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":"50 1 1","pages":""},"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":"150 1","pages":""},"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":"188 1","pages":""},"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":"27 1","pages":""},"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":"1 1","pages":""},"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}
Pub Date : 2015-08-05DOI: 10.2140/memocs.2019.7.239
Justine Louis
In [3], the low temperature ratchet current in a multilevel system is considered. In this note, we give an explicit expression for it and find its numerical value as the number of states goes to infinity.
{"title":"Low-temperature ratchet current","authors":"Justine Louis","doi":"10.2140/memocs.2019.7.239","DOIUrl":"https://doi.org/10.2140/memocs.2019.7.239","url":null,"abstract":"In [3], the low temperature ratchet current in a multilevel system is considered. In this note, we give an explicit expression for it and find its numerical value as the number of states goes to infinity.","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":"158 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2015-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82647205","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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