In this study, the exact solutions of the Biswas-Arshed equation with the beta time derivative, which has an important role and physically means that it represents the pulse propagation in an optical fiber, nuclear, and particle physics, are obtained using the modified exponential function method. Exact solutions consisting of hyperbolic, trigonometric, rational trigonometric, and rational function solutions demonstrate the competence and relevance of the proposed method. In addition, the physical properties of the obtained exact solutions are shown by making graphical representations according to different parameter values. It is seen that the method used is an effective technique, since these solution functions obtained with all these cases have periodic function properties.
{"title":"The Modified Exponential Function Method for Beta Time Fractional Biswas-Arshed Equation","authors":"Y. Pandir, Tolga Akturk, Y. Gurefe, Hussain Juya","doi":"10.1155/2023/1091355","DOIUrl":"https://doi.org/10.1155/2023/1091355","url":null,"abstract":"In this study, the exact solutions of the Biswas-Arshed equation with the beta time derivative, which has an important role and physically means that it represents the pulse propagation in an optical fiber, nuclear, and particle physics, are obtained using the modified exponential function method. Exact solutions consisting of hyperbolic, trigonometric, rational trigonometric, and rational function solutions demonstrate the competence and relevance of the proposed method. In addition, the physical properties of the obtained exact solutions are shown by making graphical representations according to different parameter values. It is seen that the method used is an effective technique, since these solution functions obtained with all these cases have periodic function properties.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47929746","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Wenjian Zheng, An Chang, Qi Wang, Jianing Shang, Mandi Cui
The correlation filtering algorithm of infrared spectral data for dim and small target tracking is studied to improve the tracking accuracy of small and weak targets and to track small and weak targets in real time. After the image noise reduction processing by the mean shift filtering algorithm, the infrared small and weak target image data model is constructed by using the denoised infrared small and weak target image. And the brightness value and position of unknown small and weak targets are obtained. The tracking and measurement model of small and weak targets is built. The joint probabilistic data association algorithm is used to calculate the probability that each measurement is associated with its possible source targets, and the particle filter is used to update the tracking status of small and weak targets to achieve real-time tracking of small and weak targets. The experimental results show that the algorithm can enhance the edge contour information of small and weak images, so as to accurately track small and weak targets moving in any track, and has good real-time tracking and accuracy. There is a small deviation between the tracking track of weak and small targets tracked by the algorithm and the actual track, and the root mean square difference of tracking weak and small targets is within 2 pixels. In addition, the detection probability of detecting weak and small targets is less affected by SNR environmental factors.
{"title":"Correlation Filtering Algorithm of Infrared Spectral Data for Dim Target Tracking","authors":"Wenjian Zheng, An Chang, Qi Wang, Jianing Shang, Mandi Cui","doi":"10.1155/2023/1240426","DOIUrl":"https://doi.org/10.1155/2023/1240426","url":null,"abstract":"The correlation filtering algorithm of infrared spectral data for dim and small target tracking is studied to improve the tracking accuracy of small and weak targets and to track small and weak targets in real time. After the image noise reduction processing by the mean shift filtering algorithm, the infrared small and weak target image data model is constructed by using the denoised infrared small and weak target image. And the brightness value and position of unknown small and weak targets are obtained. The tracking and measurement model of small and weak targets is built. The joint probabilistic data association algorithm is used to calculate the probability that each measurement is associated with its possible source targets, and the particle filter is used to update the tracking status of small and weak targets to achieve real-time tracking of small and weak targets. The experimental results show that the algorithm can enhance the edge contour information of small and weak images, so as to accurately track small and weak targets moving in any track, and has good real-time tracking and accuracy. There is a small deviation between the tracking track of weak and small targets tracked by the algorithm and the actual track, and the root mean square difference of tracking weak and small targets is within 2 pixels. In addition, the detection probability of detecting weak and small targets is less affected by SNR environmental factors.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":"1 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"64789653","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, the dynamics of the fuzzy fractional order enzyme Michaelis Menten model are investigated. To study problems with uncertainty, fuzzy fractional technique is applied. Using fuzzy theory, the sequential iterations of the model are calculated by applying fractional calculus theory and the homotopy perturbation method. A comparison is given for fractional and fuzzy results, and the numerical findings validate the fuzzy fractional case. Using MATLAB software, the results are simulated for various fractional orders, corresponding to the provided data. The simulations demonstrate the model’s appropriateness.
{"title":"Analysis of Fuzzy Differential Equation with Fractional Derivative in Caputo Sense","authors":"Q. Ain, Muhammad Nadeem, Devendra Kumar, M. Shah","doi":"10.1155/2023/4009056","DOIUrl":"https://doi.org/10.1155/2023/4009056","url":null,"abstract":"In this article, the dynamics of the fuzzy fractional order enzyme Michaelis Menten model are investigated. To study problems with uncertainty, fuzzy fractional technique is applied. Using fuzzy theory, the sequential iterations of the model are calculated by applying fractional calculus theory and the homotopy perturbation method. A comparison is given for fractional and fuzzy results, and the numerical findings validate the fuzzy fractional case. Using MATLAB software, the results are simulated for various fractional orders, corresponding to the provided data. The simulations demonstrate the model’s appropriateness.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-04-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48211476","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this study, the free convection of nanofluids between a rectangular enclosure and a sinusoidal cylinder is numerically analyzed using the finite element method (FEM). Two-phase Buongiorno’s formulation was used to model the fluid layer, and Brinkman-Forchheimer equation was used to formulate the porous layer. The enclosure has a low temperature, while the cylinder is maintained at a high temperature. The governing equations are expressed in PDEs and converted into weak formulations (Galerkin FEM). In numerical simulations, the average concentration, the amplitude of undulated cylinder, the number of undulated, and the Rayleigh number are investigated. It is observed that the homogeneous nanofluid model could be valid for low heating intensity with higher waviness frequency and/or higher amplitude. The higher the alumina concentration, the higher the heat transfer rate. The heat transfer rate can be boosted by up to 13% by suspending 1% alumina particles. The heat transfer enhancement decreases with increasing the amplitude and/or increasing the waviness number.
{"title":"Use of Finite Element Method for Free Convection of Nanofluids between a Rectangular Enclosure and a Sinusoidal Cylinder Using Buongiorno’s Two-Phase Model","authors":"A. Alhashash, H. Saleh","doi":"10.1155/2023/8426825","DOIUrl":"https://doi.org/10.1155/2023/8426825","url":null,"abstract":"In this study, the free convection of nanofluids between a rectangular enclosure and a sinusoidal cylinder is numerically analyzed using the finite element method (FEM). Two-phase Buongiorno’s formulation was used to model the fluid layer, and Brinkman-Forchheimer equation was used to formulate the porous layer. The enclosure has a low temperature, while the cylinder is maintained at a high temperature. The governing equations are expressed in PDEs and converted into weak formulations (Galerkin FEM). In numerical simulations, the average concentration, the amplitude of undulated cylinder, the number of undulated, and the Rayleigh number are investigated. It is observed that the homogeneous nanofluid model could be valid for low heating intensity with higher waviness frequency and/or higher amplitude. The higher the alumina concentration, the higher the heat transfer rate. The heat transfer rate can be boosted by up to 13% by suspending 1% alumina particles. The heat transfer enhancement decreases with increasing the amplitude and/or increasing the waviness number.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47744070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper retrieves the vector-coupled version of the generalized anticubic nonlinearity model in fiber Bragg gratings. With the help of the trial equation approach and the complete discriminant system for polynomial, nine families of the optical solitons solutions and single traveling wave solutions for the fiber Bragg gratings with generalized anticubic nonlinearity are obtained. Under specific parameter values, three-dimensional diagrams, two-dimensional diagrams, density plots, and contour plots of the obtained solutions are displayed. Moreover, the solutions obtained in the paper further demonstrated their accurate physical behaviors.
{"title":"Optical Solitons and Single Traveling Wave Solutions for the Fiber Bragg Gratings with Generalized Anticubic Nonlinearity","authors":"Dan-Mei Chen, Zhao Li","doi":"10.1155/2023/6283436","DOIUrl":"https://doi.org/10.1155/2023/6283436","url":null,"abstract":"This paper retrieves the vector-coupled version of the generalized anticubic nonlinearity model in fiber Bragg gratings. With the help of the trial equation approach and the complete discriminant system for polynomial, nine families of the optical solitons solutions and single traveling wave solutions for the fiber Bragg gratings with generalized anticubic nonlinearity are obtained. Under specific parameter values, three-dimensional diagrams, two-dimensional diagrams, density plots, and contour plots of the obtained solutions are displayed. Moreover, the solutions obtained in the paper further demonstrated their accurate physical behaviors.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45253438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The main purpose of this paper is to investigate the bifurcation and traveling wave solution of the Fokas system in monomode optical fibers by using the method of planar dynamical system. Firstly, the Fokas systems are reduced to two-dimensional planar dynamic system by using the traveling wave transformation. Secondly, by selecting fixed parameters, the phase portraits are drawn by using the Maple software. Finally, the Jacobi elliptic function solutions, the hyperbolic function solutions, and trigonometric function solutions of the Fokas system are obtained.
{"title":"Phase Portraits and Traveling Wave Solutions of Fokas System in Monomode Optical Fibers","authors":"Chao Tang, Zhao Li","doi":"10.1155/2023/8783222","DOIUrl":"https://doi.org/10.1155/2023/8783222","url":null,"abstract":"The main purpose of this paper is to investigate the bifurcation and traveling wave solution of the Fokas system in monomode optical fibers by using the method of planar dynamical system. Firstly, the Fokas systems are reduced to two-dimensional planar dynamic system by using the traveling wave transformation. Secondly, by selecting fixed parameters, the phase portraits are drawn by using the Maple software. Finally, the Jacobi elliptic function solutions, the hyperbolic function solutions, and trigonometric function solutions of the Fokas system are obtained.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45518374","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Cunlin Li, Hongyu Zhang, Rui Yuan, Y. H. Min, Tzu-Chien Yin
In this paper, a Stieltjes integral approximation method for uncertain variational inequality problem (UVIP) is studied. Firstly, uncertain variables are introduced on the basis of variational inequality. Since the uncertain variables are based on nonadditive measures, there is usually no density function. Secondly, the expected value model of UVIP is established after the expected value is discretized by the Stieltjes integral. Furthermore, a gap function is constructed to transform UVIP into an uncertain constraint optimization problem, and the optimal value of the constraint problem is proved to be the solution of UVIP. Finally, the convergence of solutions of the Stieltjes integral discretization approximation problem is proved.
{"title":"An Approximation Method for Variational Inequality with Uncertain Variables","authors":"Cunlin Li, Hongyu Zhang, Rui Yuan, Y. H. Min, Tzu-Chien Yin","doi":"10.1155/2023/5127277","DOIUrl":"https://doi.org/10.1155/2023/5127277","url":null,"abstract":"In this paper, a Stieltjes integral approximation method for uncertain variational inequality problem (UVIP) is studied. Firstly, uncertain variables are introduced on the basis of variational inequality. Since the uncertain variables are based on nonadditive measures, there is usually no density function. Secondly, the expected value model of UVIP is established after the expected value is discretized by the Stieltjes integral. Furthermore, a gap function is constructed to transform UVIP into an uncertain constraint optimization problem, and the optimal value of the constraint problem is proved to be the solution of UVIP. Finally, the convergence of solutions of the Stieltjes integral discretization approximation problem is proved.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47161595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
<jats:p>This paper studies the free boundary problem of a multistable equation with a Robin boundary condition, which may be used to describe the spreading of the invasive species with the solution representing the density of species and the free boundary representing the boundary of the spreading region. The Robin boundary condition <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"> <msub> <mrow> <mi>u</mi> </mrow> <mrow> <mi>x</mi> </mrow> </msub> <mfenced open="(" close=")"> <mrow> <mi>t</mi> <mo>,</mo> <mn>0</mn> </mrow> </mfenced> <mo>=</mo> <mi>τ</mi> <mi>u</mi> <mfenced open="(" close=")"> <mrow> <mi>t</mi> <mo>,</mo> <mn>0</mn> </mrow> </mfenced> </math> </jats:inline-formula> means that there is a flux of species at <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"> <mi>x</mi> <mo>=</mo> <mn>0</mn> </math> </jats:inline-formula>. By studying the asymptotic properties of the bounded solution, we obtain the following two situations: (i) four types of survival states: the solution is either big spreading (the solution converges to a big stationary solution defined on the half-line) or small spreading (the solution converges to a small stationary solution defined on the half-line) or small equilibrium state (the survival interval <jats:inline-formula> <math xmlns="http://www.w3.org/1998/Math/MathML" id="M3"> <mfenced open="[" close="]"> <mrow> <mn>0</mn> <mo>,</mo> <mi>h</mi> <mfenced open="(" close=")"> <mrow> <mi>t</mi> </mrow> </mfenced> </mrow> </mfenced> </math> </jats:inline-formula> tends to a finite interval and the solution tends to a small compactly supported solution) or vanishing happens (the solution and the interval <
本文研究了具有Robin边界条件的多稳态方程的自由边界问题，该问题可用于描述入侵物种的扩散，其解表示物种密度，自由边界表示扩散区域的边界。Robin边界条件u x t，0=τ，0意味着在x=0处存在物种的通量。通过研究有界解的渐近性质，我们得到了以下两种情况：（i）四种生存状态：解要么是大展开（解收敛于半线上定义的大平稳解），要么是小展开（解会聚于半线上限定的小平稳解）或是小平衡状态（生存期0，h t趋向于有限区间，并且解趋向于小的紧支撑解）或消失（解和区间0，h t收缩为0作为t⟶ T表示T+∞）；（ii）解的三重生存状态：大扩散、大平衡状态和消失。
{"title":"On a Multistable Type of Free Boundary Problem with a Flux at the Boundary","authors":"","doi":"10.1155/2023/8944465","DOIUrl":"https://doi.org/10.1155/2023/8944465","url":null,"abstract":"<jats:p>This paper studies the free boundary problem of a multistable equation with a Robin boundary condition, which may be used to describe the spreading of the invasive species with the solution representing the density of species and the free boundary representing the boundary of the spreading region. The Robin boundary condition <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M1\">\u0000 <msub>\u0000 <mrow>\u0000 <mi>u</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>x</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mi>t</mi>\u0000 <mo>,</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 </mfenced>\u0000 <mo>=</mo>\u0000 <mi>τ</mi>\u0000 <mi>u</mi>\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mi>t</mi>\u0000 <mo>,</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula> means that there is a flux of species at <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M2\">\u0000 <mi>x</mi>\u0000 <mo>=</mo>\u0000 <mn>0</mn>\u0000 </math>\u0000 </jats:inline-formula>. By studying the asymptotic properties of the bounded solution, we obtain the following two situations: (i) four types of survival states: the solution is either big spreading (the solution converges to a big stationary solution defined on the half-line) or small spreading (the solution converges to a small stationary solution defined on the half-line) or small equilibrium state (the survival interval <jats:inline-formula>\u0000 <math xmlns=\"http://www.w3.org/1998/Math/MathML\" id=\"M3\">\u0000 <mfenced open=\"[\" close=\"]\">\u0000 <mrow>\u0000 <mn>0</mn>\u0000 <mo>,</mo>\u0000 <mi>h</mi>\u0000 <mfenced open=\"(\" close=\")\">\u0000 <mrow>\u0000 <mi>t</mi>\u0000 </mrow>\u0000 </mfenced>\u0000 </mrow>\u0000 </mfenced>\u0000 </math>\u0000 </jats:inline-formula> tends to a finite interval and the solution tends to a small compactly supported solution) or vanishing happens (the solution and the interval <","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43042337","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The time-fractional diffusion equation coupled with a first-order irreversible reaction is investigated by employing integral transforms. We derive Green’s functions for short and long times via approximations of the Mittag-Leffler function. The time value for which the crossover between short- and long-time asymptotic holds is presented in explicit form. Based on the developed Green’s functions, the exact analytic asymptotic solutions of the time-fractional reaction-diffusion equation are obtained. The applicability of the obtained solutions is demonstrated via quantification of the reaction-diffusion kinetics during heterogeneous catalytic chitin conversion to chitosan.
{"title":"Green’s Functions on Various Time Scales for the Time-Fractional Reaction-Diffusion Equation","authors":"A. Zhokh, P. Strizhak","doi":"10.1155/2023/6646284","DOIUrl":"https://doi.org/10.1155/2023/6646284","url":null,"abstract":"The time-fractional diffusion equation coupled with a first-order irreversible reaction is investigated by employing integral transforms. We derive Green’s functions for short and long times via approximations of the Mittag-Leffler function. The time value for which the crossover between short- and long-time asymptotic holds is presented in explicit form. Based on the developed Green’s functions, the exact analytic asymptotic solutions of the time-fractional reaction-diffusion equation are obtained. The applicability of the obtained solutions is demonstrated via quantification of the reaction-diffusion kinetics during heterogeneous catalytic chitin conversion to chitosan.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":" ","pages":""},"PeriodicalIF":1.2,"publicationDate":"2023-04-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44287709","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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