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DOE OSTI2024

Machine Learning Driven Sensitivity Analysis of E3SM Land Model Parameters for Wetland Methane Emissions

Methane (CH 4 ) is globally the second most critical greenhouse gas after carbon dioxide, contributing to 16%–25% of the observed atmospheric warming. Wetlands are the primary natural source of methane emissions globally. However, wetland methane emission estimates from biogeochemistry models contain considerable uncertainty. One of the main sources of this uncertainty arises from the numerous uncertain model parameters within various physical, biological, and chemical processes that influence methane production, oxidation, and transport. Sensitivity Analysis (SA) can help identify critical parameters for methane emission and achieve reduced biases and uncertainties in future projections. This study performs SA for 19 selected parameters responsible for critical biogeochemical processes in the methane module of the Energy Exascale Earth System Model (E3SM) land model (ELM). The impact of these parameters on various CH 4 fluxes is examined at 14 FLUXNET- CH 4 sites with diverse vegetation types. Given the extensive number of model simulations needed for global variance-based SA, we employ a machine learning (ML) algorithm to emulate the complex behavior of ELM methane biogeochemistry. We found that parameters linked to CH 4 production and diffusion generally present the highest sensitivities despite apparent seasonal variation. Comparing simulated emissions from perturbed parameter sets against FLUXNET-CH 4 observations revealed that better performances can be achieved at each site compared to the default parameter values. This presents a scope for further improving simulated emissions using parameter calibration with advanced optimization techniques.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Efficient Sampling of Complex Interdependent and Multiplex Networks

Efficient sampling of interdependent and multiplex infrastructure networks is critical for effectively applying failure and recovery algorithms in real-world settings, as well as to generate property-preserving reduced-order graph-based ensembles that address topological uncertainties. In this paper, we first explore the performance, i.e. the success in preserving graph properties, of graph sampling algorithms for interdependent and multiplex networks with synthetic and real-world graphs. We simulate sampling algorithms under different parameter settings. These settings include probabilistic graph generators, coupling patterns, and various performance metrics. Our results show that while Random Node and Random Walk sampling algorithms perform best for interdependent networks, Random Edge and Forest Fire sampling algorithms perform best for multiplex networks. Second, we propose and implement a novel similarity-based sampling algorithm for multiplex networks that samples only log(N) number of layers of an N-layer multiplex network while yielding computational savings with performance guarantees. Experimental results show that similarity sampling outperforms complete sampling of all layers while decreasing performance costs from a linear scale to a logarithmic one. Our results also indicate that similarity-based sampling outperforms complete sampling and random selection in nearly all scenarios when tested with real-world data.

Subasi, Omer↗

DOE OSTI2021

Prediction of DIII-D Pedestal Structure From Externally Controllable Parameters

The sharp increase of pressure at the edge of a high confinement mode (H-mode) plasma, the pedestal, strongly impacts overall plasma performance. Predicting the pedestal is a necessity to control and optimize tokamak operations. Here, an experimental data-driven machine learning (ML) approach is presented that predicts the pedestal heights and widths of electron density (n e ) and electron temperature (T e ) profiles as well as the separatrix ne from externally controllable parameters such as the plasma shape, heating method and power, and gas puff rate and integrated gas puff. The OMFIT framework was used with DIII-D data to efficiently, robustly, and automatically build a database of pedestal parameters to train machine learning models. Database creation was enabled by the search engine tool for DIII-D data, TokSearch, which parallelizes data fetching, enabling fast searches through basic signals of thousands of DIII-D shots and selection of relevant time intervals. Principal Component Analysis (PCA) separated the database into three clusters that represent classes of plasma shapes that are regularly used in DIII-D. The most important parameters for setting the pedestal structure were plasma current (I p ), toroidal magnetic field (B Φ ), neutral beam heating power (P NBI ) and shaping quantities. The Deep Jointly Informed Neural Networks (DJINN) algorithm was applied to identify suitable neural network (NN) architectures that appropriately capture the features of the pedestal database. Separate NNs were implemented for each pedestal parameter, and ensembling methods were used to improve the prediction accuracy and allowed estimation of the prediction uncertainty. The pedestal predictions of the test dataset lie within the measurement uncertainties of the pedestal parameters. The NN outperformed simple Linear Regression (LR) analysis, indicating non-linear dependencies in the pedestal structure. The presented achievements illustrate a promising path for future research, using feature extraction to infer experimental trends and thereby improve pedestal models as well as deploying NN for a fast pedestal prediction in DIII-D scenario development.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Extending SEER for Extreme Heterogeneity

Heterogeneous and multi-device nodes are increasingly common in high-performance computing and data centers, yet existing programming models often lack simple, transparent, and portable support for these diverse architectures. The main contribution of this work is the development of novel SEER capabilities to address this challenge by providing a descriptive programming model that allows applications to seamlessly leverage heterogeneous nodes across various device types. SEER uses efficient memory management and can select the proper device[s] depending on the computational cost of the applications. This is completely transparent to the programmer, thereby providing a highly productive programming environment. Integrating extreme heterogeneity into the SEER library as shown with the use of NVIDIA and AMD GPUs simultaneously allows it to expand and exploit the performance possibilities. Our analysis based on the well-known Conjugate Gradient algorithm reports accelerations above 1.5 × on computationally demanding steps of such an algorithm by using both architectures simultaneously.

Teranishi, Keita [ORNL] (ORCID:0000000166472690)↗

DOE OSTI2024

Sparsified time-dependent Fourier neural operators for fusion simulations

This paper presents a sparsified Fourier neural operator for coupled time-dependent partial differential equations (ST-FNO) as an efficient machine learning surrogate for fluid and particle-based fusion codes such as NIMROD (Non-Ideal Magnetohydrodynamics with Rotation - Open Discussion) and GTC (Gyrokinetic Toroidal Code). ST-FNO leverages the structures in the governing equations and utilizes neural operators to represent Green's function-like numerical operators in the corresponding numerical solvers. Once trained, ST-FNO can rapidly and accurately predict dynamics in fusion devices compared with first-principle numerical algorithms. In general, ST-FNO represents an efficient and accurate machine learning surrogate for numerical simulators for multi-variable nonlinear time-dependent partial differential equations, with the proposed architectures and loss functions. The efficacy of ST-FNO has been demonstrated using quiescent H-mode simulation data from NIMROD and kink-mode simulation data from GTC. The ST-FNO H-mode results show orders of magnitude reduction in memory and central processing unit usage in comparison with the numerical solvers in NIMROD when computing fields over a selected poloidal plane. The ST-FNO kink-mode results achieve a factor of 2 reduction in the number of parameters compared to baseline FNO models without accuracy loss.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Determination of the Maturation Status of Dendritic Cells by Applying Pattern Recognition to High-Resolution Images

The maturation or activation status of dendritic cells (DCs) directly correlates with their behavior and immunofunction. A common means to determine the maturity of dendritic cells is from high-resolution images acquired via scanning electron microscopy (SEM) or atomic force microscopy (AFM). While direct and visual, the determination has been made by directly looking at the images by researchers. Here we report a machine learning approach using pattern recognition in conjunction with cellular biophysical knowledge of dendritic cells to determine the maturation status of dendritic cells automatically. The determination from AFM images reaches 100% accuracy. The results from SEM images reaches 94.9%. The results demonstrate the accuracy of using machine learning for accelerating data analysis, extracting information, and drawing conclusions from high-resolution cellular images, paving the way for future applications requiring high-throughput and automation, such as cellular sorting and selection based on morphology, quantification of cellular structure, and DC-based immunotherapy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2025

WigglyRivers: A tool to characterize the multiscale nature of meandering channels

Channel sinuosity is ubiquitous along river networks, producing complex patterns that encapsulate and influence morphodynamic processes and ecosystem services. Accurately characterizing these patterns is challenging with traditional curvature-based algorithms. Here, in this study, we present WigglyRivers, a Python package that builds on existing wavelet-based methods to create an unsupervised meander identification and characterization tool. The package uses planimetric information the user provides or from the USGS’s High-Resolution National Hydrography Dataset to characterize individual reaches or entire river networks. WigglyRivers also includes a supervised river identification tool for manually selecting individual meandering features. Here, we provide examples of idealized river transects and show the capabilities of WigglyRivers. We also use the supervised identification tool to validate the unsupervised identification on river transects across the continental US. WigglyRivers is a tool to understand better the multiscale characteristics of river networks and the link between river geomorphology and river corridor connectivity.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

General Multifidelity Surrogate Models: Framework and Active-Learning Strategies for Efficient Rare Event Simulation

Estimating the probability of failure for complex real-world systems using high-fidelity computational models is often prohibitively expensive, especially when the probability is small. Exploiting low-fidelity models can make this process more feasible, but merging information from multiple low-fidelity and high-fidelity models poses several challenges. Here, this paper presents a robust multi-fidelity surrogate modeling strategy in which the multi-fidelity surrogate is assembled using an active learning strategy using an on-the-fly model adequacy assessment set within a subset simulation framework for efficient reliability analysis. The multi-fidelity surrogate is assembled by first applying a Gaussian process correction to each low-fidelity model and assigning a model probability based on the model's local predictive accuracy and cost. Three strategies are proposed to fuse these individual surrogates into an overall surrogate model based on model averaging and deterministic/stochastic model selection. The strategies also dictate which model evaluations are necessary. No assumptions are made about the relationships between low-fidelity models, while the high-fidelity model is assumed to be the most accurate and most computationally expensive model. Through two analytical and two numerical case studies, including a case study evaluating the failure probability of Tristructural isotropic-coated (TRISO) nuclear fuels, the algorithm is shown to be highly accurate while drastically reducing the number of high-fidelity model calls (and hence computational cost).

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2020

X-ray diffraction at the National Ignition Facility

We report details of an experimental platform implemented at the National Ignition Facility to obtain in situ powder diffraction data from solids dynamically compressed to extreme pressures. Thin samples are sandwiched between tamper layers and ramp compressed using a gradual increase in the drive-laser irradiance. Pressure history in the sample is determined using high-precision velocimetry measurements. Up to two independently timed pulses of x rays are produced at or near the time of peak pressure by laser illumination of thin metal foils. The quasi-monochromatic x-ray pulses have a mean wavelength selectable between 0.6 Å and 1.9 Å depending on the foil material. The diffracted signal is recorded on image plates with a typical 2 θ x-ray scattering angle uncertainty of about 0.2° and resolution of about 1°. Analytic expressions are reported for systematic corrections to 2 θ due to finite pinhole size and sample offset. A new variant of a nonlinear background subtraction algorithm is described, which has been used to observe diffraction lines at signal-to-background ratios as low as a few percent. Variations in system response over the detector area are compensated in order to obtain accurate line intensities; this system response calculation includes a new analytic approximation for image-plate sensitivity as a function of photon energy and incident angle. This experimental platform has been used up to 2 TPa (20 Mbar) to determine the crystal structure, measure the density, and evaluate the strain-induced texturing of a variety of compressed samples spanning periods 2–7 on the periodic table.

47 OTHER INSTRUMENTATION↗

DOE OSTI2023

Evaluation of Electron Tomography Capabilities for Shale Imaging

Despite the advantageous resolution of electron tomography (ET), reconstruction of three-dimensional (3D) images from multiple two-dimensional (2D) projections presents several challenges, including small signal-to-noise ratios, and a limited projection range. This study evaluates the capabilities of ET for thin sections of shale, a complex nanoporous medium. A numerical phantom with 1.24 nm pixel size is constructed based on the tomographic reconstruction of a Barnett shale. A dataset of 2D projection images is numerically generated from the 3D phantom and studied over a range of conditions. First, common reconstruction techniques are used to reconstruct the shale structure. The reconstruction uncertainty is quantified by comparing overall values of storage and transport metrics, as well as the misclassification of pore voxels compared to the phantom. We then select the most robust reconstruction technique and we vary the acquisition conditions to quantify the effect of artifacts. We find a strong agreement for large pores over the different acquisition workflows, while a wider variability exists for nanometer-scale features. Furthermore, the limited projection range and reconstruction are identified as the main experimental bottlenecks, thereby suggesting that sample thinning, advanced holders, and advanced reconstruction algorithms offer opportunities for improvement.

3D scanning transmission electron microscopy↗

DOE OSTI2023

The Calar Alto Legacy Integral Field Area survey: extended and remastered data release

ABSTRACT This paper describes the extended data release (eDR) of the Calar Alto Legacy Integral Field Area (CALIFA) survey. It comprises science-grade quality data for 895 galaxies obtained with the Potsdam Multi Aperture Spectograph/PPak instrument at the 3.5-m telescope at the Calar Alto Observatory along the last 12 yr, using the V500 setup [3700–7500 Å, 6 Å/full-width at half-maximum (FWHM)] and the CALIFA observing strategy. It includes galaxies of any morphological type, star formation stage, a wide range of stellar masses (∼107–1012 M⊙), at an average redshift of ∼0.015 (90 per cent within 0.005 < z < 0.05). Primarily selected based on the projected size and apparent magnitude, we demonstrate that it can be volume corrected resulting in a statistically limited but representative sample of the population of galaxies in the nearby Universe. All the data were homogeneous re-reduced, introducing a set of modifications to the previous reduction. The most relevant is the development and implementation of a new cube-reconstruction algorithm that provides with an (almost) seeing-limited spatial resolution (FWHMPSF ∼ 1.0 arcsec). To illustrate the usability and quality of the data, we extracted two aperture spectra for each galaxy (central 1.5 arcsec and fully integrated), and analyse them using pyFIT3D. We obtain a set of observational and physical properties of both the stellar populations and the ionized gas, that have been compared for the two apertures, exploring their distributions as a function of the stellar masses and morphologies of the galaxies, comparing with recent results in the literature.

Sánchez, S. F. (ORCID:0000000164449307)↗

DOE OSTI2025

Post-hoc reweighting of hadron production in the Lund string model

We present a method for reweighting flavor selection in the Lund string fragmentation model. This is the process of calculating and applying event weights enabling fast and exact variation of hadronization parameters on pre-generated event samples. The procedure is post hoc, requiring only a small amount of additional information stored per event, and allowing for efficient estimation of hadronization uncertainties without repeated simulation. Weight expressions are derived from the hadronization algorithm itself, and validated against direct simulation for a wide range of observables and parameter shifts. The hadronization algorithm can be viewed as a hierarchical Markov process with stochastic rejections, a structure common to many complex simulations outside of high-energy physics. This perspective makes the method modular, extensible, and potentially transferable to other domains. We demonstrate the approach in Pythia, including both coverage considerations and timing benefits. For the purpose of this paper, our goal is to develop and demonstrate the the formalism, and we therefore exclude several model variations for baryon production (popcorn model, junction production) needed for proton collisions. These will be the topic of a future paper.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2019

Development and Validation of a Conjugate Heat Transfer Model for the Two-Phase CFD Code NEK-2P

A project is underway to develop, verify and validate an advanced two-phase flow modeling capability for the highly-scalable, high-performance CFD code NEK5000. The goal of the project is to develop a new two-phase version of the NEK5000 code, named NEK-2P, to simulate the two-phase flow and heat transfer phenomena that occur in a Boiling Water Reactor (BWR) fuel bundle under various operating conditions. The NEK-2P two-phase flow models follow the approach used for the Extended Boiling Framework (EBF) [2-3] previously developed at Argonne, but include more fundamental physical models of boiling phenomena and advanced numerical algorithms for improved computational accuracy, robustness, and computational speed. The development of the NEK-2P two-phase solver and the implementation of the Extended Boiling Framework two-phase models were initially supported by Argonne National Laboratory (Argonne) through a Laboratory Directed Research and Development (LDRD) project during FY2014-2016. The development and validation of the two-phase models through analyses of selected two-phase boiling flow experiments was supported by the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program in FY2017-2019. This report focuses on the FY2019 development and validation of the Conjugate Heat Transfer (CHT) model for the NEK-2P Two-Phase, Computational Fluid Dynamics (CFD) code. The NEK-2P CHT model calculates the coupled behavior of the fluid and solid domains. In the fluid domain NEK-2P calculates the vapor and liquid phase temperatures, velocities and mass fractions. In the solid domain only the temperatures are calculated. The fluid and solid domains are coupled with a heat flux boundary condition at the fluid-solid interface. The heat flux and the wall temperatures at the fluid-solid interface are updated using the NEK-2P wall heat-flux partitioning model. A wall heat flux boundary condition is also applied to the exterior surface of the solid domain. The CHT model validation was illustrated through the analysis of three of the Becker Critical Heat Flux (CHF) tests. Reasonably good agreement with measured data was obtained in predicting the CHF location and post CHF wall temperature behavior illustrating the ability of the NEK-2P CHT model to simulate the CHF phenomena for a wide range of thermal-hydraulic conditions. Apart from the CHT model development and validation, initial simulations were performed for the Virginia Tech. (VT) 3x3 bare rod bundle experiments including both cold and boiling flow simulations.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2020

Development and Validation of a Two-Phase Thermal-Hydraulic CFD Code NEK-2P

A project is underway to develop, verify and validate an advanced two-phase flow modeling capability for the highly-scalable, high-performance Computational Fluid Dynamics (CFD) code NEK5000. The goal of this work is to verify and validate the two-phase version of the NEK5000 code, named NEK-2P, to simulate the two-phase flow and heat transfer phenomena that occur in a Boiling Water Reactor (BWR) fuel bundle under various operating conditions. The NEK-2P two-phase flow models follow the approach used for the Extended Boiling Framework (EBF) previously developed at Argonne but include more fundamental physical models of boiling phenomena and advanced numerical algorithms for improved computational accuracy, robustness, and computational speed. The development of the NEK-2P two-phase solver and the implementation of the Extended Boiling Framework two-phase models were initially supported by Argonne National Laboratory (Argonne) through a Laboratory Directed Research and Development (LDRD) project during FY2014-2016. The development and validation of the two-phase models through analyses of selected two-phase boiling flow experiments was supported by the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program in FY2017-2020. This report focuses on verification and validation of the water-steam boiling model NEK-2P Two-Phase, CFD code. The NEK-2P was validated with Nuclear Power Engineering Corporation (NUPEC) Pressurized Water Reactor (PWR) Sub-channel and Bundle Test (PSBT) void distribution benchmark. Three different simulations were performed and analyzed for various operating conditions such as wall-heat flux and sub-cooled inlet temperatures. Reasonably good agreement with measured data was obtained in predicting the measured void distributions. Simulations were performed for Virginia Tech. (VT) 3x3 rod bundle geometry with and without spacers. The preliminary results were presented for Simplified Spacer Grid (SSG). In addition, the implementation of interface reconstruction model was tested with one of the Becker benchmark Critical Heat Flux (CHF) experiments.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2024

Carbon storage cost modeling for the offshore Gulf of Mexico

Groundbreaking for geologic carbon storage (GCS) projects in the offshore Gulf of Mexico is imminent, and there is great interest in utilizing this region for GCS projects. Offshore saline reservoirs provide a significant and accessible resource for GCS. However, conducting GCS in the offshore environment will pose distinct challenges pertaining to site selection, operations, infrastructure use, and monitoring compared to operating onshore that ultimately affect technoeconomic assessment of offshore GCS projects. Carbon storage and transport costs are critical to project developers looking to deploy carbon storage in the offshore environment. We present CO2_S_COM_Offshore, a model developed by the National Energy Technology Laboratory (NETL) as a screening-level offshore saline GCS cost modeling tool. Based on NETL’s widely used CO2_S_COM cost model for onshore saline CS, CO2_S_COM_Offshore enables technoeconomic analysis of GCS in offshore areas. This model comprehensively incorporates multiple facets of offshore GCS projects, from regional evaluation and site selection to permitting, transport, operations, monitoring, site closure, and decommissioning. In general, the model can explore the cost implications for potential offshore GCS project(s) by enabling the user to change several project operational and financial attribute configurations. Key inputs include offshore storage formation options, CO2 injection rate and duration, infrastructure types, monitoring intensity, project financing, and post-injection site care duration. Supporting cost algorithms within CO2_S_COM_Offshore were compiled utilizing S&P Global’ s QUE$TORTM cost estimation software alongside a variety of open-source scientific literature. In addition to reviewing key model components, we discuss several sensitivity analyses, input variabilities, and results on analysis of break-even CO2 price required by a project based on different regulation/policy and operational scenarios for the offshore Gulf of Mexico. These results indicate the value of modeling offshore GCS specifically, and the potential of offshore GCS within a decarbonization value chain. Presented at the 41st USAEE/IAEE North American Conference, 3-6 November 2024, Baton Rouge, LA, United States.

Mark-Moser, Mackenzie K.↗

DOE OSTI2020

Flexible Reinforcement Learning Framework for Building Control using EnergyPlus-Modelica Energy Models

In recent years, reinforcement learning (RL) methods have been greatly enhanced by leveraging deep learning approaches. RL methods applied to building control have shown potential in many applications due to their ability to complement or replace conventional methods such as model-based or rule-based controls. However, RL-based building control software is likely tailored either to one target building system or to a specific RL method so that significant additional effort would be required to customize the RL-based controller for use in other building systems or with other RL approaches. Also, RL-based building controls usually depend on building energy simulations to train controllers, so emulating building dynamics (i.e., thermal dynamics and control dynamics) and capturing sub-hourly dynamic profiles are crucial to further the development of effective RL-based building control methods. To address these challenges, we present an open source RL-based control software employing a high-fidelity hybrid EnergyPlus-Modelica building energy model which emulates building dynamics at 1-minute resolution. This software consists of decoupled components (environment, building emulator, control agent, and RL algorithm), which allows for quick prototyping and benchmarking of standard RL algorithms in different systems; for example, a single component can be replaced without revising all of the software. To demonstrate this software framework, we conducted a benchmark study using an EnergyPlus-Modelica building energy model for a Chicago office building with an RL-based controller to dynamically control the chilled water temperature setpoint and the air handling unit supply air temperature setpoint on selected floors.

Lee, Joon-Yong↗

DOE OSTI2022

Machine Learning Guided Synthesis of Flash Graphene

Advances in nanoscience have enabled the synthesis of nanomaterials, such as graphene, from low-value or waste materials through flash Joule heating. Though this capability is promising, the complex and entangled variables that govern nanocrystal formation in the Joule heating process remain poorly understood. In this work, machine learning (ML) models are constructed to explore the factors that drive the transformation of amorphous carbon into graphene nanocrystals during flash Joule heating. An XGBoost regression model of crystallinity achieves an r 2 score of 0.8051 ± 0.054. Feature importance assays and decision trees extracted from these models reveal key considerations in the selection of starting materials and the role of stochastic current fluctuations in flash Joule heating synthesis. Furthermore, partial dependence analyses demonstrate the importance of charge and current density as predictors of crystallinity, implying a progression from reaction-limited to diffusion-limited kinetics as flash Joule heating parameters change. Finally, a practical application of the ML models is shown by using Bayesian meta-learning algorithms to automatically improve bulk crystallinity over many Joule heating reactions. Furthermore, these results illustrate the power of ML as a tool to analyze complex nanomanufacturing processes and enable the synthesis of 2D crystals with desirable properties by flash Joule heating.

01 COAL, LIGNITE, AND PEAT↗

DOE OSTI2019

Mean-Field and Monte Carlo Studies of the Magnetic Properties of a Spin-7/2 and Spin-5/2 Ising Bilayer Film

We use standard Monte Carlo simulations based on the Metropolis algorithm and mean-field calculations to investigate the magnetic properties of an Ising bilayer film consisting of two superposed ferromagnetic squared lattices A and B whose magnetic atoms have spin 7/2 and 5/2 respectively. Crystal-field and external magnetic field effects on the spins are considered in the model. The magnetic order parameters and response functions are calculated as functions of the temperature for selected values of the model parameters and this enables one to devise thermal phase diagrams by both methods. Our calculations only reveal second-order phase boundaries. Under appropriate conditions, compensation point phenomena are detected in the calculations below the critical temperatures. When the system is exposed to the external magnetic constraint, attracting hysteresis phenomena are sometimes generated. The temperature dependence of the coercitive field for various values of the crystal-field is singled out.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗