scholarly journals A New Accurate Numerical Method Based on Shifted Chebyshev Series for Nuclear Reactor Dynamical Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Yasser Mohamed Hamada
Keyword(s):  
Nuclear Reactor ◽  
Approximate Solutions ◽  
Time Interval ◽  
Neutron Density ◽  
Chebyshev Series ◽  
System A ◽  
Temperature Feedback ◽  
Exponential Rate Of Convergence ◽  
Point Kinetics ◽  
The Given

A new method based on shifted Chebyshev series of the first kind is introduced to solve stiff linear/nonlinear systems of the point kinetics equations. The total time interval is divided into equal step sizes to provide approximate solutions. The approximate solutions require determination of the series coefficients at each step. These coefficients can be determined by equating the high derivatives of the Chebyshev series with those obtained by the given system. A new recurrence relation is introduced to determine the series coefficients. A special transformation is applied on the independent variable to map the classical range of the Chebyshev series from [-1,1] to [0,h]. The method deals with the Chebyshev series as a finite difference method not as a spectral method. Stability of the method is discussed and it has proved that the method has an exponential rate of convergence. The method is applied to solve different problems of the point kinetics equations including step, ramp, and sinusoidal reactivities. Also, when the reactivity is dependent on the neutron density and step insertion with Newtonian temperature feedback reactivity and thermal hydraulics feedback are tested. Comparisons with the analytical and numerical methods confirm the validity and accuracy of the method.

scholarly journals Solution of Point Reactor Neutron Kinetics Equations with Temperature Feedback by Singularly Perturbed Method

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Wenzhen Chen ◽  
Jianli Hao ◽  
Ling Chen ◽  
Haofeng Li
Keyword(s):  
Nuclear Reactor ◽  
Large Range ◽  
Accurate Solution ◽  
Average Density ◽  
Singularly Perturbed ◽  
Neutron Density ◽  
Delayed Neutron ◽  
Small Step ◽  
Neutron Kinetics ◽  
Temperature Feedback

The singularly perturbed method (SPM) is proposed to obtain the analytical solution for the delayed supercritical process of nuclear reactor with temperature feedback and small step reactivity inserted. The relation between the reactivity and time is derived. Also, the neutron density (or power) and the average density of delayed neutron precursors as the function of reactivity are presented. The variations of neutron density (or power) and temperature with time are calculated and plotted and compared with those by accurate solution and other analytical methods. It is shown that the results by the SPM are valid and accurate in the large range and the SPM is simpler than those in the previous literature.

An Integral Method for Solving the Point Reactor Neutron Kinetics Equations with Newtonian Temperature Feedback

2013 ◽  
Vol 732-733 ◽  
pp. 83-89
Author(s):  
Gen Fan ◽  
Wen Bin Liu
Keyword(s):  
Basis Function ◽  
Integral Method ◽  
Numerical Evaluation ◽  
Power Reactor ◽  
Neutron Density ◽  
Delayed Neutron ◽  
Time Step ◽  
Neutron Kinetics ◽  
Temperature Feedback ◽  
Point Kinetics

A numerical integral method to efficiently solve the point kinetics equations with Newtonian temperature feedback is described and investigated, which employs the better basis function (BBF) for the approximation of the neutron density in integral of one time step. The numerical evaluation is performed by the developed BBF code. The code can solve the general non-linear kinetics problems with six groups of delayed neutron. For the application purposes, the developed code and the method are tested by using a variety of problems, including ramp reactivity input with or without temperature feedback. The results are shown that the BBF method is clearly an effective and accurate numerical method for solving the point kinetics equations with Newtonian temperature feedback, and it can be used in real time power reactor forecasting in order to prevent the reactivity accidents.

Utilization of remote sensing for estimation of scale of cutting and growing of forest zones

2017 ◽  
Vol 920 (2) ◽  
pp. 57-60
Author(s):  
F.E. Guliyeva
Keyword(s):  
Remote Sensing ◽  
Fixed Time ◽  
Time Interval ◽  
Time Points ◽  
Average Value ◽  
Time Period ◽  
Remote Estimation ◽  
The Given ◽  
Forest Cutting

The study of results of relevant works on remote sensing of forests has shown that the known methods of remote estimation of forest cuts and growth don’t allow to calculate the objective average value of forests cut volume during the fixed time period. The existing mathematical estimates are not monotonous and make it possible to estimate primitively the scale of cutting by computing the ratio of data in two fixed time points. In the article the extreme properties of the considered estimates for deforestation and reforestation models are researched. The extreme features of integrated averaged values of given estimates upon limitations applied on variables, characterizing the deforestation and reforestation processes are studied. The integrated parameter, making it possible to calculate the averaged value of estimates of forest cutting, computed for all fixed time period with a fixed step is suggested. It is shown mathematically that the given estimate has a monotonous feature in regard of value of given time interval and make it possible to evaluate objectively the scales of forest cutting.

scholarly journals Optimal Control and Positional Controllability in a One-Sector Economy

Games ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 11
Author(s):  
Nikolai Grigorenko ◽  
Lilia Luk’yanova
Keyword(s):  
Optimal Control ◽  
Production Capacity ◽  
Quality Criterion ◽  
Zero Order ◽  
Suboptimal Control ◽  
Time Interval ◽  
Bounded Control ◽  
Optimal Value ◽  
Current Production ◽  
The Given

A model of production funds acquisition, which includes two differential links of the zero order and two series-connected inertial links, is considered in a one-sector economy. Zero-order differential links correspond to the equations of the Ramsey model. These equations contain scalar bounded control, which determines the distribution of the available funds into two parts: investment and consumption. Two series-connected inertial links describe the dynamics of the changes in the volume of the actual production at the current production capacity. For the considered control system, the problem is posed to maximize the average consumption value over a given time interval. The properties of optimal control are analytically established using the Pontryagin maximum principle. The cases are highlighted when such control is a bang-bang, as well as the cases when, along with bang-bang (non-singular) portions, control can contain a singular arc. At the same time, concatenation of singular and non-singular portions is carried out using chattering. A bang-bang suboptimal control is presented, which is close to the optimal one according to the given quality criterion. A positional terminal control is proposed for the first approximation when a suboptimal control with a given deviation of the objective function from the optimal value is numerically found. The obtained results are confirmed by the corresponding numerical calculations.

Evaluation of Effect of Nd:YAG and Er:YAG Lasers on the Periodontal Pathogens: A Systematic Review

2020 ◽  
Author(s):  
Hosein Eslami
Keyword(s):  
Systematic Review ◽  
Chronic Periodontitis ◽  
Complementary Therapy ◽  
Root Surface ◽  
Laser Wavelength ◽  
Time Interval ◽  
Periodontal Pathogens ◽  
Probing Depth ◽  
Treatment Procedures ◽  
The Given

Introduction: By removing the periodontal pathogens and even the invasive bacteria attacking the tissues as well as the lack of normal periodontal treatment procedures, using a laser, as a complementary therapy, can have positive and useful impacts. The present study aims at investigating the impacts of Nd:YAG and Er:YAG laser on periodontal pathogens. Materials and Methods: In this systematic review, articles in the databases of Google Scholar, PubMed and Scopus were searched within 2000-2020. All information is classified into a table. Results: In searching the aforementioned databases and considering the given time interval, 78 articles were found in connection to the searched keywords and abstracts. Once the repeated titles and articles were deleted, 25 studies were selected which were decreased to 16 by the meticulous review by the assessment team. The full text of these 16 articles was reviewed. To make the final choice, 8 articles had the inclusion criteria which included the objectives of this study. Conclusion: To use the laser in treating the chronic periodontitis, an evidence-based study seems to be conducted. A few scientific pieces of evidence are indicating the advantage of a special laser wavelength in the common treatments.Based on most researches reviewed in this study, the results of the complementary application of Nd:YAG and Er:YAG lasers in treating the chronic periodontitis are the better than the ones obtained from the normal teeth scaling and planning the teeth root surface in terms of the reduced probing depth and subgingival bacteria population. The decision was made to use the laser in periodontal surgery based on the advantages such as hemostasis and less pain after the treatment. However, more studies are needed to apply the laser in periodontal treatments.

Development and Application of Multi-Physics Safety Analysis Code for Advanced Liquid Metal Cooled Reactor

2018 ◽  
Author(s):  
Chi Wang ◽  
Xuebei Zhang ◽  
Jingchao Feng ◽  
Muhammad Shehzad Khan ◽  
Minyou Ye ◽  
...  
Keyword(s):  
Nuclear Reactor ◽  
Safety Analysis ◽  
Coolant Temperature ◽  
Medium Size ◽  
High Tech ◽  
Fuel Temperature ◽  
Flow Phenomena ◽  
Nuclear Reactor Safety ◽  
Cfd Method ◽  
Point Kinetics

The simulation of 3D thermal-hydraulic problem for the pool type fast reactors, is one of the necessary and great importance. Most system codes can’t be used to simulate multi-dimensional thermal-hydraulics problems, whereas, the CFD method is suitable to deal with these type of simulation challenges. Based on the CFD method, a neutronics and thermohydraulic coupling code FLUENT/PK for nuclear reactor safety analysis by coupling the commercial CFD code FLUENT with the point kinetics model (PKM) and the pin thermal model (PTM) is developed by University of Science and Technology of China (USTC). The coupled code is verified by comparing with a series of benchmarks on beam interruptions in a lead-bismuth-cooled and MOX-fuelled accelerator-driven system. The variations of transient power, fuel temperature and outlet coolant temperature all agree well with the benchmark results. The validation results show that the code can be used to simulate the transient accidents of critical and sub-critical lead/lead-bismuth cooled reactors. Then this coupling code is used to evaluate the safety performance of MYRRHA (Multi-purpose Hybrid Research Reactor for High-tech Applications) at unprotected beam over-power (UBOP) accident, and M2LFR-1000 (Medium-size Modular Lead-cooled Fast Reactor) at the unprotected transient over-power (UTOP) and unprotected loss of flow (ULOF) accident. The transient power, the temperature of coolant and fuel and multi-dimensional flow phenomena in upper plenum and lower plenum are presented and discussed in this paper.

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