Abstract This paper presents a comparative study between a large number of different existing sequential quadrature schemes suitable for Robust Design Optimization (RDO), with the inclusion of two partly original approaches. Efficiency of the different integration strategies is evaluated in terms of accuracy and computational effort: main goal of this paper is the identification of an integration strategy able to provide the integral value with a prescribed accuracy using a limited number of function samples. Identification of the different qualities of the various integration schemes is obtained utilizing both algebraic and practical test cases. Differences in the computational effort needed by the different schemes is evidenced, and the implications on their application to practical RDO problems is highlighted.
{"title":"Sequential quadrature methods for RDO","authors":"D. Peri","doi":"10.1515/caim-2016-0017","DOIUrl":"https://doi.org/10.1515/caim-2016-0017","url":null,"abstract":"Abstract This paper presents a comparative study between a large number of different existing sequential quadrature schemes suitable for Robust Design Optimization (RDO), with the inclusion of two partly original approaches. Efficiency of the different integration strategies is evaluated in terms of accuracy and computational effort: main goal of this paper is the identification of an integration strategy able to provide the integral value with a prescribed accuracy using a limited number of function samples. Identification of the different qualities of the various integration schemes is obtained utilizing both algebraic and practical test cases. Differences in the computational effort needed by the different schemes is evidenced, and the implications on their application to practical RDO problems is highlighted.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"7 1","pages":"23 - 47"},"PeriodicalIF":1.3,"publicationDate":"2016-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67376027","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}
Abstract The rising motion in free space of a pulsating spherical bubble of gas and vapour driven by the gravitational force, in an isochoric, inviscid liquid is investigated. The liquid is at rest at the initial time, so that the subsequent flow is irrotational. For this reason, the velocity field due to the bubble motion is described by means of a potential, which is represented through an expansion based on Legendre polynomials. A system of two coupled, ordinary and nonlinear differential equations is derived for the vertical position of the bubble center of mass and for its radius. This latter equation is a modified form of the Rayleigh-Plesset equation, including a term proportional to the kinetic energy associated to the translational motion of the bubble.
{"title":"Dynamics of a bubble rising in gravitational field","authors":"Enrico De Bernardis, G. Riccardi","doi":"10.1515/caim-2016-0018","DOIUrl":"https://doi.org/10.1515/caim-2016-0018","url":null,"abstract":"Abstract The rising motion in free space of a pulsating spherical bubble of gas and vapour driven by the gravitational force, in an isochoric, inviscid liquid is investigated. The liquid is at rest at the initial time, so that the subsequent flow is irrotational. For this reason, the velocity field due to the bubble motion is described by means of a potential, which is represented through an expansion based on Legendre polynomials. A system of two coupled, ordinary and nonlinear differential equations is derived for the vertical position of the bubble center of mass and for its radius. This latter equation is a modified form of the Rayleigh-Plesset equation, including a term proportional to the kinetic energy associated to the translational motion of the bubble.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"7 1","pages":"48 - 67"},"PeriodicalIF":1.3,"publicationDate":"2016-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/caim-2016-0018","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67375800","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}
Abstract The planar interactions between pair of vortices in an inviscid fluid are analytically investigated, by assuming one of the two vortices pointwise and the other one uniform. A novel approach using the Schwarz function of the boundary of the uniform vortex is adopted. It is based on a new integral relation between the (complex) velocity induced by the uniform vortex and its Schwarz function and on the time evolution equation of this function. They lead to a singular integrodifferential problem. Even if this problem is strongly nonlinear, its nonlinearities are confined inside two terms, only. As a consequence, its solution can be analytically approached by means of successive approximations. The ones at 0th (nonlinear terms neglected) and 1st (nonlinear terms evaluated on the 0-order solution) orders are calculated and compared with contour dynamics simulations of the vortex motion. A satisfactory agreement is keept for times which are small with respect to the turn-over time of the vortex pair.
{"title":"A study of the interactions between uniform and pointwise vortices in an inviscid fluid","authors":"G. Riccardi","doi":"10.1515/caim-2016-0016","DOIUrl":"https://doi.org/10.1515/caim-2016-0016","url":null,"abstract":"Abstract The planar interactions between pair of vortices in an inviscid fluid are analytically investigated, by assuming one of the two vortices pointwise and the other one uniform. A novel approach using the Schwarz function of the boundary of the uniform vortex is adopted. It is based on a new integral relation between the (complex) velocity induced by the uniform vortex and its Schwarz function and on the time evolution equation of this function. They lead to a singular integrodifferential problem. Even if this problem is strongly nonlinear, its nonlinearities are confined inside two terms, only. As a consequence, its solution can be analytically approached by means of successive approximations. The ones at 0th (nonlinear terms neglected) and 1st (nonlinear terms evaluated on the 0-order solution) orders are calculated and compared with contour dynamics simulations of the vortex motion. A satisfactory agreement is keept for times which are small with respect to the turn-over time of the vortex pair.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"7 1","pages":"22 - 4"},"PeriodicalIF":1.3,"publicationDate":"2016-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/caim-2016-0016","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67375758","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 issue is the second of a recent feature in the journal, the themed issue. Started in 2014, CAIM dedicated special issues have proven to be a very popular vehicle for publishing together papers that have a common theme. Seeking to publish focused, coherent thematic volumes that will be of lasting use to the community, well cited, and of the highest quality, we hope to attract the attention of a broader community of readers and help to continue the growth of CAIM. Indeed, the number of special issue published pages has progressively increased from 2014 onwards. We believe that this growth is a very positive sign of the quality and popularity of these special issues. For this reason, we plan to continue to publish a themed issues once or more per year. The first themed issue, entitled Fractional Calculus, Probability and Non-local Operators: Applications and Recent Developments and edited by Gianni Pagnini and Enrico Scalas contained a selection of paper presented at a workshop organised on the occasion of the retirement of Prof. Francesco Mainardi in Bilbao, Basque Country, Spain, on November 2013. CAIM Vol. 6 (2015) consist of two separate issues containing contributions of many outstanding researchers on fractional calculus that span either theoretical or applied topics on the interaction of fractional calculus, probability and non-local operators. We hereby launch the second CAIM themed issue. Under the title Constitutive Equations for Heat Conduction in Nanosystems and Nonequilibrium Processes, Guest Editors Vito Antonio Cimmelli and David Jou have assembled contributions from world-class experts in their fields that cover diverse topics related to the modelling of heat transport at nanoscale and in far-from-equilibrium processes. This issue is an outcome of the special session with the same title they organised at the First Joint Interna-
这一期是该杂志最近一期专题的第二期，即主题期。从2014年开始，CAIM专题特刊已经被证明是一个非常受欢迎的工具，可以将具有共同主题的论文发表在一起。寻求出版重点突出、连贯的主题卷，这些卷将对社区有持久的用处，被广泛引用，质量最高，我们希望吸引更广泛的读者社区的注意，并帮助CAIM继续发展。事实上，自2014年以来，特刊出版页数逐步增加。我们认为，这种增长是这些特刊质量和受欢迎程度的一个非常积极的迹象。因此，我们计划继续每年出版一次或多次主题问题。第一期主题为《分数阶微积分、概率和非局部算子:应用和最新发展》，由Gianni Pagnini和Enrico Scalas编辑，收录了2013年11月为纪念Francesco Mainardi教授在西班牙巴斯克地区毕尔巴鄂退休而组织的研讨会上发表的论文。CAIM Vol. 6(2015)由两个独立的问题组成，其中包含许多杰出的分数阶微积分研究人员的贡献，涵盖分数阶微积分，概率和非局部算子的相互作用的理论或应用主题。我们在此推出第二期CAIM主题杂志。在《纳米系统和非平衡过程中的热传导本构方程》的标题下，客座编辑Vito Antonio cimmeli和David Jou汇集了来自各自领域的世界级专家的贡献，涵盖了与纳米尺度和非平衡过程中的热传输建模相关的各种主题。本期专题是他们在首届联合国际会议上组织的同名特别会议的成果
{"title":"Editor’s Note","authors":"Giorgio Fotia","doi":"10.1515/caim-2016-0001","DOIUrl":"https://doi.org/10.1515/caim-2016-0001","url":null,"abstract":"This issue is the second of a recent feature in the journal, the themed issue. Started in 2014, CAIM dedicated special issues have proven to be a very popular vehicle for publishing together papers that have a common theme. Seeking to publish focused, coherent thematic volumes that will be of lasting use to the community, well cited, and of the highest quality, we hope to attract the attention of a broader community of readers and help to continue the growth of CAIM. Indeed, the number of special issue published pages has progressively increased from 2014 onwards. We believe that this growth is a very positive sign of the quality and popularity of these special issues. For this reason, we plan to continue to publish a themed issues once or more per year. The first themed issue, entitled Fractional Calculus, Probability and Non-local Operators: Applications and Recent Developments and edited by Gianni Pagnini and Enrico Scalas contained a selection of paper presented at a workshop organised on the occasion of the retirement of Prof. Francesco Mainardi in Bilbao, Basque Country, Spain, on November 2013. CAIM Vol. 6 (2015) consist of two separate issues containing contributions of many outstanding researchers on fractional calculus that span either theoretical or applied topics on the interaction of fractional calculus, probability and non-local operators. We hereby launch the second CAIM themed issue. Under the title Constitutive Equations for Heat Conduction in Nanosystems and Nonequilibrium Processes, Guest Editors Vito Antonio Cimmelli and David Jou have assembled contributions from world-class experts in their fields that cover diverse topics related to the modelling of heat transport at nanoscale and in far-from-equilibrium processes. This issue is an outcome of the special session with the same title they organised at the First Joint Interna-","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"7 1","pages":"1 - 3"},"PeriodicalIF":1.3,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/caim-2016-0001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67375143","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}
{"title":"A note from the Editor","authors":"G. Fotia","doi":"10.1515/caim-2016-0015","DOIUrl":"https://doi.org/10.1515/caim-2016-0015","url":null,"abstract":"","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"7 1","pages":"1 - 3"},"PeriodicalIF":1.3,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67376118","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 : 2015-12-30DOI: 10.1685/JOURNAL.CAIM.540
G. Pagnini, E. Scalas
It is a pleasure for us to introduce the second and final part of a special issue of Communications in Applied and Industrial Mathematics containing contributions presented at the Workshop Fractional Calculus, Probability and Non–local Operators: Applications and Recent Developments. The Workshop was organised on 6–8 November 2013 in Bilbao, Basque Country, Spain, as a tribute to the career of Professor Francesco Mainardi, on the occasion of his retirement.
{"title":"Guest Editorial: Fractional Calculus, Probability and Non–local Operators: Applications and Recent Developments, Part 2","authors":"G. Pagnini, E. Scalas","doi":"10.1685/JOURNAL.CAIM.540","DOIUrl":"https://doi.org/10.1685/JOURNAL.CAIM.540","url":null,"abstract":"It is a pleasure for us to introduce the second and final part of a special issue of Communications in Applied and Industrial Mathematics containing contributions presented at the Workshop Fractional Calculus, Probability and Non–local Operators: Applications and Recent Developments. The Workshop was organised on 6–8 November 2013 in Bilbao, Basque Country, Spain, as a tribute to the career of Professor Francesco Mainardi, on the occasion of his retirement.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"6 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2015-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67590220","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}
Abstract In this paper, we propose a numerical approach to solve a kinetic model of chemotaxis phenomena. This scheme is shown to be uniformly stable with respect to the small parameter, consistent with the uid-di usion limit (Keller-Segel model). Our approach is based on the micro-macro decomposition which leads to an equivalent formulation of the kinetic model that couples a kinetic equation with macroscopic ones. This method is validated by various test cases and compared to other standard methods.
{"title":"An Asymptotic Preserving Scheme for Kinetic Models for Chemotaxis Phenomena","authors":"A. Bellouquid, Jacques Tagoudjeu","doi":"10.2478/caim-2018-0010","DOIUrl":"https://doi.org/10.2478/caim-2018-0010","url":null,"abstract":"Abstract In this paper, we propose a numerical approach to solve a kinetic model of chemotaxis phenomena. This scheme is shown to be uniformly stable with respect to the small parameter, consistent with the uid-di usion limit (Keller-Segel model). Our approach is based on the micro-macro decomposition which leads to an equivalent formulation of the kinetic model that couples a kinetic equation with macroscopic ones. This method is validated by various test cases and compared to other standard methods.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"9 1","pages":"61 - 75"},"PeriodicalIF":1.3,"publicationDate":"2015-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69186790","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 : 2015-06-18DOI: 10.1685/JOURNAL.CAIM.504
A. Mentrelli, G. Pagnini
Modelling the propagation of interfaces is of interest in several fields of applied sciences, such as those involving chemical reactions where the reacting interface separates two different compounds. When the front propagation occurs in systems characterized by an underlying random motion, the front gets a random character and a tracking method for fronts with a random motion is desired. The Level Set Method, which is a successful front tracking technique widely used for interfaces with deterministic motion, is here randomized assuming that the motion of the interface is characterized by a random diffusive process. In particular, here we consider the case of a motion governed by the time-fractional diffusion equation, leading to a probability density function for the interface particle displacement given by the M-Wright/Mainardi function. Some numerical results are shown and discussed.
{"title":"Random front propagation in fractional diffusive systems","authors":"A. Mentrelli, G. Pagnini","doi":"10.1685/JOURNAL.CAIM.504","DOIUrl":"https://doi.org/10.1685/JOURNAL.CAIM.504","url":null,"abstract":"Modelling the propagation of interfaces is of interest in several fields of applied sciences, such as those involving chemical reactions where the reacting interface separates two different compounds. When the front propagation occurs in systems characterized by an underlying random motion, the front gets a random character and a tracking method for fronts with a random motion is desired. The Level Set Method, which is a successful front tracking technique widely used for interfaces with deterministic motion, is here randomized assuming that the motion of the interface is characterized by a random diffusive process. In particular, here we consider the case of a motion governed by the time-fractional diffusion equation, leading to a probability density function for the interface particle displacement given by the M-Wright/Mainardi function. Some numerical results are shown and discussed.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"6 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2015-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67589975","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 : 2015-06-18DOI: 10.1685/JOURNAL.CAIM.536
Changpin Li, Rifang Wu, Heng-fei Ding
In this paper, a high order approximation with convergence order $$O( {{tau ^{3 - alpha }}})$$ to Caputo derivative $$_{C}D_{0,t}^{alpha}f(t)$$ for $$alphain(0,1)$$ is introduced. Furthermore, two high-order algorithms for Caputo type advection-diffusion equation are obtained. The stability and convergence are rigorously studied which depend upon the derivative order alpha. The corresponding convergence orders are $$O(tau^{3-alpha}+h^2)$$ and $$O(tau^{3-alpha}+h^4)$$ where tau is the time stepsize, h the space stepsize, respectively. Finally, numerical examples are given to support the theoretical analysis.
{"title":"High-order approximation to Caputo derivatives and Caputo-type advection-diffusion equations","authors":"Changpin Li, Rifang Wu, Heng-fei Ding","doi":"10.1685/JOURNAL.CAIM.536","DOIUrl":"https://doi.org/10.1685/JOURNAL.CAIM.536","url":null,"abstract":"In this paper, a high order approximation with convergence order \u0000$$O( {{tau ^{3 - alpha }}})$$ to Caputo derivative $$_{C}D_{0,t}^{alpha}f(t)$$ for \u0000$$alphain(0,1)$$ is introduced. Furthermore, two high-order algorithms for Caputo type advection-diffusion equation are obtained. The stability and convergence are rigorously studied which depend upon the derivative order alpha. The corresponding convergence orders are $$O(tau^{3-alpha}+h^2)$$ and $$O(tau^{3-alpha}+h^4)$$ where tau is the time stepsize, h the space stepsize, respectively. Finally, numerical examples are given to support the theoretical analysis.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"6 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2015-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67589913","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 : 2015-06-18DOI: 10.1685/JOURNAL.CAIM.538
F. Costa, E. C. Grigoletto, J. Vaz, E. C. Oliveira
The fractional version for the diffusion of neutrons in a material medium is studied. The concept of fractional derivative is presented, in the Caputo and Riesz senses. Using this concept, we discuss a fractional partial differential equation associated with the slowing-down of neutrons, whose analytical solution is presented in terms of Fox's H function. As a convenient limiting case, the classical solution is recovered.
{"title":"Slowing-down of neutrons: a fractional model","authors":"F. Costa, E. C. Grigoletto, J. Vaz, E. C. Oliveira","doi":"10.1685/JOURNAL.CAIM.538","DOIUrl":"https://doi.org/10.1685/JOURNAL.CAIM.538","url":null,"abstract":"The fractional version for the diffusion of neutrons in a material medium is studied. The concept of fractional derivative is presented, in the Caputo and Riesz senses. Using this concept, we discuss a fractional partial differential equation associated with the slowing-down of neutrons, whose analytical solution is presented in terms of Fox's H function. As a convenient limiting case, the classical solution is recovered.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"52 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2015-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67589932","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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