Monte Carlo Program Research Articles

The Simulations Chain of the MURAVES Experiment

The MUon RAdiography of VESuvius (MURAVES) project aims at the study of the summital cone of Mt. Vesuvius, an active and hazardous volcano near Naples, Italy. A detailed Monte Carlo simulation framework is necessary in order to investigate the effects of the experimental constraints and to perform comparisons with the actual observations. Our Monte Carlo setup combines a variety of Monte Carlo programs that address different aspects of cosmic muon simulation, from muon generation in the Earth's upper atmosphere to the response of the detector, including the interactions with the material of the volcano. We will elaborate on the rationale for our technical choices, including trade-off between speed and accuracy, and on the lessons learned, which are of general interest for similar use cases in muon radiography.

Production of vector mesons in the string+P30 model of polarized quark fragmentation

The production of vector mesons in the fragmentation process of polarized quarks is studied within the recursive String+${}^3P_0$ model, improving a previous version of the model in which the production of pseudoscalar mesons only was considered. Two types of couplings of the vector meson to quarks are introduced, their coupling constants being the additional free parameters of the model. The angular distribution of the decay products of the polarized vector meson is deduced from the spin density matrix of the meson and the spin information is propagated along the fragmentation chain taking into account the entanglement of spin states. The new model is implemented in a stand alone Monte Carlo program utilized to investigate in detail kinematic distributions and transverse spin asymmetries. The sensitivity of these observables to the new free parameters is discussed and the Monte Carlo results are compared with experimental data on transverse spin asymmetries.

Computing the dynamic friction coefficient and evaluation of radiation shielding performance for AISI 304 stainless steel

The cold rolling deformation (CRD) has been employed to produce the different AISI 304 stainless-steel (AISI 304 S) samples containing different percent of the martensitic phase. The microstructure observations have appeared the different percentages of the martensitic phase included in the austenitic phase. The hardness amelioration mainly relied on the character, growth, and distribution of the martensitic phase. Additionally, the findings of wear tests clarify that the sliding wear rate decrease with the increase of the martensite phase. The worn surfaces have revealed the debris mechanism associated with delamination spots is predominant during wear tests. Also, the present study extends to evaluate the dynamic friction coefficients (μ) using temperature-time curve throughout performing the dry sliding wear tests. The comparison of measured and computed values of μ has revealed the good agreement between both. Moreover, neutrons and gamma-rays shielding performance of AISI 304 S were studied using Monte Carlo (MCNP5) and WinXCom programs. The MCNP5 calculations were performed for neutrons in the energy range of 10−5 eV to 20 MeV. While the shielding parameters of gamma rays were done in the energy range of 0.015–15 MeV. The results of radiation shielding showed that the AISI 304 S owns a good shielding performance against neutrons and gamma-rays compared to previously published studies.

Neutronic and Thermal-Mechanical Coupling Schemes for Heat Pipe-Cooled Reactor Designs

Abstract Space fission power systems can enable ambitious solar-system and deep-space science missions. The heat pipe-cooled reactor is one of the most potential candidates for near-term space power supply, featuring safety, simplicity, reliability, and modularity. Heat pipe-cooled reactors are solid-state and high-temperature (up to 1500 K) reactors, where the thermal expansion is remarkable and the mechanical response significantly influences the neutronics and thermal analyses. Due to the considerable difference between heat pipe-cooled reactors and traditional water reactors in the structure and design concept, the coupling solutions for light water reactors cannot be directly applied to heat pipe-cooled reactor analyses. Therefore, a new coupling framework and program need to consider the coupling effects among neutronics, heat transfer, and mechanics. Based on the Monte Carlo program rmc and commercial finite element program ansysmechanicalansys parametric design language (APDL), this work introduces the three coupling fields of neutronics (N), thermal (T), and mechanics (M) for heat pipe cooled reactors. Besides, the finite element method and the Monte Carlo program use different meshes and geometry construction methods. Therefore, the spatial mapping and geometry reconstruction are also essential for the N/T-M coupling, which is discussed and established in detail. Furthermore, the N/T-M coupling methods are applied to the preliminary self-designed 10 kWel space heat pipe cooled reactor. Coupling shows that the thermal-mechanical feedback in the solid-state reactor has negative reactivity feedback (about −2000 pcm) while it has a deterioration in heat transfer due to the expansion in the gas gap.

Calculation researches for the formation of high-level and long-life medium-level radioactive waste of activation origin for the WWER-1200 reactor of Belarusian NPP

The study of the issue of constructing a disposal facility for high-activity radioactive waste in the Republic of Belarus is associated with an assessment of the volume of radioactive waste to be deeply disposed of, generated as a result of the activation of structural materials of the VVER-1200 reactor of the Belarusian NPP. This paper presents the results of computational studies of the formation of solid high-level radioactive waste (HLW) and long-lived intermediate level radioactive waste (ILW-LL) during neutron activation of materials adjacent to the core of the VVER-1200 reactor structures of the Belarusian NPP. The assessment of the volumes of HLW and ILW-LL of activation origin, formed over 60 years of operation of the VVER-1200 reactor, was carried out on the basis of computational studies of the induced activity of structural and shielding materials using reactor and Monte Carlo program codes (SERPENT 2, TVS-M, DYN3D, MCU- PD). As a result of the research, it was found that when neutrons activate materials of the sections of the VVER-1200 reactor structures of the Belarusian NPP adjacent to the core (in the steel structures of the baffle, shaft, surfacing, part of the reactor vessel, structures of the protective tube unit (PTU), the space under the core, in heat insulation materials, rods of absorbing elements (Dy2TiO5)) are formed by HLW and ILW-LL with a total weight of 272,5 tons and a volume of 43 m3 . Calculated studies of the activation of dry protection materials, building concrete, support truss and biological protection showed that these structural elements will not belong to either HLW or ILW-LL.

A new evaluation index of rockburst tendency considering tunnel excavation and fracture distribution

Rockburst risk and tendency analysis of fractured rock mass after excavation and unloading has been gaining importance. Within the framework of a constitutive model based on internal variable thermodynamics, the energy dissipation rate is proposed as a new evaluation index of rockburst tendency. Taking the numerical simulation of a traffic tunnel in western China as an example to carry out the rockburst tendency analysis, the models with parallel fractures of different dip angles were established in FLAC3D by Monte-Carlo method and MATLAB programming. Combined with the estimated in-situ stress of the deep-buried tunnel and the inversion results of constitutive parameters of rock mass, the influence of fracture dip angles on rockburst tendency of the surrounding rock is analyzed. The analysis results under different calculation conditions show that with the increase of fracture dip angle, the possible location of rockburst gradually transfers from the vault to the left arch waist. In addition, the comparison with the stress index verifies that the energy dissipation rate index can effectively evaluate the potential dangerous areas and rockburst positions after excavation and unloading of fractured rock mass, which has a reference value for the rockburst risk assessment in deep-buried tunnels.

Simulation of the response of SiPMs; Part I: Without saturation effects

A Monte Carlo program is presented which simulates the response of SiPMs in the linear regime in which saturation effects can be ignored. Inputs to the program are the mean number and the time distribution of Geiger discharges from photons, as well as the dark-count rate. For every primary Geiger discharge, correlated Geiger discharges due to prompt and delayed cross-talk and after-pulses are simulated, and a table, called Geiger Array, of the amplitudes and times of all Geiger discharges in a specified time window is generated.A number of different physics-based models and statistical treatments for the simulation of correlated Geiger discharges can be selected. The Geiger Arrays for many events together with different options for the pulse shapes of single Geiger discharges can be used to simulate charge spectra, as measured by a current-integrating charge-to-digital converter. In addition, current transients convolved with electronics response functions, as recorded by a digital oscilloscope, and time-difference distributions can be simulated. The program can be used to compare simulation results with different assumptions to experimental data, and thus find out which model is the most appropriate for a given SiPM, optimise the operating conditions and readout for a given application, and test programs for extracting SiPM parameters from experimental data. A Python version of the program is available on request.

Absolute measurements of bremsstrahlung double differential cross sections of C and Al atoms by 5–25 keV electron impact

Absolute measurements of the bremsstrahlung double differential cross sections (DDCSs) for photons radiated at 90° generated by the collisions of 5–25 keV electrons and down to 1–2 keV photon energy with two thin targets C (Z = 6) and Al (Z = 13) are presented. A parallelized version of the PENELOPE Monte Carlo program has been used to correct the effects of electron multiple scattering and the backscattering from the target substrate on the experimental results. Comparisons between the experiments and the theories reveal some discrepancies between the measured data and the theoretical bremsstrahlung predictions.

Position reconstruction for segmented detectors

The topic of the paper is the position reconstruction from signals of segmented detectors. With the help of a simple simulation, it is shown that the position reconstruction using the centre-of-gravity method is strongly biased, if the width of the charge (or e.g. light) distribution at the electrodes (or photo detectors) is less than the read-out pitch. A method is proposed which removes this bias for events with signals in two or more read-out channels and thereby improves the position resolution. The method also provides an estimate of the position–response function for every event. Examples are given for which its width as a function of the reconstructed position varies by as much as an order of magnitude.A fast Monte Carlo program is described which simulates the signals from a silicon pixel detector traversed by charged particles under different angles, and the results obtained with the proposed reconstruction method and with the centre-of-gravity method are compared. The simulation includes the local energy-loss fluctuations, the position-dependent electric field, the diffusion of the charge carriers, the electronics noise and charge thresholds for clustering, A comparison to test-beam-data is used to validate the simulation.

Fully Geant4 compatible package for the simulation of Dark Matter in fixed target experiments

We present the package for the simulation of DM (Dark Matter) particles in fixed target experiments. The most convenient way of this simulation (and the only possible way in the case of beam-dump) is to simulate it in the framework of the Monte-Carlo program performing the particle tracing in the experimental setup. The Geant4 toolkit framework was chosen as the most popular and versatile solution nowadays.Specifically, the package includes the codes for the simulation of the processes of DM particles production via electron and muon bremsstrahlung off nuclei, resonant in-flight positron annihilation on atomic electrons and gamma to ALP (axion-like particles) conversion on nuclei. Four types of DM mediator particles are considered: vector, scalar, pseudoscalar and axial vector. The total cross sections of bremsstrahlung processes are calculated numerically at exact tree level (ETL).The code handles both the case of invisible DM decay and of visible decay into e+e− (μ+μ− for Z′, γγ for ALP).The proposed extension implements native Geant4 application programming interfaces (API) designed for these needs and can be unobtrusively embedded into the existing applications.As an example of its usage, we discuss the results obtained from the simulation of a typical active beam-dump experiment. We consider 5×1012 100 GeV electrons impinging on a lead/plastic heterogeneous calorimeter playing a role of an active thick target. The expected sensitivity of the experiment to the four types of DM mediator particles mentioned above is then derived. Program summaryProgram Title: DMG4CPC Library link to program files:https://doi.org/10.17632/6m3yhx4ssw.1Licensing provisions: GNU General Public License 3Programming language: c++Nature of problem: The optimal way to simulate Dark Matter production processes in fixed target experiments in most cases is to do it inside the program for the full simulation of the experimental setup and not separately, in event generators. The code that can be easily embedded in such programs is needed. The code should be able to simulate various DM production processes that happen in a thick target, in particular on nuclei, with maximal accuracy.Solution method: We created a Geant4 compatible DM simulation package for this purpose. The choice of this simulation framework is suggested by its popularity and versatility. The code includes the cross sections precalculated at exact tree level for a wide variety of DM particles.

Assessment of multi-energy inter-pixel coincidence counters for photon-counting detectors at the presence of charge sharing and pulse pileup: A simulation study.

Spectral distortion due to charge sharing (CS) and pulse pileup (PP) in photon-counting detectors (PCDs) degrades the quality of PCD data. We recently proposed multi-energy inter-pixel coincidence counters (MEICC) that provided spectral cross-talk information related to CS. When PP was absent, the normalized Cramér-Rao lower bounds (nCRLBs) of 225-µm pixel PCDs with MEICC was comparable to those of 450-µm pixel PCD without MEICC. The aim of this study was to assess the performance of PCDs with MEICC in the presence of both CS and PP using computer simulations. An in-house Monte Carlo program was modified to incorporate the following four temporal elements: (1) A pulse shape with a pulse duration of 20ns, (2) delays of up to 10ns in anode arrival times when photons were incident on pixel boundaries, (3) offsets proportional to a vertical separation between the primary and secondary charge clouds at the rate of ±4ns per ±100µm, and (4) a stochastic fluctuation of anode arrival times for all of the charge clouds with a standard deviation of 2ns. We assessed the performance of five PCDs, (a)-(f), for three spectral tasks, (A)-(C): (a) The conventional PCD, (b) a PCD with MEICC, (c) a PCD with one coincidence counter (1CC), (d) a PCD with a 3×3 analog charge summing scheme (ACS), and (e) a PCD with a 3×3 digital count summing scheme (DCS); (A) conventional CT imaging with water (i.e., linear attenuation coefficient maps), (B) water-bone material decomposition, and (C) K-edge imaging with tungsten. The tube current was changed from 1mA to 1000mA and the nCRLB was assessed. The recorded count rate curves were fitted by the non-paralyzable detection model with the effective deadtime parameter. The best fit was achieved by 25.8ns for the conventional PCD, 18.6ns for MEICC and 1CC, 140.5ns for ACS, and 209.0ns for DCS. The nCRLBs were strongly dependent on count rates. MEICC provided the best nCRLBs for all of the imaging tasks over the count rate range investigated except for a few conditions such as K-edge imaging at 1mA. PP decreased the merit of MEICC over the conventional PCD in addressing CS. Nonetheless, MEICC consistently provided better nCRLBs than the conventional PCD did. The nCRLBs of MEICC were in the range of 49-58% of those of the conventional PCD for K-edge imaging, 45-76% for water-bone material decomposition, and 81-88% for the conventional CT imaging (i.e., linear attenuation coefficient maps). ACS provided better nCRLBs than the conventional PCD did only when the effect of PP was minor (e.g., when the counting efficiency of the conventional PCD was higher than 0.95 with the tube current of up to 100mA). Besides a few cases, MEICC provides the best nCRLBs for all of the tasks at all of the count rates. ACS and DCS provide better nCRLBs than the conventional PCD does only when count rates are very low.

Energy-efficient user association with load-balancing for cooperative IIoT network within B5G era

As one of the key technologies of 5G wireless communication technology, cooperative multi-access edge computing allows one device to associate multiple edge nodes simultaneously, namely multi-association, which can provide scalable communication services with characteristics of high reliability, massive connectivity and low latency for promising Industrial Internet of Things (IIoT). Effective association between edge nodes and devices is the prerequisite for providing high quality communication services in dense deployed IIoT networks. Most of state of art researches focus on the user association problem in single-association scenario. There are rarely no solutions presented for the considered user association problem with multi-association. In this paper, user association, power allocation and edge node deployment are jointly considered for load balance and energy efficiency under the multi-association mechanism. The problem is formulated as a nested knapsack optimization problem (NKOP) with energy efficiency and load balancing as objective functions and power and signal quality as constraints. Differential evolution with Monte Carlo and sequential quadratic programming (DMS) algorithm is proposed to solve this problem, which decouples the problem into three parts, user association, power allocation and optimizing the location of edge nodes. Numerical results show that: (1) Compared with the single-association, multi-association with power allocation can provide better signal quality and improve energy efficiency; (2) Proposed DMS algorithm is feasible and stable for optimal deployment of edge nodes. These works together provide good reference for edge node deployment of high-density IIoT application scenarios.

A machine-learning method to derive the parameters of contact binaries

Abstract Contact binary stars are important research objects in astrophysics. The calculation speed of deriving the parameters of contact binaries with the Wilson–Devinney program and the Phoebe with Markov chain Monte Carlo (MCMC) program is relatively slow. It is unrealistic to derive the parameters in batches with the program for sky survey data. We obtain a neural network model of supervised learning with the training of synthetic light curves with Phoebe. We calculate the parameters of eight special targets from the simulated data and the Kepler data. Then, we generate the new light curve to fit the light curve of the special target base on these parameters. The correlation index R2 of the fitting result is more than 0.98. The method can be used to fit the target which has orbital inclinations greater than 50°. By fitting the Kepler data and the observed data on the ground, the method has a good generalization ability to these targets, which have some noise and some starspots. The calculation speed of one light curve with this method is less than seconds. We can derive the parameters quickly in batches to undertake some statistical work for sky survey data with the method.

ESTIMATION OF THE ORGAN AND EFFECTIVE DOSE TO PATIENTS UNDERGOING MEDICAL DIAGNOSTIC X-RAY EXAMINATIONS IN SAUDI ARABIA.

Quantifying the radiological risk from diagnostic radiography is essential for patients' safety. Effective dose is considered the best quantity to determine the stochastic risk associated with the radiological examinations. Therefore, the present work investigated organ and effective dose for adult patients in the most common type of X-ray examinations, such as the chest (PA/LAT), abdomen (AP) and lumbar spine (AP/LAT) projections. The PCXMC version 2 Monte Carlo program was used to estimate the organ and effective dose for 547 patients who underwent a radiographic examination at the King Abdulaziz Hospital, Saudi Arabia. The results showed wide variation in organ doses. The largest organ dose in each X-ray examination were 2.72mGy for the spleen in the lumbar spine (LAT), 1.98mGy for the urinary bladder in the lumbar spine (AP), 0.40mGy for the spleen in the chest (PA), 0.11mGy for the kidney in the chest (LAT) and 1.78mGy for the testicles in the abdomen (AP) examinations. Values for the effective dose were estimated for each investigated X-ray examination, and the results were compared with the published values available in the literature. The obtained values for effective dose were relatively lower than those reported by the European Commission and the United Nations Scientific Committee on the Effects of Atomic Radiation for the same examinations. The results presented here will help establish a database that will be useful for future comparisons and monitoring in radiographic procedures.

Closed-loop well construction optimization (CLWCO) using stochastic approach under time uncertainty

There is a digital step change taking place in well construction today. More and better data will become available for a vast number of analyses. The well construction process is complicated and includes several hundred parameters. There are many inhouse drilling analytics tools used by service and consulting companies. The objective of this paper is to aim at a complete time optimization and to improve health, safety and the environment (HSE) in a time-effective way. In this paper we establish and apply a full approach methodology for closed Loop well construction optimization (CLWCO) under time uncertainty. CLWCO involves six major steps: data gathering,a work-breakdown structure (WBS) in drilling scenarios, time estimation (budget time &technical time),time simulation (MCS&PERT), scenario analysis & optimization and finally updating time model. CLWCO involves three major concepts: optimizing the time plan based on current time knowledge, drilling new wells and collecting time data, finally updating multiple time models based on all of the available data. In the CLWCO step, work breakdown structure (W.B.S), time and controls for new wells are optimized by Monte-Carlo Simulation and program evaluation review technique (PERT). This paper goals are to identify and in best case quantify “the value of Monte Carlo simulation and Program Evaluation Review Technique (PERT) in batch & conventional time drilling optimization” in offshore wells for clients or operating company. Batch drilling does not combine professionally with modern techniques yet.we fill this gap by using modern techniques to optimize and enhance drilling work. We evaluate and analysis above-mentioned approach for batch drilling which has become increasingly prevalent in the petroleum industry as large and small investors alike seek to increase their profit margin. The insight of many of these oil and gas companies was to drill and complete wells using new techniques with the desire of considerable reduction in drilling time and cost for the field. when similar hole sections such as 32″,24″,16″,12 ¼″ and 8 ½″ of different wells were drilled one after the other efficiency and profits would be greatly increased. According to obtained results in closed loop well construction optimization (CLWCO), these methods are successful as it needs less time and cost to drill a lot of wells using the same platform. we simulated a drilling program for the case study of SP field by Monte-Carlo Simulation and program evaluation review technique (PERT),at the end we propose the optimum probable time to do future drilling program in SP field. The time versus depth graph of drilling project show that the improved drilling efficiency for drilling project designed as 11 wells would reduce the total drilling time around 15% in compare of previous drilling projects in phase SP6,SP7 and SP8,totally average drilling time have been improved between 2.5 and 8 days in MCS and PERT simulation technique for each well by using CLWCO.We presented the optimal plan coupling with batch drilling could be implemented in the future phases of SP field, which has resulted in decreasing drilling time to 30 days by using casing-drilling and liner-drilling technology.

BAli-Phy version 3: model-based co-estimation of alignment and phylogeny.

We describe improvements to BAli-Phy, a Markov chain Monte Carlo (MCMC) program that jointly estimates phylogeny, alignment and other parameters from unaligned sequence data. Version 3 is substantially faster for large trees, and implements covarion models, additional codon models and other new models. It implements ancestral state reconstruction, allows prior selection for all model parameters, and can also analyze multiple genes simultaneously. Software is available for download at http://www.bali-phy.org. C++ source code is freely available on Github under the GPL2 License. Supplementary data are available at Bioinformatics online.

Monte Carlo simulation of the passage of γ-rays and α-particles in CsI

Theoretical and computational methods for simulating the creation of ionization tracks by fast ions in solids were applied to the passage of α-particles in CsI, an inorganic scintillator commonly used for radiation detection. The methods were implemented in a Monte Carlo program to simulate the interaction of α-particles, with incident energies of up to 1 MeV, with CsI. The simulations followed the fate of individual electron-hole pairs and included the formation of Frenkel pairs and thus allowed for a detailed description of the microscopic structure of ionization and defect tracks created by incident radiation. Simulations were also performed with γ-rays of the same energy to compare and contrast the ionization tracks obtained with both types of particles. Intrinsic properties such as the mean energy per electron-hole pair, Fano factor, maximum theoretical light yield, and spatial distributions of electron-hole pairs were computed for both α-particles and γ-rays. α-Particles created cylindrical tracks that were initially aligned with the incident direction and with initial radii of a few tens of nanometers, whereas γ-rays showed significant scattering, resulting in probability distributions with lower intensities and much greater radial extents.

Semi-Analytical Monte Carlo Method to Simulate the Signal of the VIP-2 Experiment

The VIP-2 collaboration runs an apparatus in the Gran Sasso underground laboratories of the Italian Institute for Nuclear Physics (INFN) designed to search for anomalous X-rays from electron-atom interactions due to violations of the fundamental antisymmetry of multi-electron wavefunctions. The experiment implements the scheme first proposed by Ramberg and Snow, where a current source injects electrons into a metal strip (the experiment’s target). In this paper we describe the structure of a Monte Carlo program to simulate a new upgrade of the experiment, where the anomalous X-ray emission is modulated by an arbitrary time-varying input current. A novel feature of the simulation algorithm is that the Monte Carlo program is based on a mixture of analytical and numerical methods. We report preliminary, exploratory results on the expected detection rate for different modulations of the injected current; these results are a starting point on the way to optimize the modulation scheme and indicate a large potential improvement of the detection sensitivity.

An adaptive optimization reverse regulation method for neutron spectrum based on standardized response module

• An adaptive optimization reverse regulation method for neutron spectrum based on standardized response module was developed. • 50 standardized response modules with different thickness and materials were designed for neutron spectrum regulation. • The differential evolution and artificial neural network algorithms are used to optimize the arrangement of response modules. • Verifications on ITER TBM and RBEC-M have confirmed the accuracy and universality of the developed method. The neutron spectrum is one of the essential parameters in the design of advanced nuclear energy systems. Neutron spectra of different nuclear energy systems have wide differences so that accurate regulation of a specific neutron spectrum is of great significance to its development. In this research, an adaptive optimization reverse regulation method for neutron spectrum based on standardized response module was developed. The proposed method designed different types of standardized response modules and calibrated it with their corresponding multi-dimensional response matrix calculated by the Monte Carlo program. Combined with an intelligent optimization algorithm and artificial neural network algorithm, the regulation scheme of the target neutron spectrum could be constructed and modified accurately and efficiently. The 14 MeV single-energy fusion neutron source was used to verify the regulated results of the proposed method on the tritium breeder blanket of a fusion reactor (ITER) whose results showed that the accuracy of the proposed method was improved by 7.69 % compared to the forward manual experiment. Also, a verification of the regulated spectrum on a fission reactor RBEC-M was done to ensure universal application of the method.

Research on the fabrication method of macroscopic cross section base on the Monte Carlo simulation

Recent studies related to Monte Carlo based homogenization have shown that we can use a one-step method to generate the macroscopic cross section database (MCSD) of each grid element of the reactor core. This paper presents a systematic study on the influence of energy groups and fuel rod groups on MCSD. The Monte Carlo method for generating multi-group MCSD is studied based on the Monte Carlo program OpenMC with ENDF-B-VII.1 continuous energy cross section library. Through Monte Carlo simulation of the whole model, a fine 69 groups MCSD of lattice level can be directly generated by a one-step method, without leakage correction, and compared with 2 and 8 groups MCSDs. Furthermore, a method is proposed to group the fuel rods in the model according to the symmetry and neutron energy spectrum similarity. OpenMOC was used to test the generated MCSDs. The effective multiplication factors and the power distribution were in good agreement between OpenMC and OpenMOC results. It demonstrates that the Monte Carlo method is feasible to generate the highly accurate multi-group MCSD by the one-step method of full model calculation and the fuel grouping method.