Pub Date : 2021-01-01DOI: 10.4236/ajcm.2021.113013
Z. M. Alaofi, Talaat Sayed Ali, F. A. Alaal, S. Dragomir
In the present paper, we introduce a non-polynomial quadratic spline method for solving third-order boundary value problems. Third-order singularly perturbed boundary value problems occur frequently in many areas of applied sciences such as solid mechanics, quantum mechanics, chemical reactor theory, Newtonian fluid mechanics, optimal control, convection-diffusion proc-esses, hydrodynamics, aerodynamics, etc. These problems have various im-portant applications in fluid dynamics. The procedure involves a reduction of a third-order partial differential equation to a first-order ordinary differential equation. Truncation errors are given. The unconditional stability of the method is analysed by the Von-Neumann stability analysis. The developed method is tested with an illustrated example, and the results are compared with other methods from the literature, which shows the applicability and feasibility of the presented method. Furthermore, a graphical comparison between analytical and approximate solutions is also shown for the illustrated example.
{"title":"Quartic Non-Polynomial Spline for Solving the Third-Order Dispersive Partial Differential Equation","authors":"Z. M. Alaofi, Talaat Sayed Ali, F. A. Alaal, S. Dragomir","doi":"10.4236/ajcm.2021.113013","DOIUrl":"https://doi.org/10.4236/ajcm.2021.113013","url":null,"abstract":"In the present paper, we introduce a non-polynomial quadratic spline method for solving third-order boundary value problems. Third-order singularly perturbed boundary value problems occur frequently in many areas of applied sciences such as solid mechanics, quantum mechanics, chemical reactor theory, Newtonian fluid mechanics, optimal control, convection-diffusion proc-esses, hydrodynamics, aerodynamics, etc. These problems have various im-portant applications in fluid dynamics. The procedure involves a reduction of a third-order partial differential equation to a first-order ordinary differential equation. Truncation errors are given. The unconditional stability of the method is analysed by the Von-Neumann stability analysis. The developed method is tested with an illustrated example, and the results are compared with other methods from the literature, which shows the applicability and feasibility of the presented method. Furthermore, a graphical comparison between analytical and approximate solutions is also shown for the illustrated example.","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70509601","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.4236/ajcm.2021.114020
Nasrin Bastani, A. Vard, Mehdi Jabalameli, Vahid Bastani
Zernike polynomials have been used in different fields such as optics, astronomy, and digital image analysis for many years. To form these polynomials, Zernike moments are essential to be determined. One of the main issues in realizing the moments is using factorial terms in their equation which causes higher time complexity. As a solution, several methods have been presented to reduce the time complexity of these polynomials in recent years. The purpose of this research is to study several methods among the most popular recursive methods for fast Zernike computation and compare them together by a global theoretical evaluation system called worst-case time complexity. In this study, we have analyzed the selected algorithms and calculated the worst-case time complexity for each one. After that, the results are represented and explained and finally, a conclusion has been made by com-paring these criteria among the studied algorithms. According to time complexity, we have observed that although some algorithms such as Wee method and Modified Prata method were successful in having the smaller time complexities, some other approaches did not make any significant difference compared to the classical algorithm.
{"title":"A Theoretical Comparison among Recursive Algorithms for Fast Computation of Zernike Moments Using the Concept of Time Complexity","authors":"Nasrin Bastani, A. Vard, Mehdi Jabalameli, Vahid Bastani","doi":"10.4236/ajcm.2021.114020","DOIUrl":"https://doi.org/10.4236/ajcm.2021.114020","url":null,"abstract":"Zernike polynomials have been used in different fields such as optics, astronomy, and digital image analysis for many years. To form these polynomials, Zernike moments are essential to be determined. One of the main issues in realizing the moments is using factorial terms in their equation which causes higher time complexity. As a solution, several methods have been presented to reduce the time complexity of these polynomials in recent years. The purpose of this research is to study several methods among the most popular recursive methods for fast Zernike computation and compare them together by a global theoretical evaluation system called worst-case time complexity. In this study, we have analyzed the selected algorithms and calculated the worst-case time complexity for each one. After that, the results are represented and explained and finally, a conclusion has been made by com-paring these criteria among the studied algorithms. According to time complexity, we have observed that although some algorithms such as Wee method and Modified Prata method were successful in having the smaller time complexities, some other approaches did not make any significant difference compared to the classical algorithm.","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70509501","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.4236/ajcm.2021.114016
Wensheng Zhang, Yijun Li
In this paper, we investigate the elastic wave full-waveform inversion (FWI) based on the trust region method. The FWI is an optimization problem of minimizing the misfit between the observed data and simulated data. Usually, the line search method is used to update the model parameters iteratively. The line search method generates a search direction first and then finds a suitable step length along the direction. In the trust region method, it defines a trial step length within a certain neighborhood of the current iterate point and then solves a trust region subproblem. The theoretical methods for the trust region FWI with the Newton type method are described. The algorithms for the truncated Newton method with the line search strategy and for the Gauss-Newton method with the trust region strategy are presented. Numerical computations of FWI for the Marmousi model by the L-BFGS method, the Gauss-Newton method and the truncated Newton method are completed. The comparisons between the line search strategy and the trust region strategy are given and show that the trust region method is more efficient than the line search method and both the Gauss-Newton and truncated Newton methods are more accurate than the L-BFGS method.
{"title":"Elastic Full Waveform Inversion Based on the Trust Region Strategy","authors":"Wensheng Zhang, Yijun Li","doi":"10.4236/ajcm.2021.114016","DOIUrl":"https://doi.org/10.4236/ajcm.2021.114016","url":null,"abstract":"In this paper, we investigate the elastic wave full-waveform inversion (FWI) based on the trust region method. The FWI is an optimization problem of minimizing the misfit between the observed data and simulated data. Usually, the line search method is used to update the model parameters iteratively. The line search method generates a search direction first and then finds a suitable step length along the direction. In the trust region method, it defines a trial step length within a certain neighborhood of the current iterate point and then solves a trust region subproblem. The theoretical methods for the trust region FWI with the Newton type method are described. The algorithms for the truncated Newton method with the line search strategy and for the Gauss-Newton method with the trust region strategy are presented. Numerical computations of FWI for the Marmousi model by the L-BFGS method, the Gauss-Newton method and the truncated Newton method are completed. The comparisons between the line search strategy and the trust region strategy are given and show that the trust region method is more efficient than the line search method and both the Gauss-Newton and truncated Newton methods are more accurate than the L-BFGS method.","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70509387","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-01-01DOI: 10.4236/ajcm.2021.114021
Liang. He, Shuanghong Chen
In this paper, we investigate the periodic wave solutions and solitary wave solutions of a (2+1)-dimensional Korteweg-de Vries (KDV) equation by ap-plying Jacobi elliptic function expansion method. Abundant types of Jacobi elliptic function solutions are obtained by choosing different coefficients p, q and r in the elliptic equation. Then these solutions are coupled into an auxiliary equation and substituted into the (2+1)-dimensional KDV equation. As a result, a large number of complex Jacobi elliptic function solutions are obtained, and many of them have not been found in other documents. As 1 m → , some complex solitary solutions are also obtained correspondingly. These solutions that we obtained in this paper will be helpful to understand the physics of the (2+1)-dimensional KDV equation.
{"title":"Periodic Wave Solutions and Solitary Wave Solutions of the (2+1)-Dimensional Korteweg-de-Vries Equatio","authors":"Liang. He, Shuanghong Chen","doi":"10.4236/ajcm.2021.114021","DOIUrl":"https://doi.org/10.4236/ajcm.2021.114021","url":null,"abstract":"In this paper, we investigate the periodic wave solutions and solitary wave solutions of a (2+1)-dimensional Korteweg-de Vries (KDV) equation by ap-plying Jacobi elliptic function expansion method. Abundant types of Jacobi elliptic function solutions are obtained by choosing different coefficients p, q and r in the elliptic equation. Then these solutions are coupled into an auxiliary equation and substituted into the (2+1)-dimensional KDV equation. As a result, a large number of complex Jacobi elliptic function solutions are obtained, and many of them have not been found in other documents. As 1 m → , some complex solitary solutions are also obtained correspondingly. These solutions that we obtained in this paper will be helpful to understand the physics of the (2+1)-dimensional KDV equation.","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70509539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-01DOI: 10.4236/ajcm.2020.104033
Y. Chu
Elegans are one of the best model organisms in neural researches, and tropism movement is a typical learning and memorizing activity. Based on one imaging technique called Fast Track-Capturing Microscope (FTCM), we investigated the movement regulation. Two movement patterns are extracted from various trajectories through analysis on turning angle. Then we applied this classification on trajectory regulation on the compound gradient field, and theoretical results corresponded with experiments well, which can initially verify the conclusion. Our breakthrough is performed computational geometric analysis on trajectories. Several independent features were combined to describe movement properties by principal composition analysis (PCA) and support vector machine (SVM). After normalizing all data sets, no-supervising machine learning was processed along with some training under certain supervision. The final classification results performed perfectly, which indicates the further application of such computational analysis in biology researches combining with machine learning.
{"title":"Computational Geometric Analysis for C. elegans Trajectories on Thermal and Salinity Gradient","authors":"Y. Chu","doi":"10.4236/ajcm.2020.104033","DOIUrl":"https://doi.org/10.4236/ajcm.2020.104033","url":null,"abstract":"Elegans are one of the best model organisms in neural researches, and tropism movement is a typical learning and memorizing activity. Based on one imaging technique called Fast Track-Capturing Microscope (FTCM), we investigated the movement regulation. Two movement patterns are extracted from various trajectories through analysis on turning angle. Then we applied this classification on trajectory regulation on the compound gradient field, and theoretical results corresponded with experiments well, which can initially verify the conclusion. Our breakthrough is performed computational geometric analysis on trajectories. Several independent features were combined to describe movement properties by principal composition analysis (PCA) and support vector machine (SVM). After normalizing all data sets, no-supervising machine learning was processed along with some training under certain supervision. The final classification results performed perfectly, which indicates the further application of such computational analysis in biology researches combining with machine learning.","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":"10 1","pages":"578-590"},"PeriodicalIF":0.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45088249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-01DOI: 10.4236/ajcm.2020.104032
H. Sarafian
Two electrically charged rings of different sizes are assembled along their common vertical symmetry axis through their centers. The bottom ring is secured on a horizontal support while the top one is loose. For a set of practical values characterizing the charged rings we envision a scenario where the mutual electric repulsion between the rings and the weight of the top ring results in stable nonlinear oscillations. To quantify the characteristics of the oscillations, we utilize a Computer Algebra System specifically Mathematica [1]. We accompany the analysis with a simulation for a comprehensive visual understanding.
{"title":"Nonlinear Oscillations of a Pair of Charged Rings","authors":"H. Sarafian","doi":"10.4236/ajcm.2020.104032","DOIUrl":"https://doi.org/10.4236/ajcm.2020.104032","url":null,"abstract":"Two electrically charged rings of different sizes are assembled along their common vertical symmetry axis through their centers. The bottom ring is secured on a horizontal support while the top one is loose. For a set of practical values characterizing the charged rings we envision a scenario where the mutual electric repulsion between the rings and the weight of the top ring results in stable nonlinear oscillations. To quantify the characteristics of the oscillations, we utilize a Computer Algebra System specifically Mathematica [1]. We accompany the analysis with a simulation for a comprehensive visual understanding.","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44641072","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-01DOI: 10.4236/ajcm.2020.104029
D. Cacuci, R. Fang
This work extends to third-order previously published work on developing the adjoint sensitivity and uncertainty analysis of the numerical model of a polyethylene-reflected plutonium (acronym: PERP) OECD/NEA reactor physics benchmark. The PERP benchmark comprises 21,976 imprecisely known (uncertain) model parameters. Previous works have used the adjoint sensitivity analysis methodology to compute exactly and efficiently all of the 21,976 first-order and (21,976)2 second-order sensitivities of the PERP benchmark’s leakage response to all of the benchmark’s uncertain parameters, showing that the largest and most consequential 1st- and 2nd-order response sensitivities are with respect to the total microscopic cross sections. These results have motivated extending the previous adjoint-based derivations to third-order, leading to the derivation, in this work, of the exact mathematical expressions of the (180)3 third-order sensitivities of the PERP leakage response with respect to these total microscopic cross sections. The formulas derived in this work are valid not only for the PERP benchmark but can also be used for computing the 3rd-order sensitivities of the leakage response of any nuclear system involving fissionable material and internal or external neutron sources. Subsequent works will use the adjoint-based mathematical expressions obtained in this work to compute exactly and efficiently the numerical values of these (180)3 third-order sensitivities (which turned out to be very large and consequential) and use them for a third-order uncertainty analysis of the PERP benchmark’s leakage response.
{"title":"Third-Order Adjoint Sensitivity Analysis of an OECD/NEA Reactor Physics Benchmark: I. Mathematical Framework","authors":"D. Cacuci, R. Fang","doi":"10.4236/ajcm.2020.104029","DOIUrl":"https://doi.org/10.4236/ajcm.2020.104029","url":null,"abstract":"This work extends to third-order previously published work on developing the adjoint sensitivity and uncertainty analysis of the numerical model of a polyethylene-reflected plutonium (acronym: PERP) OECD/NEA reactor physics benchmark. The PERP benchmark comprises 21,976 imprecisely known (uncertain) model parameters. Previous works have used the adjoint sensitivity analysis methodology to compute exactly and efficiently all of the 21,976 first-order and (21,976)2 second-order sensitivities of the PERP benchmark’s leakage response to all of the benchmark’s uncertain parameters, showing that the largest and most consequential 1st- and 2nd-order response sensitivities are with respect to the total microscopic cross sections. These results have motivated extending the previous adjoint-based derivations to third-order, leading to the derivation, in this work, of the exact mathematical expressions of the (180)3 third-order sensitivities of the PERP leakage response with respect to these total microscopic cross sections. The formulas derived in this work are valid not only for the PERP benchmark but can also be used for computing the 3rd-order sensitivities of the leakage response of any nuclear system involving fissionable material and internal or external neutron sources. Subsequent works will use the adjoint-based mathematical expressions obtained in this work to compute exactly and efficiently the numerical values of these (180)3 third-order sensitivities (which turned out to be very large and consequential) and use them for a third-order uncertainty analysis of the PERP benchmark’s leakage response.","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41597716","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-01DOI: 10.4236/ajcm.2020.104031
R. Fang, D. Cacuci
The (180)3 third-order mixed sensitivities of the leakage response of a polyethylene-reflected plutonium (PERP) experimental benchmark with respect to the benchmark’s 180 microscopic total cross sections have been computed in accompanying works [1] [2]. This work quantifies the contributions of these (180)3 third-order mixed sensitivities to the PERP benchmark’s leakage response distribution moments (expected value, variance and skewness) and compares these contributions to those stemming from the corresponding first- and second-order sensitivities of the PERP benchmark’s leakage response with respect to the total cross sections. The numerical results obtained in this work reveal that the importance of the 3rd-order sensitivities can surpass the importance of the 1st- and 2nd-order sensitivities when the parameters’ uncertainties increase. In particular, for a uniform standard deviation of 10% of the microscopic total cross sections, the 3rd-order sensitivities contribute 80% to the response variance, whereas the contribution stemming from the 1st- and 2nd-order sensitivities amount only to 2% and 18%, respectively. Consequently, neglecting the 3rd-order sensitivities could cause a very large non-conservative error by under-reporting the response variance by a factor of 506%. The results obtained in this work also indicate that the effects of the 3rd-order sensitivities are to reduce the response’s skewness in parameter space, rendering the distribution of the leakage response more symmetric about its expected value. The results obtained in this work are the first such results ever published in reactor physics. Since correlations among the group-averaged microscopic total cross sections are not available, only the effects of typical standard deviations for these cross sections could be considered. Due to this lack of correlations among the cross sections, the effects of the mixed 3rd-order sensitivities could not be quantified exactly at this time. These effects could be quantified only when correlations among the group-averaged microscopic total cross sections would be obtained experimentally by the nuclear physics community.
{"title":"Third Order Adjoint Sensitivity and Uncertainty Analysis of an OECD/NEA Reactor Physics Benchmark: III. Response Moments","authors":"R. Fang, D. Cacuci","doi":"10.4236/ajcm.2020.104031","DOIUrl":"https://doi.org/10.4236/ajcm.2020.104031","url":null,"abstract":"The (180)3 third-order mixed sensitivities of the leakage response of a polyethylene-reflected plutonium (PERP) experimental benchmark with respect to the benchmark’s 180 microscopic total cross sections have been computed in accompanying works [1] [2]. This work quantifies the contributions of these (180)3 third-order mixed sensitivities to the PERP benchmark’s leakage response distribution moments (expected value, variance and skewness) and compares these contributions to those stemming from the corresponding first- and second-order sensitivities of the PERP benchmark’s leakage response with respect to the total cross sections. The numerical results obtained in this work reveal that the importance of the 3rd-order sensitivities can surpass the importance of the 1st- and 2nd-order sensitivities when the parameters’ uncertainties increase. In particular, for a uniform standard deviation of 10% of the microscopic total cross sections, the 3rd-order sensitivities contribute 80% to the response variance, whereas the contribution stemming from the 1st- and 2nd-order sensitivities amount only to 2% and 18%, respectively. Consequently, neglecting the 3rd-order sensitivities could cause a very large non-conservative error by under-reporting the response variance by a factor of 506%. The results obtained in this work also indicate that the effects of the 3rd-order sensitivities are to reduce the response’s skewness in parameter space, rendering the distribution of the leakage response more symmetric about its expected value. The results obtained in this work are the first such results ever published in reactor physics. Since correlations among the group-averaged microscopic total cross sections are not available, only the effects of typical standard deviations for these cross sections could be considered. Due to this lack of correlations among the cross sections, the effects of the mixed 3rd-order sensitivities could not be quantified exactly at this time. These effects could be quantified only when correlations among the group-averaged microscopic total cross sections would be obtained experimentally by the nuclear physics community.","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":"10 1","pages":"559-570"},"PeriodicalIF":0.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49046043","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-01DOI: 10.4236/ajcm.2020.104034
Weiwei Ji, She-xiao Zou, Jishan Liu, Quanben Sun, L. Xia
In the article, we established a non-autonomous vector infectious disease model, studied the long-term dynamic behavior of the system, and obtained sufficient conditions for the extinction and persistence of infectious diseases by constructing integral functions.
{"title":"Dynamic of Non-Autonomous Vector Infectious Disease Model with Cross Infection","authors":"Weiwei Ji, She-xiao Zou, Jishan Liu, Quanben Sun, L. Xia","doi":"10.4236/ajcm.2020.104034","DOIUrl":"https://doi.org/10.4236/ajcm.2020.104034","url":null,"abstract":"In the article, we established a non-autonomous vector infectious disease model, studied the long-term dynamic behavior of the system, and obtained sufficient conditions for the extinction and persistence of infectious diseases by constructing integral functions.","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":"10 1","pages":"591-602"},"PeriodicalIF":0.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43350980","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-12-01DOI: 10.4236/ajcm.2020.104030
R. Fang, D. Cacuci
This work presents the results of the exact computation of (180)3 = 5,832,000 third-order mixed sensitivities of the leakage response of a polyethylene-reflected plutonium (PERP) experimental benchmark with respect to the benchmark’s 180 microscopic total cross sections. This computation was made possible by applying the Third-Order Adjoint Sensitivity Analysis Methodology developed by Cacuci. The numerical results obtained in this work revealed that many of the 3rd-order sensitivities are significantly larger than their corresponding 1st- and 2nd-order ones, which is contrary to the widely held belief that higher-order sensitivities are all much smaller and hence less important than the first-order ones, for reactor physics systems. In particular, the largest 3rd-order relative sensitivity is the mixed sensitivity of the PERP leakage response with respect to the lowest energy-group (30) total cross sections of 1H (“isotope 6”) and 239Pu (“isotope 1”). These two isotopes are shown in this work to be the two most important parameters affecting the PERP benchmark’s leakage response. By comparison, the largest 1st-order sensitivity is that of the PERP leakage response with respect to the lowest energy-group total cross section of isotope 1H, having the value , while the largest 2nd-order sensitivity is . The 3rd-order sensitivity analysis presented in this work is the first ever such analysis in the field of reactor physics. The consequences of the results presented in this work on the uncertainty analysis of the PERP benchmark’s leakage response will be presented in a subsequent work.
{"title":"Third Order Adjoint Sensitivity and Uncertainty Analysis of an OECD/NEA Reactor Physics Benchmark: II. Computed Sensitivities","authors":"R. Fang, D. Cacuci","doi":"10.4236/ajcm.2020.104030","DOIUrl":"https://doi.org/10.4236/ajcm.2020.104030","url":null,"abstract":"This work presents the results of the exact computation of (180)3 = 5,832,000 third-order mixed sensitivities of the leakage response of a polyethylene-reflected plutonium (PERP) experimental benchmark with respect to the benchmark’s 180 microscopic total cross sections. This computation was made possible by applying the Third-Order Adjoint Sensitivity Analysis Methodology developed by Cacuci. The numerical results obtained in this work revealed that many of the 3rd-order sensitivities are significantly larger than their corresponding 1st- and 2nd-order ones, which is contrary to the widely held belief that higher-order sensitivities are all much smaller and hence less important than the first-order ones, for reactor physics systems. In particular, the largest 3rd-order relative sensitivity is the mixed sensitivity of the PERP leakage response with respect to the lowest energy-group (30) total cross sections of 1H (“isotope 6”) and 239Pu (“isotope 1”). These two isotopes are shown in this work to be the two most important parameters affecting the PERP benchmark’s leakage response. By comparison, the largest 1st-order sensitivity is that of the PERP leakage response with respect to the lowest energy-group total cross section of isotope 1H, having the value , while the largest 2nd-order sensitivity is . The 3rd-order sensitivity analysis presented in this work is the first ever such analysis in the field of reactor physics. The consequences of the results presented in this work on the uncertainty analysis of the PERP benchmark’s leakage response will be presented in a subsequent work.","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43747781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：