presents a Tom’s Obvious Minimal Language (TOML)-based representation of input for the US Nuclear Regulatory Commission’s TRAC/RELAP Advanced Computational Engine (TRACE) thermal hydraulics code. Implemented using the Workbench Analysis Sequence Processor (WASP), the approach maps traditional TRACE input structures to a hierarchical format composed of named parameters, typed values, and native data collections. The resulting representation preserves TRACE’s existing modeling capabilities while providing a modern, structured interface for model development and management. WASP further extends TOML through a file import directive that supports modular model composition and reusable input organization. In addition, WASP provides extended array data entry convenience with various data repeat and interpolation capabilities. Examples of the new TOML syntax are provided for major TRACE input categories, including hydraulic components, heat structures, control systems, and trip logic. The TOML representation establishes a foundation for improved validation, tooling, automation, and model maintainability while remaining compatible with existing TRACE workflows. To facilitate migration to the TOML-based input format, the TRACE executable now supports conversion of native TRACE input into an intermediate JSON representation. A Python utility subsequently transforms the JSON data into an equivalent TOML model. Lastly, the TRACE executable now supports execution using TOML-formatted input.

Lefebvre, Robert A. [Oak Ridge National Laboratory↗
DOE OSTI2024

A FFT-based mesoscale continuum dislocation mechanics with defect energy: Applications to composites and polycrystals

A crystal plasticity elastoviscoplastic FFT (fast Fourier transform) formulation with a mesoscale continuum field dislocation mechanics model is presented, which incorporates a defect energy density that depends on GND densities and an associated material length scale. This allows to thermodynamically derive internal length scale dependent intra-crystalline backstress and Peach–Koehler force acting on GND densities. The model considers GND density evolution through a filtered numerical spectral approach, which is coupled with stress equilibrium through the elastoviscoplastic FFT algorithm. The discrete Fourier transform (DFT) method together with finite difference (FD) schemes is applied to solve both the backstress tensor and the Fourier–Green operator. Numerical results are first reported for two-phase laminate composites with plastic single crystal channels and elastic precipitates for shear loadings. Channel size effects are simulated and analyzed on the overall and local hardening behaviors during monotonous loadings. In addition, the evolutions of GND densities and the role of their associated backstress on size effects are examined during reversible shear loading. In a second part, the role of the defect energy internal length scale on polycrystal’s hardening during tension–compression is discussed. The results are compared to those obtained using FFT-based continuum field dislocation mechanics without defect energy.

36 MATERIALS SCIENCE↗
NASA NTRS1988

Inflation in a renormalizable cosmological model and the cosmic no hair conjecture

The possibility of having inflation in a renormalizable cosmological model is investigated. The Cosmic No Hair Conjecture is proved to hold for all Bianchi types except Bianchi IX. By the use of a conformal transformation on the metric it is shown that these models are equivalent to the ones described by the Einstein-Hilbert action for gravity minimally coupled to a set of scalar fields with inflationary potentials. Henceforth, it is proven that inflationary solutions behave as attractors in solution space, making it a natural event in the evolution of such models.

Maeda, Kei-Ichi↗