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15 results on '"University of Zagreb-University of Zagreb"'

1. Sobolev norm estimates for a class of bilinear multipliers

Author

Vjekoslav Kovač, Frédéric Bernicot, Laboratoire de Mathématiques Jean Leray (LMJL), Centre National de la Recherche Scientifique (CNRS)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN), Department of Mathematics, Department of Mathematics [Zagreb], Faculty of Science [Zagreb], University of Zagreb-University of Zagreb-Faculty of Science [Zagreb], University of Zagreb-University of Zagreb, and ANR-11-JS01-0001,AFoMEN,Analyse de Fourier Multilineaire et EDPs Nonlineaires(2011)

Subjects
Spatial variable, Pure mathematics, Pseudodifferential operators, Applied Mathematics, 010102 general mathematics, Bilinear interpolation, bilinear Hilbert transform, bilinear multiplier, paraproduct, pseudodifferential operator, Sobolev space, General Medicine, [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA], 01 natural sciences, 030207 dermatology & venereal diseases, 03 medical and health sciences, 0302 clinical medicine, Operator (computer programming), Mathematics - Classical Analysis and ODEs, Norm (mathematics), 0101 mathematics, 42B15, Analysis, Mathematics
Abstract

We consider bilinear multipliers that appeared as a distinguished particular case in the classification of two-dimensional bilinear Hilbert transforms by Demeter and Thiele [9]. In this note we investigate their boundedness on Sobolev spaces. Furthermore, we study structurally similar operators with symbols that also depend on the spatial variables. The new results build on the existing L^p estimates for a paraproduct-like operator previously studied by the authors in [5] and [10]. Our primary intention is to emphasize the analogies with Coifman-Meyer multipliers and with bilinear pseudodifferential operators of order 0., Comment: 11 pages

Published
2013
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2. Analytic moduli for parabolic Dulac germs

Author

Pavao Mardešić, Maja Resman, Institut de Mathématiques de Bourgogne [Dijon] (IMB), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB), Department of Mathematics [Zagreb], Faculty of Science [Zagreb], University of Zagreb-University of Zagreb, Croatian Unity Through Knowledge Fund (UKF) 'My first collaboration grant'16Croatian Science Foundation (HRZZ) - European Social FundUIP-2017-05-1020PZS-2019-02-3055EIPHI Graduate SchoolANR-17-EURE-0002UKF grant, and ANR-17-EURE-0002,EIPHI,Ingénierie et Innovation par les sciences physiques, les savoir-faire technologiques et l'interdisciplinarité(2017)

Subjects
Pure mathematics, Class (set theory), Mathematics::Dynamical Systems, General Mathematics, Dulac germ, Dynamical Systems (math.DS), 01 natural sciences, Moduli, Mathematics::Algebraic Geometry, 0103 physical sciences, FOS: Mathematics, Mathematics - Dynamical Systems, [MATH]Mathematics [math], 0101 mathematics, transseries, Mathematics, Sequence, Mathematics::Complex Variables, 010102 general mathematics, State (functional analysis), 37C15, 37F75, analytic invariants, Gevrey summability, Almost regular germ, Ecalle-Voronin moduli, ecalle-Voronin moduli, 010307 mathematical physics
Abstract

In this paper we give moduli of analytic classification for parabolic Dulac i.e. almost regular germs. Dulac germs appear as first return maps of hyperbolic polycycles. Their moduli are given by a sequence of Ecalle-Voronin-like germs of analytic diffeomorphisms. We state the result in a bigger class of parabolic generalized Dulac germs having power-logarithmic asymptotic expansions., 63 pages, 5 figures

Published
2021
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3. Nilpotence of orbits under monodromy and the length of Melnikov functions

Author

Pavao Mardesić, Jessie Pontigo-Herrera, Dmitry Novikov, L. Ortiz-Bobadilla, Institut de Mathématiques de Bourgogne [Dijon] (IMB), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB), Department of Mathematics [Zagreb], Faculty of Science [Zagreb], University of Zagreb-University of Zagreb, Department of Mathematics (Weizmann Institute of Science), Weizmann Institute of Science [Rehovot, Israël], Instituto de Matematicas [México], and Universidad Nacional Autónoma de México (UNAM)

Subjects
Physics, Pure mathematics, Sequence, Polynomial, Conjecture, Melnikov function, Abelian integrals, 010102 general mathematics, Statistical and Nonlinear Physics, Iterated integrals, Condensed Matter Physics, 01 natural sciences, Nilpotence class, Foliation, Displacement function, Limit cycles, Monodromy, Simple (abstract algebra), [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], Product (mathematics), 0103 physical sciences, 010307 mathematical physics, 0101 mathematics, Orbit (control theory), ComputingMilieux_MISCELLANEOUS
Abstract

Let F ∈ ℂ [ x , y ] be a polynomial, γ ( z ) ∈ π 1 ( F − 1 ( z ) ) a non-trivial cycle in a generic fiber of F and let ω be a polynomial 1-form, thus defining a polynomial deformation d F + e ω = 0 of the integrable foliation given by F . We study different invariants: the orbit depth k , the nilpotence class n , the derivative length d associated with the couple ( F , γ ) . These invariants bind the length l of the first nonzero Melnikov function of the deformation d F + e ω along γ . We analyze the variation of the aforementioned invariants in a simple but informative example, in which the polynomial F is defined by a product of four lines. We study as well the relation of this behavior with the length of the corresponding Godbillon–Vey sequence. We formulate a conjecture motivated by the study of this example.

Published
2021
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4. Absolute Root Separation

Author

Andrej Dujella, Bruno Salvy, Yann Bugeaud, Tomislav Pejković, Wenjie Fang, Institut de Recherche Mathématique Avancée (IRMA), Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics [Zagreb], Faculty of Science [Zagreb], University of Zagreb-University of Zagreb, Laboratoire d'Informatique Gaspard-Monge (LIGM), Centre National de la Recherche Scientifique (CNRS)-Fédération de Recherche Bézout-ESIEE Paris-École des Ponts ParisTech (ENPC)-Université Paris-Est Marne-la-Vallée (UPEM), Arithmetic and Computing (ARIC), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de l'Informatique du Parallélisme (LIP), École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), ANR-14-CE25-0018,Fast Relax,Approximation rapide et fiable(2014), Université Paris-Est Marne-la-Vallée (UPEM)-École des Ponts ParisTech (ENPC)-ESIEE Paris-Fédération de Recherche Bézout-Centre National de la Recherche Scientifique (CNRS), Arithmétiques des ordinateurs, méthodes formelles, génération de code (ARIC), Laboratoire de l'Informatique du Parallélisme (LIP), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Inria Lyon, and Institut National de Recherche en Informatique et en Automatique (Inria)

Subjects
Computer Science - Symbolic Computation, FOS: Computer and information sciences, Polynomial, Current (mathematics), General Mathematics, Root (chord), Absolute value, 0102 computer and information sciences, Symbolic Computation (cs.SC), 01 natural sciences, Integer, ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Applied mathematics, Number Theory (math.NT), 0101 mathematics, Mathematics, [INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC], Mathematics - Number Theory, Degree (graph theory), 010102 general mathematics, Symmetric function, Mathematics - Classical Analysis and ODEs, 010201 computation theory & mathematics, Bounded function, polynomials, root separation
Abstract

International audience; The absolute separation of a polynomial is the minimum nonzero difference between the absolute values of its roots. In the case of polynomials with integer coefficients, it can be bounded from below in terms of the degree and the height (the maximum absolute value of the coefficients) of the polynomial. We improve the known bounds for this problem and related ones. Then we report on extensive experiments in low degrees, suggesting that the current bounds are still very pessimistic.

Published
2019
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5. Tubular neighborhoods of orbits of power-logarithmic germs

Author

Vesna Županović, J.P. Rolin, Pavao Mardesić, Maja Resman, Institut de Mathématiques de Bourgogne [Dijon] (IMB), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB), Department of Mathematics [Zagreb], Faculty of Science [Zagreb], University of Zagreb-University of Zagreb, Department of Applied Mathematics [Zagreb], and Faculty of Electrical Engineering and Computing [Zagreb] (FER)

Subjects
MSC : 28A75, 37C05, 37C15, 34C07, 30B10, 34E05, 37C10, Logarithm, Dulac map, Transseries, 010102 general mathematics, Order (ring theory), Function (mathematics), Characterization (mathematics), 01 natural sciences, Fractal properties of orbits, ε-Neighborhoods, Power-logarithm asymptotic expansions, Formal and analytic invariants, Embedding in a flow, 010101 applied mathematics, Iterated logarithm, Combinatorics, Conjugacy class, Iterated function, [MATH]Mathematics [math], 0101 mathematics, Asymptotic expansion, Power-logarithmasymptotic expansions, Analysis, Mathematics
Abstract

We consider a class of power-logarithmic germs. We call them parabolic Dulac germs, as they appear as Dulac germs (first-return germs) of hyperbolic polycycles. In view of formal or analytic characterization of such a germ f by fractal properties of several of its orbits, we study the tubular $$\varepsilon $$ -neighborhoods of orbits of f with initial points $$x_0$$ . We denote by $$A_f(x_0,\varepsilon )$$ the length of such a tubular $$\varepsilon $$ -neighborhood. We show that, even if f is an analytic germ, the function $$\varepsilon \mapsto A_f(x_0,\varepsilon )$$ does not have a full asymptotic expansion in $$\varepsilon $$ in the scale of powers and (iterated) logarithms. Hence, this partial asymptotic expansion cannot contain necessary information for analytic classification. In order to overcome this problem, we introduce a new notion: the continuous time length of the $$\varepsilon $$ -neighborhood $$A^c_f(x_0,\varepsilon )$$ . We show that this function has a full transasymptotic expansion in $$\varepsilon $$ in the power, iterated logarithm scale. Moreover, its asymptotic expansion extends the initial, existing part of the asymptotic expansion of the classical length $$\varepsilon \mapsto A_f(x_0,\varepsilon )$$ . Finally, we prove that this initial part of the asymptotic expansion determines the class of formal conjugacy of the Dulac germ f.

Published
2019
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6. An invariance principle for sums and record times of regularly varying stationary sequences

Author

Bojan Basrak, Philippe Soulier, Hrvoje Planinić, Department of Mathematics [Zagreb], Faculty of Science [Zagreb], University of Zagreb-University of Zagreb, Modélisation aléatoire de Paris X (MODAL'X), and Université Paris Nanterre (UPN)

Subjects
Statistics and Probability, Asymptotic analysis, Sequence, Series (mathematics), Point process, Regular variation, Invariance principle, Functional limit theorem, Record times, Stochastic process, Probability (math.PR), 010102 general mathematics, Asymptotic distribution, Scale invariance, 16. Peace & justice, 01 natural sciences, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 010104 statistics & probability, 60F17, 60G51, 60G52, 60G55, 60G70, FOS: Mathematics, Applied mathematics, Limit (mathematics), 0101 mathematics, Statistics, Probability and Uncertainty, Mathematics - Probability, Analysis, Mathematics
Abstract

We prove a sequence of limiting results about weakly dependent stationary and regularly varying stochastic processes in discrete time. After deducing the limiting distribution for individual clusters of extremes, we present a new type of point process convergence theorem. It is designed to preserve the entire information about the temporal ordering of observations which is typically lost in the limit after time scaling. By going beyond the existing asymptotic theory, we are able to prove a new functional limit theorem. Its assumptions are satisfied by a wide class of applied time series models, for which standard limiting theory in the space $D$ of \cadlag\ functions does not apply. To describe the limit of partial sums in this more general setting, we use the space~$E$ of so--called decorated \cadlag\ functions. We also study the running maximum of partial sums for which a corresponding functional theorem can be still expressed in the familiar setting of space $D$. We further apply our method to analyze record times in a sequence of dependent stationary observations, even when their marginal distribution is not necessarily regularly varying. Under certain restrictions on dependence among the observations, we show that the record times after scaling converge to a relatively simple compound scale invariant Poisson process., 40 pages, 4 figures. Version 2 a new expression for the location parameter in the case $\alpha=1$ is provided

Published
2018
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7. Derivation of a poroelastic elliptic membrane shell model

Author

Andro Mikelić, Josip Tambača, Modélisation mathématique, calcul scientifique (MMCS), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics [Zagreb], Faculty of Science [Zagreb], University of Zagreb-University of Zagreb, and ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010)

Subjects
74Q15, Nuclear Theory, Poromechanics, SHELL model, AMS subject classification, Shell (structure), asymptotic methods, Biot's quasi-static equations, 01 natural sciences, Domain (mathematical analysis), Physics::Geophysics, 010305 fluids & plasmas, Physics::Fluid Dynamics, Membrane poroelastic shell, 0103 physical sciences, Physics::Atomic and Molecular Clusters, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], MSC 76S, 0101 mathematics, Mathematics, Deformation (mechanics), Biot number, 74K25, Applied Mathematics, 010102 general mathematics, Mechanics, Physics::Classical Physics, 35B25, 74F10, Membrane, Flow (mathematics), elliptic-parabolic, systems, Membrane poroelastic shell, Biot’s quasi-static equations, elliptic–parabolic systems, asymptotic methods, Analysis
Abstract

A derivation of the model for a poroelastic elliptic membrane shell is undertaken. The flow and deformation in a three-dimensional shell domain is described by the quasi-static Biot equations of linear poroelasticity. We consider the limit when the shell thickness goes to zero and look for the limit equations. Using the technique developed in the seminal articles by Ciarlet, Lods, Miara et al.and the recent results on the rigorous derivation of the equations for poroelastic plates and flexural poroelastic shells by Marciniak-Czochra, Mikelić, and Tambača, we present a rigorous derivation of the linear poroelastic elliptic membrane shell model. After rescaling, the corresponding velocity and the pressure field are close in the C([0, T] ; (H1x)2×(L2x)2) norm and the stresses in C([0, T] ; (L2x)9) norm. We note the major difference with respect to the flexural case: (i) it is not anymore the rescaled total stress divided by the scaling parameter, but the rescaled total stress itself which converges ; (ii) the same comment applies to the pore fluid pressure ; and (iii) there is a deterioration of the convergence for the vertical component of the rescaled displacement. Consequence of the above differences is that the effective model remains of the 2nd order in space. In the case of a spherical membrane shell, we confirm the results by Taber from the literature.

Published
2018
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8. The Fatou coordinate for parabolic Dulac germs

Author

Vesna Županović, Maja Resman, Pavao Mardešić, Jean-Philippe Rolin, Institut de Mathématiques de Bourgogne [Dijon] (IMB), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB), Department of Mathematics [Zagreb], Faculty of Science [Zagreb], University of Zagreb-University of Zagreb, Department of Applied Mathematics [Zagreb], Faculty of Electrical Engineering and Computing [Zagreb] (FER), This research was supported by: Croatian Science Foundation (HRZZ) project no. 2285, French ANR project STAAVF, French–Croatian bilateral Cogito project 33003TJClassification de points fixes et de singularités à l'aide d'epsilon-voisinages d'orbites et de courbes, Croatian UKF project Classifications of Dulac maps and epsilon-neighborhoods, My first collaboration grant 2018, project no. 7, the University of Zagreb research support for 2015 and 2016., and ANR-11-BS01-0009,STAAVF,Singularités de Trajectoires de Champs de Vecteurs Analytiques et Algébriques(2011)

Subjects
Pure mathematics, Monomial, Class (set theory), Mathematics::Dynamical Systems, Constructive proof, Logarithm, Transseries, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], orbits, Dulac germ, Asymptotic expansion, Dynamical Systems (math.DS), 01 natural sciences, MSC: 37C05, 34C07, 30B10, 30B12, 39A06, 34E05, 37C10, 37C15, 37C05, 34C07, 30B10, 30B12, 39A06, 34E05, 37C10, 37C15, Mathematics::Algebraic Geometry, FOS: Mathematics, 0101 mathematics, Mathematics - Dynamical Systems, Mathematics, Fatou coordinate, Embedding in a flow, diffeomorphisms, Mathematics::Complex Variables, Applied Mathematics, 010102 general mathematics, 010101 applied mathematics, classification, normal forms, epsilon-neighborhoods, Analysis
Abstract

We study the class of parabolic Dulac germs of hyperbolic polycycles. For such germs we give a constructive proof of the existence of a unique Fatou coordinate, admitting an asymptotic expansion in the power-iterated log scale., 31 pages. arXiv admin note: text overlap with arXiv:1606.02581

Published
2019
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9. Normal forms and embeddings for power-log transseries

Author

Jean-Philippe Rolin, Maja Resman, Pavao Mardešić, Vesna Županović, Institut de Mathématiques de Bourgogne [Dijon] ( IMB ), Université de Bourgogne ( UB ) -Centre National de la Recherche Scientifique ( CNRS ), Department of Applied Mathematics, Faculty of Electrical Engineering and Computing, University of Zagreb, University of Zagreb-Faculty of Electrical Engineering and Computing, University of Zagreb-University of Zagreb, Croatian Science Foundation (HRZZ) project. Grant number : 2285, French-Croatian bilateral Cogito project Classification de points fixes et de singularites a l'aide d'epsilon-voisinages d'orbites et de courbes, University of Zagreb, ANR-11-BS01-0009,STAAVF,Singularités de Trajectoires de Champs de Vecteurs Analytiques et Algébriques ( 2011 ), Institut de Mathématiques de Bourgogne [Dijon] (IMB), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB), Department of Applied Mathematics [Zagreb], Faculty of Electrical Engineering and Computing [Zagreb] (FER), and ANR-11-BS01-0009,STAAVF,Singularités de Trajectoires de Champs de Vecteurs Analytiques et Algébriques(2011)

Subjects
Mathematics::Dynamical Systems, [ MATH.MATH-CA ] Mathematics [math]/Classical Analysis and ODEs [math.CA], Transseries, General Mathematics, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [ MATH.MATH-DS ] Mathematics [math]/Dynamical Systems [math.DS], MSC: 34C20, 37C10, 39B12, 46A19, 28A75, 58K50, 26A12, [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA], Normal forms, 01 natural sciences, Iteration theory, Dulac map, normal forms, embedding in a flow, transseries, 0101 mathematics, Algebra over a field, Mathematics, Series (mathematics), formal normal forms, parabolic transseries, Mathematics::History and Overview, 010102 general mathematics, Power (physics), 010101 applied mathematics, Algebra, Embedding, Embedding in a flow
Abstract

First return maps in the neighborhood of hyperbolic polycycles have their asymptotic expansion as Dulac series, which are series with power-logarithm monomials. We extend the class of Dulac series to an algebra of power-logarithm transseries. Inside this new algebra, we provide formal normal forms of power-log transseries and a formal embedding theorem. The questions of classifications and of embeddings of germs into flows of vector fields are common problems in dynamical systems. Aside from that, our motivation for this work comes from fractal analysis of orbits of first return maps around hyperbolic polycycles. This is a joint work with Pavao Mardešić, Jean-Philippe Rolin and Vesna Županović.

Published
2016
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10. Effective pressure boundary condition for the filtration through porous medium via homogenization

Author

Eduard Marušić-Paloka, Thomas Carraro, Andro Mikelić, IAM Heidelberg, Universität Heidelberg [Heidelberg], Department of Mathematics [Zagreb], Faculty of Science [Zagreb], University of Zagreb-University of Zagreb, Modélisation mathématique, calcul scientifique (MMCS), Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Ce travail a été réalisé grâce au soutien financier du LABEX MILYON (ANR-10-LABX-0070) de l'Université de Lyon, dans le cadre du programme 'Investissements d'Avenir' (ANR-11-IDEX-0007) géré par l'Agence Nationale de la Recherche (ANR)., and ANR-10-LABX-0070,MILYON,Community of mathematics and fundamental computer science in Lyon(2010)

Subjects
010103 numerical & computational mathematics, Boundary layer thickness, 01 natural sciences, 010305 fluids & plasmas, Physics::Fluid Dynamics, 0103 physical sciences, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], Boundary value problem, 0101 mathematics, [MATH]Mathematics [math], Mathematics, Applied Mathematics, [SPI.FLUID]Engineering Sciences [physics]/Reactive fluid environment, Mathematical analysis, General Engineering, General Medicine, Robin boundary condition, Computational Mathematics, Boundary layer, Boundary conditions in CFD, Blasius boundary layer, No-slip condition, Homogenization, Stationary Navier–Stokes equations, Stress boundary conditions, Effective tangential velocity jump, Porous media, Porous medium, General Economics, Econometrics and Finance, Analysis
Abstract

We present homogenization of the viscous incompressible porous media flows under stress boundary conditions at the outer boundary. In addition to Darcy’s law describing filtration in the interior of the porous medium, we derive rigorously the effective pressure boundary condition at the outer boundary. It is a linear combination of the outside pressure and the applied shear stress. We use the two-scale convergence in the sense of boundary layers, introduced by Allaire and Conca (1997) to obtain the boundary layer structure next to the outer boundary. The approach allows establishing the strong L 2 -convergence of the velocity corrector and identification of the effective boundary velocity slip jump. The theoretical results are confirmed through numerical experiments.

Published
2018
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11. Absolute real root separation

Author

Yann Bugeaud, Bruno Salvy, Tomislav Pejković, Andrej Dujella, Institut de Recherche Mathématique Avancée (IRMA), Université de Strasbourg (UNISTRA)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics [Zagreb], Faculty of Science [Zagreb], University of Zagreb-University of Zagreb, Arithmetic and Computing (ARIC), Inria Grenoble - Rhône-Alpes, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de l'Informatique du Parallélisme (LIP), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), ANR-14-CE25-0018,Fast Relax,Approximation rapide et fiable(2014), Došlić, Tomislav, Martinjak, Ivica, Centre National de la Recherche Scientifique (CNRS)-Université de Strasbourg (UNISTRA), École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL), and Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL)

Subjects
[INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC], integer polynomials, root separation, Mathematics - Number Theory, General Mathematics, 010102 general mathematics, Separation (statistics), Mathematical analysis, Root (chord), [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA], 010103 numerical & computational mathematics, 01 natural sciences, Properties of polynomial roots, Absolute (philosophy), ComputingMethodologies_SYMBOLICANDALGEBRAICMANIPULATION, FOS: Mathematics, Number Theory (math.NT), 0101 mathematics, Mathematics, Polynomials
Abstract

International audience; While the separation (the minimal nonzero distance) between roots of a polynomial is a classical topic, its absolute counterpart (the minimal nonzero distance between their absolute values) does not seem to have been studied much. We present the general context and give tight bounds for the case of real roots.

Published
2017
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12. Effects of rough boundary and nonzero boundary conditions on the lubrication process with micropolar fluid

Author

Igor Pažanin, Francisco Javier Suárez-Grau, Matthieu Bonnivard, Bonnivard, Matthieu, Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics [Zagreb], Faculty of Science [Zagreb], University of Zagreb-University of Zagreb, Departemento Ecuaciones Diferenciales y Analisis Numerico, and Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico

Subjects
Asymptotic analysis, General Physics and Astronomy, Boundary (topology), 02 engineering and technology, numerical results, 01 natural sciences, Physics::Fluid Dynamics, rough boundary, 0203 mechanical engineering, nonzero boundary conditions, Nonzero boundary conditions, [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP], lubrication process, Boundary value problem, 0101 mathematics, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Mathematical Physics, Mathematics, Mathematical analysis, Mechanics, Mixed boundary condition, [MATH.MATH-NA] Mathematics [math]/Numerical Analysis [math.NA], Lubrication process, Micropolar fluid, Singular boundary method, Lubrication theory, 010101 applied mathematics, micropolar fluid, Boundary conditions in CFD, asymptotic analysis, 020303 mechanical engineering & transports, Rough boundary, Numerical results, Lubrication, No-slip condition, micropolar fluid, [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
Abstract

The lubrication theory is mostly concerned with the behavior of a lubricant flowing through a narrow gap. Motivated by the experimental findings from the tribology literature, we take the lubricant to be micropolar fluid and study its behavior in a thin domain with rough boundary. Instead of considering (commonly used) simple zero boundary condition, we impose physically relevant (nonzero) boundary condition for microrotation and perform asymptotic analysis of the corresponding 3D boundary value problem. We formally derive a simplified mathematical model acknowledging the roughness-induced effects and the effects of the nonzero boundary conditions on the macroscopic flow. Using the obtained asymptotic model, we study numerically the influence of the specific rugosity profile on the performance of a linear slider bearing. The numerical results clearly indicate that the use of the rough surfaces may contribute to enhance the mechanical performance of such device. Croatian Science Foundation University of Zagreb Ministerio de Economía y Competitividad Junta de Andalucía

Published
2017

13. A two level scaling-up method for multiphase flow in porous media; numerical validation and comparison with other methods

Author

Alain Bourgeat, Mladen Jurak, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics [Zagreb], Faculty of Science [Zagreb], University of Zagreb-University of Zagreb, and Reymond, Aurélie

Subjects
Hydrogeology, Multiphase flow, 010103 numerical & computational mathematics, Mechanics, 01 natural sciences, Computer Science Applications, 010101 applied mathematics, Computational Mathematics, Computational Theory and Mathematics, Flow (mathematics), Nuclear waste repository, Two-phase flow, Porous media, Scale up, Coarsening, Transport migration, SCALE-UP, Geotechnical engineering, 0101 mathematics, Computers in Earth Sciences, Numerical validation, Porous medium, Scaling, ComputingMilieux_MISCELLANEOUS, Geology
Abstract

We present a robust and accurate strategy for upscaling two-phase flow in heterogeneous porous media composed of different rock-types. The method is tested by means of numerical simulations and compared with other upscaling methods.

Published
2009
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14. Scaling up of an underground nuclear waste repository including a possibly damaged zone

Author

Alain Bourgeat, Andrey Piatnitski, Eduard Marušić-Paloka, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Narvik University College, Department of Mathematics [Zagreb], Faculty of Science [Zagreb], University of Zagreb-University of Zagreb, and Reymond, Aurélie

Subjects
Physics, upscaling, homogenization, convection–diffusion equation, General Mathematics, 010102 general mathematics, Macroscopic model, Radioactive waste, Mechanics, 01 natural sciences, Homogenization (chemistry), 010101 applied mathematics, 0101 mathematics, Convection–diffusion equation, Scaling, ComputingMilieux_MISCELLANEOUS
Abstract

We derive a macroscopic model for an underground nuclear waste repository consisting of long storage cells linked by a possibly damaged drifts. As the first result we find a simple first-order approximation. Secondly, we compute a corrector using a matched expansion around the drift. We prove an appropriate convergence result.

Published
2010

15. Two phase partially miscible flow and transport modeling in porous media: application to gas migration in a nuclear waste repository

Author

Mladen Jurak, Alain Bourgeat, Farid Smaï, Institut Camille Jordan [Villeurbanne] (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université Jean Monnet [Saint-Étienne] (UJM)-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics [Zagreb], Faculty of Science [Zagreb], and University of Zagreb-University of Zagreb

Subjects
Materials science, Hydrogen, Two-phase flow, Porous medium, Modeling, Underground nuclear waste management, Capillary action, 0207 environmental engineering, FOS: Physical sciences, chemistry.chemical_element, 010103 numerical & computational mathematics, 02 engineering and technology, Thermal diffusivity, 01 natural sciences, 7. Clean energy, [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph], Geotechnical engineering, 0101 mathematics, Computers in Earth Sciences, 020701 environmental engineering, ComputingMilieux_MISCELLANEOUS, Mathematical Physics, Radioactive waste, porous medium, modeling, Mathematical Physics (math-ph), Mechanics, Computer Science Applications, Computational Mathematics, Computational Theory and Mathematics, chemistry, 13. Climate action, Compressibility, Deep geological repository, underground nuclear waste management
Abstract

We derive a compositional compressible two-phase, liquid and gas, flow model for numerical simulations of hydrogen migration in deep geological repository for radioactive waste. This model includes capillary effects and the gas high diffusivity. Moreover, it is written in variables (total hydrogen mass density and liquid pressure) chosen in order to be consistent with gas appearance or disappearance. We discuss the well possedness of this model and give some computational evidences of its adequacy to simulate gas generation in a water-saturated repository.

Published
2008

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