Pub Date : 2021-09-01DOI: 10.17512/jamcm.2021.3.01
R. Autar, Anuj Kumar
. A simple mathematical model for the temperature evolution in the cornea exposed to short-pulsed Ho: YAG laser under Laser Thermo Keratoplasty (LTK) treatment is developed by incorporating both the heat flux phase-lag and temperature gradient phase-lag in Fourier’s heat transfer model. An analytical solution to the mathematical model is obtained using the Laplace transformation technique. The computational results for the temperature profile and the temperature variation with time are presented through the graphs. The effect of some typical parameters: the heat flux phase-lag and the temperature gradient phase-lag on the temperature distribution and temperature variations are illustrated and discussed. MSC 2010: 92B05, 80A20, 78A60, 35L20
{"title":"Mathematical modeling of short pulsed laser irradiation in the cornea: a dual phase lag model","authors":"R. Autar, Anuj Kumar","doi":"10.17512/jamcm.2021.3.01","DOIUrl":"https://doi.org/10.17512/jamcm.2021.3.01","url":null,"abstract":". A simple mathematical model for the temperature evolution in the cornea exposed to short-pulsed Ho: YAG laser under Laser Thermo Keratoplasty (LTK) treatment is developed by incorporating both the heat flux phase-lag and temperature gradient phase-lag in Fourier’s heat transfer model. An analytical solution to the mathematical model is obtained using the Laplace transformation technique. The computational results for the temperature profile and the temperature variation with time are presented through the graphs. The effect of some typical parameters: the heat flux phase-lag and the temperature gradient phase-lag on the temperature distribution and temperature variations are illustrated and discussed. MSC 2010: 92B05, 80A20, 78A60, 35L20","PeriodicalId":43867,"journal":{"name":"Journal of Applied Mathematics and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44077467","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 : 2021-09-01DOI: 10.17512/jamcm.2021.3.03
D. P. Rao, Swaminathan Thiagarajan, Vajha Srinivasa Kumar
. Tangent hyperbolic fluid is one of the non-Newtonian fluids in which the constitutive equation is valid for low and high shear rates and used mostly in laboratory experiments and industries. The Darcy-Forchheimer flow model is substantial in the fields where the high flow rate effect is the common phenomenon, for instance, in petroleum engineering. With these things in mind, in this article, we analysed the mixed convective dissipative Darcy-Forchheimer flow of tangent hyperbolic fluid by an inclined plate with Joule heating. Flow administering equations were altered as nonlinear ODEs and then resolved using shooting strategy. Pertinent outcomes are explained through graphs. It is discovered that fluid velocity minifies with the rise in the power law index parameter and Forchheimer number. It is detected that the thermal buoyancy parameter minimizes fluid temperature, and the magnetic field parameter ameliorates the same. What’s more, we noticed that Forchheimer number minimizes the skin friction coefficient, and the heat transfer rate is minified with the larger Eckert number. Furthermore, we have verified our results with former results for the Nusselt number and noticed a satisfactory agreement
{"title":"Heat transfer in Darcy-Forchheimer flow of tangent hyperbolic fluid over an inclined plate with Joule heating","authors":"D. P. Rao, Swaminathan Thiagarajan, Vajha Srinivasa Kumar","doi":"10.17512/jamcm.2021.3.03","DOIUrl":"https://doi.org/10.17512/jamcm.2021.3.03","url":null,"abstract":". Tangent hyperbolic fluid is one of the non-Newtonian fluids in which the constitutive equation is valid for low and high shear rates and used mostly in laboratory experiments and industries. The Darcy-Forchheimer flow model is substantial in the fields where the high flow rate effect is the common phenomenon, for instance, in petroleum engineering. With these things in mind, in this article, we analysed the mixed convective dissipative Darcy-Forchheimer flow of tangent hyperbolic fluid by an inclined plate with Joule heating. Flow administering equations were altered as nonlinear ODEs and then resolved using shooting strategy. Pertinent outcomes are explained through graphs. It is discovered that fluid velocity minifies with the rise in the power law index parameter and Forchheimer number. It is detected that the thermal buoyancy parameter minimizes fluid temperature, and the magnetic field parameter ameliorates the same. What’s more, we noticed that Forchheimer number minimizes the skin friction coefficient, and the heat transfer rate is minified with the larger Eckert number. Furthermore, we have verified our results with former results for the Nusselt number and noticed a satisfactory agreement","PeriodicalId":43867,"journal":{"name":"Journal of Applied Mathematics and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46882664","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 : 2021-09-01DOI: 10.17512/jamcm.2021.3.02
G. C. Rana
{"title":"Effects of rotation on Jeffrey nanofluid flow saturated by a porous medium","authors":"G. C. Rana","doi":"10.17512/jamcm.2021.3.02","DOIUrl":"https://doi.org/10.17512/jamcm.2021.3.02","url":null,"abstract":"","PeriodicalId":43867,"journal":{"name":"Journal of Applied Mathematics and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47147061","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 : 2021-06-01DOI: 10.17512/jamcm.2021.2.03
Hami Gündoğdu, Ömer Faruk Gözükɩzɩl
. In the present paper, the fractional-order cubic nonlinear Schr¨odinger equation is considered. The Schr¨odinger equation with time and space fractional derivative is studied at the same time. Different types of travelling wave solutions including the kink solution, soliton solution, periodic solution, and singular solution for the mentioned equation are obtained by using the Jacobi elliptic functions expansion method. It is shown that the solutions turn into the exact solutions when the fractional orders go to 1. This method can be relied on gaining the solutions to time or space fractional order partial differential equations as well as ordinary ones. Throughout this work, the fractional derivative is given in a conformable sense.
{"title":"Cubic nonlinear fractional Schrödinger equation with conformable derivative and its new travelling wave solutions","authors":"Hami Gündoğdu, Ömer Faruk Gözükɩzɩl","doi":"10.17512/jamcm.2021.2.03","DOIUrl":"https://doi.org/10.17512/jamcm.2021.2.03","url":null,"abstract":". In the present paper, the fractional-order cubic nonlinear Schr¨odinger equation is considered. The Schr¨odinger equation with time and space fractional derivative is studied at the same time. Different types of travelling wave solutions including the kink solution, soliton solution, periodic solution, and singular solution for the mentioned equation are obtained by using the Jacobi elliptic functions expansion method. It is shown that the solutions turn into the exact solutions when the fractional orders go to 1. This method can be relied on gaining the solutions to time or space fractional order partial differential equations as well as ordinary ones. Throughout this work, the fractional derivative is given in a conformable sense.","PeriodicalId":43867,"journal":{"name":"Journal of Applied Mathematics and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45661075","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 : 2021-06-01DOI: 10.17512/jamcm.2021.2.02
Süleyman Çetinkaya, A. Demir
{"title":"Solution of hybrid time fractional diffusion problem via weighted inner product","authors":"Süleyman Çetinkaya, A. Demir","doi":"10.17512/jamcm.2021.2.02","DOIUrl":"https://doi.org/10.17512/jamcm.2021.2.02","url":null,"abstract":"","PeriodicalId":43867,"journal":{"name":"Journal of Applied Mathematics and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49459344","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 : 2021-06-01DOI: 10.17512/jamcm.2021.2.06
Subrata Roy, Sandip Saha, S. Raut, A. Das
. In this article, using the standard reductive perturbation technique (RPT) to the basic governing equations for plasma comprising stationary ions, cold electrons and hot electrons abiding by vortex-like distribution, nonplanar Schamel Burger (NSB) equations is derived. In order to study the propagating properties of Electron acoustic (EA), progressive wave solution is obtained by employing the weighted residual method (WRM). Most of the observations of the EA wave are limited to the plasma environment where the effects of viscosity, collisions, ion streaming velocity are totally neglected. In our present observation, propagation of EA waves in a viscous plasma is described considering a weak damping (by adding a Burgers term) due to the inner particle collision and viscosity. Special attention has been given to study the impact of the other physical parameters in wave propagation in the framework of the Schamel Burgers medium.
{"title":"Studies on the effect of kinematic viscosity on electron-acoustic cylindrical and spherical solitary waves in a plasma with trapped electrons","authors":"Subrata Roy, Sandip Saha, S. Raut, A. Das","doi":"10.17512/jamcm.2021.2.06","DOIUrl":"https://doi.org/10.17512/jamcm.2021.2.06","url":null,"abstract":". In this article, using the standard reductive perturbation technique (RPT) to the basic governing equations for plasma comprising stationary ions, cold electrons and hot electrons abiding by vortex-like distribution, nonplanar Schamel Burger (NSB) equations is derived. In order to study the propagating properties of Electron acoustic (EA), progressive wave solution is obtained by employing the weighted residual method (WRM). Most of the observations of the EA wave are limited to the plasma environment where the effects of viscosity, collisions, ion streaming velocity are totally neglected. In our present observation, propagation of EA waves in a viscous plasma is described considering a weak damping (by adding a Burgers term) due to the inner particle collision and viscosity. Special attention has been given to study the impact of the other physical parameters in wave propagation in the framework of the Schamel Burgers medium.","PeriodicalId":43867,"journal":{"name":"Journal of Applied Mathematics and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48794502","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 : 2021-06-01DOI: 10.17512/jamcm.2021.2.01
Dilara Altan Koç, Mustafa Gülsu
In this study, the locally one dimensional (LOD) method is used to solve the two dimensional time fractional diffusion equation. The fractional derivative is the Caputo fractional derivative of order α. The rate of convergence of the finite difference method is presented. It is seen that this method is in agreement with the obtained numerical solutions with acceptable central processing unit time (CPU time). Error estimates, numerical and exact results are tabulated. The graphics of errors are given. MSC 2010: 65M06, 65M22, 34K37
{"title":"A new numerical scheme for solving the two dimensional fractional diffusion equation","authors":"Dilara Altan Koç, Mustafa Gülsu","doi":"10.17512/jamcm.2021.2.01","DOIUrl":"https://doi.org/10.17512/jamcm.2021.2.01","url":null,"abstract":"In this study, the locally one dimensional (LOD) method is used to solve the two dimensional time fractional diffusion equation. The fractional derivative is the Caputo fractional derivative of order α. The rate of convergence of the finite difference method is presented. It is seen that this method is in agreement with the obtained numerical solutions with acceptable central processing unit time (CPU time). Error estimates, numerical and exact results are tabulated. The graphics of errors are given. MSC 2010: 65M06, 65M22, 34K37","PeriodicalId":43867,"journal":{"name":"Journal of Applied Mathematics and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49153046","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 : 2021-06-01DOI: 10.17512/jamcm.2021.2.04
R. Kvit, T. Salo
The model of a plate brittle material reinforced with randomly sized and placed rigid rectilinear inclusions that do not interact with each other is considered. The geometric parameters of inclusions (length and orientation) are statistically independent random variables, with certain given laws of probability distribution. Diagrams of statistical strength criterion for such plates are constructed under conditions of comprehensive tension-compression. The diagrams are constructed for plates using a material of a different structural inhomogeneity and Poisson’s ratio of an elastic homogeneous matrix. The statistical nature of the scale effect is studied, the intensity of which depends on the type of stress state. MSC 2010: 74R10, 74R99, 60K35, 82C03
{"title":"Diagrams of statistical strength criterion for reinforced composite materials","authors":"R. Kvit, T. Salo","doi":"10.17512/jamcm.2021.2.04","DOIUrl":"https://doi.org/10.17512/jamcm.2021.2.04","url":null,"abstract":"The model of a plate brittle material reinforced with randomly sized and placed rigid rectilinear inclusions that do not interact with each other is considered. The geometric parameters of inclusions (length and orientation) are statistically independent random variables, with certain given laws of probability distribution. Diagrams of statistical strength criterion for such plates are constructed under conditions of comprehensive tension-compression. The diagrams are constructed for plates using a material of a different structural inhomogeneity and Poisson’s ratio of an elastic homogeneous matrix. The statistical nature of the scale effect is studied, the intensity of which depends on the type of stress state. MSC 2010: 74R10, 74R99, 60K35, 82C03","PeriodicalId":43867,"journal":{"name":"Journal of Applied Mathematics and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44462588","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 : 2021-06-01DOI: 10.17512/jamcm.2021.2.05
P. Puchała
. We take under consideration Young measures – objects that can be interpreted as generalized solutions of a class of certain nonconvex optimization problems arising among others in nonlinear elasticity or micromagnetics. They can be looked at from several points of view. We look at Young measures as at a class of weak ∗ measurable, measure-valued mappings and consider the basic existence theorem for them. On the basis of this theorem, an imbedding of the set of bounded Borel functions into the set of Young measures is defined. Using the weak ∗ denseness of the set of Young measures associated with simple functions in the set of Young measures, it is shown that this imbedding assigns the Young measure associated with any bounded Borel function.
{"title":"On a certain embedding in the space of measures","authors":"P. Puchała","doi":"10.17512/jamcm.2021.2.05","DOIUrl":"https://doi.org/10.17512/jamcm.2021.2.05","url":null,"abstract":". We take under consideration Young measures – objects that can be interpreted as generalized solutions of a class of certain nonconvex optimization problems arising among others in nonlinear elasticity or micromagnetics. They can be looked at from several points of view. We look at Young measures as at a class of weak ∗ measurable, measure-valued mappings and consider the basic existence theorem for them. On the basis of this theorem, an imbedding of the set of bounded Borel functions into the set of Young measures is defined. Using the weak ∗ denseness of the set of Young measures associated with simple functions in the set of Young measures, it is shown that this imbedding assigns the Young measure associated with any bounded Borel function.","PeriodicalId":43867,"journal":{"name":"Journal of Applied Mathematics and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45360024","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 : 2021-03-01DOI: 10.17512/JAMCM.2021.1.08
S. Qureshi
. Closed form solutions for mathematical systems are not easy to find in many cases. In particular, linear systems such as the population growth/decay model, RLC circuit, mixing problems in chemistry, first-order kinetic reactions, and mass spring damper system in mechanical and mechatronic engineering can be handled with tools available in theoretical study of linear systems. One such linear system has been investigated in the present research study. The second order linear ordinary differential equation called the mass spring damper system is explored under the Caputo type differential operator while using the Sumudu integral transform. The closed form solution has been found in terms of the Fox H-function wherein different aspects of the solution can be obtained with variation in α ∈ ( 1 , 2 ] and β ∈ ( 0 , 1 ] . The classical mass spring damper model is retrieved for α = β = 1 . MSC 2010: 26A33, 34M03.
{"title":"Fox H-functions as exact solutions for Caputo type mass spring damper system under Sumudu transform","authors":"S. Qureshi","doi":"10.17512/JAMCM.2021.1.08","DOIUrl":"https://doi.org/10.17512/JAMCM.2021.1.08","url":null,"abstract":". Closed form solutions for mathematical systems are not easy to find in many cases. In particular, linear systems such as the population growth/decay model, RLC circuit, mixing problems in chemistry, first-order kinetic reactions, and mass spring damper system in mechanical and mechatronic engineering can be handled with tools available in theoretical study of linear systems. One such linear system has been investigated in the present research study. The second order linear ordinary differential equation called the mass spring damper system is explored under the Caputo type differential operator while using the Sumudu integral transform. The closed form solution has been found in terms of the Fox H-function wherein different aspects of the solution can be obtained with variation in α ∈ ( 1 , 2 ] and β ∈ ( 0 , 1 ] . The classical mass spring damper model is retrieved for α = β = 1 . MSC 2010: 26A33, 34M03.","PeriodicalId":43867,"journal":{"name":"Journal of Applied Mathematics and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46426607","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：