Pub Date : 2023-01-01DOI: 10.4236/ajcm.2023.132012
Yoshihiro Tanaka
{"title":"Average Probability of an Element Being a Generator in the Cyclic Group","authors":"Yoshihiro Tanaka","doi":"10.4236/ajcm.2023.132012","DOIUrl":"https://doi.org/10.4236/ajcm.2023.132012","url":null,"abstract":"","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70510561","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 : 2022-07-13DOI: 10.4236/ajcm.2022.123021
H. Baty
In this study, the hyperbolic method is adopted to explore the flow field states of incompressible flow in a four-sided lid-driven square cavity. In particular, we focus on the flow bifurcation obtained at the critical Reynolds number R e (cid:39) 130. In the hyperbolic method, the diffusive term is transformed into an hyperbolic one by introducing a diffusion flux term, which is the solution of an additional equation. A classical Riemann-like solver with a finite-volume discretization is thus employed for the full flux (splitted into advective and diffusive parts), in order to solve the steady-state incompressible Navier-Stokes equation. The incompressibility of the flow is treated via the artificial pseudo-compressibility method. It is shown that our numerical code is able to detect the bifurcation, by the analysis of the residual term relaxation during the pseudo-time iteration procedure. Moreover, depending on the combination choice of slope limiters for the two spatial directions, our method is able to select the first or the second stable solution among the double flow field state obtained when the Reynolds number is higher than the critical value that is estimated to be 129 . 4 in our study.
{"title":"Hyperbolic Method to Explore Multiplicity Flow Solutions in a Four-Sided Lid-Driven Cavity","authors":"H. Baty","doi":"10.4236/ajcm.2022.123021","DOIUrl":"https://doi.org/10.4236/ajcm.2022.123021","url":null,"abstract":"In this study, the hyperbolic method is adopted to explore the flow field states of incompressible flow in a four-sided lid-driven square cavity. In particular, we focus on the flow bifurcation obtained at the critical Reynolds number R e (cid:39) 130. In the hyperbolic method, the diffusive term is transformed into an hyperbolic one by introducing a diffusion flux term, which is the solution of an additional equation. A classical Riemann-like solver with a finite-volume discretization is thus employed for the full flux (splitted into advective and diffusive parts), in order to solve the steady-state incompressible Navier-Stokes equation. The incompressibility of the flow is treated via the artificial pseudo-compressibility method. It is shown that our numerical code is able to detect the bifurcation, by the analysis of the residual term relaxation during the pseudo-time iteration procedure. Moreover, depending on the combination choice of slope limiters for the two spatial directions, our method is able to select the first or the second stable solution among the double flow field state obtained when the Reynolds number is higher than the critical value that is estimated to be 129 . 4 in our study.","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41312610","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 : 2022-01-01DOI: 10.4236/ajcm.2022.121001
H. Sarafian
Oscillations due to three different forces in three areas of physics: electrostatic, nuclear, and mechanics, are analyzed. The electrostatic long-range Coulomb force has a different character than the nucleonic short-range Yukawa force. Both are different from the linear Hooke’s force. The equation of motion of each case is solved applying a Computer Algebra System (CAS). It is shown that these oscillations have similarities and differences. Phase diagrams of all three cases are compared.
{"title":"Coulomb, Yukawa, and Hooke’s Oscillations","authors":"H. Sarafian","doi":"10.4236/ajcm.2022.121001","DOIUrl":"https://doi.org/10.4236/ajcm.2022.121001","url":null,"abstract":"Oscillations due to three different forces in three areas of physics: electrostatic, nuclear, and mechanics, are analyzed. The electrostatic long-range Coulomb force has a different character than the nucleonic short-range Yukawa force. Both are different from the linear Hooke’s force. The equation of motion of each case is solved applying a Computer Algebra System (CAS). It is shown that these oscillations have similarities and differences. Phase diagrams of all three cases are compared.","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":"12 1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70509617","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 : 2022-01-01DOI: 10.4236/ajcm.2022.122010
H. Sarafian
We envision utilizing the versatility of a Computer Algebra System, specifi-cally Mathematica to explore designing physics problems. As a focused project, we consider for instance a thermo-mechanical-physics problem showing its development from the ground up. Following the objectives of this investiga-tion first by applying the fundamentals of physics principles we solve the problem symbolically. Applying the solution we investigate the sensitivities of the quantities of interest for various scenarios generating feasible numeric parameters. Although a physics problem is investigated, the proposed methodol-ogy may as well be applied to other scientific fields. The codes needed for this particular project are included enabling the interested reader to duplicate the results, extend and modify them as needed to explore various extended scenarios.
{"title":"Designing Physics Problems with <i>Mathematica</i>","authors":"H. Sarafian","doi":"10.4236/ajcm.2022.122010","DOIUrl":"https://doi.org/10.4236/ajcm.2022.122010","url":null,"abstract":"We envision utilizing the versatility of a Computer Algebra System, specifi-cally Mathematica to explore designing physics problems. As a focused project, we consider for instance a thermo-mechanical-physics problem showing its development from the ground up. Following the objectives of this investiga-tion first by applying the fundamentals of physics principles we solve the problem symbolically. Applying the solution we investigate the sensitivities of the quantities of interest for various scenarios generating feasible numeric parameters. Although a physics problem is investigated, the proposed methodol-ogy may as well be applied to other scientific fields. The codes needed for this particular project are included enabling the interested reader to duplicate the results, extend and modify them as needed to explore various extended scenarios.","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70509814","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 : 2022-01-01DOI: 10.4236/ajcm.2022.124025
H. Sarafian
{"title":"Impact of a Mobile Void within a Charge Distribution on the Electric Field","authors":"H. Sarafian","doi":"10.4236/ajcm.2022.124025","DOIUrl":"https://doi.org/10.4236/ajcm.2022.124025","url":null,"abstract":"","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70509726","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 : 2022-01-01DOI: 10.4236/ajcm.2022.121009
Joachim Moussounda Mouanda
We construct sequences of positive integers which are solutions of the equation z . We introduce Mouanda’s choice functions which allow us to construct galaxies of sequences of positive integers. We give many examples of galaxies of numbers. We show that the equation has no integer solutions. We prove that the equation has no solutions in . We introduce the notion of the planetary representation of a galaxy of numbers which allow us to predict the structure, laws of the universe and life in every planet system of every galaxy of the universe. We show that every multiverse contains a finite number of
{"title":"On Fermat’s Last Theorem and Galaxies of Sequences of Positive Integers","authors":"Joachim Moussounda Mouanda","doi":"10.4236/ajcm.2022.121009","DOIUrl":"https://doi.org/10.4236/ajcm.2022.121009","url":null,"abstract":"We construct sequences of positive integers which are solutions of the equation z . We introduce Mouanda’s choice functions which allow us to construct galaxies of sequences of positive integers. We give many examples of galaxies of numbers. We show that the equation has no integer solutions. We prove that the equation has no solutions in . We introduce the notion of the planetary representation of a galaxy of numbers which allow us to predict the structure, laws of the universe and life in every planet system of every galaxy of the universe. We show that every multiverse contains a finite number of","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70509802","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 : 2022-01-01DOI: 10.4236/ajcm.2022.122015
H. Sarafian
{"title":"Characteristics of an Accelerated Transverse Mechanical Pulse and Its Implications","authors":"H. Sarafian","doi":"10.4236/ajcm.2022.122015","DOIUrl":"https://doi.org/10.4236/ajcm.2022.122015","url":null,"abstract":"","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70509864","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 : 2022-01-01DOI: 10.4236/ajcm.2022.121002
N. O. Al-Atawi, D. Mashat
{"title":"Synovial Joint Study","authors":"N. O. Al-Atawi, D. Mashat","doi":"10.4236/ajcm.2022.121002","DOIUrl":"https://doi.org/10.4236/ajcm.2022.121002","url":null,"abstract":"","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70510073","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 : 2022-01-01DOI: 10.4236/ajcm.2022.121005
D. Cacuci
This work presents the mathematical framework of the “Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N),” which generalizes and extends all of the previous works performed to date on this subject. The 5th-CASAM-N enables the exact and efficient computation of all sensitivities, up to and including fifth-order, of model responses to uncertain model parameters and uncertain boundaries of the system’s domain of definition, thus enabling, inter alia, the quantification of uncertainties stemming from manufacturing tolerances. The 5th-CASAM-N provides a fundamental step towards overcoming the curse of dimensionality in sensitivity and uncertainty analysis.
{"title":"Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N): I. Mathematical Framework","authors":"D. Cacuci","doi":"10.4236/ajcm.2022.121005","DOIUrl":"https://doi.org/10.4236/ajcm.2022.121005","url":null,"abstract":"This work presents the mathematical framework of the “Fifth-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems (5th-CASAM-N),” which generalizes and extends all of the previous works performed to date on this subject. The 5th-CASAM-N enables the exact and efficient computation of all sensitivities, up to and including fifth-order, of model responses to uncertain model parameters and uncertain boundaries of the system’s domain of definition, thus enabling, inter alia, the quantification of uncertainties stemming from manufacturing tolerances. The 5th-CASAM-N provides a fundamental step towards overcoming the curse of dimensionality in sensitivity and uncertainty analysis.","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70509709","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 : 2022-01-01DOI: 10.4236/ajcm.2022.121006
H. Sarafian
Utilizing Mathematica this report shows how from a practitioner’s point of view useful quantities some known, and some unknown and fresh properties about the Maxwell-Boltzmann distribution are calculated. We shortcut circling the usage of antiquated incomplete tabulated error functions given in the textbooks and professional literature replacing them with efficient up-grades. And, utilizing the animation features of Mathematica displaying the temperature-dependence of the distribution function assists in visualizing the character of the distribution
{"title":"Maxwell-Boltzmann Distribution Mathematica Based Practitioner’s Approach","authors":"H. Sarafian","doi":"10.4236/ajcm.2022.121006","DOIUrl":"https://doi.org/10.4236/ajcm.2022.121006","url":null,"abstract":"Utilizing Mathematica this report shows how from a practitioner’s point of view useful quantities some known, and some unknown and fresh properties about the Maxwell-Boltzmann distribution are calculated. We shortcut circling the usage of antiquated incomplete tabulated error functions given in the textbooks and professional literature replacing them with efficient up-grades. And, utilizing the animation features of Mathematica displaying the temperature-dependence of the distribution function assists in visualizing the character of the distribution","PeriodicalId":64456,"journal":{"name":"美国计算数学期刊(英文)","volume":"26 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70509750","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}
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