Pub Date : 2019-09-19DOI: 10.11648/J.IJAMTP.20190503.14
A. Mahmud, Suhana Perveen, Md Nazmul Hasan, M. Samsuzzoha, N. Islam
There has been renewed interest in the flow behaviour within tubes with periodically varying cross-section with the recognition that they can be used as particle separation devices. In this paper, we present a numerical study of the effect of tube geometry on creeping flow of viscous incompressible fluid through sinusoidally constricted periodic tube which is axisymmetric but longitudinally asymmetric. The boundary element method is used to solve for the flow in the tube by specifying the pressure drop across the ends of the tube. The boundary element equations have been formulated for an infinite periodic tube by writing the velocity in terms of the integrals over the tube boundary and is used to calculate the force on the tube boundary, to obtain the detailed velocity distribution within the tube and to determine the effect of amplitude and wavelength of corrugation on the structure of the flow. We have found that the highest axial velocity is at throat region and lowest axial velocity is at expansion region. Also, we have discovered that the maximum radial velocity occurs at diverging cross-section and minimum radial velocity occurs at converging cross-section. The tangential force on the tube wall is examined for different amplitudes and wavelengths of corrugation and observed that the tangential force is greater in the constricted region than in the expansion region. The physical quantities (such as velocity and force) increase with increasing amplitude and decrease with increasing wavelength. Finally, we have compared our results with the work of Hemmat and Borhan [3] and have found good agreement with them.
{"title":"Numerical Study of Creeping Flow Through Sinusoidally Periodic Tube","authors":"A. Mahmud, Suhana Perveen, Md Nazmul Hasan, M. Samsuzzoha, N. Islam","doi":"10.11648/J.IJAMTP.20190503.14","DOIUrl":"https://doi.org/10.11648/J.IJAMTP.20190503.14","url":null,"abstract":"There has been renewed interest in the flow behaviour within tubes with periodically varying cross-section with the recognition that they can be used as particle separation devices. In this paper, we present a numerical study of the effect of tube geometry on creeping flow of viscous incompressible fluid through sinusoidally constricted periodic tube which is axisymmetric but longitudinally asymmetric. The boundary element method is used to solve for the flow in the tube by specifying the pressure drop across the ends of the tube. The boundary element equations have been formulated for an infinite periodic tube by writing the velocity in terms of the integrals over the tube boundary and is used to calculate the force on the tube boundary, to obtain the detailed velocity distribution within the tube and to determine the effect of amplitude and wavelength of corrugation on the structure of the flow. We have found that the highest axial velocity is at throat region and lowest axial velocity is at expansion region. Also, we have discovered that the maximum radial velocity occurs at diverging cross-section and minimum radial velocity occurs at converging cross-section. The tangential force on the tube wall is examined for different amplitudes and wavelengths of corrugation and observed that the tangential force is greater in the constricted region than in the expansion region. The physical quantities (such as velocity and force) increase with increasing amplitude and decrease with increasing wavelength. Finally, we have compared our results with the work of Hemmat and Borhan [3] and have found good agreement with them.","PeriodicalId":367229,"journal":{"name":"International Journal of Applied Mathematics and Theoretical Physics","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134391813","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 : 2019-08-26DOI: 10.11648/J.IJAMTP.20190503.13
Konan Firmin N'gohisse, D. Nabongo, Lassane Traoré
Theoretical study of the phenomenon of blow-up solutions for semilinear Schrodinger equations has been the subject of investigations of many authors. It is said that the maximal time interval of existence of the solution blows up in a finite time when this time is finite, and the solution develops a singularity in a finite time. In fact, semilinear Schrhodinger equation models a lot of physical phenomenon such as nonlinear optics, energy transfer in molecular systems, quantum mechanics, seismology, plasma physics. In the past, certain authors have used numerical methods to study the phenomenon of blow-up for semilinear Schrodinger equations. They have considered the same problem and one proves that the energy of the system is conserved, and the method used to show blow-up solutions are based on the energy's method. This paper proposes a method based on a modification of the method of Kaplan using eigenvalues and eigenfunctions to show that the semidiscrete solution blows up in a finite time under some assumptions. The semidiscrete blow-up time is also estimate. Similar results are obtain replacing the reaction term by another form to generalise the result. Finally, this paper propose two schemes for some numerical experiments and a graphics is given to illustrate the analysis.
{"title":"Blow-up for Semidiscretisations of a Semilinear Schrodinger Equation with Dirichlet Condition","authors":"Konan Firmin N'gohisse, D. Nabongo, Lassane Traoré","doi":"10.11648/J.IJAMTP.20190503.13","DOIUrl":"https://doi.org/10.11648/J.IJAMTP.20190503.13","url":null,"abstract":"Theoretical study of the phenomenon of blow-up solutions for semilinear Schrodinger equations has been the subject of investigations of many authors. It is said that the maximal time interval of existence of the solution blows up in a finite time when this time is finite, and the solution develops a singularity in a finite time. In fact, semilinear Schrhodinger equation models a lot of physical phenomenon such as nonlinear optics, energy transfer in molecular systems, quantum mechanics, seismology, plasma physics. In the past, certain authors have used numerical methods to study the phenomenon of blow-up for semilinear Schrodinger equations. They have considered the same problem and one proves that the energy of the system is conserved, and the method used to show blow-up solutions are based on the energy's method. This paper proposes a method based on a modification of the method of Kaplan using eigenvalues and eigenfunctions to show that the semidiscrete solution blows up in a finite time under some assumptions. The semidiscrete blow-up time is also estimate. Similar results are obtain replacing the reaction term by another form to generalise the result. Finally, this paper propose two schemes for some numerical experiments and a graphics is given to illustrate the analysis.","PeriodicalId":367229,"journal":{"name":"International Journal of Applied Mathematics and Theoretical Physics","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132828945","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 : 2019-08-07DOI: 10.11648/J.IJAMTP.20190502.12
Bazuaye Frank Etin-Osa
Over the years, the Quadrature Algorithm as a method of solving initial value problems in ordinary differential equations is known to be of low accuracy compared to other well known methods. However, It has been shown that the method perform well when applied to moderately stiff problems. In this present study, the nonlinear method based on the Heronian Mean (HeM), of the function value for the solution of initial value problems is developed. Stability investigation is in agreement with the known Trapezoidal method.
{"title":"Solution of an Initial Value Problemin Ordinary Differential Equations Using the Quadrature Algorithm Based on the Heronian Mean","authors":"Bazuaye Frank Etin-Osa","doi":"10.11648/J.IJAMTP.20190502.12","DOIUrl":"https://doi.org/10.11648/J.IJAMTP.20190502.12","url":null,"abstract":"Over the years, the Quadrature Algorithm as a method of solving initial value problems in ordinary differential equations is known to be of low accuracy compared to other well known methods. However, It has been shown that the method perform well when applied to moderately stiff problems. In this present study, the nonlinear method based on the Heronian Mean (HeM), of the function value for the solution of initial value problems is developed. Stability investigation is in agreement with the known Trapezoidal method.","PeriodicalId":367229,"journal":{"name":"International Journal of Applied Mathematics and Theoretical Physics","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122928890","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 : 2019-06-21DOI: 10.11648/J.IJAMTP.20190502.11
D. Lei, Lizhen Wang, Z. Ou
With the rapid development of nanotechnology, nano-components and nano-materials will be widely concerned and applied. At the nano-scale, due to the obvious increase the ratio of surface area to the volume effect and surface effect of nano-components and nano-materials are significant, making their mechanical properties significantly different from the material properties under the macroscopic conditions. And in the practical cases, the interface is not always perfect and smooth, they always have a certain form of defects. Therefore, the wave function expansion method is used in the analytical solutions of dynamic stress concentration factor (DSCF) around a coated fiber with an imperfect interface at nano-scale. The stress boundary conditions on the interface are obtained by using the generalized Young-Laplace equation and the imperfect displacement boundary conditions on the interface are modeled by a spring model. Considering the effects of surface and spring model, the influence of spring stiffness, the number of incident wave and the surface effects on the DSCF are analyzed. The results show that the frequency of incident wave, the spring stiffness and the surface energy have significant effects on the dynamic stress concentration distributions of the nano-sized coated fiber. The smaller the spring coefficient is, the stronger the interface imperfection is, and the stronger the stress concentration at the boundary is. When the spring coefficient reaches a certain value, it is almost close to the dynamic stress value under the ideal interface. The DSCF are obviously different under different incident wave frequencies.
{"title":"Surface Effects on a Coated Fiber with an Imperfect Interface Subjected to Plane Compressional Wave","authors":"D. Lei, Lizhen Wang, Z. Ou","doi":"10.11648/J.IJAMTP.20190502.11","DOIUrl":"https://doi.org/10.11648/J.IJAMTP.20190502.11","url":null,"abstract":"With the rapid development of nanotechnology, nano-components and nano-materials will be widely concerned and applied. At the nano-scale, due to the obvious increase the ratio of surface area to the volume effect and surface effect of nano-components and nano-materials are significant, making their mechanical properties significantly different from the material properties under the macroscopic conditions. And in the practical cases, the interface is not always perfect and smooth, they always have a certain form of defects. Therefore, the wave function expansion method is used in the analytical solutions of dynamic stress concentration factor (DSCF) around a coated fiber with an imperfect interface at nano-scale. The stress boundary conditions on the interface are obtained by using the generalized Young-Laplace equation and the imperfect displacement boundary conditions on the interface are modeled by a spring model. Considering the effects of surface and spring model, the influence of spring stiffness, the number of incident wave and the surface effects on the DSCF are analyzed. The results show that the frequency of incident wave, the spring stiffness and the surface energy have significant effects on the dynamic stress concentration distributions of the nano-sized coated fiber. The smaller the spring coefficient is, the stronger the interface imperfection is, and the stronger the stress concentration at the boundary is. When the spring coefficient reaches a certain value, it is almost close to the dynamic stress value under the ideal interface. The DSCF are obviously different under different incident wave frequencies.","PeriodicalId":367229,"journal":{"name":"International Journal of Applied Mathematics and Theoretical Physics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116132475","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 : 2019-04-19DOI: 10.11648/J.IJAMTP.20190501.13
Zakaria Ndemo
Upon observing with concern that the majority of high school students experienced severe language related difficulties when solving contextualized differential equations, the researcher then decided to investigate the kinds of such challenges and their impact on students’ learning of differential equations. A sample of 10 mathematics students was selected from one urban high school in one province in Zimbabwe. Written tasks and follow up interviews were employed as data collection tools for the study. Content analysis technique was applied to the written responses and interview transcriptions to obtain a revealing picture of how the kinds of the language related challenges interfere with the growth of mathematical content. The study revealed that the students struggled with interpreting and formulating differential equations from given mathematical situations. Further, interpretation of given initial conditions posed a challenge to the learners. A major consequence of these language related challenges was that the students could not generate complete solutions and lack of interplay between conceptual and procedural fluency was one of the insights generated from this study with regards to the learning of differential equations. The study findings have important implications for instruction in high school mathematics lessons such as the need to develop and foster the students’ abilities to engage in adaptive reasoning and use multiple modes of presenting content in order to promote students’ understanding of contextualized differential equations.
{"title":"High School Students’ Language Related Struggles with Contextualized Differential Equations","authors":"Zakaria Ndemo","doi":"10.11648/J.IJAMTP.20190501.13","DOIUrl":"https://doi.org/10.11648/J.IJAMTP.20190501.13","url":null,"abstract":"Upon observing with concern that the majority of high school students experienced severe language related difficulties when solving contextualized differential equations, the researcher then decided to investigate the kinds of such challenges and their impact on students’ learning of differential equations. A sample of 10 mathematics students was selected from one urban high school in one province in Zimbabwe. Written tasks and follow up interviews were employed as data collection tools for the study. Content analysis technique was applied to the written responses and interview transcriptions to obtain a revealing picture of how the kinds of the language related challenges interfere with the growth of mathematical content. The study revealed that the students struggled with interpreting and formulating differential equations from given mathematical situations. Further, interpretation of given initial conditions posed a challenge to the learners. A major consequence of these language related challenges was that the students could not generate complete solutions and lack of interplay between conceptual and procedural fluency was one of the insights generated from this study with regards to the learning of differential equations. The study findings have important implications for instruction in high school mathematics lessons such as the need to develop and foster the students’ abilities to engage in adaptive reasoning and use multiple modes of presenting content in order to promote students’ understanding of contextualized differential equations.","PeriodicalId":367229,"journal":{"name":"International Journal of Applied Mathematics and Theoretical Physics","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114727702","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 : 2019-03-21DOI: 10.11648/J.IJAMTP.20190501.12
L. Moukala
The quantum mystery began with the probabilistic interpretation of the wave function. However, this usefulness is definitive in Quantum Mechanics while the suspense continues. The present paper aims to investigate the origin of such a mystery. Hence, considering a relativistic charged particle in quantum vacuum, it appeared that: (i) from a classical association, this electromagnetismself-consistent derives from the usual wave function, which corresponds to the scalar nature in addition to the vector one. (ii) Such duplicity is only justifiable when the related gauge fields describe fermions, in accordance with the previous theory of duality field-matter. This occurrence then corresponds to the appearance of bosons at cell intersections in vacuum lattice, whatever is the field. (iii) From the related gauge couplings, the scalar function must have an unknown vector companion. Both appear as originating the related conservation laws on one side. On the other side, specific variations of the field front would explain their physical origin. (iv) Moreover, both define an original gauge field to which that of law conservation is sensible. (v) Due to definition validity in any reference system, their possible quantization should lead to that of scalar and vector fields of stationary states. At last, the results highlight the connection between waves and fields associable to any object, emphasizing the field unification framework.
{"title":"Duality Occurrences: Physical Origin of Wave Functions","authors":"L. Moukala","doi":"10.11648/J.IJAMTP.20190501.12","DOIUrl":"https://doi.org/10.11648/J.IJAMTP.20190501.12","url":null,"abstract":"The quantum mystery began with the probabilistic interpretation of the wave function. However, this usefulness is definitive in Quantum Mechanics while the suspense continues. The present paper aims to investigate the origin of such a mystery. Hence, considering a relativistic charged particle in quantum vacuum, it appeared that: (i) from a classical association, this electromagnetismself-consistent derives from the usual wave function, which corresponds to the scalar nature in addition to the vector one. (ii) Such duplicity is only justifiable when the related gauge fields describe fermions, in accordance with the previous theory of duality field-matter. This occurrence then corresponds to the appearance of bosons at cell intersections in vacuum lattice, whatever is the field. (iii) From the related gauge couplings, the scalar function must have an unknown vector companion. Both appear as originating the related conservation laws on one side. On the other side, specific variations of the field front would explain their physical origin. (iv) Moreover, both define an original gauge field to which that of law conservation is sensible. (v) Due to definition validity in any reference system, their possible quantization should lead to that of scalar and vector fields of stationary states. At last, the results highlight the connection between waves and fields associable to any object, emphasizing the field unification framework.","PeriodicalId":367229,"journal":{"name":"International Journal of Applied Mathematics and Theoretical Physics","volume":"431 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131995174","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 : 2017-11-14DOI: 10.11648/J.IJAMTP.20190503.12
R. Andriambololona, Ravo Tokiniaina Ranaivoson, Hanitriarivo Rakotoson
This work is a continuation of our previous works concerning linear canonical transformations and phase space representation of quantum theory. It is mainly focused on the description of an approach which allows to establish spinorial representation of linear canonical transformations. This description is started with the presentation of a suitable parameterization of linear canonical transformations which permits to represent them with special pseudo-orthogonal transformations in an operator space. Then the establishment of the spinorial representation is deduced using the well-known relation existing between special pseudo-orthogonal and spin groups. The cases of one dimension and general multidimensional theory are both studied.
{"title":"Study on a Spinorial Representation of Linear Canonical Transformation","authors":"R. Andriambololona, Ravo Tokiniaina Ranaivoson, Hanitriarivo Rakotoson","doi":"10.11648/J.IJAMTP.20190503.12","DOIUrl":"https://doi.org/10.11648/J.IJAMTP.20190503.12","url":null,"abstract":"This work is a continuation of our previous works concerning linear canonical transformations and phase space representation of quantum theory. It is mainly focused on the description of an approach which allows to establish spinorial representation of linear canonical transformations. This description is started with the presentation of a suitable parameterization of linear canonical transformations which permits to represent them with special pseudo-orthogonal transformations in an operator space. Then the establishment of the spinorial representation is deduced using the well-known relation existing between special pseudo-orthogonal and spin groups. The cases of one dimension and general multidimensional theory are both studied.","PeriodicalId":367229,"journal":{"name":"International Journal of Applied Mathematics and Theoretical Physics","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121432930","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 : 1900-01-01DOI: 10.11648/j.ijamtp.20210704.15
L. Deswita, Ponco Hidayah, Ali Mohamed Ali Hassan Ali, Syamsudhuha Syamdhuha
{"title":"Analysis of COVID-19 Disease Using Fractional Order SEIR Model","authors":"L. Deswita, Ponco Hidayah, Ali Mohamed Ali Hassan Ali, Syamsudhuha Syamdhuha","doi":"10.11648/j.ijamtp.20210704.15","DOIUrl":"https://doi.org/10.11648/j.ijamtp.20210704.15","url":null,"abstract":"","PeriodicalId":367229,"journal":{"name":"International Journal of Applied Mathematics and Theoretical Physics","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128158682","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 : 1900-01-01DOI: 10.11648/j.ijamtp.20210704.14
I. Thiam, Babou Khady Thiam, I. Faye
{"title":"Numerical Simulation of Ocean Currents with Hermite IFinite Elements","authors":"I. Thiam, Babou Khady Thiam, I. Faye","doi":"10.11648/j.ijamtp.20210704.14","DOIUrl":"https://doi.org/10.11648/j.ijamtp.20210704.14","url":null,"abstract":"","PeriodicalId":367229,"journal":{"name":"International Journal of Applied Mathematics and Theoretical Physics","volume":"33 8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127471038","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：