Pub Date : 2018-07-26DOI: 10.2140/MEMOCS.2018.6.251
Elena Lopez Tomas, A. Scheuer, E. Abisset-Chavanne, F. Chinesta
{"title":"On the effect of phase transition on the manifold dimensionality: application to the Ising model","authors":"Elena Lopez Tomas, A. Scheuer, E. Abisset-Chavanne, F. Chinesta","doi":"10.2140/MEMOCS.2018.6.251","DOIUrl":"https://doi.org/10.2140/MEMOCS.2018.6.251","url":null,"abstract":"","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2018-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89164525","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 : 2018-07-26DOI: 10.2140/MEMOCS.2018.6.213
H. Abdoul-Anziz, P. Seppecher
We determine the effective behavior of periodic structures made of welded elastic bars. Taking into account the fact that flexural and torsional stiffnesses are much smaller than the extensional one we overpass classical homogenization formula and obtain totally different types of effective energies. We work in the framework of linear elasticity. We give different examples of two dimensional or three dimensional micro-structures which lead to generalized 1D, 2D or 3D continua like Timoshenko beam, Mindlin-Reissner plate, strain gradient, Cosserat, or micromorphic continua.
{"title":"Strain gradient and generalized continua obtained by homogenizing frame lattices","authors":"H. Abdoul-Anziz, P. Seppecher","doi":"10.2140/MEMOCS.2018.6.213","DOIUrl":"https://doi.org/10.2140/MEMOCS.2018.6.213","url":null,"abstract":"We determine the effective behavior of periodic structures made of welded elastic bars. Taking into account the fact that flexural and torsional stiffnesses are much smaller than the extensional one we overpass classical homogenization formula and obtain totally different types of effective energies. We work in the framework of linear elasticity. We give different examples of two dimensional or three dimensional micro-structures which lead to generalized 1D, 2D or 3D continua like Timoshenko beam, Mindlin-Reissner plate, strain gradient, Cosserat, or micromorphic continua.","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2018-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77209870","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 : 2018-07-26DOI: 10.2140/memocs.2018.6.137
Gianpietro Del Piero
{"title":"The variational structure of classical plasticity","authors":"Gianpietro Del Piero","doi":"10.2140/memocs.2018.6.137","DOIUrl":"https://doi.org/10.2140/memocs.2018.6.137","url":null,"abstract":"","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2018-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82963368","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 : 2018-07-26DOI: 10.2140/MEMOCS.2018.6.201
S. Kumar, D. Mandal
{"title":"Generation of SH-type waves due to shearing stress discontinuity in an anisotropic layer overlying an initially stressed elastic half-space","authors":"S. Kumar, D. Mandal","doi":"10.2140/MEMOCS.2018.6.201","DOIUrl":"https://doi.org/10.2140/MEMOCS.2018.6.201","url":null,"abstract":"","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2018-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80443388","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 : 2018-07-26DOI: 10.2140/MEMOCS.2018.6.181
L. Russo
The paper summarizes and discusses the main theses exposed in a previous book (L' America dimenticata, Mondadori Universita, 2013 [in Italian]) in light of more recent results. Specifically, the work addresses the problem of explaining the origin of the systematic error on longitudes in Ptolemy's Geographia and its logical relation with the reduced estimate for the dimension of the Earth there given. The thesis is sustained that, conversely to a frequently advanced conjecture, the shrinking of the dimension of the Earth is a consequence of the scale error on the longitudes, which, in turn, was originated by a misidentification of the Islands of the Blessed. The location of the Islands of the Blessed according the source of Ptolemy is identified in the Caribbean. The analysis of a passage by Pliny provides an independent and quantitative confirmation of the proposed identification, which sheds new light on possible contact among civilizations.
本文总结并讨论了前一本书(L' America dimenticata, Mondadori Universita, 2013[意大利语])中暴露的主要论文，并结合了最近的研究结果。具体地说，这项工作解决了解释托勒密的《地理学》中经度系统误差的起源问题，以及它与那里给出的地球尺寸缩减估计的逻辑关系。与经常提出的猜想相反，这个论点得到了支持，即地球尺寸的缩小是经度刻度误差的结果，而经度刻度误差又源于对受祝福岛屿的错误识别。根据托勒密的来源，受祝福的岛屿的位置被确定在加勒比海。对普林尼的一篇文章的分析为提出的鉴定提供了独立和定量的证实，这为文明之间可能的接触提供了新的线索。
{"title":"Far-reaching Hellenistic geographical knowledge\u0000hidden in Ptolemy’s data","authors":"L. Russo","doi":"10.2140/MEMOCS.2018.6.181","DOIUrl":"https://doi.org/10.2140/MEMOCS.2018.6.181","url":null,"abstract":"The paper summarizes and discusses the main theses exposed in a previous book (L' America dimenticata, Mondadori Universita, 2013 [in Italian]) in light of more recent results. Specifically, the work addresses the problem of explaining the origin of the systematic error on longitudes in Ptolemy's Geographia and its logical relation with the reduced estimate for the dimension of the Earth there given. The thesis is sustained that, conversely to a frequently advanced conjecture, the shrinking of the dimension of the Earth is a consequence of the scale error on the longitudes, which, in turn, was originated by a misidentification of the Islands of the Blessed. The location of the Islands of the Blessed according the source of Ptolemy is identified in the Caribbean. The analysis of a passage by Pliny provides an independent and quantitative confirmation of the proposed identification, which sheds new light on possible contact among civilizations.","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2018-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77901468","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 : 2018-05-29DOI: 10.2140/MEMOCS.2018.6.69
I. Benjamini, G. Kalai
We did not meet Lucio Russo in person but his mathematical work greatly influenced our own and his wide horizons and interests in physics, mathematics, philosophy, and history greatly inspired us. We describe here two directions of study following early work of Russo. The first section follow the famous Russo-Seymour-Welsh theorem regarding critical planar percolation. The second section follows the basic ”Russo’s lemma” and deep ”Russo’s 0-1 law”. In each direction we present one central conjecture.
{"title":"Around two theorems and a lemma by Lucio Russo","authors":"I. Benjamini, G. Kalai","doi":"10.2140/MEMOCS.2018.6.69","DOIUrl":"https://doi.org/10.2140/MEMOCS.2018.6.69","url":null,"abstract":"We did not meet Lucio Russo in person but his mathematical work greatly influenced our own and his wide horizons and interests in physics, mathematics, philosophy, and history greatly inspired us. We describe here two directions of study following early work of Russo. The first section follow the famous Russo-Seymour-Welsh theorem regarding critical planar percolation. The second section follows the basic ”Russo’s lemma” and deep ”Russo’s 0-1 law”. In each direction we present one central conjecture.","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2018-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83935781","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 : 2018-05-29DOI: 10.2140/MEMOCS.2018.6.77
L. Placidi, E. Barchiesi, A. Misra
{"title":"A strain gradient variational approach to damage: a comparison with damage gradient models and numerical results","authors":"L. Placidi, E. Barchiesi, A. Misra","doi":"10.2140/MEMOCS.2018.6.77","DOIUrl":"https://doi.org/10.2140/MEMOCS.2018.6.77","url":null,"abstract":"","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2018-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77293680","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 : 2018-05-29DOI: 10.2140/MEMOCS.2018.6.125
Xu Wang, P. Schiavone
{"title":"An arbitrarily shaped Eshelby inclusion interacting with a circular piezoelectric inhomogeneity penetrated by a semi-infinite crack","authors":"Xu Wang, P. Schiavone","doi":"10.2140/MEMOCS.2018.6.125","DOIUrl":"https://doi.org/10.2140/MEMOCS.2018.6.125","url":null,"abstract":"","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2018-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79416912","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-10-28DOI: 10.2140/memocs.2018.6.101
R. Segev, J. Sniatycki
The paper considers the formulation of higher-order continuum mechanics on differentiable manifolds devoid of any metric or parallelism structure. For generalized velocities modeled as sections of some vector bundle, a variational kth order hyper-stress is an object that acts on jets of generalized velocities to produce power densities. The traction hyper-stress is introduced as an object that induces hyper-traction fields on the boundaries of subbodies. Additional aspects of multilinear algebra relevant to the analysis of these objects are reviewed.
{"title":"On jets, almost symmetric tensors, and traction hyper-stresses","authors":"R. Segev, J. Sniatycki","doi":"10.2140/memocs.2018.6.101","DOIUrl":"https://doi.org/10.2140/memocs.2018.6.101","url":null,"abstract":"The paper considers the formulation of higher-order continuum mechanics on differentiable manifolds devoid of any metric or parallelism structure. For generalized velocities modeled as sections of some vector bundle, a variational kth order hyper-stress is an object that acts on jets of generalized velocities to produce power densities. The traction hyper-stress is introduced as an object that induces hyper-traction fields on the boundaries of subbodies. Additional aspects of multilinear algebra relevant to the analysis of these objects are reviewed.","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2017-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85935354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2017-09-06DOI: 10.2140/memocs.2019.7.203
M. Olive
We propose a general algorithm to compute all the symmetry classes of any $mathrm{SO}(3)$ or $mathrm{O}(3)$ linear representation. This method relies on the introduction of a binary operator between sets of conjugacy classes of closed subgroups, called the clips. We compute explicit tables for this operation which allows to solve definitively the problem.
{"title":"Effective computation of SO(3) and O(3) linear\u0000representation symmetry classes","authors":"M. Olive","doi":"10.2140/memocs.2019.7.203","DOIUrl":"https://doi.org/10.2140/memocs.2019.7.203","url":null,"abstract":"We propose a general algorithm to compute all the symmetry classes of any $mathrm{SO}(3)$ or $mathrm{O}(3)$ linear representation. This method relies on the introduction of a binary operator between sets of conjugacy classes of closed subgroups, called the clips. We compute explicit tables for this operation which allows to solve definitively the problem.","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":null,"pages":null},"PeriodicalIF":1.9,"publicationDate":"2017-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77243415","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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