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7 results on '"Institute of Mathematics 'Octav Mayer'"'

1. Nonstandard micro-inertia terms in the relaxed micromorphic model: well-posedness for dynamics

Author

Ionel-Dumitrel Ghiba, Patrizio Neff, Sebastian Owczarek, Marco Valerio d'Agostino, Faculty of Mathematics and Information Science [Warszawa], Warsaw University of Technology [Warsaw], Alexandru Ioan Cuza University of Iași [Romania], Institute of Mathematics 'Octav Mayer', Romanian Academy, Mécanique des Matériaux et des Structures (M2S), Géomécanique, Matériaux et Structures (GEOMAS), Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA), Fakultät für Mathematik der Universität Duisburg-Essen, Universität Duisburg-Essen [Essen], and Thework of I.D. Ghiba was supported by Alexandru Ioan Cuza University of Iasi (UAIC) under the grant GI-17458,within the internal grant competition for young researchers.

Subjects
Wave propagation, General Mathematics, media_common.quotation_subject, FOS: Physical sciences, generalized continua, 02 engineering and technology, Inertia, 01 natural sciences, Mathematics - Analysis of PDEs, 0203 mechanical engineering, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], General Materials Science, Fakultät für Mathematik, ddc:510, 0101 mathematics, Mathematical Physics, media_common, Physics, Dynamics (mechanics), Metamaterial, Mathematical Physics (math-ph), 010101 applied mathematics, 020303 mechanical engineering & transports, Classical mechanics, Mechanics of Materials, Mathematik, micro-inertia, Focus (optics), Well posedness, Analysis of PDEs (math.AP)
Abstract

International audience; We study the existence of solutions arising from the modelling of elastic materials using generalized theories of continua. In view of some evidence from physics of metamaterials, we focus our effort on two recent nonstandard relaxed micromorphic models including novel micro-inertia terms. These novel micro-inertia terms are needed to better capture the band-gap response. The existence proof is based on the Banach fixed-point theorem.

Published
2019
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2. Real wave propagation in the isotropic-relaxed micromorphic model

Author

Gabriele Barbagallo, Angela Madeo, Marco Valerio d'Agostino, Rafael Abreu, Ionel-Dumitrel Ghiba, Patrizio Neff, Universität Duisburg-Essen [Essen], Laboratoire de Génie Civil et d'Ingénierie Environnementale (LGCIE), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA), Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne] (LaMCoS), Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Université de Lyon-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Institut für Geophysik [Münster], Westfälische Wilhelms-Universität Münster (WWU), Alexandru Ioan Cuza University of Iași [Romania], Institute of Mathematics 'Octav Mayer', and Romanian Academy

Subjects
Wave propagation, AMS 2010: 74A10, 74A30, 74A60, 74E15, 74M25, 74Q15, General Mathematics, generalized continuum, [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], FOS: Physical sciences, General Physics and Astronomy, 02 engineering and technology, ellipticity, [PHYS.MECA.SOLID]Physics [physics]/Mechanics [physics]/Mechanics of the solides [physics.class-ph], 01 natural sciences, planar harmonic waves, real wave velocity, Planar, 0203 mechanical engineering, acoustic tensor, micromorphic, 0101 mathematics, Mathematical Physics, Research Articles, positive-definiteness, Physics, Cosserat, Continuum (measurement), Mathematical analysis, Isotropy, Linear elasticity, Wave velocity, General Engineering, Mathematical Physics (math-ph), 74A10, 74A30, 74A60, 74E15, 74M25, 74Q15, 010101 applied mathematics, rank-one convexity, 020303 mechanical engineering & transports, Positive definiteness, micropolar, Mathematik
Abstract

For the recently introduced isotropic-relaxed micromorphic generalized continuum model, we show that, under the assumption of positive-definite energy, planar harmonic waves have real velocity. We also obtain a necessary and sufficient condition for real wave velocity which is weaker than the positive definiteness of the energy. Connections to isotropic linear elasticity and micropolar elasticity are established. Notably, we show that strong ellipticity does not imply real wave velocity in micropolar elasticity, whereas it does in isotropic linear elasticity.

Published
2017
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3. When some variational properties force convexity

Author

Jean-Baptiste Hiriart-Urruty, Michel Volle, Constantin Zălinescu, Laboratoire d'Analyse non linéaire et Géométrie (LANLG), Avignon Université (AU), Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Octav Mayer Institute of Mathematics, Romanian Academy of Sciences, EA2151 Laboratoire de Mathématiques d'Avignon (LMA), Mathématiques pour l'Industrie et la Physique (MIP), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), University 'Al. I. Cuza' Iasi Faculty of Mathematics, Université 'Al. I. Cuza' Iasi, Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse III - Paul Sabatier (UT3), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Alexandru Ioan Cuza University of Iași [Romania], Institute of Mathematics 'Octav Mayer', and Romanian Academy

Subjects
Pure mathematics, Control and Optimization, Mathematics::Optimization and Control, Banach space, 01 natural sciences, Convexity, Order (group theory), Metric projection, [MATH]Mathematics [math], 0101 mathematics, best approximation, ComputingMilieux_MISCELLANEOUS, Mathematics, Convex analysis, essential smoothness, Mathematics::Functional Analysis, Convex duality, 010102 general mathematics, Mathematical analysis, Function (mathematics), 010101 applied mathematics, Computational Mathematics, Control and Systems Engineering, convex duality, 49J53 (46G05 49J50), well posed optimization problem, Convex function, essential strict convexity
Abstract

International audience; The notion of adequate (resp. strongly adequate) function has been recently introduced to characterize the essentially strictly convex (resp. essentially firmly subdifferentiable) functions among the weakly lower semicontinuous (resp. lower semicontinuous) ones. In this paper we provide various necessary and sufficient conditions in order that the lower semicontinuous hull of an extended real-valued function on a reflexive Banach space is essentially strictly convex. Some new results on nearest (farthest) points are derived from this approach.

Published
2013
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4. A new view on boundary conditions in the Grioli–Koiter–Mindlin–Toupin indeterminate couple stress model

Author

Patrizio Neff, Angela Madeo, Ingo Münch, Ionel-Dumitrel Ghiba, Laboratoire de Génie Civil et d'Ingénierie Environnementale (LGCIE), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA), International Research Center for the Mathematics & Mechanics of Complex Systems (MEMOCS), Università degli Studi dell'Aquila (UNIVAQ), Universität Duisburg-Essen [Essen], Alexandru Ioan Cuza University of Iași [Romania], Institute of Mathematics 'Octav Mayer', Romanian Academy, Karlsruhe Institute of Technology (KIT), and The work of the second author was partial supported by a grant of the Romanian National Authority for Scientific Research and Innovation, CNCS-UEFISCDI, project number PN II-ID-PCE-2011-3-0521, contract nr. 144/2011.

Subjects
74A30, 74A35, Traction (engineering), General Physics and Astronomy, Boundary (topology), FOS: Physical sciences, 02 engineering and technology, 01 natural sciences, Generalized continua, Mathematics - Analysis of PDEs, 0203 mechanical engineering, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], Calculus, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], General Materials Science, Boundary value problem, 0101 mathematics, Equivalence (measure theory), Mathematical Physics, Mathematics, Mechanical Engineering, Mathematical analysis, Isotropy, Indeterminate couple stress model, Mixed boundary condition, Mathematical Physics (math-ph), [SPI.MECA]Engineering Sciences [physics]/Mechanics [physics.med-ph], Robin boundary condition, 010101 applied mathematics, 020303 mechanical engineering & transports, Mechanics of Materials, Mathematik, Second gradient elasticity, Consistency of mixed boundary conditions, Indeterminate, Analysis of PDEs (math.AP)
Abstract

International audience; In this paper we consider the Grioli–Koiter–Mindlin–Toupin linear isotropic indeterminate couple stress model. Our main aim is to show that, up to now, the boundary conditions have not been completely understood for this model. As it turns out, and to our own surprise, restricting the well known boundary conditions stemming from the strain gradient or second gradient models to the particular case of the indeterminate couple stress model, does not always reduce to the Grioli–Koiter–Mindlin–Toupin set of accepted boundary conditions. We present, therefore, a proof of the fact that when specific “mixed” kinematical and traction boundary conditions are assigned on the boundary, no “a priori” equivalence can be established between Mindlin's and our approach.

Published
2016
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5. On some fundamental misunderstandings in the indeterminate couple stress model. A comment on recent papers of A.R. Hadjesfandiari and G.F. Dargush

Author

Ionel-Dumitrel Ghiba, Ingo Münch, Patrizio Neff, Angela Madeo, Universität Duisburg-Essen [Essen], Karlsruhe Institute of Technology (KIT), Alexandru Ioan Cuza University of Iași [Romania], Institute of Mathematics 'Octav Mayer', Romanian Academy, Laboratoire de Génie Civil et d'Ingénierie Environnementale (LGCIE), Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA), International Research Center for the Mathematics & Mechanics of Complex Systems (MEMOCS), and Università degli Studi dell'Aquila (UNIVAQ)

Subjects
Size effects, Modified couple stress model, 74A30, 74A35, Strain gradient elasticity, FOS: Physical sciences, 02 engineering and technology, Generalized continua, Theoretical physics, Mathematics - Analysis of PDEs, 0203 mechanical engineering, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], Symmetric Cauchy stresses, FOS: Mathematics, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], General Materials Science, Boundary value problem, Virtual work, Tensor, Boltzmann axiom, Conformal invariance, Microstructure, Mathematical Physics, Mathematics, Continuum (measurement), Continuum mechanics, Applied Mathematics, Mechanical Engineering, Isotropy, Mathematical Physics (math-ph), Elasticity (physics), [SPI.MECA]Engineering Sciences [physics]/Mechanics [physics.med-ph], 021001 nanoscience & nanotechnology, 16. Peace & justice, Condensed Matter Physics, Consistent traction boundary conditions, Gradient elasticity, 020303 mechanical engineering & transports, Mechanics of Materials, Modeling and Simulation, Mathematik, Preprint, 0210 nano-technology, Symmetry of couple stress tensor, Analysis of PDEs (math.AP)
Abstract

In a series of papers which are either published [A.R. Hadjesfandiari and G.F. Dargush, Couple stress theory for solids, Int. J. Solids Struct. 48, 2496-2510, 2011; A.R. Hadjesfandiari and G.F. Dargush, Fundamental solutions for isotropic size-dependent couple stress elasticity, Int. J. Solids Struct. 50, 1253-1265, 2013] or available as preprints Hadjesfandiari and Dargush have reconsidered the linear indeterminate couple stress model. They are postulating a certain physically plausible split in the virtual work principle. Based on this postulate they claim that the second-order couple stress tensor must always be skew-symmetric. Since they use an incomplete set of boundary conditions in their virtual work principle their statement contains unrecoverable errors. This is shown by specifying their development to the isotropic case. However, their choice of constitutive parameters is mathematically possible and still yields a well-posed boundary value problem., arXiv admin note: text overlap with arXiv:1504.00868

Published
2016
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6. Internal nonnegative stabilization for some parabolic equations

Author

Bedr'Eddine Ainseba, Sebastian Aniţa, Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Tools of automatic control for scientific computing, Models and Methods in Biomathematics (ANUBIS), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1 (UB)-Inria Bordeaux - Sud-Ouest, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), Institute of Mathematics 'Octav Mayer', Romanian Academy, Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), and Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Inria Bordeaux - Sud-Ouest

Subjects
education.field_of_study, Applied Mathematics, Mathematical analysis, Population, General Medicine, Parabolic cylinder function, 01 natural sciences, Parabolic partial differential equation, Domain (mathematical analysis), 010305 fluids & plasmas, 010101 applied mathematics, Elliptic operator, Elliptic partial differential equation, Parabolic cylindrical coordinates, 0103 physical sciences, 0101 mathematics, education, ComputingMilieux_MISCELLANEOUS, Analysis, Eigenvalues and eigenvectors, Mathematics
Abstract

The internal zero-stabilization of the nonnegative solutions to some parabolic equations is investigated. We provide a necessary and a sufficient condition for nonnegative stabilizability in terms of the sign of the principal eigenvalue of a certain elliptic operator. This principal eigenvalue is related to the rate of the convergence of the solution. We give some evaluations of this principal eigenvalue with respect to the geometry of the domain and of the support of the control. A stabilization result for an age-dependent population dynamics with diffusion is also established.

Published
2008
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7. The interplay between models and public health policies: Regional control for a class of spatially structured epidemics (think globally, act locally).

Author

Capasso V and Aniţa S

Subjects
Algorithms, Ecosystem, Epidemiology, Health Policy, Humans, Nonlinear Dynamics, Poisson Distribution, Seasons, Stochastic Processes, Time Factors, Communicable Diseases epidemiology, Epidemics, Public Health methods
Abstract

A review is presented here of the research carried out, by a group including the authors, on the mathematical analysis of epidemic systems. Particular attention is paid to recent analysis of optimal control problems related to spatially structured epidemics driven by environmental pollution. A relevant problem, related to the possible eradication of the epidemic, is the so called zero stabilization. In a series of papers, necessary conditions, and sufficient conditions of stabilizability have been obtained. It has been proved that it is possible to diminish exponentially the epidemic process, in the whole habitat, just by reducing the concentration of the pollutant in a nonempty and sufficiently large subset of the spatial domain. The stabilizability with a feedback control of harvesting type is related to the magnitude of the principal eigenvalue of a certain operator. The problem of finding the optimal position (by translation) of the support of the feedback stabilizing control is faced, in order to minimize both the infected population and the pollutant at a certain finite time.

Published
2018
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