Directional Distribution Research Articles

Effects of an Explicit Time-dependent Radiation Pressure Force on Trajectories of Primary Neutral Hydrogen in the Heliosphere

Radiation pressure exerted by solar photon output is salient to the motion of primary neutral hydrogen atoms streaming into the inner heliosphere directly from the local interstellar medium. The action of a time-dependent radiation pressure force, when coupled with the usual gravitational force, changes the characteristic velocities, and therefore energies, of the atoms when they reach regions in which explorer probes are present. A study is presented that uses a 2D code to backtrace neutral hydrogen trajectories from representative target points located 1 au from the Sun. It makes use of both a radiation pressure function and a function for the photoionization rate at 1 au that both oscillate with time based on measurements over a typical solar cycle, as well as a time-independent charge exchange ionization rate at 1 au. Assuming a Maxwellian distribution in the distant upwind direction, phase space data is calculated at the target points, at different moments in time. The dependence of the force on the radial particle velocity has been omitted in the analysis, such that the emphasis is on the effects of the global solar UV intensity variations through the solar cycle. This process allows for the analysis of direct and indirect Maxwellian components through time and space in the time-dependent force environment. Additionally, pseudo-bound orbits caused by energy losses associated with this force environment are observed, and their properties are evaluated with the aim of determining their effects on potential measurements by explorer probes.

Evaluation of Different Numerical Approaches to Modeling Flood Flows Over Groynes

AbstractThe hydraulic resistance of groynes is an important factor in the determination of design flood water levels on rivers and the assessment of how much these levels are lowered by modifying the groynes. In standard one‐ or two‐dimensional numerical hydrodynamic models for flood risk management, groynes are commonly represented as subgrid features with a local energy loss according to a weir formula. We tested this representation by using a two‐dimensional horizontal mesh at various groyne submergence degrees by comparing the results with those of flume experiments. We also compared the results with simulations using different 2D and 3D approaches on finer grids that incorporate groynes in the bed topography. In one of the two tested 3D models, complete Reynolds‐averaged Navier‐Stokes equations were solved. The second tested 3D model was constructed simpler by assuming hydrostatic pressure distribution in the vertical direction. We employed Delft3D software in construction and execution of all models. One of the 3D models did predict the hydraulic resistance at low submergence better than the standard model, but it slightly underestimated the resistance at higher submergences. Despite differences in flow characteristics, weirs and groynes were found to produce similar flow resistances for the same height and boundary conditions. Simulations of groyne modifications showed that hydraulic resistance decreased nonlinearly with groyne lowering and streamlining.

Evaluation Method of Out‐of‐Plane Deformation on Kirigami Structure with Repetitive Slit Patterns on Concentric Circles

In this study, we devised an evaluation method and a quantitative index for the radial distribution of the out‐of‐plane deformation of kirigami structures with a slit pattern on concentric circles. The concentric kirigami structure was deformed in the out‐of‐plane direction by pulling the center of the structure, and the out‐of‐plane deformation distribution in the radial direction was changed by changing the distance between the slits in the radial direction of the circle and the length on the circumference of the circle. We used a single quantitative index to express the radial distribution of out‐of‐plane deformation. If the design of the kirigami structure can be freely determined from the quantification index, it can significantly contribute to the realization of useful devices which uses the concentric kirigami structure. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

A Circular-Linear Probabilistic Model Based on Nonparametric Copula with Applications to Directional Wind Energy Assessment.

The joint probability density function of wind speed and wind direction serves as the mathematical basis for directional wind energy assessment. In this study, a nonparametric joint probability estimation system for wind velocity and direction based on copulas is proposed and empirically investigated in Inner Mongolia, China. Optimal bandwidth algorithms and transformation techniques are used to determine the nonparametric copula method. Various parameter copula models and models without considering dependency relationships are introduced and compared with this approach. The results indicate a significant advantage of employing the nonparametric copula model for fitting joint probability distributions of both wind speed and wind direction, as well as conducting correlation analyses. By utilizing the proposed KDE-COP-CV model, it becomes possible to accurately and reliably analyze how wind power density fluctuates in relation to wind direction. This study reveals the researched region possesses abundant wind resources, with the highest wind power density being highly dependent on wind direction at maximum speeds. Wind resources in selected regions of Inner Mongolia are predominantly concentrated in the northwest and west directions. These findings can contribute to improving the accuracy of micro-siting for wind farms, as well as optimizing the design and capacity of wind turbine generators.

Experimental study on tensile and fracture properties of continuous directional steel fibre reactive powder concrete

In this paper, an orientation method with pre-tensioning at both ends is proposed to successfully prepare continuously directional steel fibre reactive powder concrete (DSFRPC). The tensile and fracture properties are determined by splitting tensile, axial tensile and three-point notch fracture tests. The paper sets three different groups named C0, Group S and Group D, which presents non-fibre, randomly distributed fibre and directional fibre, respectively. The test results showed that: the splitting strength of Group D specimens increased quite significantly with the increase of fibre dosage. Compared to the Group S, the splitting strength of Group D was improved by 46.5%, 69.8%, and 66.1%, respectively. The specimens of C0 and Group S in the axial tensile test suffered typical single-seam brittle failure, which showed obvious strain softening characteristics. With the increase of fibre dosage, the damage mode of specimens in Group D changed from single-seam brittle damage to multi-seam ductile damage, showing better energy dissipation capacity. Under the same converted fibre dosage, the fracture energy enhancement ratios of Group D specimens were 14.7, 18.9 and 19.55, respectively. At a lower water-cement ratio, the toughening effect of continuous directional steel fibre specimens is more obvious. The toughening effect of the reactive powder concrete (RPC) of with continuous directional steel fibre is mainly reflected in the directional distribution of steel fibre produced by the interfacial adhesion and friction caused by the increase in energy dissipation, as well as the maintenance of a stronger grip between the “dispersed rebar” and the matrix. Based on current study, the future research should be focused on a wider range of materials, structural design, and environmental conditions to verify the effectiveness and reliability of DSFRPC in various applications.

On the Application Limits of the Parameter in Studying Variations of the Ancient Geomagnetic Field

To describe secular geomagnetic variation on geological timescales, statistical models have been widely used in recent decades. Currently, the most popular among these is the TK03 model (Tauxe and Kent, 2004). As other statistical models, TK03 numerically characterizes the amplitude of secular geomagnetic variation and the shape of the distribution of paleomagnetic directions which are considered as directly reflecting the directions of the geomagnetic field on the considered interval of geological time. For this purpose, three main parameters are used: the scatter Sb (or S) of the virtual geomagnetic poles, the elongation E of the distribution of paleomagnetic directions, and the direction of elongation of the distribution of paleomagnetic directions. The correct application of these parameters to describe ancient secular variation requires the satisfaction of certain, sometimes rather strict conditions. These conditions for the Sb and E parameters were considered in a number of previous publications, while the limits and conditions of application of parameter have not been studied in detail so far. This paper presents the results of mathematical modeling that allow us to evaluate the stability of the calculated values of this parameter as a function of the latitude of sampling, the number of samples used for its determination, the length of the time series on which this parameter is determined, as well as inclination shallowing and the degree of averaging when is estimated in sedimentary rocks. We also consider the extent to which the parameter can be sensitive to the presence and characteristics of the equatorial dipole component in the total geomagnetic field.

Micromechanics of contact-bound cohesive granular materials in confined compression.

The mechanical behavior of granular materials results from interparticle interactions, which are predominantly frictional. With the presence of even very small amounts of cohesion this frictional interparticle behavior significantly changes. In this study, we introduce trace amounts of cohesive binder between the intergranular contacts in a sample of quartz particles and apply one-dimensional (1D) compression loading. X-ray computed tomography is performed in situ during 1D compression. We make observations at three different length scales. At the macroscopic or ensemble scale, we track the evolution of the porosity, particle size and the stress-strain response during this compression. At the microstructure or interparticle scale, we compute the directional distribution of contacts and the particles. We also track the evolution of the fabric chains with continued compression. We also evaluate particle rotations, displacements, contact twist, rotation, and sliding. We show through our experiments that even a small amount of cohesion (as low as 1% by weight) significantly changes the response at multiple length scales. This interparticle cohesion suppresses the fragmentation of grains, alters force transmission and changes the structure of the ensemble.

The analysis of pedestrian flow in the smart city by improved DWA with robot assistance

With the acceleration of urbanization in China, the urban population continues to grow, leading to frequent occurrences of crowded public spaces, which in turn trigger traffic congestion and even safety accidents. In order to more effectively control pedestrian flow, enhance the efficiency and safety of public spaces, this experiment conducts in-depth research and improvement on the traditional Dynamic Window Approach (DWA), and applies it to the fine control of pedestrian flow. Specifically, this study comprehensively reviews and analyzes the characteristics of pedestrian traffic flow and the working principles of traditional DWA. Based on this, the shortcomings of traditional DWA in dealing with complex pedestrian flow scenarios are identified, and targeted improvement solutions are proposed. The core of this improvement scheme lies in the introduction of a new evaluation function, enabling DWA to more accurately balance various factors in the decision-making process, including pedestrian movement speed, direction, and spatial distribution. Subsequently, the improved DWA is validated through simulation experiments. The experimental scenario is set in an area of 18 m*18 m, and compared with traditional DWA, the improved DWA shows significant advantages in trajectory length and travel time. Specifically, the trajectory length of the traditional DWA robot is 19.4 m, with a required time of 34.8 s, while the trajectory length of the improved DWA robot is shortened to 18.7 m, and the time is reduced to 18.6 s. This result fully demonstrates the effectiveness of the improved DWA in optimizing pedestrian flow control. The improved DWA proposed in this study not only has strong scientific validity but also demonstrates high efficiency in practical applications. This study has important reference value for improving the safety of urban public spaces and improving pedestrian traffic flow conditions, and provides new ideas for the further development of pedestrian flow control technology in the future.

Pengaruh Online Customer Review Dan Perceived Risk Terhadap Keputusan Pembelian

Currently, the beauty care industry is experiencing significant sales growth. However, in 2022, the number of monthly web visits to Sociolla decreased. High perceived risk can make consumers hesitant to make purchases. Similarly, online customer reviews can greatly impact consumer confidence. This study aims to determine the effect of online customer reviews and perceived risk on purchasing decisions for Sociolla consumers in Medan city. The research employed a quantitative approach with an associative design. The study focused on Sociolla application users in Medan City, with a sample size of 96 respondents selected through non-probability purposive sampling. Primary data was collected through direct distribution of questionnaires, while secondary data was obtained through literature review. The study results suggest that online customer reviews have a significant positive impact on purchasing decisions. The t-count value of 4.478 (>1.985) and a significance value of 0.000 (<0.05) indicate this. Additionally, perceived risk also has a significant positive effect on purchasing decisions, with a t-count value of 2.049 (>1.985) and a significance value of 0.043 (<0.05), and a regression coefficient value of 0.134. During simultaneous testing, the variable of online customer reviews and perceived risk have a combined effect with a level of influence of 21.3%. The remaining 78.7% is influenced by factors outside the scope of this study.

Study on the distribution of average wind speeds at a mountainous bridge site for structural durability design

Conventional wind speed distribution methods (e.g., Rayleigh distribution and Weibull distribution) may not adequately capture complex characteristics of wind fields in mountainous areas. To address this problem, this study proposes a semi-parametric mix method for modeling the distribution of average wind speeds based on the combination of nonparametric Kernel Density Estimation (KDE) and Generalized Pareto Distribution (GPD). In the proposed method, KDE focuses on capturing the distribution in the main part of average wind speeds, while GPD aims at performing the distribution in terms of those in the extreme part. The segment point (i.e., the threshold) between KDE and GPD distributions is determined based on the combination of conditional mean excesses criterion and empirical rule. Meanwhile, the selection of modeling parameters should ensure that the mix distribution model is continuous and differentiable at the identified threshold point. Then, the commonly-used conditional probability model is further introduced to describe the wind direction distribution. Finally, a case study based on the measured 10-min average wind speeds at a mountainous bridge site is employed to demonstrate the effectiveness of the proposed method. The results indicate that: (1) the distribution of omnidirectional average wind speeds in the mountainous bridge site exhibits an obviously single-peak characteristic, while those considering wind directionality present a certain bimodal characteristic; (2) the proposed method can effectively describe wind speed distributions with different statistical characteristics, and the fitting accuracy outperforms the frequently-employed Weibull distribution model.

Optimal permeance ratio, flux direction and layer distribution in composite asymmetric membranes composed of sequences of layers obeying real-power flux laws

In this study, the optimal permeance ratio and layers distribution in multilayer membranes and thin films in which each layer obeys the following real-power law: Flux=πi(P1,ini−P2,ini) are determined for any positive real values of ni. Such an exponent has a physical meaning in several cases, such as: diffusion-controlled permeation of hydrogen in metal membranes i) under infinite-dilution conditions (n = 0.5), and ii) under higher-concentration ones (0.5 < n < 1.5), iii) desorption-limited permeation (n = 1) in the same type of membranes, Knudsen-type diffusional mechanism (n = 1) and viscous flow (n = 2) in microporous membranes. Furthermore, n is equal to 4 in radiation-driven thermal flux. The work considers two generic layers of different thicknesses and exponents, for which it is proven the existence of a general optimal permeance ratio π1/π2 maximising the flux ratio, which is found to be equal to the inverse of the ratio between the respective maximum theoretical driving forces that can be established in each layer. Such an optimal permeance ratio is also proven to be a global optimum. Afterwards, we provide a theoretical generalisation of this optimality to whatever types of driving forces. Then, we provide a demonstration that the highest species permeating flux is always established when feeding it from the layer side with the highest exponent independently of the permeance ratio. As an important consequence, to maximise flux, a multilayer membrane/thin film should be fabricated by depositing the layers in cascade according to the ascending or descending exponents, and should be used in a configuration in which the flux flows from the layer with the highest pressure exponent to the layer with the lowest one. It is also shown that there exists an optimal value of the lower exponent n1 that maximizes the flux ratio keeping constant the other parameters. Finally, we showed that a virial-type linear combination of polynomial driving forces can be approximated by the empirical flux law investigated. Overall, our results are valid not only for whatever type of composite membranes and thin films (metallic, ceramic, polymeric and hybrid ones), but also for any sequential system involving a flux of whatever physical entity obeying the aforementioned law, such as heat transfer in the presence of radiation, non-linear electrical resistances and possible others.

Three-dimensional forest structure features extraction based on TomoSAR

Abstract. Forest structure is an important indicator for evaluating forest ecosystem and an indispensable input parameter for estimating forest carbon sink. Synthetic Aperture Radar (SAR) Tomography (TomoSAR), as a novel microwave remote sensing technique with 3D imaging capability, has been demonstrated to be an valuable tool for accurate inversion of forest structure. At present, the forest vertical structure parameters inversion is almost all concentrated on the forest height estimation. However, the spatial structure of forests is complex, and it is not enough to only use the forest height to express the forest structure. This fails to identify tree canopy, branch layer and underlying vegetation layer, etc., resulting in the partial and inaccurate forest vertical structure information. To solve this problem, this paper constructs 3D structural indices from tomograms, namely Horizontal Structure Index (HS) and Vertical Structure Index (VS). The HS primarily describes canopy density, compensating for the lack of information on the horizontal dimension of forest structure provided by traditional TomoSAR techniques; while VS describes the complexity of canopy distribution in the altitude direction, further enriching information on forest structure vertically. In order to verify their feasibility and validity, HS and VS are extracted using six fully-polarized L-band SAR images covering the Krycklan watershed in Sweden. Moreover, the accuracy is verified by using external high-precision LiDAR data. The results indicate a strong correlation between the structural indices extracted from TomoSAR and those extracted from LiDAR.

Rapid determination of seismic influence field based on mobile communication big data-A case study of the Luding Ms 6.8 earthquake in Sichuan, China.

Smartphone location data provide the most direct field disaster distribution data with low cost and high coverage. The large-scale continuous sampling of mobile device location data provides a new way to estimate the distribution of disasters with high temporal-spatial resolution. On September 5, 2022, a magnitude 6.8 earthquake struck Luding County, Sichuan Province, China. We quantitatively analyzed the Ms 6.8 earthquake from both temporal and geographic dimensions by combining 1,806,100 smartphone location records and 4,856 spatial grid locations collected through communication big data with the smartphone data under 24-hour continuous positioning. In this study, the deviation of multidimensional mobile terminal location data is estimated, and a methodology to estimate the distribution of out-of-service communication base stations in the disaster area by excluding micro error data users is explored. Finally, the mathematical relationship between the seismic intensity and the corresponding out-of-service rate of communication base stations is established, which provides a new technical concept and means for the rapid assessment of post-earthquake disaster distribution.

Spatial and Temporal Characteristic Analysis and Risk Assessment of Global Highly Pathogenic Avian Influenza H5N8 Subtype

H5N8 HPAI is a highly infectious avian disease that now poses a serious threat and potential risk to poultry farming, wild birds, and public health. In this study, to investigate the seasonality and transmission directionality of global H5N8 HPAI, the spatial and temporal analysis of H5N8 HPAI was conducted using time series decomposition and directional distribution analysis. An ecological niche model was developed for H5N8 HPAI in poultry to identify areas at high risk of H5N8 HPAI in poultry and associated risk factors. The results indicated that three global pandemics of H5N8 HPAI emerged from 2014 to 2022, all showing a southeast–northwest distribution direction. H5N8 HPAI occurred more frequently in winter and less frequently in summer. The southwestern border region and the southeastern region of North America, the southern region of South America, most of Europe, the southern border region and the northern border region of Africa, and the southwestern region and the southeastern region of Asia provide the suitable environment for the occurrence of H5N8 HPAI in poultry. Chicken density, duck density, population density, bio1 (annual mean temperature), and land cover were considered important variables for the occurrence of H5N8 HPAI in poultry. This study can help optimize the use of resources and provide new information for policymakers to carry out prevention and control efforts.

Preparation of large-area superhydrophobic and anti-icing 3D micro-nano-structures using femtosecond Bessel beams with fluorination treatment

This study proposes a simple strategy for overcoming the adverse effects of icing on material surfaces and improving the anti-icing performance of these surfaces. First, a femtosecond Gaussian beam is transformed into a femtosecond Bessel beam through spatial shaping to improve its energy distribution in the propagation direction while avoiding the adverse effects of defocusing during processing, thereby achieving large-area, consistent micro-nano-fabrication. Subsequently, the surface wettability of the considered material is controlled through the preparation of a functionalized three-dimensional micro-nano-structure using fluorination, transforming the material surface from superhydrophilic to superhydrophobic, thereby directly preventing the adhesion of subcooled droplets. Static-droplet condensation tests and dynamic anti-icing tests in simulated freezing-rain environments demonstrated that the proposed strategy can considerably increase the droplet condensation time and reduce the amount of surface icing. Overall, the strategy provides an efficient, high-quality, highly reproducible solution to the problem of surface icing.

Process design for flexible T-profile-rolling of tailored thickness stringers with different cross sections

A new process, called flexible T-profile-rolling, is being developed to produce T-profiles with variable thickness distribution in longitudinal direction by flexible rolling. These tailored thicknesses allow for load-adapted and weight-optimised design of stringer profiles for aircrafts. The new process can replace the chemical milling currently used in the production of stringers and enables a more environmentally friendly and resource-saving production of the thickness changes. In order to achieve uniform thicknesses in the web and flange of the T-profile, a new rolling stand with rolls inclined against the T-profile and varying roll radii was developed. However, the varying roll radii cause different longitudinal strains in the profile cross-section due to the varied contact areas between the roll and the rolling stock, resulting in unwanted profile bowing. This bowing depends on the profile dimensions, as the adjacent roll radii vary over the profile cross-sections.This paper demonstrates the effects of profile dimensions on deflection through numerical investigations with different web heights, flange widths and thickness reductions. A straightening method is presented to obtain straight profiles as a function of the profile dimensions. The results show that this process can produce almost straight T-profiles with variable thicknesses for different cross section dimensions.

Evaluation of RPV closure head penetration integrity considering fitting and residual stresses

To ensure the structure integrity of the Reactor Pressure Vessel (RPV), the main challenge is the embrittlement of beltline material. However, the stress is more complex for the regions of Closure Head Penetration (CHP). Feedback of leakage at the CHP has been found during in-service inspection. Although the detailed mechanical evaluation of the RPV head and the CHP has been carried out by many international institutions, there are limited studies to concern structure integrity of CHP tube. The systematic analysis of the influence of material strength matching, assemble stress, the Welding Residual (WR) stress and work pressure load on the fracture is also limited. In this paper, the systematic influence of these factors is analyzed, and the distribution characteristics of Stress Intensity Factor (SIF) and the crack propagation characteristics are studied. The 2D model and accurate 3D model are carried out using the finite element method. The results show that the WR stress on the outer surface of the CHP and the area adjacent to the weld is larger than the yield strength of the material. There is a gap between the RPV and the upper part of the CHP. The attenuation rate of the WR stress in the outlet direction of RPV is lower than that in the inlet direction, so cracks are more likely to occur in the out of direction. The influence of WR stress on the circumferential stress distribution and fracture parameters in the wall thickness direction of CHP is bigger than the influence of assemble load and design condition load. However, the overall stress of CHP is low. The SIF values along the crack front have an asymmetric distribution, and the SIF value is very small. As the fatigue crack propagation life is much longer than the assumed limit in the design lifetime, the risk of fracture and crack fatigue propagation caused by mechanical stress is low.

Determining Critical Points in Fish Distribution and Calculation of Income UD. Sumber Rezeki Laut, Tuban Regency

This study aims to evaluate the fish distribution activities in UD. Sumber Rezeki Laut, alongside the fish handling during distribution, and critical points of fish quality decline during distribution. This research uses descriptive analysis, critical point analysis, organoleptic tests, and income analysis. Distribution handling is divided into two types, namely direct distribution handling and indirect distribution handling. The most important handling of both types of distribution includes maintaining the right temperature during the process, transferring fish to UD. Sumber Rezeki Laut, changing fish containers, cleaning and soaking fish, and distributing fish to Balekambang Market. However, the long travel distance required to distribute the fishes has the potential to reduce the quality of the fish, as evidenced by the decrease in fish quality observed during the distribution trials. Organoleptic test results showed that the quality of the fish decreased from when it was purchased until it reached the wholesaler. Meanwhile, when calculating distribution costs, the highest result for direct distribution was IDR1,335,987, and the lowest was IDR372,995. The highest income from indirect distribution was IDR1,544,001, while the lowest was IDR399,993. To ensure good fish quality, UD. Sumber Rezeki Laut needs to improve its human resource capabilities to become more efficient and produce quality products for consumers.

Modified calculation model of train-induced aerodynamic pressure on vertical noise barriers considering the train geometry effect

High-speed trains (HSTs) generate air disturbance, leading to significant aerodynamic pressure on the noise barriers. Differences in train geometry result in variations in the aerodynamic pressure on noise barriers, implying that existing European standard calculation models may not necessarily be suitable for all types of HSTs. In this paper, the influence of the width, height, and nose length of the train on the aerodynamic pressure on vertical noise barriers was studied using computational fluid dynamics (CFD) simulations. Results showed that taller and wider trains result in greater aerodynamic loads on noise barriers. Conversely, an increase in the nose length of a train leads to a reduction in such pressure. Using grey relational analysis, correlation of various factors with the train-induced aerodynamic pressure is, from strong to weak: distance to the track center, width, height, and nose length of the train. Building upon the EN 14067-4 calculation model, the shape coefficients of trains with varying geometric characteristics were derived using the simulation data obtained in this study. A modified pressure calculation model was established accounting for the differences in geometric features of HSTs and pressure distribution in the vertical direction of noise barriers and validated using relevant data from the literature.

Neutronic simulation of Traveling Wave Reactor (TWR) core in multi-cycles using Monte Carlo method

Abstract An ingenious design, Traveling Wave Reactor (TWR) has been suggested for full exploitation of uranium resources in next generation of nuclear reactors. This design involves the slow propagation of a nuclear fission wave through a long initially subcritical core and the transmutation of nuclear fuel. It has been widely proven that the initiation and propagation of fission waves are feasible prompting the Terra Power Company to conduct preliminary commercialization studies on this project. In equilibrium state, the shapes of the neutron flux, nuclide densities and power density distribution remain constant but the burning region moves in axial (or radial) directions. In this case the in situ fissile material production and consumption drives the operation. Only natural or depleted uranium is required for fresh fuel region. However, in equilibrium state, the burning region contains a spectrum of fission products as well as higher actinides whose are not easily available for initial TWR core construction. One solution is based on the use of enriched uranium in the first cycle to ignite the fission wave and then employment of the composition in subsequent cycles up to the equilibrium state. The main objective of this work is the feasibility study of forming a fission wave as well as the neutronic analysis of a Gas-Cooled Traveling Wave Reactor in various cycles up to the equilibrium one. The MCNP Monte Carlo code was utilized for the analysis of criticality and burn-up calculation. In each cycle, the axial fresh fuel loading and spent fuel discharge, were subjected to analysis. Results showed that the equilibrium state can be obtained by using special arrays of absorbers, from the third cycle where the shape of neutron flux and the power density distribution in axial direction remain unchanged.