Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “advanced modelling and simulation”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 721 records · Page 40

Two-Dimensional Silk Crystal Films as Matrix Layer for High-Performance Microelectronics

This study explores a bio-inspired approach for memristive devices by combining Keggin-type polyoxometalates (POMs)-[SiW 12 O 40 ] 4 (POM-T) and [PW 12 O 40 ] 3 (POM-P), with silk fibroin (SF) to create 2D SF–POM layers on highly ordered pyrolytic graphite (HOPG) as resistive switching layers for memristors. We propose that the ordered SF layer template 0D POMs facilitate the formation of conductive filaments, thereby enhancing the variability of the manufactured memristors. AFM analysis revealed that both SF and SF–POM layers shared similar morphologies, while SF–POM–T formed larger aggregates, likely due to the stronger acidity of POM-T, which probably caused SF to aggregate and alter its secondary structure. Scanning Kelvin probe microscopy (SKPM) revealed that POMs reduced the contact potential difference of HOPG, resulting in lower work functions. Compared to an SF device, the SF–POM–P device showed improved memristive behavior, with a larger current gap and good repeatability over multiple sweeps; whereas the SF–POM–T device did not exhibit memristor activity, likely due to acidity-induced disruption of the SF template’s order and CF formation. More importantly, SF–POM–P devices also demonstrated programmable memristive states. Finally, combining simulation-driven memristor modeling, we showcase a co-design workflow for advancing bioinspired memristors through new materials design, synthesis, and device modeling and development.

36 MATERIALS SCIENCE↗

Estimating Drizzle Parameters by Aircraft Sampling

In-cloud supersaturation is calculated from aircraft derived measurements of the in-cloud vertical gradient of liquid water content, vertical velocity, the pt and 3 rd cloud droplet radius moments and a parameter related to the heat and mass transport during condensation and evaporation of cloud droplets. The aircraft data where taken during the VOCALS 2008 study in marine stratocumulus clouds off the coast of Chile. Approximately 16000 discrete samples, 2.5 meter in length, were used in the present analysis of in-cloud supersaturation and its variability, both of which are indicative of turbulent processes within the cloud and their significant impact on drizzle formation. Two additional drizzle parameters, the eddy persistence time and the variance of fluctuations in in-cloud droplet growth rate were also estimated from this data set. These results will help to constrain parameterizations of underlying turbulent microphysical processes of clouds and thereby advance the future development of warm cloud and precipitation models for climate simulation.

54 ENVIRONMENTAL SCIENCES↗

Operational Probabilistic Tools for Solar Uncertainty (OPTSUN) (Final Project Report for DOE Solar Forecasting II Project)

Increasing levels of solar PV can challenge system operations and may require novel methods to operate the power system reliably and efficiently. Power system operating plans generally use deterministic forecasts, in which the variable energy resources are represented by the expected value for each interval of the decision horizon. Probabilistic forecasts are relatively new but have the potential to address the shortfalls of deterministic forecasts. However, understanding how best to use such forecasts is still a key gap in industry and was the focus of this project. The project had three workstreams. In a forecasting workstream, improvements were made to baseline probabilistic forecasts using a number of new approaches such as machine learning methods and improved input data. In a design workstream, advanced simulation tools used these forecasts to investigate newly proposed reserve determination methods. Lastly, in a demonstration workstream a scheduling management platform (SMP) was developed to leverage probabilistic forecasts in a modular and customizable manner. In order to study the benefits that could be accrued, the project team collaborated with three utility partners (Duke Energy, Southern Company and Hawaiian Electric) to deliver improved probabilistic forecasts for each region and to model each region in case studies using advanced production cost modeling tools. Different methods to determine operating reserve requirements from probabilistic forecasts were developed, simulated, and tested across each region. The benefits of using these newly proposed methods varied by utility, but, in general, using probabilistic forecasts as well as historical data to set the reserve requirements seems to improve reliability related results, with less risk of reserve or supply shortfalls. The cost implications were not always straightforward; in some cases the new methods could show a reduction in expected operating costs, but often the increase in reserves associated with better risk mitigation using probabilistic forecasts could result in an increase in operating costs in the simulations. The SMP tool was developed to process probabilistic forecasts from their initial receipt through to scheduling decisions. This open-source tool consists of several modules for scenario development, reserve requirements calculation, and visualization. The SMP tool was demonstrated to a wide range of operators and stakeholders at all three utilities and further improved based on their feedback. The tool will be available on www.epri.com/optsun. The proposed probabilistic information-based reserve determination approaches have the potential to be implemented by different regions to ensure an economic and reliable power system operation on power systems integrating increasing levels of variable renewable resources. The innovative yet practical methods developed in this project demonstrated tangible benefits from using probabilistic forecasts beyond just study-based assessments to include three unique balancing areas. The demonstrated benefits across the multiple utility environments, are expected to provide system operators in all regions the confidence required and a platform to adopt the new forecasting and operating methods.

14 SOLAR ENERGY↗

Towards Next-Generation Urban Decision Support Systems through AI-Powered Construction of Scientific Ontology Using Large Language Models—A Case in Optimizing Intermodal Freight Transportation

The incorporation of Artificial Intelligence (AI) models into various optimization systems is on the rise. However, addressing complex urban and environmental management challenges often demands deep expertise in domain science and informatics. This expertise is essential for deriving data and simulation-driven insights that support informed decision-making. In this context, we investigate the potential of leveraging the pre-trained Large Language Models (LLMs) to create knowledge representations for supporting operations research. By adopting ChatGPT-4 API as the reasoning core, we outline an applied workflow that encompasses natural language processing, Methontology-based prompt tuning, and Generative Pre-trained Transformer (GPT), to automate the construction of scenario-based ontologies using existing research articles and technical manuals of urban datasets and simulations. From these ontologies, knowledge graphs can be derived using widely adopted formats and protocols, guiding various tasks towards data-informed decision support. The performance of our methodology is evaluated through a comparative analysis that contrasts our AI-generated ontology with the widely recognized pizza ontology, commonly used in tutorials for popular ontology software. We conclude with a real-world case study on optimizing the complex system of multi-modal freight transportation. Our approach advances urban decision support systems by enhancing data and metadata modeling, improving data integration and simulation coupling, and guiding the development of decision support strategies and essential software components.

96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗

AGGREGATE: dAta-driven modelinG preservinG contRollable dEr for outaGe mAnagemenT and rEsiliency (Report for Task 13: Functional Specification Report(Deliverable D9))

This report provides functional specification for the AGGREGATE project and associated modules/ tools being developed for outage management and restoration with the Distributed Energy Resources (DERs). This report also provide initial validation of the developed modules and performance metrics. The AGGREGATE team at this stage has been collaborating with General Electric (GE) and Seattle City Light (SCL) to move forward from offline validation to online validation using commercial advanced distribution management system (ADMS). Hence, the functional specifications documents, which outline the requirement of various modules, is provided to address the integration of the modules, including 1) real-time model update and aggregation tools module, 2) observability and controllability metric module, 3) fault location solution service restoration module, 4) transmission-distribution co-simulation module, and 5) advanced distribution management system module. integration of different AGGREGATE modules and functional specification provides the foundation for online multi-scenario testing using SCL system model.

42 ENGINEERING↗

Understanding Dynamics and Thermodynamics of ENSO and Its Complexity Simulated by E3SM and Other Climate Models

Despite the seeming success of most state-of-the-art climate models in simulating the El Niño-Southern Oscillation (ENSO), there is strong evidence that models achieve realistic levels of ENSO activity do so often for wrong reasons. This is owing to an often occurred near cancelation of large errors in terms of contributions to ENSO growth rate from coupled dynamic and thermodynamic feedback processes. Climate models remain deficient in simulating the observed ENSO’s spatial and temporal complexity that involves interplays of coupled dynamic and thermodynamic feedbacks, interactions across multiple scales, nonlinear processes in the tropical atmosphere and ocean system, biases in mean sate and physical processes, and influences external to equatorial Pacific coupled ENSO dynamics. Our proposed research aims at advancing predictive and process-level understandings of ENSO simulated in E3SM and other climate models under current and future climate conditions with two main objectives: (i) better understanding the aforementioned broad range interactive processes and sources that control fundamental properties of ENSO in E3SM and CIMP6 outputs as well as in observational (reanalysis) data sets, using a hierarchical of coupled dynamical frameworks consisting of theoretical analysis, intermediate complexity modeling, and coupled dynamic diagnostics; (ii) to use this understanding to explore pathways towards improving E3SM’s capability of simulating ENSO and its complexity. More specifically, we will focus on four main thrusts of research: (1) ENSO’s dynamic and thermodynamic feedbacks; (2) the across-scale interactions of ENSO with annual cycle and MJO/WWB/TIW (Madden Julian Oscillation/Westerly Wind Burst/Tropical Instability Wave) activity; (3) key nonlinear processes of ENSO involving atmospheric convective thresholds, nonlinear ocean dynamic heating, and thermocline outcropping; and (4) the impacts of climate mean-state biases/changes and perturbed physical processes on simulated ENSO and its complexity.

54 ENVIRONMENTAL SCIENCES↗

FY2019 Analysis Program Annual Progress Report

The VTO Analysis Program supports mission-critical technology, economic, and interdisciplinary analyses to assist in prioritizing VTO technology investments and to inform research portfolio planning. These efforts provide essential vehicle and market data, modeling and simulation, and integrated and applied analyses, using the unique capabilities, analytical tools, and expertise resident in the national laboratory system.

33 ADVANCED PROPULSION SYSTEMS↗

Advancing material modeling in hydrocodes using a concurrent finite-element and molecular dynamics multiscale framework

We present a multiscale simulation framework that couples the finite-element method with molecular dynamics. Bypassing traditional equations of state (EOS) by using in-line atomistic simulations, the method offers the advantage of incorporating detailed microscale physics not easily represented with coarse-grained models. Coupling consistency with the continuum code is ensured through the use of lifting and restriction operators, in line with heterogeneous multiscale methods. The concurrent continuum-atomistic framework is validated through comparison with experimental results and conventional EOS models, and demonstrated in a shock-driven hydrodynamic flow simulation under extreme conditions. We further evaluate the framework's usability by comparing it to state-of-the-art EOS models of deuterium. A computational performance study reveals that the atomistic EOS evaluation is a feasible alternative to conventional approaches, and demonstrates a weak scaling of 99% efficiency. These results highlight the framework's potential for large-scale multiscale modeling across a broad range of materials and conditions.

Computer science↗

Open‐Source Anaerobic Digestion Modeling Platform, Anaerobic Digestion Model No. 1 Fast (ADM1F)

An open‐source modeling platform, called Anaerobic Digestion Model No. 1 Fast (ADM1F), is introduced to achieve fast and numerically stable simulations of anaerobic digestion processes. ADM1F is compatible with an iPython interface to facilitate model configuration, simulation, data analysis, and visualization. Faster simulations and more stable results are accomplished by implementing an advanced open‐source library of numerical methods called Portable Extensive Toolkit for Scientific Computation (PETSc) to solve the ADM1 system of equations. Leveraging PETSc, ADM1F can consistently complete a steady‐state simulation under 0.2 s, over 99% faster than a benchmark ADM1 model implemented with MATLAB while achieving agreement of model outputs within 1% of those obtained with the benchmark model. For dynamic simulations, however, ADM1F has a computational speed advantage only when the influent characteristics update more frequently than every 4 h. The ability of ADM1F to be useful as a tool to study anaerobic digestion systems is demonstrated through two example implementations of ADM1F: (1) a two‐phase co‐digestion scenario evaluating the impact of the organic loading rate and the substrate composition on reactor performance and stability, and (2) a conventional digester scenario assessing the effectiveness of recovery strategies after disruptions that led to instability. These examples demonstrate how the high simulation speed and the convenience of the iPython interface allow ADM1F to complete complex analyses within minutes, much faster than computational strategies currently reported in the literature.

anaerobic co-digestion↗

Heterogeneous Computing

To leverage the increasing heterogeneity in modern computing resources, Geant4 incorporates advanced software tools and a task-based framework (G4Tasking) that enables efficient parallelism at event, sub-event, and track levels. Ongoing R&D efforts focus on integrating GPUs into high-energy physics (HEP) simulations, including optical photon simulation with Opticks/NVIDIA OptiX, offloading electromagnetic particle transport using G4HepEM/AdePT and Celeritas, and employing advanced surface-based geometry models such as VecGeom2.0 and ORANGE. As Geant4 continues evolving toward high-performance computing (HPC) and heterogeneous architectures, it remains a key tool for large-scale simulations in HEP and beyond.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Interface capturing simulations of bubble population effects in PWR subchannels

As the computational power of high-performance computing (HPC) facilities grows, so too does the feasibility of using first principle based simulation to study turbulent two-phase flows within complex pressurized water reactor (PWR) geometries. Direct numerical simulation (DNS), integrated with an interface capturing method, allows for the collection of high-fidelity numerical data using advanced analysis techniques. The research presented here employs the massively parallel, finite-element based, unstructured mesh code, PHASTA, to simulate a set of two-phase bubbly flows through PWR subchannel geometries including auxiliary structures (spacer grids and mixing vanes). The main objective of the presented work is to analyze bubble dynamics and turbulence interactions at varying bubble concentrations to support the development of advanced two-phase flow closure models. Turbulent two-phase flows in PWR subchannels were simulated at hydraulic Reynolds numbers of 81,000 with bubble concentrations of 3%–15% by gas volume fraction (768–3928 resolved bubbles, respectively) and compared against a 1% void fraction case (262 bubbles) that had been previously simulated. The finite element mesh utilized for the study at higher bubble concentrations was composed of 1.55 billion elements, compared to the previous study which employed 1.11 billion elements, ensuring all turbulence scales and individual bubbles within the flow are fully resolved. For each case, the resolved initial bubble size was 0.65 mm in diameter (resolved with 25 grid points across the diameter). The simulations were analyzed to find flow features such as the mean velocity profile, bubble relative velocity and the effect of the bubbles on the turbulent conditions.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Stress Birth and Death: Disruptive Computational Mechanics and Novel Diagnostics for Fluid-to-Solid Transitions

Many materials of interest to Sandia transition from fluid to solid or have regions of both phases coexisting simultaneously. Currently there are, unfortunately, no material models that can accurately predict this material response. This is relevant to applications that "birth stress" related to geoscience, nuclear safety, manufacturing, energy production and bioscience. Accurately capturing solidification and residual stress enables fully predictive simulations of the evolving front shape or final product. Accurately resolving flow of proppants or blood could reduce environmental impact or lead to better treatments for heart attacks, thrombosis, or aneurism. We will address a science question in this proposal: When does residual stress develop during the critical transition from liquid to solid and how does it affect material deformation? Our hypothesis is that these early phases of stress development are critical to predictive simulation of material performance, net shape, and aging. In this project, we use advanced constitutive models with yield stress to represent both fluid and solid behavior simultaneously. The report provides an abbreviated description of the results from our LDRD "Stress Birth and Death: Disruptive Computational Mechanics and Novel Diagnostics for Fluid-to-Solid Transitions," since we have written four papers that document the work in detail and which we reference. We give highlights of the work and describe the gravitationally driven flow visualization experiment on a model yield stress fluid, Carbopol, at various concentrations and flow rates. We were able to collapse the data on a single master curve by showing it was self-similar. We also describe the Carbopol rheology and the constitutive equations of interest including the Bingham-Carreau-Yasuda model, the Saramito model, and the HB-Saramito model including parameter estimation for the shear and oscillatory rheology. We present several computational models including the 3D moving mesh simulations of both the Saramito models and Bingham-Carreau-Yasuda (BCY) model. We also show results from the BCY model using a 3D level set method and two different ways of handling reduced order Hele-Shaw modeling for generalized Newtonian fluids. We present some first ever two-dimensional results for the modified Jeffries Kamani-Donley-Rogers constitutive equation developed during this project. We include some recent results with a successful Saramito-level set coupling that allows us to tackle problems with complex geometries like mold filling in a thin gap with an obstacle, without the need for remeshing or remapping. We report on some experiments for curing systems where fluorescent particles are used to track material flow. These experiments were carried out in an oven on Sylgard 184 as a model polymerizing system. We conclude the report with a summary of accomplishments and some thoughts on follow-on work.

36 MATERIALS SCIENCE↗

Development and Validation of MALAMUTE model for Electric Field Assisted Sintering of Structural Materials

Fusion power plant designs feature extreme material performance requirements for structural material candidates. In addition to conventional alloys, more advanced composites and oxide dispersion strengthened (ODS) alloys are being explored, however, achieving the desired microstructures to maximize performance using traditional manufacturing methods can be challenging. The advanced manufacturing (AM) electric field-assisted sintering (EFAS) technique offers improved control over the final microstructure through higher heating and cooling rates and moderate pressures. Modeling and simulation tools show promise in elucidating the process-structure-property-performance (PSPP) correlation for AM-produced parts, including the EFAS process. An inherently multiscale process, the EFAS technique aligns well with the multiscale modeling capability of the open-source Multiphysics Object-Oriented Simulation Environment (MOOSE)[cite]. We present here an electro-thermo-mechanical approach to modeling the EFAS process using the MOOSE Application Library for Advanced Manufacturing UTilitiEs (MALAMUTE) code. Prediction of the field and gradient distributions across the EFAS tooling is required to accurately describe the conditions for the lower-scale microstructural evolution models. In this work we present the MALAMUTE model developed to predict the electrical potential, temperature, and mechanical stress distribution across the EFAS graphite tooling and part at the larger engineering-scale. Validation of the MALAMUTE engineering-scale model is completed using data from experimental densification and pre-densified runs of iron powder via EFAS at 1000oC. These runs were conducted using a Thermal Technology DCS-5 EFAS system. Data collected during the experiment runs include the direct current (DC) supplied to the graphite tooling, the temperature of the graphite tooling as measured with a pyrometer, and the force applied to the top of the graphite tooling stack, and the data were recorded every 10 seconds. Our validation approach used the current and force data from the EFAS run as boundary condition inputs to the MAMALUTE simulation; the temperature data were used to evaluate the MALAMUTE EFAS model prediction. Results of the MALAMUTE simulations are employed to connect the external pyrometer temperature measurement to the temperature profile across the part undergoing consolidation. We investigate the impact of material property variation and mesh deformation on the temperature profile as predicted by MALAMUTE. We conclude by highlighting projects where the MALAMUTE EFAS modeling and simulation capabilities will be used to assist experimental design.

36 - MATERIALS SCIENCE↗

Beyond Magic Barrels: Digital manufacturing for crystallization, process development and optimization of explosive materials: Part II Resveratrol Exemplar

This SAND report summarizes work supported by an Engineering Sciences Research Foundation (ESRF) Lab Directed Research and Development (LDRD) project entitled “Beyond Magic Barrels: Digital manufacturing for crystallization, process development and optimization of explosive materials.” This SAND report is written in two parts with Part 1 discusses recrystallization of our explosive exemplar and Part 2 summarizing our work with recrystallization of resveratrol. We have studied resveratrol recrystallization with a multiscale approach combining experiments, modeling and simulation. At the single crystal scale, microscopy experiments illuminate crystal time-dependent growth rates using advanced image analysis. Bench scale experiments were carried out to look at growth of multiple particles in a small reactor creating thousands of particles and analyzing the results with microscopy and μCT. For the modeling we combine kinetic Monte Carlo (kMC) models with subscale information from density functional theory (DFT) or molecular dynamics. This work is discussed in Part 1 and can also be found in a paper from the project discussing a coarse-grained kMC model specifically developed for resveratrol. For well-mixed systems, we have population balance equations (PBE) linked with species mass conservation forming a set of ordinary differential equations that can be solved quickly. For more complicated geometries, such as the vat crystallization used throughout the complex, a coupled computational fluid dynamic (CFD)/PBE method was developed to account for gradients in temperature and concentration and differences in crystallization rates throughout the domain. These simulations are more complex and require high performance computing. We present results for two cases: 5% seed fast cool with parameters fit to the well-mixed case and 5% seed slow cool using the same parameters. We show reasonable agreement with experiments though are particles are significantly larger than the experiments.

36 MATERIALS SCIENCE↗

Simulation of natural circulation cartridge loop experiments and application to molten salt reactors

This work uses the TRAC/RELAP Advanced Computational Engine (TRACE) thermal hydraulics (TH) code to model natural circulation cartridge loop experiments previously conducted at Oak Ridge National Laboratory (ORNL) using water and compares the simulated and experimental results. TRACE is also used to characterize natural circulation in the cartridge loop vehicle using FLiNaK as the working fluid. The experimental vehicle is a buoyancy-aided, annular cartridge loop, referred to as a thermosyphon, and is designed to aid in qualifying liquid–fueled and/or liquid–cooled irradiation experiments for the Versatile Test Reactor (VTR), which is currently being designed in the United States. Out-of-pile water experiments have been conducted using the cartridge and the Thermosyphon Test Loop facility at ORNL, and future experiments are anticipated that would use other molten salt surrogates as the working fluid, followed by eventual insertion of a similar cartridge into VTR. Additionally, this work aims to determine how well TRACE can replicate the natural convection conditions that were observed experimentally; this serves as an initial step for validating the modeling tool for design and safety calculations to support future irradiation experiments in VTR. Initial predictions of potential experiments were made using FLiNaK as the natural circulation fluid to demonstrate the relevance of the cartridge design to molten salt reactors (MSRs). Results from this study indicate that TRACE can accurately capture natural convection phenomena in the thermosyphon and that several design changes to the current cartridge vehicle are necessary to achieve hydraulic conditions similar to those expected in MSRs.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Estimating Uncertainty in Simulated ENSO Statistics

Abstract Large ensembles of model simulations are frequently used to reduce the impact of internal variability when evaluating climate models and assessing climate change induced trends. However, the optimal number of ensemble members required to distinguish model biases and climate change signals from internal variability varies across models and metrics. Here we analyze the mean, variance and skewness of precipitation and sea surface temperature in the eastern equatorial Pacific region often used to describe the El Niño–Southern Oscillation (ENSO), obtained from large ensembles of Coupled model intercomparison project phase 6 climate simulations. Leveraging established statistical theory, we develop and assess equations to estimate, a priori, the ensemble size or simulation length required to limit sampling‐based uncertainties in ENSO statistics to within a desired tolerance. Our results confirm that the uncertainty of these statistics decreases with the square root of the time series length and/or ensemble size. Moreover, we demonstrate that uncertainties of these statistics are generally comparable when computed using either pre‐industrial control or historical runs. This suggests that pre‐industrial runs can sometimes be used to estimate the expected uncertainty of statistics computed from an existing historical member or ensemble, and the number of simulation years (run duration and/or ensemble size) required to adequately characterize the statistic. This advance allows us to use existing simulations (e.g., control runs that are performed during model development) to design ensembles that can sufficiently limit diagnostic uncertainties arising from simulated internal variability. These results may well be applicable to variables and regions beyond ENSO.

54 ENVIRONMENTAL SCIENCES↗

A review of thermo-hydro-mechanical modeling of coupled processes in fractured rock: From continuum to discontinuum perspective

Coupled thermo-hydro-mechanical (THM) processes in fractured rock are playing a crucial role in geoscience and geoengineering applications. Diverse and conceptually distinct approaches have emerged over the past decades in both continuum and discontinuum perspectives leading to significant progress in their comprehending and modeling. This review paper offers an integrated perspective on existing modeling methodologies providing guidance for model selection based on the initial and boundary conditions. By comparing various models, one can better assess the uncertainties in predictions, particularly those related to the conceptual models. The review explores how these methodologies have significantly enhanced the fundamental understanding of how fractures respond to fluid injection and production, and improved predictive capabilities pertaining to coupled processes within fractured systems. It emphasizes the importance of utilizing advanced computational technologies and thoroughly considering fundamental theories and principles established through past experimental evidence and practical experience. The selection and calibration of model parameters should be based on typical ranges and applied to the specific conditions of applications. The challenges arising from inherent heterogeneity and uncertainties, nonlinear THM coupled processes, scale dependence, and computational limitations in representing field scale fractures are discussed. Realizing potential advances on computational capacity calls for methodical conceptualization, mathematical modeling, selection of numerical solution strategies, implementation, and calibration to foster simulation outcomes that intricately reflect the nuanced complexities of geological phenomena. Future research efforts should focus on innovative approaches to tackle the hurdles and advance the state-of-the-art in this critical field of study.

Coupling scheme↗