Benchmark Simulation Research Articles

A Novel Permeability–Tortuosity–Porosity Model for Evolving Pore Space and Mineral-Induced Clogging in Porous Medium

Hydrogeochemical processes contribute to long-term alterations in key physical properties of a porous medium, including porosity, tortuosity, and permeability, making it essential to understand their evolution and address clogging-dominated problems in hydrogeological systems such as acid rock drainage treatment and aquifer storage and recovery. However, accurately simulating extreme cases of evolving pore space presents challenges due to the inherent heterogeneity and nonlinear reactions in a porous medium. In response, this study introduces a comprehensive model that integrates the effects of tortuosity on permeability and surface area on reactivity during oxidative precipitation of Fe(II) in a porous medium. Benchmark simulations include an innovative permeability–tortuosity–porosity model accounting for Fe precipitation, as well as the occurrence of complete clogging from localized precipitation, which leads to a reduction of permeability and outflow. The outcomes demonstrate complete pore clogging when Fe(II) concentration reaches 10 mmol/L and a significant decrease in outflow at a Fe(II) concentration of 100 mmol/L. The model’s predictions provide detailed insights into the evolution of the pore matrix during hydrogeochemical reactions and support the development of regional engineering-scale models for applications in mining, agriculture, and environmental management.

Differences for Cooling Capacity of a Cable Tunnel System: Install One or Three Additional Cable Troughs with Cable Circuit for 100/70 Heat Loads – A Numerical Study

The purpose of this report was to compare the numerical analysis for different cooling efficiency of a cable tunnel system when installing one additional cable trough or three cable troughs for cable circuit 100% or 70% heat load. Cable tunnel system is widely known for it is use for high voltage transmission in an underground. Due to the cables generating large quantities of heat, water pipes and air ventilation were used in the tunnel to cool down the transmission cable. To investigate the cooling efficiency of a tunnel, research for benchmark case was carried out. A Computational Fluid Dynamic (CFD) benchmark analysis about 2D natural convection inside the square cavity was investigated to further understand the air movement inside the square medium. Ansys Fluent was carried out for benchmark cases of heat transfer natural convection inside the square cavity and to check whether Ansys Fluent can be used for any CFD and heat transfer purposes by validating the results with previous studies. The benchmark case used a 2D square with different active temperature side walls and adiabatic walls for top and bottom side. From the benchmark simulations with different Rayleigh Number, a number representing buoyancy-driven of a fluid from 103 to 105 affected air differently and the heat transfer natural convection inside the square. At different Rayleigh Number air forms a recirculation passing the active walls and adiabatic walls. After investigated the benchmark, the results were used to validate with previous studies. To validate the results was by using Nusselt Number, ratio of convective to conductive. The benchmark case results were validated and Ansys Fluent proven can be used for CFD and heat transfer purposes. Two 3D cable tunnel were modelled with 100-meter length after concluded the benchmark. The two tunnel models were based on the number of cable troughs installed. The first tunnel was with one cable trough and two cable circuits on the bottom, as for the second tunnel was with one bottom cable circuit and three cable troughs. Cable tunnel simulations were based on cable circuit for 100% heat load and 70% heat load with each heat load case was given different water flow rate of 4.25 L/s and 6.5 L/s. A total of eight scenario cases were carried out to determine which provided a better cooling efficiency choice. The analysis for cable tunnel cases on how the copper cables cooled down through heat transfer of natural convection inside the cable trough, which the heat then was removed from the cable circuit by air and continue to the outside of the tunnel. During the heat transfer processes, conductivity was present as not all heat were removed by air and water, but continue to through the walls of the tunnel and to the ground soil. Based on the simulations, a cable tunnel with three cable troughs was proven more cooling efficiency compared tunnel with one cable trough. Some scenarios did not meet the criteria, due to insufficient heat relocation by air and water. The cooling efficiency was determined by which has the better balance heat relocation by air, water, and ground, also considering the comfort and safety of human inside the tunnel.

RAMSES-yOMP: Performance Optimizations for the Astrophysical Hydrodynamic Simulation Code RAMSES

Abstract Developing an efficient code for large, multiscale astrophysical simulations is crucial in preparing for the upcoming era of exascale computing. RAMSES is an astrophysical simulation code that employs parallel processing based on the message-passing interface (MPI). However, it has limitations in computational and memory efficiency when using a large number of CPU cores. The problem stems from inefficiencies in workload distribution and memory allocation that inevitably occur when a volume is simply decomposed into domains equal to the number of working processors. We present RAMSES-yOMP, which is a modified version of RAMSES designed to improve parallel scalability. Major updates include the incorporation of open multiprocessing into the MPI parallelization to take advantage of both the shared and distributed memory models. Utilizing this hybrid parallelism in high-resolution benchmark simulations with full prescriptions for baryonic physics, we achieved an increase in performance by a factor of 2 in the total run-time, while using 75% less memory and 30% less storage than the original code, when using the same number of processors. These improvements allow us to perform larger or higher-resolution simulations than what was feasible previously.

Four-dimensional phase space tomography from one-dimensional measurements of a hadron beam

In this paper, we use one-dimensional measurements to infer the four-dimensional phase space density of an accumulated proton beam in the Spallation Neutron Source (SNS) accelerator. The reconstruction was performed by maximizing the distribution’s entropy subject to the measurement constraints and thus represents the most conservative inference from the data. The reconstructed distribution reproduces the measured profiles down to the noise level, and simulations indicate that the problem is reasonably well constrained. Similar measurements could serve as benchmarks for beam dynamics simulations in the SNS or hadron accelerators. Published by the American Physical Society 2024

Score matching for differential abundance testing of compositional high-throughput sequencing data.

The class of a-b power interaction models, proposed by Yu et al. (2024), provides a general framework for modeling sparse compositional count data with pairwise feature interactions. This class includes many distributions as special cases and enables modeling of zero counts through power transformations, making it particularly suitable for modern high-throughput sequencing data with excess zeros, including single-cell RNA-Seq and microbial amplicon data. Here, we present an extension of this class of models that allows inclusion of covariate information, thus enabling accurate characterization of covariate dependencies in heterogeneous populations. Combining this model with a tailored differential abundance (DA) test leads to a novel DA testing scheme, cosmoDA, that can reduce false positive detection rate caused by correlated features. cosmoDA uses penalized generalized score matching for parsimonious model fitting. We show on simulated benchmarks that cosmoDA can accurately estimate feature interactions in the presence of population heterogeneity and significantly reduces the false discovery rate when testing for differential abundance of correlated features. Using single-cell and amplicon data, we illustrate cosmoDA's ability to estimate data-adaptive Box-Cox-type data transformations and assess the impact of zero replacement and power transformations on downstream differential abundance results. cosmoDA is available at https://github.com/bio-datascience/cosmoDA.

Open-jet testing: Investigating turbulence and geometric scale effects on surface pressures in the atmospheric boundary layer

Bluff body aerodynamics is essential for the design and safety of structures exposed to wind forces. Traditional atmospheric boundary layer wind testing often fails to replicate the complex turbulence characteristics of real-world flows, necessitating innovative testing methodologies. We developed an open-jet testing approach and conducted experiments on scaled models (1:7.6 and 1:10) at Reynolds numbers ranging from 0.5 × 106 to 1 × 106, significantly higher than those typically achieved in conventional testing. This methodology produced integral length scales approximately ten times larger than those observed in traditional methods, resulting in 25%–300% higher peak pressures than those from small-scale tests, closely aligning with full-scale field data. Our findings emphasize the necessity of testing under complete atmospheric boundary layer turbulence to ensure accurate wind pressure predictions. Insights into the effects of advanced flow on separation, reattachment, and pressure distribution inform new experimental protocols and have significant implications for the design and safety of structures in wind-prone regions. By establishing a robust benchmark for future experimental and computational simulations in wind engineering, this approach promotes the development of safer, more resilient, and economically viable building designs capable of withstanding extreme wind events exacerbated by climate change, contributing to sustainable infrastructure advancement.

Benchmarking a dual-scale hybrid simulation framework for small globular proteins combining the CHARMM36 and Martini2 models.

Multi-scale models in which varying resolutions are considered in a single molecular dynamics simulation setup are gaining importance in integrative modeling. However, combining atomistic and coarse-grain resolutions, especially for coarse-grain force fields derived from top-down approaches, have not been well explored. In this study, we have implemented and tested a dual-resolution simulation approach to model globular proteins in atomistic detail (represented by the CHARMM36 model) with the surrounding solvent in Martini2 coarse-grain detail. The hybrid scheme considered is an extension of a model implemented earlier for mainly lipid and water molecules. We have considered a set of small globular proteins and have extensively compared to atomistic benchmark simulations as well as a host of experimental observables. We show that the protein structural dynamics sampled in the hybrid scheme is robust, and the intra-protein contact maps are reproduced, despite increased fluctuations of the loop regions. A good match is observed with experimental small angle X-ray scattering (SAXS) and NMR observables, such as chemical shifts and [Formula: see text] -coupling, with the best match obtained for the chemical shifts. However, deviations are observed in the water dynamics and protein-water interactions which we attribute to the limitation of solvent screening in the coarse-grain force field. The computational speed-up achieved is about 2-3 times compared to an all-atom system. Overall, the hybrid model is able to retain the main features of the underlying atomistic conformational landscape with a two-fold speed-up in computational cost.

A note on the analysis of groundwater travel times for injection–abstraction doublets

The solutions of Lippmann and Tsang (1980, Ground Water , 18, 452–458) for the temperature changes in an injection-abstraction doublet have been revisited as benchmarks for numerical simulations developed to assess the feasibility of open-loop geothermal systems. The Lippmann–Tsang solution for the evolution of the temperature at the abstraction well was developed for the case of no ambient groundwater flow in an aquifer that is sealed across its top and bottom. The results of testing confirm some puzzling aspects of the solution. In this note, it is shown that while some elements of the Lippmann–Tsang solution are correct, results for the temperature history at an abstraction well deviate substantially from solutions presented elsewhere in the literature.

A Multivariable Probability Density-Based Auto-Reconstruction Bi-LSTM Soft Sensor for Predicting Effluent BOD in Wastewater Treatment Plants.

The precise detection of effluent biological oxygen demand (BOD) is crucial for the stable operation of wastewater treatment plants (WWTPs). However, existing detection methods struggle to meet the evolving drainage standards and management requirements. To address this issue, this paper proposed a multivariable probability density-based auto-reconstruction bidirectional long short-term memory (MPDAR-Bi-LSTM) soft sensor for predicting effluent BOD, enhancing the prediction accuracy and efficiency. Firstly, the selection of appropriate auxiliary variables for soft-sensor modeling is determined through the calculation of k-nearest-neighbor mutual information (KNN-MI) values between the global process variables and effluent BOD. Subsequently, considering the existence of strong interactions among different reaction tanks, a Bi-LSTM neural network prediction model is constructed with historical data. Then, a multivariate probability density-based auto-reconstruction (MPDAR) strategy is developed for adaptive updating of the prediction model, thereby enhancing its robustness. Finally, the effectiveness of the proposed soft sensor is demonstrated through experiments using the dataset from Benchmark Simulation Model No.1 (BSM1). The experimental results indicate that the proposed soft sensor not only outperforms some traditional models in terms of prediction performance but also excels in avoiding ineffective model reconstructions in scenarios involving complex dynamic wastewater treatment conditions.

Assessment of Slow Feature Analysis and Its Variants for Fault Diagnosis in Process Industries

Accurate monitoring of complex industrial plants is crucial for ensuring safe operations and reliable management of desired quality. Early detection of abnormal events is essential to preempt serious consequences, enhance system performance, and reduce manufacturing costs. In this work, we propose a novel methodology for fault detection based on Slow Feature Analysis (SFA) tailored for time series models and statistical process control. Fault detection is critical in process monitoring and can ensure that systems operate efficiently and safely. This study investigates the effectiveness of various multivariate statistical methods, including Slow Feature Analysis (SFA), Kernel Slow Feature Analysis (KSFA), Dynamic Slow Feature Analysis (DSFA), and Principal Component Analysis (PCA) in detecting faults within the Tennessee Eastman (TE), Benchmark Simulation Model No. 1 (BSM 1) datasets and Beijing wastewater treatment plant (real world). Our comprehensive analysis indicates that KSFA and DSFA significantly outperform traditional methods by providing enhanced sensitivity and fault detection capabilities, particularly in complex, nonlinear, and dynamic data environments. The comparative analysis underscores the superior performance of KSFA and DSFA in capturing comprehensive process behavior, making them robust, cutting-edge choices for advanced fault detection applications. Such methodologies promise substantial improvements in industrial plant monitoring, contributing to heightened system reliability, safety, and overall operational efficiency.

FastSLAM-MO-PSO: A Robust Method for Simultaneous Localization and Mapping in Mobile Robots Navigating Unknown Environments

In the realm of mobile robotics, the capability to navigate and map uncharted territories is paramount, and Simultaneous Localization and Mapping (SLAM) stands as a cornerstone technology enabling this capability. While traditional SLAM methods like Extended Kalman Filter (EKF) and FastSLAM have made strides, they often struggle with the complexities of non-linear dynamics and non-Gaussian noise, particularly in dynamic settings. Moreover, these methods can be computationally intensive, limiting their applicability in real-world scenarios. This paper introduces an innovative enhancement to the FastSLAM framework by integrating Multi-Objective Particle Swarm Optimization (MO-PSO), aiming to bolster the robustness and accuracy of SLAM in mobile robots. We outline the theoretical underpinnings of FastSLAM and underscore its significance in robotic autonomy for mapping and exploration. Our approach innovates by crafting a specialized fitness function within the MO-PSO paradigm, which is instrumental in optimizing the particle distribution and addressing the challenges inherent in traditional particle filtering methods. This strategic fusion of MO-PSO with FastSLAM not only circumvents the pitfalls of particle degeneration, but also enhances the overall robustness and precision of the SLAM process across a spectrum of operational environments. Our empirical evaluation involves testing the proposed method on three distinct simulation benchmarks, comparing its performance against four other algorithms. The results indicate that our MO-PSO-enhanced FastSLAM method outperforms the traditional particle filtering approach by significantly reducing particle degeneration and ensuring more reliable and precise SLAM performance in challenging environments. This research demonstrates that the integration of MO-PSO with FastSLAM is a promising direction for improving SLAM in mobile robots, providing a robust solution for accurate mapping and localization even in complex and unknown settings.

Retrofit Measures for Aircraft Noise Reduction: Simulation Benchmark and Impact Assessment

DLR, German Aerospace Center, has developed a low-noise retrofit to reduce noise generation of a conventional midrange transportation aircraft, i.e., measures to the airframe and engine exhaust nozzle. Selected measures have been installed onboard of DLR’s flying testbed Advanced Technology Research Aircraft and been subject to a flyover noise campaign. The aircraft in its original configuration and the modified aircraft have been tested and measured in flyover campaigns in 2016 and 2019, respectively. Initial simulation models have been derived from the results and previous component simulations and wind tunnel tests to account for the new reduction measures within DLR’s system noise prediction tool Parametric Aircraft Noise Analysis Module (PANAM). This paper presents the developed measures as selected for the flight test campaigns. An overview of the conducted flight tests is provided. The overall noise simulation process, including aircraft and engine design, flight simulation, and noise prediction, is presented. Simulation results obtained from this process are then compared to the measured levels from the flight campaigns. Estimated simulation uncertainties from PANAM can now be directly compared to differences between measured and simulated levels. Finally, a parameter study is conducted in order to assess the reduction potential of the novel retrofit measures along different simulated flight procedures. Spatial noise distribution in sound exposure level contours is assessed.

Data-Driven Tube-Based Robust Predictive Control for Constrained Wastewater Treatment Process.

The wastewater treatment process (WWTP) is characterized by unknown nonlinearity and external disturbances, which complicates the tracking control of dissolved oxygen concentration (DOC) within operational constraints. To address this issue, a data-driven tube-based robust predictive control (DTRPC) strategy is proposed to achieve stable tracking control of DOC and satisfy the system constraints. First, a tube-based robust predictive control (TRPC) strategy is designed to deal with system constraints and external disturbances. Specifically, a nominal controller is designed to ensure that the nominal output accurately tracks the set-point under tightened constraints, while an auxiliary feedback controller is designed to suppress disturbances and restore the nominal performance of the disturbed WWTP. Second, two fuzzy neural network identifiers are employed to provide accurate predictive outputs for the control process, overcoming the challenges of modeling the WWTP with strong nonlinearity and unknown dynamics. Third, the generalized multiplier method is utilized to solve the constrained optimization problem to obtain the nominal control law, and the gradient descent algorithm is used to obtain the auxiliary control law. The implementation of this composite controller ensures the satisfaction of the system constraints and the effective suppression of disturbances. Finally, the feasibility and stability of the proposed DTRPC strategy are guaranteed through rigorous theoretical analysis, and its effectiveness is demonstrated through the simulations on the benchmark simulation model No.1.

Benchmark Simulation of Laminar Reactive Micromixing Using Lattice Boltzmann Methods

Micromixers are chemical processing devices with complex flow patterns applied for both mixing and reaction of chemical species. In current research, laminar reacting multicomponent flows are considered. Despite the laminar streaming regime (e.g., Re = 186), there exist secondary flow microstructures. For this setup, accurate predictions of those structures are possible with a large-eddy simulation on a fine mesh resolving till the Batchelor microscales. Utilizing the open-source lattice Boltzmann method (LBM) framework, OpenLB, a benchmark simulation of the reacting micromixer, is re-established with new, more precise computation results. In this context, a Schmidt-number-based stabilization method for LBM-discretized reactive advection–diffusion equations by laminar secondary flow structures is used. A convergence study is performed, which is also a novelty. All computations have been performed on the high-performance computing cluster HoreKa using up to 160 NVIDIA A100 graphics processing units.

CIPHER: Cybersecurity Intelligent Penetration-Testing Helper for Ethical Researcher.

Penetration testing, a critical component of cybersecurity, typically requires extensive time and effort to find vulnerabilities. Beginners in this field often benefit from collaborative approaches with the community or experts. To address this, we develop Cybersecurity Intelligent Penetration-testing Helper for Ethical Researchers (CIPHER), a large language model specifically trained to assist in penetration testing tasks as a chatbot. Unlike software development, penetration testing involves domain-specific knowledge that is not widely documented or easily accessible, necessitating a specialized training approach for AI language models. CIPHER was trained using over 300 high-quality write-ups of vulnerable machines, hacking techniques, and documentation of open-source penetration testing tools augmented in an expert response structure. Additionally, we introduced the Findings, Action, Reasoning, and Results (FARR) Flow augmentation, a novel method to augment penetration testing write-ups to establish a fully automated pentesting simulation benchmark tailored for large language models. This approach fills a significant gap in traditional cybersecurity Q&A benchmarks and provides a realistic and rigorous standard for evaluating LLM's technical knowledge, reasoning capabilities, and practical utility in dynamic penetration testing scenarios. In our assessments, CIPHER achieved the best overall performance in providing accurate suggestion responses compared to other open-source penetration testing models of similar size and even larger state-of-the-art models like Llama 3 70B and Qwen1.5 72B Chat, particularly on insane difficulty machine setups. This demonstrates that the current capabilities of general large language models (LLMs) are insufficient for effectively guiding users through the penetration testing process. We also discuss the potential for improvement through scaling and the development of better benchmarks using FARR Flow augmentation results.

Modeling of bed-to-wall heat transfer coefficient in fluidized adsorption bed by gene expression programming approach

Adsorption cooling and desalination methods with adsorption chillers (AC) are promising in energy technologies. However, the low-performance coefficient and bulkiness of traditional packed-bed ACs, primarily due to the high voidage of the sorbent beds leading to low heat transfer coefficients, pose significant challenges. Despite numerous attempts, a practical solution to this problem is yet to be found.In response to this challenge, we propose a novel approach: a fluidized adsorbent bed instead of the traditional packed bed. We also introduce gene expression programming (GEP) as an innovative artificial intelligence (AI) method for modeling the bed-to-wall heat transfer coefficient in the adsorption bed. Our study includes calculations and model validation for a heat transfer adsorption bed reactor designed for low-pressure adsorption processes. The fluidizing agent of the adsorbent bed was water vapor generated in the evaporator. Silica gel was used as the parent adsorption material in our tests. The heat transfer coefficient was successfully validated and determined through experiments and estimated using the formulated (b-t-wHTc) meta-model. The data evaluated by the model aligns well with the experimental results. Our calculations demonstrate that the GEP-based model accurately predicts the heat transfer coefficient and is suitable for analyzing the fluidized adsorption bed reactor.The outlined studies serve as a benchmark for subsequent simulations of the intensified heat transfer adsorption bed reactor, as they are integral to project No. 2018/29/B/ST8/00442, titled “Research on sorption process intensification methods in modified construction of adsorbent beds,” supported by the National Science Center in Poland.

Molecular simulation using transfer-learned potentials for the disordered nanoscale structure of nitrogen-doped nanoporous carbons

Machine learning (ML)-based molecular dynamics (MD) simulations of the formation of a class of N-doped nanoporous carbons are performed to assess their disordered partially graphitized nanoscale structure. The study is motivated by the effectiveness of so-called nitrogen assembly carbons (NACs) for catalysis applications. Benchmark simulations for pure-C disordered graphitic systems reveal the importance of reliably capturing the vdW component of the potentials in order to accurately describe the tendency for layering of disordered graphene-like sheets. In our modeling, this is achieved by a transfer learning strategy incorporating features of the energetics from the optB88-vdW DFT functional into potentials initially trained with a less expensive functional, thereby providing a superior description of the pure-C systems. Generation from MD simulations of realistic partially graphitized structures is significantly more challenging for N-doped versus for pure C systems. However, such structures are achieved by a tailored MD simulation protocol mimicking the experimental synthesis process and in particular incorporating an annealing and subsequent quenching stages. Simulated PXRD patterns effectively reproduce the features of experimental observations for NACs, including the appearance of a prominent but broad (002) peak at around 25∘, and the development of another weaker feature associated with in-layer ordering of mixed C-N graphene-like sheets.

The Transition from Aerosol- to Updraft-Limited Susceptibility Regime in Large-Eddy Simulations with Bulk Microphysics

Large-eddy simulation (LES) is often used as a benchmark simulation in climate science and is suggested as a fundamental tool to examine, e.g., marine cloud brightening. Therefore, it is necessary to critically evaluate if these high-resolution models can skillfully simulate expected physical phenomena. This study focuses on the first indirect aerosol effect in warm stratocumulus clouds. We investigate if an LES code with explicit aerosol-cloud interactions and a widely used two-moment bulk microphysical scheme can reproduce well-known cloud droplet number susceptibility regimes previously identified by observations and supported by detailed parcel model simulations—the updraft-limited regime (typically occurring at high aerosol number concentrations and low updraft speeds) and the aerosol-limited regime (typically occurring at low aerosol number concentrations and high updraft speeds). Our simulations show that the LES in its default configuration cannot reproduce the two regimes if the initial droplet radius of newly activated droplets (rid) is estimated by integrating the wet aerosol size distribution. The main reason is related to the relatively coarse (but commonly used) time step in the model (Δt ≈ 1s), which is too long to resolve relevant microphysical processes adequately at high aerosol concentrations. A regime transition does occur if the timestep is decreased to Δt ≈ 0.1s and if a renormalization procedure is applied, which limits the number of activated droplets so that the water mass of the newly activated droplets cannot exceed the available amount of supersaturated water vapor. Another way to obtain a regime transition is to increase rid to values >1 µm. However, a clear recommendation for the choice of rid cannot be made upon physical arguments. An alternative solution could be to introduce a sub-time-stepping or adaptive time-stepping algorithm to calculate droplet formation and growth, particularly for updraft-limited conditions. Our study highlights the importance of critically evaluating LES results to guarantee that relevant physical processes are properly represented.

Simulating column splice fracture and post‐fracture response for seismic assessment of steel moment frames

AbstractMitigating fracture in welded column splices is an important challenge for the safety of existing steel moment‐resisting frames. While models to predict splice fracture have recently been developed, suitable approaches are not available to simulate the response of frames after splice fracture. Motivated by this, a two‐dimensional displacement‐based fiber element construct, termed the Splice Fracture Element (SFE), is presented. The SFE includes numerous features: (1) representation of the loss of strength in any fiber at a critical stress determined from fracture mechanics, (2) the ability to simulate the loss of shear strength of the cross‐section when the entire section is severed – a phenomenon not readily simulated in conventional fiber elements, and (3) the ability to track the kinematics of the severed parts of the column to represent transfer of compressive stresses on contact. This formulation is implemented into an open‐source software (OpenSees) and applied to conduct Nonlinear Response History Analysis (NLRHA) of two demonstration problems, including a 1‐story frame and a 20‐story frame. Benchmark simulations that do not simulate splice fracture or represent it without the loss of shear strength are also conducted. The results indicate that the SFE element can successfully simulate the key phenomena associated with splice fracture and post‐fracture response.

Publisher’s Note: “Benchmark simulations of radiative transfer in participating binary stochastic mixtures in two dimensions” [Matter Radiat. Extremes 9, 067802 (2024)

Publisher’s Note: “Benchmark simulations of radiative transfer in participating binary stochastic mixtures in two dimensions” [Matter Radiat. Extremes 9, 067802 (2024)