Pub Date : 2022-01-19DOI: 10.2140/memocs.2022.10.171
Tomoyuki Oka
. The present paper concerns a space-time homogenization problem for nonlinear diffusion equations with periodically oscillating (in space and time) coefficients. Main results consist of corrector results (i.e., strong convergences of solutions with corrector terms) for gradients, diffusion fluxes and time-derivatives without assumptions for smoothness of coefficients. Proofs of the main results are based on the space-time version of the unfolding method, which is deeply concerned with the strong two-scale convergence theory.
{"title":"Corrector results for space-time homogenization of nonlinear diffusion","authors":"Tomoyuki Oka","doi":"10.2140/memocs.2022.10.171","DOIUrl":"https://doi.org/10.2140/memocs.2022.10.171","url":null,"abstract":". The present paper concerns a space-time homogenization problem for nonlinear diffusion equations with periodically oscillating (in space and time) coefficients. Main results consist of corrector results (i.e., strong convergences of solutions with corrector terms) for gradients, diffusion fluxes and time-derivatives without assumptions for smoothness of coefficients. Proofs of the main results are based on the space-time version of the unfolding method, which is deeply concerned with the strong two-scale convergence theory.","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":"11 2","pages":""},"PeriodicalIF":1.9,"publicationDate":"2022-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72588376","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 : 2021-12-31DOI: 10.2140/memocs.2021.9.367
Estefania Nuñez del Prado, N. Challamel, V. Picandet
{"title":"Discrete and nonlocal solutions for the lattice\u0000Cattaneo–Vernotte heat diffusion equation","authors":"Estefania Nuñez del Prado, N. Challamel, V. Picandet","doi":"10.2140/memocs.2021.9.367","DOIUrl":"https://doi.org/10.2140/memocs.2021.9.367","url":null,"abstract":"","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":"1 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90863049","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 : 2021-12-31DOI: 10.2140/memocs.2021.9.397
I. Giorgio
{"title":"A variational formulation for one-dimensional linear thermoviscoelasticity","authors":"I. Giorgio","doi":"10.2140/memocs.2021.9.397","DOIUrl":"https://doi.org/10.2140/memocs.2021.9.397","url":null,"abstract":"","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":"14 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86947806","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 : 2021-12-31DOI: 10.2140/memocs.2021.9.231
E. Babilio, L. Cascini, F. Fraternali, M. R. Scoppettuolo
{"title":"Investigating the evolution of landslides via dimensionless displacement trends","authors":"E. Babilio, L. Cascini, F. Fraternali, M. R. Scoppettuolo","doi":"10.2140/memocs.2021.9.231","DOIUrl":"https://doi.org/10.2140/memocs.2021.9.231","url":null,"abstract":"","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":"119 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77460762","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 : 2021-12-31DOI: 10.2140/memocs.2021.9.413
L. Placidi, M. E. El Sherbiny, P. Baragatti
{"title":"Experimental investigation for the existence of frequency band gap in a microstructure model","authors":"L. Placidi, M. E. El Sherbiny, P. Baragatti","doi":"10.2140/memocs.2021.9.413","DOIUrl":"https://doi.org/10.2140/memocs.2021.9.413","url":null,"abstract":"","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":"30 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80650138","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 : 2021-12-31DOI: 10.2140/memocs.2021.9.337
A. Morch, J. Witz, B. Desmorat, R. Desmorat, M. Brieu
{"title":"Kelvin decomposition for nonlinear hyperelastic modeling in large deformation","authors":"A. Morch, J. Witz, B. Desmorat, R. Desmorat, M. Brieu","doi":"10.2140/memocs.2021.9.337","DOIUrl":"https://doi.org/10.2140/memocs.2021.9.337","url":null,"abstract":"","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":"524 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75019578","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 : 2021-12-31DOI: 10.2140/memocs.2021.9.293
S. Eugster
To study nonlinear wave propagation phenomena in pantographic sheets, we propose a dynamic model that consists of an assembly of interconnected planar nonlinear Euler–Bernoulli beams. The interconnections are either formulated as perfect bilateral constraints or by onedimensional generalized force laws. Accordingly, the spatially discretized system is described by a differential algebraic system of equations, which is solved with an appropriate numerical solution strategy. We analyze various wave propagation phenomena by changing the kind of excitation.
{"title":"Numerical analysis of nonlinear wave propagation\u0000in a pantographic sheet","authors":"S. Eugster","doi":"10.2140/memocs.2021.9.293","DOIUrl":"https://doi.org/10.2140/memocs.2021.9.293","url":null,"abstract":"To study nonlinear wave propagation phenomena in pantographic sheets, we propose a dynamic model that consists of an assembly of interconnected planar nonlinear Euler–Bernoulli beams. The interconnections are either formulated as perfect bilateral constraints or by onedimensional generalized force laws. Accordingly, the spatially discretized system is described by a differential algebraic system of equations, which is solved with an appropriate numerical solution strategy. We analyze various wave propagation phenomena by changing the kind of excitation.","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":"106 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88007825","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 : 2021-10-15DOI: 10.2140/memocs.2021.9.423
D. Benedetto, E. Caglioti, S. Rossi
Many interesting physical systems can be described at the microscopic level as particle dynamics and at the mesoscopic level with kinetic equations. In the wide field of two-body interactions, the link between these two regimes is mathematically well understood in the case of the mean-field limit, i.e. when the density of the particles diverges with their number N , the mean free path vanishes as 1{N and the interaction intensity scales with 1{N . In this limit, each particle feels the interaction with the others as a mean. A rigorous mathematical proof of this result can be done in the case of two-body interactions with sufficiently regular potentials. This classical achievement has been obtained independently by several authors in the ’70s (see [5, 14, 27]) and its explanation is particularly clear in the Dobrushin’s argument [14] where the result follows by noticing that the empirical measure associated with the particle system is a weak solution of the mean-field equation; the proof follows by showing the weak continuity, w.r.t the initial datum, of the weak solutions. Although the theory for regular pairwise interactions is sufficiently well understood, going beyond it considering singular potentials, is instead a harder task. This is the case of the three-dimensional VlasovPoisson equation, which is the most important equation of plasma physics and of galactic dynamics, based on the choice of the Coulomb or Newton potential, respectively. In this equation, the potential 1{r is singular at the origin and does not belong to any L space. Although the mean-field limit for the Vlasov-Poisson equation remains an open
{"title":"Mean-field limit for particle systems with topological interactions","authors":"D. Benedetto, E. Caglioti, S. Rossi","doi":"10.2140/memocs.2021.9.423","DOIUrl":"https://doi.org/10.2140/memocs.2021.9.423","url":null,"abstract":"Many interesting physical systems can be described at the microscopic level as particle dynamics and at the mesoscopic level with kinetic equations. In the wide field of two-body interactions, the link between these two regimes is mathematically well understood in the case of the mean-field limit, i.e. when the density of the particles diverges with their number N , the mean free path vanishes as 1{N and the interaction intensity scales with 1{N . In this limit, each particle feels the interaction with the others as a mean. A rigorous mathematical proof of this result can be done in the case of two-body interactions with sufficiently regular potentials. This classical achievement has been obtained independently by several authors in the ’70s (see [5, 14, 27]) and its explanation is particularly clear in the Dobrushin’s argument [14] where the result follows by noticing that the empirical measure associated with the particle system is a weak solution of the mean-field equation; the proof follows by showing the weak continuity, w.r.t the initial datum, of the weak solutions. Although the theory for regular pairwise interactions is sufficiently well understood, going beyond it considering singular potentials, is instead a harder task. This is the case of the three-dimensional VlasovPoisson equation, which is the most important equation of plasma physics and of galactic dynamics, based on the choice of the Coulomb or Newton potential, respectively. In this equation, the potential 1{r is singular at the origin and does not belong to any L space. Although the mean-field limit for the Vlasov-Poisson equation remains an open","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":"9 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2021-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82569583","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 : 2020-11-09DOI: 10.2140/memocs.2020.8.287
D. George, R. Allena, C. Bourzac, S. Pallu, M. Bensidhoum, H. Portier, Y. Rémond
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. A new comprehensive approach for bone remodeling under medium and high mechanical load based on cellular activity Rachele Allena, Daniel George, Céline Bourzac, Stéphane Pallu, Yves Rémond, Morad Bensidhoum, Hugues Portier
{"title":"A new comprehensive approach for bone remodeling under medium and high mechanical load based on cellular activity","authors":"D. George, R. Allena, C. Bourzac, S. Pallu, M. Bensidhoum, H. Portier, Y. Rémond","doi":"10.2140/memocs.2020.8.287","DOIUrl":"https://doi.org/10.2140/memocs.2020.8.287","url":null,"abstract":"HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. A new comprehensive approach for bone remodeling under medium and high mechanical load based on cellular activity Rachele Allena, Daniel George, Céline Bourzac, Stéphane Pallu, Yves Rémond, Morad Bensidhoum, Hugues Portier","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":"12 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2020-11-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80773503","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 : 2019-08-10DOI: 10.2140/MEMOCS.2019.7.189
M. Guzev, G. Tsitsiashvili, M. Osipova
{"title":"The object detection by autonomous apparatus as a solution of the Buffon needle problem","authors":"M. Guzev, G. Tsitsiashvili, M. Osipova","doi":"10.2140/MEMOCS.2019.7.189","DOIUrl":"https://doi.org/10.2140/MEMOCS.2019.7.189","url":null,"abstract":"","PeriodicalId":45078,"journal":{"name":"Mathematics and Mechanics of Complex Systems","volume":"133 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2019-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74804883","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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