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

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At least 1,279 records · Page 71
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Data-Driven Optimization of the Processing Window for 316H Components Fabricated Using Laser Powder Bed Fusion

The Advanced Materials and Manufacturing Technologies Program is focused on accelerating the development and deployment of advanced materials and components fabricated via additive manufacturing with a specific focus on laser powder bed fusion (LPBF). As an initial case study, the program has selected 316H stainless steel (SS) as an initial material around which to develop a code case development strategy. This strategy involves two parallel approaches: (1) an equivalency approach whereby round-robin testing across multiple collaborating laboratories demonstrates repeatability in processing and direct comparisons with conventional wrought 316H material and (2) a revolutionary approach to code qualification combining in situ data collection and high-fidelity modeling to capture, predict, and bound the performance of LPBF 316HSS components. As part of this campaign, this work package has initiated an extensive process optimization campaign across three laboratories, each printing variations of LPBF 316HSS using three different LPBF units (Concept Laser, EOS, and Renishaw). In FY23, ORNL has focused on unique experimental designs spanning wide ranges in energy inputs and turning knobs such as scan speed, laser power, hatch spacing, layer thickness, spot size, scan rotation, and more. On the Concept Laser M2, 72 different combinations of processing variables were investigated with duplicate samples and different powder compositions. In total, 252 samples were printed with combined in situ sensing data. A parallel design of experiments was conducted on the Renishaw AM400 with an additional 390 printed specimens for analysis. All 642 miniature specimens, each with unique features included in each print to capture geometry-related heterogeneity, were subjected to high-throughput x-ray computed tomography (XCT) analysis to enable the downselection of specific processing parameters of interest. Then, using electrical discharge machining (EDM), miniature tensile specimens were extracted for mechanical testing and microscopy investigations. From the analysis performed in FY23, it was found that powder composition drastically affects the resulting microstructure and mechanical performance of 316SS. Specifically, changing from 316L to 316HSS powder results in a wide range of grain sizes with varying degrees of preferred grain orientation, which increases as a function of energy density. It was also found that due to stored heat in thin fin–type features, large microstructural differences can be seen within one part printed with one set of processing parameters. These variations in microstructure features, including grain size, the nanoscale dislocation structure, and grain texture, will all affect the irradiation performance and high-temperature mechanical performance of LPBF 316HSS parts. Two sets of concept laser processing parameters, spanning both refined and columnar grain structures, were scaled to print larger 316H builds for campaign testing (high-temperature creep and irradiation). In addition, at least two optimized processing parameter sets were identified for the Renishaw AM400 for round-robin testing in FY24 with Argonne National Laboratory. Future work includes printing samples using identical parameters identified by partner institutions, providing material for corrosion and high-temperature mechanical testing, and continuing evaluations of heterogeneity in larger printed parts.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Parallel interior-point solver for block-structured nonlinear programs on SIMD/GPU architectures

Here, we investigate how to port the standard interior-point method to new exascale architectures for block-structured nonlinear programs with state equations. Computationally, we decompose the interior-point algorithm into two successive operations: the evaluation of the derivatives and the solution of the associated Karush-Kuhn-Tucker (KKT) linear system. Our method accelerates both operations using two levels of parallelism. First, we distribute the computations on multiple processes using coarse parallelism. Second, each process uses SIMD/GPU accelerators locally to accelerate the operations using fine-grained parallelism. The KKT system is reduced by eliminating the inequalities and the state variables from the corresponding equations. We demonstrate our method's capability on the supercomputer Polaris, a testbed for the future exascale Aurora system. Each node is equipped with four GPUs, a setup amenable to our two-level approach. Our experiments on the stochastic optimal power flow problem show that the reduction method is 50x faster than the sparse linear solver HSL MA57 running in serial on the CPU, and 6x faster than Pardiso running in parallel on CPU on the same number of processes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Optimal Power Flow of Radial Networks and Its Variations: A Sequential Convex Optimization Approach

This paper proposes a sequential convex optimization method to solve broader classes of optimal power flow (OPF) problems over radial networks. The non-convex branch power flow equation is decomposed as a second-order cone inequality and a non-convex constraint involving the difference of two convex functions. Provided with an initial solution offered by an inexact second-order cone programming relaxation model, this approach solves a sequence of convexified penalization problems, where concave terms are approximated by linear functions and updated in each iteration. It could recover a feasible power flow solution, which usually appears to be very close, if not equal, to the global optimal one. Two variations of the OPF problem, in which non-cost related objectives are optimized subject to power flow constraints and the convex relaxation is generally inexact, are elaborated in detail. One is the maximum loadability problem, which is formulated as a special OPF problem that seeks the maximal distance to the boundary of power flow insolvability. The proposed method is shown to outperform commercial nonlinear solvers in terms of robustness and efficiency. The other is the bi-objective OPF problem. A non-parametric scalarization model is suggested, and is further reformulated as an extended OPF problem by convexifying the objective function. It provides a single trade-off solution without any subjective preference. The proposed computation framework also helps retrieve the Pareto front of the bi-objective OPF via the e-constraint method or the normal boundary intersection method. This paper also discusses extensions for OPF problems over meshed networks based on the semidefinite programming relaxation method.

bi-objective optimization↗
DOE OSTI2018

Backfilling of Geological Disposal Facilities - Development of Optimized Backfill Material - 18146

In Belgium, low- and intermediate-level waste (B-waste) will be conditioned in concrete monoliths and high-level waste (C-waste) in so-called Super-containers (SCs). The Belgian radioactive waste management program has focused on the disposal of these waste types in two emplacement fields of a geological disposal facility (GDF). When the disposal waste packages (DWP) have been emplaced, backfilling of the galleries is supposed to be carried out in order to stabilize the galleries, to reduce voids, to guarantee a favourable chemical milieu with regard to the retention of the radionuclides, to minimize a possible gas pressure build-up, to dissipate radioactive decay heat and to enable good conditions for a potential retrieval of the DWP. The current reference solution is to mix the backfill at the surface and then to pump the mixture through pipeline distribution systems into the underground structures. The catalogue of backfill material requirements comprises common, but also different requirements due to the characteristics of the B and C waste packages and differences in the backfilling systems. It was found that two backfill material recipes have to be developed. Different requirements, such as high porosity (low strength and low gas threshold pressure) and high thermal conductivity have contrary consequences for the material. In addition, during backfill production quality variations of the raw materials that influence the backfill material properties can occur. Different lengths of the delivery pipeline may require adjustments of the material composition. In order to consider the practical experiences of backfill material production, one focus of the development programs was to identify compositional ranges that guarantee the respective material property. A combination of the individual 'conformity fields' results in optimal solutions for the standard operating conditions as well as a compositional range that guarantees compliance with the required material specifications. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2023

Experimental Evidence on Latency in a Fleet of Controllable Water Heaters

Demand response is an important emerging part of smart grids with wide coverage in theoretical and modeling research. However, experimental evidence on the real-life behavior of controllable loads is still limited. We present observations regarding latency and communication aspects of the operation on a fleet of residential water heaters in a smart neighborhood in Atlanta, GA. Our analysis shows that latency in water heaters is not constant and does not follow a Gaussian distribution. We also find that there is a systematic relationship between latency and hour of the day. Latency was found to increase during morning and evening hours compared to the afternoon. These findings could help better plan deployment of control for demand response programs. Understanding delays associated with controlling smart devices is crucial for proper design and algorithm development for optimization, frequency of dispatch, and override detection.

communication delay↗
DOE OSTI2024

An Evaluation of The Dynamic Physical Security Risk Assessment Methodology for Fleet-Wide Applications

The requirements for U.S. nuclear power plants to maintain a large onsite physical security force contribute to their high operational costs. The cost of maintaining the current physical security posture is approximately 10% of the overall operation and maintenance budget for commercial nuclear power plants. The goal of the Light Water Reactor Sustainability (LWRS) program’s physical security pathway is to develop tools, methods, and technologies and provide the technical basis for an optimized physical security posture. The conservatisms built into current security postures may be analyzed and minimized to reduce security costs while still ensuring adequate security and operational safety. The research performed at Idaho National Laboratory within LWRS program’s physical security pathway has successfully developed a dynamic force-on-force modeling framework using various computer simulation tools and integrating them with the dynamic assessment Event Modeling Risk Assessment using Linked Diagrams (EMRALD) tool. This integrated process for physical security analysis is named Modeling and Analysis for Safety Security using Dynamic EMRALD Framework (MASS-DEF). This document provides an update on the progress in applying the MASS-DEF process to an operating commercial nuclear power plant as well as additional industry feedback regarding use of the tool for other physical security risk-informed topics. This report is only a summary of the progress and does not contain specific modeling results as those contain sensitive security information. Previous reports described how a user could integrate their plant-specific force-on-force models with the dynamic simulation tool EMRALD, model operator actions, and integrate with probabilistic risk assessment tools, such as CAFTA (Computer Aided Fault Tree Analysis System) or SAPHIRE (Systems Analysis Programs for Hands-on Integrated Reliability Evaluations), and with thermal-hydraulic tools, such as RELAP-5 or MAAP. Previous reports applied various combinations of available simulations codes with EMRALD using generic plant models to demonstrate how to perform the analysis. This report is an update the progress of applying the dynamic computational framework to an actual nuclear facility using their security scenarios and timelines. This report also provides an update to the procedural guidance for the MASS-DEF process and an overview of the generic models available for use by utilities. This report does not contain any plant’s sensitive information and/or safeguards information. This study’s purpose was to verify that the results achieved using generic models are similar to actual plant results and refine our guidance on the use of the framework. This assessment enables further analysis, such as what-if scenarios and staff-reduction evaluation, thereby optimizing physical security at plants.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Design and analysis of optimal pre-cooling in residential buildings

Existing pre-cooling strategies provide a means of shifting or reducing the peak demand and/or energy cost in residential buildings. However, majority of them are rule-based and therefore may not be optimal in terms of cost saving, leaving room for improvement. In this paper, an integer linear programming problem that accounts for the thermal properties of a specific home, HVAC system capacity, utility rate structure, and weather conditions and makes use of a home thermal model is formulated. This problem determines the HVAC on/off control signal that minimizes the 24-h energy cost while maintaining thermal comfort and calculates the corresponding optimal indoor air temperature. The model is constructed using home thermal properties identified via data training in real-time. Through simulation, the energy performance of the proposed optimal pre-cooling strategy is investigated and compared with three rule-based operation strategies from the literature. It is found that the optimal strategy requires the least energy consumption without sacrificing thermal comfort. The superb energy performance of the optimal strategy is attributed to a longer runtime of the HVAC system in cool outdoor air conditions and to the elimination of deadband in HVAC operation, which is required by the rule-based strategies, to allow the indoor air temperature to stay near the thermal comfort upper bound as much as possible. In terms of energy cost, the rule-based operation strategies require 3.52, 1.90, and 2.79, respectively, while the optimal strategy only requires 1.52. These figures represent a saving of 56.82%, 20.00%, and 45.52%, respectively. The results suggest that the optimal strategy is indeed significantly more effective than the existing rule-based operation strategies.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2018

Parallelized hybrid optimization methods for nonsmooth problems using NOMAD and linesearch

Two parallelized hybrid methods are presented for single-function optimization problems with side constraints. The optimization problems are difficult not only due to possible existence of local minima and nonsmoothness of functions, but also due to the fact that objective function and constraint values for a solution vector can only be obtained by querying a black box whose execution requires considerable computational effort. Examples are optimization problems in Engineering where objective function and constraint values are computed via complex simulation programs, and where local minima exist and smoothness of functions is not assured. The hybrid methods consist of the well-known method NOMAD and two new methods called DENCON and DENPAR that are based on the linesearch scheme CS-DFN. The hybrid methods compute for each query a set of solution vectors that are evaluated in parallel. The hybrid methods have been tested on a set of difficult optimization problems produced by a certain seeding scheme for multiobjective optimization. We compare computational results with solution by NOMAD, DENCON, and DENPAR as stand-alone methods. It turns out that among the stand-alone methods, NOMAD is significantly better than DENCON and DENPAR. However, the hybrid methods are definitely better than NOMAD.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

H–J–B Equations of Optimal Consumption-Investment and Verification Theorems

We consider a consumption-investment problem on infinite time horizon maximizing discounted expected HARA utility for a general incomplete market model. Based on dynamic programming approach we derive the relevant H–J–B equation and study the existence and uniqueness of the solution to the nonlinear partial differential equation. By using the smooth solution we construct the optimal consumption rate and portfolio strategy and then prove the verification theorems under certain general settings.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

High Yield, Economical and Environmentally Benign Production of Rare Earth Elements from Coal Ash (Phase II Final Summary Report)

Fly ash stored in landfills and ponds across the United States is an attractive, abundant domestic resource for the cost-effective recovery of rare earth elements (REE) and other critical minerals (CM). Physical Sciences Inc. (PSI) and its team members, Winner Water Services (WWS) and University of Kentucky/Center for Applied Energy Research (UK/CAER) successfully executed a multiphase program that developed technologies and their implementation in a pilot plant. We demonstrated plant operations for cost-effective and environmentally-friendly production of rare earth element oxide (REO) concentrates, and the critical minerals scandium and aluminum (in the forms of salts or oxide products), from coal ash. We also constructed and demonstrated a research-scale (0.5 kg/day) micropilot facility to validate the key physical and chemical processing operations, predict yields, and troubleshoot process bottlenecks. The project team then designed, constructed and operated two decoupled pilot plants: (1) an operational pilot plant for physical separation processes with capacity of 0.4 metric tons per day (tpd), where we optimized processes to produce selected ash fractions as the feedstock for chemical processing and as valuable byproducts such as cenospheres, magnetic ash, and secondary fuel carbon, and (2) an operational pilot plant for chemical ash processing with a capacity of 0.5 tpd that developed optimized processes for the production of: (a) REO concentrates, (b) critical minerals (Sc, Al), and (c) beneficiated ash as a valuable byproduct suitable for cement applications. In Phase I, the project team (with Equinox Chemicals in place of WWS) developed and demonstrated the feasibility of the physical and chemical separation processes, developed the design of a pilot plant, and began the development of a preliminary techno-economic model. In the baseline (initial) Phase II program, the project team developed and demonstrated the above pilot scale plant, producing salable REE concentrates, including Y and Sc (REYSc), plus commercially viable byproducts, using environmentally safe and high-yield physical and chemical enrichment processes. The team successfully demonstrated chemical pilot design, construction, shakedown, and operations of the plant. We produced the Phase II deliverable REYSc concentrate ((50 g of >60 wt.% purity REYSc salts on elemental basis), generated the feed for the Phase II follow-on program, identified processing challenges for future optimizations, and refined the techno-economic model. In the Phase II follow-on program, the project team: (1) developed and demonstrated processes to increase the REE amount by 3X (content basis) and convert the Phase II REE salt mixture to an oxide mixture, (2) produced/delivered >38 g of REO mixture with >85 wt.% purity (elemental basis); (3) developed processes to recover critical minerals scandium and aluminum from intermediate streams; (4) produced/delivered > 1 g of scandium salt mixture with >85 wt. % purity (elemental basis); (5) produced/delivered > 100 g of aluminum oxide type material with >70% wt. purity (elemental basis); and (6) updated the techno-economic model from the baseline Phase II program to assess CAPEX and OPEX of a commercial operation. This program has developed extensive databases on process chemistry, unit operations, plant engineering, and techno-economics that will enable further scale-up toward commercial plant design. Specific future developments will be focused on achieving dramatic savings in energy, reagent usage, and operating costs. The combined results will contribute significantly for maturing the technologies of REE recovery from coal byproducts and promote the establishment of domestic REE and CM supply chains.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2024

Decomposing a renewable energy design and dispatch model

We address a mixed-integer linear programming model which selects a cost-minimizing set of available technologies with which to design a renewable energy system and prescribe their associated dispatch decisions. Realistically sized instances of such models pose computational challenges. To this end, we develop a Lagrangian heuristic based on a decomposition methodology which partitions the model into blocks and optimizes these more manageable, smaller subproblems. It also provides a lower bound to assess solution quality. In conclusion, we apply this methodology to the National Renewable Energy Laboratory's Renewable Energy Integration and Optimization (REopt TM ) model to generate near-optimal solutions to realistic instances containing, on average, approximately 300,000 variables and at least as many constraints, with a mean 30% optimality gap improvement using a five-minute solution time limit, compared to directly solving the original monolith.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Plant-specific Model and Data Analysis using Dynamic Security Modeling and Simulation

The requirements for U.S. nuclear power plants to maintain a large on-site physical security force contribute to their high operational costs. The cost of maintaining the current physical security posture is approximately 10% of the overall operation and maintenance budget for commercial nuclear power plants. The goal of the Light Water Reactor Sustainability (LWRS) program’s physical security pathway is to develop tools, methods, and technologies and provide the technical basis for an optimized physical security posture. The conservatisms built into current security postures may be analyzed and minimized in order to reduce security costs while still ensuring adequate security and operational safety. The research performed at Idaho National Laboratory within LWRS program’s physical security pathway has successfully developed a dynamic force-on-force modeling framework using various computer simulation tools and integrating them with the dynamic assessment Event Modeling Risk Assessment using Linked Diagrams (EMRALD) tool. This document provides an update on the progress in applying a dynamic computational framework that links results from a commercially available force-on-force simulation tool, a commercially available thermal-hydraulic tool, and EMRALD to an operating commercial nuclear power plant. This report is only a summary of the progress and does not contain specific modeling results as those contain sensitive security information. This process of including plant procedures and multiple analysis results is being called Modeling and Analysis for Safety Security using Dynamic EMRALD Framework or MASS-DEF. Previous reports described how a user could integrate their plant-specific force-on-force models with the dynamic simulation tool EMRALD, model operator actions, integrate with probabilistic risk assessment tools, such as CAFTA (Computer Aided Fault Tree Analysis System) or SAPHIRE (Systems Analysis Programs for Hands-on Integrated Reliability Evaluations), and with thermal-hydraulic tools, such as RELAP-5. Previous reports applied various combinations of available simulations codes with EMRALD using generic plant models to demonstrate how to perform the analysis. This report documents the results of applying the dynamic computational framework to an actual nuclear facility using their security scenarios and timelines. This report does not contain any plant's sensitive information and/or Safeguards Information. The purpose of this study was to verify that results achieved using generic models are similar to actual plant results and to refine our guidance on the use of the framework. This assessment enables further analysis, such as what-if scenarios and staff-reduction evaluation, thereby optimizing physical security at plants.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2015

Pareto Efficient Policy for Supervisory Power Management Control

n this paper we address the problem of online optimization of the supervisory power management control in parallel hybrid electric vehicles (HEVs). We model HEV opera- tion as a controlled Markov chain using the long-run expected average cost per unit time criterion, and we show that the control policy yielding the Pareto optimal solution minimizes the average cost criterion online. The effectiveness of the proposed solution is validated through simulation and compared to the solution derived with dynamic programming using the average cost criterion.

Markov chain↗
DOE OSTI2021

A Scalable Meter Placement Method for Distribution System State Estimation

This paper studies the optimal meter placement problem for distribution system state estimation given limited measurement resources. We formulate the problem as a mixed integer semi-definite programming that minimizes the worst case estimation errors over a set of operating points. To solve the problem, we first relax the problem as a convex optimization problem. Motivated by the lack of scalability of existing solvers, we next leverage the special structure of the cost function and propose an algorithm based on barrier method that solves the problem with significantly better numerical performance. The proposed method has been validated on the IEEE 13-bus, IEEE 123-bus, and IEEE 8,500-bus feeders.

barrier method↗
DOE OSTI2016

A Study on Vitrification for LLW Radioactive Wastes - 16235

Ash and ion exchange resin wastes to be vitrified were considered among various radioactive wastes in the Japanese nuclear industry. The appropriate glass composition for the waste is calculated using the computer program. The glass composition is systematically studied using a ternary diagram, considering viscosity, electrical conductivity, and durability. The optimized glass composition based on calculated parameters of vitrification process and the convenience of mixing wastes is selected for crucible experiment. Since differences between calculated values and measured values may occur upon evaluation of glass formulations using glass formulation computer simulation program, the calculated glass formulations should be verified through experiments on a laboratory scale for more meticulous development of glass formulations. For the follow-up development of glass formulations, several glass formulations are planned to be developed. The candidate glasses for treatment of ash and ion exchange resin were melted and fabricated using reagents, respectively. The chemicals were weighed out to produce the desired batch compositions and mixed thoroughly and then put into clay crucibles for melting. Next, the crucibles were introduced into an electric furnace at 1,150 deg. C in the ambient atmosphere and pressure with occasional stirring by a quartz rod. A hold time of 1 hour was introduced to promote homogenization. Finally, the melted material was poured on a graphite plate to be rapidly cooled. The viscosities of all fabricated glasses were in the desired range. After rapid cooling, the micro-structure of the glasses was analyzed using the SEM. They exhibited amorphous structure with good homogeneity. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

Toward a scalable robust security-constrained optimal power flow using a proximal projection bundle method

Robust security-constrained optimal power flow (rSCOPF) aims to find the worst-case contingencies of alternating current optimal power flow (ACOPF) in power systems. With the rise of GPU architectures on the upcoming supercomputer architectures, optimization algorithms that rely on sparse linear algebra and indefinite linear systems are becoming increasingly hard to solve efficiently (e.g. interior-point method). To address this we revisit a maximin optimization formulation of the rSCOPF and the single-level mixed-integer semidefinite programming (MISDP) reformulation, which is obtained by taking the Lagrangian relaxation of the inner minimization ACOPF problem. In this paper, we focus on the development of a proximal projection bundle method (PPBM) for solving continuous relaxation node subproblems of the MISDP problem, based primarily on the well-known alternating direction method of multipliers. Cutting planes reminiscent of bundle method ideas are also applied in coordination with updates of the proximal parameter. The cutting-plane method can generate a large number of linear inequalities, leading to a large scale but decomposable quadratic programming (QP) subproblem that is amenable to GPUs. We present the numerical results on the IEEE 30, 57, 118, and 300-bus systems by using our PBMM method. We discuss the main computational bottleneck of our method, which is the time taken to solve each iteration of a QP subproblem instance of the PPBM, and how GPU architectures can accelerate this solution process.

bundle method↗
DOE OSTI2022

Towards Digital and Performance-Based Supervisory HVAC Control Delivery

Upgrading supervisory HVAC control in commercial buildings is one of the most attractive decarbonization tools at our disposal. Modern controls are software programs and can in theory be deployed at scale and with a low up-front carbon "pulse". In practice, however, control delivery is a disjointed and inefficient process, dominated by manual handoffs of imprecise English language documents. A particularly high barrier exists between control implementation and building energy modeling (BEM) which results in control sequences typically not being tested for correctness or performance before implementation. Together with industry partners, DOE and the national labs are developing an ecosystem of tools and standards that can support fully digital performance-based control delivery workflows. This paper describes this ecosystem, which consists of three mutually supportive efforts. Semantic models of buildings and their systems enable automatic configuration and installation of control software. Platform-neutral control descriptions separate control algorithms from control platforms and enable the creation of libraries of reference control implementations. Dynamic whole-building energy-control simulation that can execute physically realistic control sequences makes it possible to test and evaluate the performance of control sequences and then directly compile them for installation and execution in control systems. In addition to digitizing and streamlining project-level control delivery, these standards and related software support benchmarking of control algorithms, both rule-based and optimization-based, and help to both advance the state of the art and to implement ratings and programs that encourage the adoption of high-performance control.

building controls↗
DOE OSTI2023

CrysFieldExplorer : rapid optimization of the crystal field Hamiltonian

A new approach to the fast optimization of crystal electric field (CEF) parameters to fit experimental data is presented. This approach is implemented in a lightweight Python-based program, CrysFieldExplorer. The main novelty of the method is the development of a unique loss function, referred to as the spectrum characteristic loss (L Spectrum ), which is based on the characteristic polynomial of the Hamiltonian matrix. Particle swarm optimization and a covariance matrix adaptation evolution strategy are used to find the minimum of the total loss function. It is demonstrated that CrysFieldExplorer can perform direct fitting of CEF parameters to any experimental data such as a neutron spectrum, susceptibility or magnetization measurements etc. CrysFieldExplorer can handle a large number of non-zero CEF parameters and reveal multiple local and global minimum solutions. Crystal field theory, the loss function, and the implementation and limitations of the program are discussed within the context of two examples.

42 ENGINEERING↗