Martin Arop, H. Kasumba, Juma Kasozi, F. Berntsson
In this paper, an optimal actuator placement problem, with a linear wave equation as the constraint, is considered. In particular, this work presents the framework for finding the best location of actuators depending upon the given initial conditions, and where the dependence on the initial conditions is averaged out. The problem is motivated by the need to control vibrations induced by pedestrian-bridge interactions. An approach based on the shape optimization techniques is used to solve the problem. Specifically, the shape sensitivities involving a cost functional are determined using the averaged adjoint approach. A numerical algorithm based on these sensitivities is used as a solution strategy. Numerical tests illustrate the theoretical results.
{"title":"Optimal actuator placement for control of vibrations induced by pedestrian-bridge interactions","authors":"Martin Arop, H. Kasumba, Juma Kasozi, F. Berntsson","doi":"10.5206/mase/15949","DOIUrl":"https://doi.org/10.5206/mase/15949","url":null,"abstract":"In this paper, an optimal actuator placement problem, with a linear wave equation as the constraint, is considered. In particular, this work presents the framework for finding the best location of actuators depending upon the given initial conditions, and where the dependence on the initial conditions is averaged out. The problem is motivated by the need to control vibrations induced by pedestrian-bridge interactions. An approach based on the shape optimization techniques is used to solve the problem. Specifically, the shape sensitivities involving a cost functional are determined using the averaged adjoint approach. A numerical algorithm based on these sensitivities is used as a solution strategy. Numerical tests illustrate the theoretical results.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70664520","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}
This paper deals with study of the plane elasticity of thermoelastic problems for inhomogenous strip. Here, the original problems are reduced to set the governing equations in the volterra integral equations by making the use of direct integration method. Further using the iteration technique the numerical calculations has been performed. The stress distribution obtained and calculated numerically and shown graphically.
{"title":"Analysis of thermal stresses to 2D plane thermoelastic inhomogeneous strip","authors":"Abhijeet B. Adhe, K. Ghadle, U. Thool","doi":"10.5206/mase/16387","DOIUrl":"https://doi.org/10.5206/mase/16387","url":null,"abstract":"This paper deals with study of the plane elasticity of thermoelastic problems for inhomogenous strip. Here, the original problems are reduced to set the governing equations in the volterra integral equations by making the use of direct integration method. Further using the iteration technique the numerical calculations has been performed. The stress distribution obtained and calculated numerically and shown graphically.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43099725","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}
The aim of this article is to study the dynamic Von-Karman model coupledwith thermoelastic equations without rotational terms, subject to a thermal dissipation. We establish the existence as well as the uniqueness of a weak solution related to the dynamic model. At the end, we apply the finite difference method for approximating the solution of our problem.
{"title":"On the weak solution of the Von Karman model with thermoelastic plates","authors":"M. Raissouli, J. Oudaani","doi":"10.5206/mase/15658","DOIUrl":"https://doi.org/10.5206/mase/15658","url":null,"abstract":"The aim of this article is to study the dynamic Von-Karman model coupledwith thermoelastic equations without rotational terms, subject to a thermal dissipation. We establish the existence as well as the uniqueness of a weak solution related to the dynamic model. At the end, we apply the finite difference method for approximating the solution of our problem.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47130043","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}
Habiba Babangida Awwalu, N. Abdullahi, M. Hussaini
Water is a basic part of our daily lives, as such effective water supply is of paramount importance. Thus, as a result of the rise in population size and water shortage there is the need for proper, suitable and optimal utilization of water resources to efficiently be distributed among the populace. The proper allocation and distribution of water in the field of network planning need to be modelled through mathematical parameters for objective of water distribution system. This mathematical approach requires of solving an optimization problem based on multi-objective function subjected to certain constraints of mixed integer linear programming objective function which is proportional to the cost of the water distribution network. This study present a conceptual model of multi-objective optimization proposed for determination of design parameters of water distribution system by considering the significant number of constraints, decision variables, cost and reliability objective functions. The model was proposed to solve the reliability problem of water production and reduce the design and operational costs.
{"title":"CONCEPTUAL MODEL OF MIXED-INTEGER LINEAR PROGRAMMING WATER DISTRIBUTION SYSTEM","authors":"Habiba Babangida Awwalu, N. Abdullahi, M. Hussaini","doi":"10.5206/mase/15591","DOIUrl":"https://doi.org/10.5206/mase/15591","url":null,"abstract":"Water is a basic part of our daily lives, as such effective water supply is of paramount importance. Thus, as a result of the rise in population size and water shortage there is the need for proper, suitable and optimal utilization of water resources to efficiently be distributed among the populace. The proper allocation and distribution of water in the field of network planning need to be modelled through mathematical parameters for objective of water distribution system. This mathematical approach requires of solving an optimization problem based on multi-objective function subjected to certain constraints of mixed integer linear programming objective function which is proportional to the cost of the water distribution network. This study present a conceptual model of multi-objective optimization proposed for determination of design parameters of water distribution system by considering the significant number of constraints, decision variables, cost and reliability objective functions. The model was proposed to solve the reliability problem of water production and reduce the design and operational costs.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44516982","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}
Relation between species and their livelihood environment in ecological systems is very complex. For that reason, in order to study predator-prey relations, modeling is essential in biomathematics. The vital components of predator-prey models are prey species' growth function in the absence of apredator and the functional response. In this article, we proposed a predator-prey model with gregarious prey. In the existing literature, square-root functional response incorporates the gregarious behavior of prey. This study considers the generalized square root functional response and theta-logistic growth of prey in the absence of a predator. The effect of functional response parameters on stability, limit cycle, and Hopf bifurcation on the proposed model has been discussed. Numerical analysis is performed on the basis of some hypothetical parameter values to analyze the model numerically.
{"title":"Dynamical study of the theta-logistic predator-prey model incorporating gregarious behavior of prey","authors":"P. Santra, G. Mahapatra","doi":"10.5206/mase/15648","DOIUrl":"https://doi.org/10.5206/mase/15648","url":null,"abstract":"Relation between species and their livelihood environment in ecological systems is very complex. For that reason, in order to study predator-prey relations, modeling is essential in biomathematics. The vital components of predator-prey models are prey species' growth function in the absence of apredator and the functional response. In this article, we proposed a predator-prey model with gregarious prey. In the existing literature, square-root functional response incorporates the gregarious behavior of prey. This study considers the generalized square root functional response and theta-logistic growth of prey in the absence of a predator. The effect of functional response parameters on stability, limit cycle, and Hopf bifurcation on the proposed model has been discussed. Numerical analysis is performed on the basis of some hypothetical parameter values to analyze the model numerically.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48459712","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}
This paper analyses a predator-prey model with Holling type II response function incorporating Allee and fear effect in the prey. The model includes intra species competition among predators. We find out the local dynamics as well as Hopf bifurcation by considering level of fear as bifurcation parameter. The condition for diffusion-driven instability and patterns are then demonstrated in relation to the system's ecological parameters and diffusion coefficients. Intra-specific competition affects the dynamics of the system and Turing pattern formation. Moreover, output of results is verified through numerical simulation. Thus, from a dynamical standpoint, the considered model seems to be relevant in the field of ecology.
{"title":"Diffusion-driven instability and pattern formation in a prey-predator model with fear and Allee effect","authors":"Debjit Pal, D. Kesh, D. Mukherjee","doi":"10.5206/mase/15231","DOIUrl":"https://doi.org/10.5206/mase/15231","url":null,"abstract":"This paper analyses a predator-prey model with Holling type II response function incorporating Allee and fear effect in the prey. The model includes intra species competition among predators. We find out the local dynamics as well as Hopf bifurcation by considering level of fear as bifurcation parameter. The condition for diffusion-driven instability and patterns are then demonstrated in relation to the system's ecological parameters and diffusion coefficients. Intra-specific competition affects the dynamics of the system and Turing pattern formation. Moreover, output of results is verified through numerical simulation. Thus, from a dynamical standpoint, the considered model seems to be relevant in the field of ecology.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42497366","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}
This paper studies a class of Hartree equations with Coulomb potential. Combined with the conservation of mass and energy, we analyze the variational characteristics of the corresponding nonlinear elliptic equation. According to the range of parameters, we construct the evolution invariant flows of the equation in different cases. Then the sharp energy thresholds for global existence and blow-up of solutions are discussed in detail.
{"title":"Energy criteria of global existence for a class of Hartree equations with Coulomb potential","authors":"Na Tang, Jian Zhang","doi":"10.5206/mase/15536","DOIUrl":"https://doi.org/10.5206/mase/15536","url":null,"abstract":"This paper studies a class of Hartree equations with Coulomb potential. Combined with the conservation of mass and energy, we analyze the variational characteristics of the corresponding nonlinear elliptic equation. According to the range of parameters, we construct the evolution invariant flows of the equation in different cases. Then the sharp energy thresholds for global existence and blow-up of solutions are discussed in detail.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44941569","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}
The dominating set of the graph G is a subset D of vertex set V, such that every vertex not in V-D is adjacent to at least one vertex in the vertex subset D. A dominating set D is a minimal dominating set if no proper subset of D is a dominating set. The number of elements in such set is called as domination number of graph and is denoted by $gamma(G)$. In this work the domination numbers are obtained for family of prism graphs such as prism CL_n, antiprism Q_n and crossed prism R_n by identifying one of their minimum dominating set.
{"title":"Minimum Dominating Set for the Prism Graph Family","authors":"Veninstine Vivik J","doi":"10.5206/mase/15775","DOIUrl":"https://doi.org/10.5206/mase/15775","url":null,"abstract":"The dominating set of the graph G is a subset D of vertex set V, such that every vertex not in V-D is adjacent to at least one vertex in the vertex subset D. A dominating set D is a minimal dominating set if no proper subset of D is a dominating set. The number of elements in such set is called as domination number of graph and is denoted by $gamma(G)$. In this work the domination numbers are obtained for family of prism graphs such as prism CL_n, antiprism Q_n and crossed prism R_n by identifying one of their minimum dominating set.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43035769","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}
The Schnakenberg model is thought to be the Caputo fractional derivative. In order to create caputo fractional differential equations for the Schnakenberg model, a discretization process is first used. The fixed points in the model are categorized topologically. Then, we show analytically that, under certain parametric conditions, a Neimark-Sacker (NS) bifurcation and a Flip-bifurcation are supported by a fractional order Schnakenberg model. Using central manifold and bifurcation theory, we demonstrate the presence and direction of NS and Flip bifurcations. The parameter values and the initial conditions have been found to have a profound impact on the dynamical behavior of the fractional order Schnakenberg model. Numerical simulations are shown to demonstrate chaotic behaviors like bifurcations, phase portraits, period 2, 4, 7, 8, 10, 16, 20 and 40 orbits, invariant closed cycles, and attractive chaotic sets in addition to validating analytical conclusions. In order to support the system’s chaotic characteristics, we also compute the maximal Lyapunov exponents and fractal dimensions quantitatively. Finally, the chaotic trajectory of the system is stopped using the OGY approach, hybrid control method, and state feedback method.
{"title":"Chaotic dynamics of the fractional order Schnakenberg model and its control","authors":"Md. Jasim Uddin, S. M. Sohel Rana","doi":"10.5206/mase/15355","DOIUrl":"https://doi.org/10.5206/mase/15355","url":null,"abstract":"The Schnakenberg model is thought to be the Caputo fractional derivative. In order to create caputo fractional differential equations for the Schnakenberg model, a discretization process is first used. The fixed points in the model are categorized topologically. Then, we show analytically that, under certain parametric conditions, a Neimark-Sacker (NS) bifurcation and a Flip-bifurcation are supported by a fractional order Schnakenberg model. Using central manifold and bifurcation theory, we demonstrate the presence and direction of NS and Flip bifurcations. The parameter values and the initial conditions have been found to have a profound impact on the dynamical behavior of the fractional order Schnakenberg model. Numerical simulations are shown to demonstrate chaotic behaviors like bifurcations, phase portraits, period 2, 4, 7, 8, 10, 16, 20 and 40 orbits, invariant closed cycles, and attractive chaotic sets in addition to validating analytical conclusions. In order to support the system’s chaotic characteristics, we also compute the maximal Lyapunov exponents and fractal dimensions quantitatively. Finally, the chaotic trajectory of the system is stopped using the OGY approach, hybrid control method, and state feedback method.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":" ","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44826688","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}
In this paper, we present a generalization of Tsallis relative operator entropy defined for positive operators and we investigate some related properties. Some inequalities involving the generalized Tsallis relative operator entropy are pointed out as well.
{"title":"On a new generalized Tsallis relative operator entropy","authors":"Lahcen Tarik, Mohamed Chergui, Bouazza El Wahbi","doi":"10.5206/mase/15397","DOIUrl":"https://doi.org/10.5206/mase/15397","url":null,"abstract":"In this paper, we present a generalization of Tsallis relative operator entropy defined for positive operators and we investigate some related properties. Some inequalities involving the generalized Tsallis relative operator entropy are pointed out as well.","PeriodicalId":93797,"journal":{"name":"Mathematics in applied sciences and engineering","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42112015","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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