Simulation Code Research Articles

Self-consistent calculation of the optical emission spectrum of an argon capacitively coupled plasma based on the coupling of particle simulation with a collisional-radiative model

We report the development of a computational framework for the calculation of the optical emission spectrum of a low-pressure argon capacitively coupled plasma (CCP), which is based on the coupling of a particle-in-cell/Monte Carlo collision simulation code with a diffusion-reaction-radiation code for Ar I excited levels. In this framework, the particle simulation provides the rates of the direct and stepwise electron-impact excitation and electron-impact de-excitation for 30 excited levels, as well as the rates of electron-impact direct and stepwise ionization. These rates are used in the solutions of the diffusion equations of the excited species in the second code, along with the radiative rates for a high number of Ar-I transitions. The calculations also consider pooling ionization, quenching reactions, and radial diffusion losses. The electron energy distribution function and the population densities of the 30 excited atomic levels are computed self-consistently. The calculations then provide the emission intensities that reproduce reasonably well the experimentally measured optical emission spectrum of a symmetric CCP source operated at 13.56 MHz with 300 V peak-to-peak voltage, in the 2–100 Pa pressure range. The accuracy of the approach appears to be limited by the one-dimensional nature of the model, the treatment of the radiation trapping through the use of escape factors, and the effects of radiative cascades from higher excited levels not taken into account in the model.

Verification, validation, and uncertainty quantification for electron-density diagnostics of polarimeter/interferometer system on experimental advanced superconducting tokamak

The verification, validation, and uncertainty quantification (VVUQ) analysis is a systematic method for identifying and quantifying uncertainties in complex engineering projects. This method has been used by the International Atomic Energy Agency as a critical assessment method in the field of high-precision plasma diagnostics in tokamaks. Starting from the basic theory to the final results, it assesses every process to obtain the uncertainties, system confidence level, and similarity between the model and experimental assessments. In this study, we evaluated the electron-density diagnosis of the polarimeter/interferometer system on an experimental advanced superconducting tokamak using a cylindrical simulation model. This study applied the VVUQ to an entire plasma diagnostic system for the first time, coupled with the statistical concepts of confidence and similarity. Through the VVUQ process, the uncertainty from the simulation code, diagnostic code, and engineering errors were identified, quantified, and minimized.

LAPS: An MPI-parallelized 3D pseudo-spectral Hall-MHD simulation code incorporating the expanding box model

Numerical simulations have been an increasingly important tool in space physics. Here, we introduce an open-source three-dimensional compressible Hall-Magnetohydrodynamic (MHD) simulation code LAPS (UCLA-Pseudo-Spectral, https://github.com/chenshihelio/LAPS). The code adopts a pseudo-spectral method based on Fourier Transform to evaluate spatial derivatives, and third-order explicit Runge-Kutta method for time advancement. It is parallelized using Message-Passing-Interface (MPI) with a “pencil” parallelization strategy and has very high scalability. The Expanding-Box-Model is implemented to incorporate spherical expansion effects of the solar wind. We carry out test simulations based on four classic (Hall)-MHD processes, namely, 1) incompressible Hall-MHD waves, 2) incompressible tearing mode instability, 3) Orszag-Tang vortex, and 4) parametric decay instability. The test results agree perfectly with theory predictions and results of previous studies. Given all its features, LAPS is a powerful tool for large-scale simulations of solar wind turbulence as well as other MHD and Hall-MHD processes happening in space.

Macroscopic and mesoscopic mechanism of hydration instability of the rock-grout coupled structure

In order to investigate the macroscopic and mesoscopic mechanism of hydration instability of rock-grout structure under the influence of moisture content, a direct shear test combined with particle flow code (PFC) simulation was conducted subject to various moisture content levels and normal stresses. The results show that a higher moisture content would compromise the load bearing capacity of soft rock anchorage structures by deteriorating the structural integrity of the surrounding rock and the bonding effect between the anchorage interfaces. The load bearing capacity of the surrounding rock is also rapidly reduced. The rock-grout structure has four main shear damage modes, which are influenced by both moisture content and normal stress. When the saturated moisture content is reached, the anchorage structure has lost its bearing capacity, and the rock is muddied and subsequently debonded from the bolt. The energy required to break the internal adhesion of the rock-grout structure under the effect of hydration is greatly reduced, resulting in easy decoupling and dispersion between the rock skeleton particles. In turn, the rock surface particles bonded by the anchor agent are separated from the deeper particles, resulting in the failure of the bonding surface and weakening the coupling effect between the anchor and the surrounding rock. According to the test results, the control measures for surrounding rock of muddy roadway are put forward.

Code Simulator with Real-Time Conferencing and Considerable Users

Abstract: The Multiuser Live Text Editor represents a dynamic platform fostering collaborative coding endeavors, enabling users to engage in real-time interaction while collectively crafting code. Boasting compatibility with prominent programming languages such as C++, Java, and Python, this innovative tool is founded upon the notion of adaptive functionality, a cornerstone of its shared editing capabilities. At its core lies pair programming, an agile methodology originating from Extreme Programming (XP), wherein two developers synergistically collaborate on a single computing environment. Tasked with jointly conceiving, implementing, and validating user stories, these pairs operate in tandem, leveraging their complementary skills to achieve shared objectives. Notably, this collaborative process thrives on the diversity of the paired developers' systems, with each individual allocated equal time at the keyboard.

NeuSIM4: A comprehensive GEANT4 based neutron simulation code

A new neutron SIMulation program based on the versatile GEANT4 toolkit, neuSIM4, has been developed to describe interactions of neutrons in the NE213 liquid scintillator from 0.1 to 3000 MeV. neuSIM4 is designed to accommodate complicated modern detector geometry setups with multiple scintillator detectors, each of which can be outfitted with more than one photo-multiplier. To address a broad spectrum of neutron energies, two new neutron interaction physics models, KSCIN and NxQMD, have been implemented in GEANT4. For neutrons with energy below 110 MeV, we incorporate a total of eleven neutron induced reaction channels on hydrogen and carbon nuclei, including nine carbon inelastic reaction channels, into KSCIN. Beyond 110 MeV, we implement a neutron induced reaction model, NxQMD, in GEANT4. We use its results as reference to evaluate other neutron-interaction physics models in GEANT4. We find that results from an existing cascade physics model (INCL) in GEANT4 agree very well with the results from NxQMD, and results from both codes agree with new and existing light response data. To connect KSCIN to NxQMD or INCL, we introduce a transition region where the contribution of neuSIM4 linearly decreases with corresponding increased contributions from NxQMD or INCL. To demonstrate the application of the new code, we simulate the light response and performance of a 2 × 2 m2 neutron detector wall array consisting of 25 2m-long scintillation bars. We are able to compare the predicted light response functions to the shape of the experimental response functions and calculate the efficiency of the neutron detector array for neutron energies up to 200 MeV. These simulation results will be pivotal for understanding the performance of modern neutron arrays with intricate geometries, especially in the measurements of neutron energy spectra in heavy-ion reactions.

Bridging the gap between machine learning and particle accelerator physics with high-speed, differentiable simulations

Machine learning has emerged as a powerful solution to the modern challenges in accelerator physics. However, the limited availability of beam time, the computational cost of simulations, and the high dimensionality of optimization problems pose significant challenges in generating the required data for training state-of-the-art machine learning models. In this work, we introduce heetah, a yorch-based high-speed differentiable linear beam dynamics code. heetah enables the fast collection of large datasets by reducing computation times by multiple orders of magnitude and facilitates efficient gradient-based optimization for accelerator tuning and system identification. This positions heetah as a user-friendly, readily extensible tool that integrates seamlessly with widely adopted machine learning tools. We showcase the utility of heetah through five examples, including reinforcement learning training, gradient-based beamline tuning, gradient-based system identification, physics-informed Bayesian optimization priors, and modular neural network surrogate modeling of space charge effects. The use of such a high-speed differentiable simulation code will simplify the development of machine learning-based methods for particle accelerators and fast-track their integration into everyday operations of accelerator facilities. Published by the American Physical Society 2024

An extended Monte Carlo simulation code for modeling gas chromatography experiments with superheavy elements and their homologs

AbstractMonte Carlo simulations are commonly used to model the behavior of chemical species of the heaviest elements and their homologs in gas chromatography experiments. In this paper, we present an extension of the fundamental Monte Carlo simulation proposed by Zvara in 1985. While preserving the core functionality, our code features two enhancements: first, it allows simulating experiments in which a primary radioisotope decays into a daughter isotope belonging to a different element, hence exhibiting different chemical properties. Second, it allows modeling scenarios where conversion of an initial chemical species to a different one can occur at temperatures high enough to overcome an activation barrier, facilitating simulations of related physisorption and chemisorption processes. This Monte Carlo code is applicable to open tubular and rectangular chromatography columns.

A Geant4-based Monte Carlo X-ray imaging simulation platform

X-ray digital radiography plays a pivotal role in accessing the internal structure of objects. Nevertheless, key imaging parameters, such as source-to-target distance or number of projected images needed for three-dimensional construction, mostly rely on real-life trials thus increasing radiation exposure risks. This paper introduces a recently developed software platform known as GMAX (Geant4-based Monte Carlo Advanced X-ray) that helps addressing above issues from a simulation perspective. GMAX employs Geant4, a Monte Carlo simulation code at its core and facilitates high-fidelity X-ray imaging, requiring no prior user experience. Compared to CAD models that only reflect object's geometrical information, GMAX simulates how objects interact with photon and can accurately evaluate important imaging parameters, such as target object to detector distance. It also provides three-dimensional construction functionality for images and therefore could be used as an effective tool for X-ray non-destructive testing and inspection.

Feasibility of a Tungsten-181 HDR brachytherapy source: Analysis of isotope production and source dosimetry

BackgroundInterest in Intensity Modulated Brachytherapy (IMBT) for High Dose Rate Brachytherapy (HDR) treatments has steadily increased in recent years. However, intensity modulation is not best optimized for currently used HDR sources since they emit high energy photons. To that end, the focus on IMBT has moved to middle energy sources, such as Ytterbium-169; yet even Yb-169 emits some high energy photons at a low yield. We present an alternative isotope, Tungsten-181 (T1/2 = 121 days) that is interesting due to its complete lack of high energy photon emissions. (Eavg = 58.9 keV, Emed = 57.5 keV) making it potentially favorable as high dose rate brachytherapy source from both a medical physics and health physics perspective. PurposeThe purpose of this study was to determine the feasibility of using W-181 as an HDR brachytherapy source; in this study we focused on W-181's production, dosimetric properties, and intensity modulation capabilities. MethodsWe determined the isotope production kinetics, its Dose Rate Constant, Radial Dose Function, photon self-absorption, and the shielding intensity modulation capabilities for a W-181 pellet source geometry using the MCNP6.2 Computer Simulations Code. All simulations were performed using a personal computer running an AMD Ryzen 5 3600 6-Core Processor 3.59 GHz. The number of histories run for each study were selected to produce relative simulation convergence errors in the MCNP tally output of less than 2%.Dosimetric calculations were made using the MCNP6.2 computer simulations code and activation analyses were determined mathematically using a Catenary kinetics analysis (also known as a Bateman Analysis) of W-181 and Tantlum-182 production from the neutron activation of a pure Tungsten-180 stable target. Since W-181 emits middle energy photons and has a high density, we also assessed the effects of photon self-absorption within a tungsten pellet. ResultsFrom our analysis, we determined that a 3.5 mm long and 0.6 mm in diameter is feasible for clinical applications. Our activation analyses found that these pellets can achieve W-181 activities up to 7.9Ci and 13Ci using neutron fluence rates of 4E14 cm−2 s−1 and 1E15 cm−2 s−1 respectively, which then would provide a dose rate of 1.84 ± 0.01 cG y/Ci/min at a depth of 1 cm from the source. Using our resulting Monte Carlo simulated Dose Rate Constant of 1.24 ± 0.02 cGy h−1∙U−1, a W-181 source in this geometry would require a source activity upwards of 10Ci for use in HDR treatments. In the intensity modulation analysis, only 0.1 mm of gold shielding was found to reduce a pellet's absorbed dose by over 50% while 0.3 mm of gold shielding, which is thin enough to theoretically fit between an HDR pellet and the inner catheter wall, was found to reduce the pellet's absorbed dose by over 85%. ConclusionsWhile W-181 has a lower specific activity than Ir-192 and Yb-169, it shows great promise as an isotope for use in Intensity Modulated Brachytherapy due to its easily shielded photons. We therefore expect that W-181 may lend itself best for use as a multi-pellet configuration in IMBT.

Rapid iodine oxoacid nucleation enhanced by dimethylamine in broad marine regions

Abstract. Recent experiments have revealed a vital nucleation process of iodic acid (HIO3) and iodous acid (HIO2) under marine boundary layer conditions. However, HIO3–HIO2 nucleation may not effectively drive the observed rapid new particle formation (NPF) in certain coastal regions influenced by urban air masses. Dimethylamine (DMA) is a promising basic precursor to enhance nucleation considering its strong ability to stabilize acidic clusters and the wide distribution in marine atmosphere, while its role in HIO3–HIO2 nucleation remains unrevealed. Hence, a method combining quantum chemical calculations and Atmospheric Cluster Dynamics Code (ACDC) simulations was utilized to study the HIO3–HIO2–DMA nucleation process. We found that DMA can preferentially accept the proton from HIO3 as a basic precursor in the most stable configurations of HIO3–HIO2–DMA clusters. Kinetically, the participation of DMA in the cluster formation pathways of the iodine oxoacid system could be significant at the 10−1 to 1 pptv level of [DMA]. Furthermore, DMA can enhance the cluster formation rates of the HIO3–HIO2 system in marine and polar regions near DMA sources more than 103-fold. Compared to the classical nucleation mechanism, the HIO3–HIO2–DMA mechanism exhibits strong nucleation ability, worthy of consideration as a promising mechanism in marine and polar regions rich in amine sources. The newly proposed HIO3–HIO2–DMA ternary mechanism might provide an explanation for some missing fluxes of atmospheric iodine particles.

Strength Simulator Codes for Different Age Groups Considering Physiological Processes of Adaptation in Conditions of Strength Fitness

Topicality. Determination of optimal load parameters in fitness, based on age-related physiological features and adaptive changes of the neuromuscular system, is one of the most debated issues among leading scientists in this field. The research purpose was to develop models of code combinations for strength training of different age groups, considering physiological processes of human body adaptation to a stressful physical stimulus in the conditions of strength fitness. Methods. A comparative analysis of the research results on the effectiveness of using the optimal combination between the parameters of an external physical stimulus and the physiological features of the human body adaptive reactions has been used over the research. The results. It was established that in the process of developing code combinations for different age groups` strength training, the nature of the physiological reactions of their neuromuscular system to a stressful stimulus depend on the features of the load regime and the structure of the exercise program. For adolescence, considering the peculiarities of the physiological process of adaptation, it is used of moderate-intensity activity in combination with a complex of isolation exercises that promotes the processes of intra-muscular and inter-muscular coordination. For youth, in the process of developing code combinations aimed at the development of the main types of strength, the entire range of load modes is actively used. Particular attention is paid to stimuli that contribute to increasing the number of active (FF) motor units. In adulthood, especially in the second period, the content of code combinations to increase strength capabilities changes significantly. In the vast majority, this applies to the parameters of the intensity of load modes, the use of which will selectively affect the hypertrophy of a certain type of muscle fibers within intermuscular coordination. For the elderly, in the process of developing code combinations for strength training, priority is given to the selective activity of agonists during moderate-intensity isolated exercises. Findings. Strength Simulator codes considering physiological processes of the neuromuscular system adaptation to a stressful physical stimulus, is one of the innovative mechanisms for improving the training program of different age groups in the conditions of strength fitness.

Parameterization of H2SO4 and organic contributions to volatile PM in aircraft plumes at ground idle.

Volatile Particulate Matter (vPM) emissions are challenging to measure and quantify, since they are not present in the condensed form at the engine exit plane and they evolve to first form in the aircraft plume and then continue to grow and change as they mix and dilute in the ambient atmosphere. To better understand the issues associated with the initial formation and growth of vPM, a modeling study has been undertaken to examine several key parameters that affect the formation and properties of the vPM that is created in the initial cooling and dilution of the aircraft exhaust. A modeling tool (Aerosol Dynamic Simulation Code, ADSC) that was developed and enhanced over a series of past research projects supported by NASA, DoD's SERDP/ESTCP, and FAA (Wong et al. 2010, 2014, 2015) was used to perform a parametric analysis of vPM. The parameters of fuel sulfur content (FSC), emitted condensable hydrocarbon (HC) concentrations, and the species profile of the HCs were used to construct a computational matrix that framed a wide range of expected parameter values. This computational matrix was executed for two representative commercial aircraft engines at ground idle and results were obtained for distances of 250 m and 1000 m downstream. From prior results, the most significant vPM emissions occur at the lowest power settings, so an engine power condition of 7% rated thrust was used. A primary goal of the parametric study is to develop an updated vPM modeling methodology and also to help interpret data collected in experimental campaigns. The parameterization proposed here allows the vPM emission composition and particle numbers to be estimated in greater detail than current methods. The aim is to provide additional understanding on how the vPM properties vary with fuel and engine parameters to increase the utility of vPM predictions.Implications: Volatile ParticulateMatter (vPM) is an important contribution to the total PM emitted by aviationengines. While vPM is not currently a part of engine emissions certificationregulations, vPM is used in aviation environmental impact assessments and forair quality modeling in and around airports. Current methods in use, such asFOA (Wayson et al. 2009), were developed before many recent advances inexperimental data acquisition and in understanding of vPM processes. Theparameterization proposed here allows the vPM emission composition and particlenumbers to be estimated in greater detail than current methods. These estimatescan be used to develop inventories and provide a better estimate of total PMemission for most aviation engines. Its use in international regulatory toolscan inform possible future regulatory actions regarding vPM.

Uncertainty quantification of the lattice Boltzmann method focussing on studies of human-scale vascular blood flow

Uncertainty quantification is becoming a key tool to ensure that numerical models can be sufficiently trusted to be used in domains such as medical device design. Demonstration of how input parameters impact the quantities of interest generated by any numerical model is essential to understanding the limits of its reliability. With the lattice Boltzmann method now a widely used approach for computational fluid dynamics, building greater understanding of its numerical uncertainty characteristics will support its further use in science and industry. In this study we apply an in-depth uncertainty quantification study of the lattice Boltzmann method in a canonical bifurcating geometry that is representative of the vascular junctions present in arterial and venous domains. These campaigns examine how quantities of interest—pressure and velocity along the central axes of the bifurcation—are influenced by the algorithmic parameters of the lattice Boltzmann method and the parameters controlling the values imposed at inlet velocity and outlet pressure boundary conditions. We also conduct a similar campaign on a set of personalised vessels to further illustrate the application of these techniques. Our work provides insights into how input parameters and boundary conditions impact the velocity and pressure distributions calculated in a simulation and can guide the choices of such values when applied to vascular studies of patient specific geometries. We observe that, from an algorithmic perspective, the number of time steps and the size of the grid spacing are the most influential parameters. When considering the influence of boundary conditions, we note that the magnitude of the inlet velocity and the mean pressure applied within sinusoidal pressure outlets have the greatest impact on output quantities of interest. We also observe that, when comparing the magnitude of variation imposed in the input parameters with that observed in the output quantities, this variability is particularly magnified when the input velocity is altered. This study also demonstrates how open-source toolkits for validation, verification and uncertainty quantification can be applied to numerical models deployed on high-performance computers without the need for modifying the simulation code itself. Such an ability is key to the more widespread adoption of the analysis of uncertainty in numerical models by significantly reducing the complexity of their execution and analysis.

Elastic overtaking collisions of large-amplitude ion-acoustic solitons

Overtaking collisions of large-amplitude solitons are investigated via fluid simulations for a plasma consisting of cold ions and Boltzmann-distributed electrons. To achieve this, a new fluid simulation code is presented. In addition, a novel approach to construct soliton initial conditions is developed. Using these ideas, initial conditions are combined that allows the simulation of overtaking collisions. It is shown that, in the small-amplitude regime, simulation results agree well with the two-soliton solution obtained from reductive perturbation theory. Interestingly, in the large amplitude regime, both the slow and fast solitons re-emerge after the collision with no significant change, showing that the collisions remain elastic. A comparison between reductive perturbation analysis and the simulations show that the only significant effect of higher order nonlinearities on overtaking collisions is a reduction in the magnitude of the phase shifts of both solitons.

Numerical simulations on loss of ICRF-heated NBI ions in EAST

The loss of ion cyclotron resonance frequencies (ICRF)-heated neutral beam injection ions in experimental advanced superconducting tokamak was numerically investigated by ORBIT code simulations. The effects of collisions and ripples on particle losses were taken into account, and the distributions of fast ions generated by different beams in combination with ICRF heating were calculated using the TRANSP code. Results showed that ICRF waves altered the orbital distributions of beam ions, causing an increase in trapped ions and fast ion losses. Additionally, for co-current injected beams, perpendicular injection resulted in higher fast ion losses in synergistic heating than tangential injection. The study also found that the synergistic effect of collisions and ripples enhanced fast ion losses, which were highly localized and generated a maximum heat load of 0.165 MW m−2 on the first wall. However, conducting synergy heating experiments at high plasma currents and low effective ion charge numbers can significantly reduce the loss of fast ions.

A GPU based accelerated solver for simulation of heat transfer during metal casting process

The metal casting process, which is one of the key drivers of the manufacturing industry, involves several physical phenomena occurring simultaneously like fluid flow, phase change, and heat transfer which affect the casting yield and quality. Casting process modeling involves numerical modeling of these phenomena on a computer. In recent decades, this has become an inevitable tool for foundry engineers to make defect-free castings. To expedite computational time graphics processing units (GPUs) are being increasingly used in the numerical modeling of heat transfer and fluid flow. Initially, in this work a CPU based implicit solver code is developed for solving the 3D unsteady energy equation including phase change numerically using finite volume method which predicts the thermal profile during solidification in the metal casting process in a completely filled mold. To address the computational bottleneck, which is identified as the linear algebraic solver based on the bi-conjugate gradient stabilized method, a GPU-based code is developed using Compute Unified Device Architecture toolkit and was implemented on the GPU. The CPU and GPU based codes are then validated against a commercial casting simulation code FLOW-3D CAST® for a simple casting part and against in-house experimental results for gravity die casting of a simple geometry. Parallel performance is analyzed for grid sizes ranging from 10 × 10 × 10 to 210 × 210 × 210 and for three time-step sizes. The performance of the GPU code based on occupancy and throughput is also investigated. The GPU code exhibits a maximum speedup of 308× compared to the CPU code for a grid size of 210 × 210 × 210 and a time-step size of 2 s.

A New Analytical Simulation Code of Acoustic-Gravity Waves of Seismic Origin and Rapid Co-Seismic Thermospheric Disturbance Energetics

A New Analytical Simulation Code of Acoustic-Gravity Waves of Seismic Origin and Rapid Co-Seismic Thermospheric Disturbance Energetics

Optimal controller for S–CO2 compressor inlet conditioning

The small, simple, and effective characteristics of a Supercritical CO2 (S–CO2) power system make it an ideal candidate for distributed power generation. However, the distributed power generation will be required with constant changes in the operating conditions to meet the varying demand. Thus, it is necessary for the S–CO2 power system to demonstrate that it can operate safely and efficiently under all anticipated operating conditions. One of the key issues in the S–CO2 power system is controlling the compressor inlet conditions. This paper focused on the control of the compressor inlet temperature. In this paper, a system dynamic simulation code is used to model the precooler system for the compressor inlet control first. Based on the analysis results to obtain the transfer function and the state space, a linear quadratic controller was designed using optimal control theory. Since the controller was estimated to have steady-state error, a disturbance observer was also used. To validate the designed controller, experiments were conducted. The experimental results show that the proposed controller can be used to maintain the S–CO2 compressor inlet conditions under various transient scenarios without additional tuning.

Application of reinforcement learning to deduce nuclear power plant severe accident scenario

Severe accident scenarios for nuclear power plants are determined through probabilistic safety analysis (PSA). In this process, it is possible to identify the failure sequence of specific components, but assessing the impact of component failure time on the severity of accident remains a challenge. In this study, a novel approach is presented that utilizes machine learning methodologies such as reinforcement learning (RL) to complement traditional PSA. The proposed process was validated by comparing whether the most severe accident scenarios obtained through critical accident simulations can be reproduced by a RL, since this is a novel use of machine learning techniques. The comparison shows feasibility of exploring critical accident scenarios using RL. To implement the reinforcement learning methodology based on the existing system code, supervised learning model that can predict the remaining time of reactor vessel failure was implemented in this study. Based on this prediction model and data from existing catastrophic accident simulation, RL was implemented. The results obtained from RL were subsequently validated with the results of severe accident code simulation. In summary, new methodology for applying machine learning techniques to the nuclear accident analysis process was presented, and the feasibility and potential of the proposed methodology were discussed.