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  • 51.
    Matsui, Kazunori
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Asymptotic analysis of an ε-Stokes problem with Dirichlet boundary conditions2019Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    In this thesis, we propose an ε-Stokes problem connecting the Stokes problem and the corresponding pressure-Poisson equation using one pa- rameter ε > 0. We prove that the solution to the ε-Stokes problem, converges as ε tends to 0 or ∞ to the Stokes and pressure-Poisson prob- lem, respectively. Most of these results are new. The precise statements of the new results are given in Proposition 3.5, Theorem 4.1, Theorem 5.2, and Theorem 5.3. Numerical results illustrating our mathematical results are also presented.

  • 52. Matsui, Kazunori
    et al.
    Muntean, Adrian
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Asymptotic analysis of an ε-Stokes problem connecting Stokes and pressure-Poisson problems2018In: Advances in Mathematical Sciences and Applications, ISSN 1343-4373, Vol. 27, no 1, p. 181-191Article in journal (Refereed)
    Abstract [en]

    In this Note, we prepare an ε-Stokes problem connecting the Stokes problem and the corresponding pressure-Poisson equation using one parameter ε > 0. We prove that the solution to the ε-Stokes problem, convergences as ε tends to 0 or ∞ to the Stokes and pressure-Poisson problem, respectively.

  • 53. Meier, Sebastian A.
    et al.
    Muntean, Adrian
    Technical University of Eindhoven.
    A two-scale reaction-diffusion system with micro-cell reaction concentrated on a free boundary2008In: Comptes rendus. Mecanique, ISSN 1631-0721, E-ISSN 1873-7234, Vol. 336, no 6, p. 481-486Article in journal (Refereed)
  • 54.
    Muntean, Adrian
    University of Bremen.
    Concentration blow up in a two-phase non-equilibrium model with source term2007In: Meccanica (Milano. Print), ISSN 0025-6455, E-ISSN 1572-9648, Vol. 42, no 4, p. 409-411Article in journal (Refereed)
  • 55.
    Muntean, Adrian
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science. Technical University of Eindhoven.
    Continuity with respect to data and parameters of weak solutions to a Stefan-like problem2009In: Acta Mathematica Universitatis Comenianae, ISSN 0862-9544, E-ISSN 0231-6986, Vol. 78, no 2, p. 205-222Article in journal (Refereed)
    Abstract [en]

    We study a reaction-diffusion system with moving boundary describing a prototypical fast reaction-diffusion scenario arising in the chemical corrosion of concrete-based materials. We prove the continuity with respect to data and parameters of weak solutions to the resulting moving-boundary system of partial differential equations. 

  • 56.
    Muntean, Adrian
    Tech Univ Eindhoven, Dept Math & Comp Sci, CASA Ctr Anal Sci Comp & Applicat, Eindhoven, Netherlands..
    Well-posedness of a moving-boundary problem with two moving reaction strips2009In: Nonlinear Analysis, ISSN 1468-1218, Vol. 10, no 4, p. 2541-2557Article in journal (Refereed)
    Abstract [en]

    We deal with a one-dimensional coupled system of semi-linear reaction-diffusion equations in two a priori unknown moving phases driven by a non-local kinetic condition. The PDEs system models the penetration of gaseous carbon dioxide in unsaturated porous materials (like concrete). The main issue is that the strong competition between carbon dioxide diffusion and the fast reaction of carbon dioxide with calcium hydroxide–which are the main active reactants–leads to a sudden drop in the alkalinity of concrete near the steel reinforcement. This process–called concrete carbonation–facilitates chemical corrosion and drastically influences the lifetime of the material. We present details of a class of moving-boundary models with kinetic condition at the moving boundary and address the local existence, uniqueness and stability of positive weak solutions. We also point out our concept of global solvability. The application of such moving-boundary systems to the prediction of carbonation penetration into ordinary concrete samples is illustrated numerically.

  • 57.
    Muntean, Adrian
    et al.
    Eindhoven Inst Technol, Inst Complex Mol Syst, Dept Math & Comp Sci, CASA Ctr Anal Sci Comp & Applicat, Eindhoven, Netherlands.
    Aki, T.
    Japan Womens Univ, Fac Sci, Dept Math & Phys, Tokyo Japan.
    Preface to "The mathematics of concrete"2014In: Networks and Heterogeneous Media, ISSN 1556-1801, E-ISSN 1556-181X, Vol. 9, no 4, p. 1-2Article in journal (Refereed)
  • 58.
    Muntean, Adrian
    et al.
    Technical University of Eindhoven.
    Böhm, M.
    University of Bremen.
    Interface conditions for fast-reaction fronts in wet porous mineral materials: the case of concrete carbonation2009In: Journal of Engineering Mathematics, ISSN 0022-0833, E-ISSN 1573-2703, Vol. 65, no 1, p. 89-100Article in journal (Refereed)
    Abstract [en]

    Reaction–diffusion processes, where slow diffusion balances fast reaction, usually exhibit internal loci where the reactions are concentrated. Some modeling and simulation aspects of using kinetic free-boundary conditions to drive fast carbonation reaction fronts into unsaturated porous cement-based materials are discussed. Providing full control on the velocity of the reaction front, such conditions offer a rich description of the coupling between transport, reaction, and change in the shape of the a priori unknown time-dependent regions. New models are formulated and validated by means of numerical simulations and experimental data.

  • 59.
    Muntean, Adrian
    et al.
    Eindhoven University of Technology, The Netherlands.
    Chalupecky, Vladimir
    Kyushu University, Japan.
    Homogenization Method and Multiscale Modeling2011Book (Other academic)
    Abstract [en]

    This mini-course addresses graduate students and young researchers in mathematics and engineering sciences interested in applying both formal and rigorous averaging methods to real-life problems described by means of partial differential equations (PDEs) posed in heterogeneous media. As a background application scenario we choose to look at the interplay between reaction, diffusion and flow in periodic porous materials, but broadly speaking, a similar procedure would apply for, e.g., acoustic and/or electromagnetic wave propagation phenomena in composite (periodic) media as well. We start off with the study of oscillatory elliptic PDEs formulated firstly in fixed and, afterwards, in periodically-perforated domains. We remove the oscillations by means of a (formal) asymptotic homogenization method. The output of this procedure consists of a “guessed” averaged model equations and explicit rules (based on cell problems) for computing the effective coefficients. As second step, we introduce the concept of two-scale convergence (and correspondingly, the two-scale compactness) in the sense of Allaire and Nguetseng and derive rigorously the averaged PDE models and coefficients obtained previously. This step uses the framework of Sobolev and Bochner spaces and relies on basic tools like weak convergence methods, compact embeddings as well as extension theorems in Sobolev spaces. We particularly emphasize the role the choice of microstructures (pores, perforations, subgrids, etc.) plays in performing the overall averaging procedure. Finally, we focus our attention on a two-scale partly dissipative reaction-diffusion system with periodically distributed microstructure modeling chemical attack on concrete structures. We present a two-scale finite difference scheme able to approximate the unique weak solution to the two-scale system and prove its convergence. We illustrate numerically the typical micro-macro behavior of the active concentrations involved in the corrosion process and give details on how a two-scale FD scheme can be implemented in C. The main objective of the course is to endow the audience with a rather flexible mathematical homogenization tool so that he/she can quickly start applying this averaging methodology to other PDEs scenarios describing physico-chemical processes in media with microstructures.

  • 60.
    Muntean, Adrian
    et al.
    Eindhoven Institute of Technology.
    Neuss-Radu, Maria
    A multiscale Galerkin approach for a class of nonlinear coupled reaction-diffusion systems in complex media2010In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 371, no 2, p. 705-718Article in journal (Refereed)
  • 61.
    Muntean, Adrian
    et al.
    Technische Universiteit Eindhoven.
    van Noorden, T. L.
    University of Erlangen-Nürnberg, Martensstraße 3, Erlangen 91058, Germany .
    Corrector estimates for the homogenization of a locally periodic medium with areas of low and high diffusivity2013In: European journal of applied mathematics (Print), ISSN 0956-7925, E-ISSN 1469-4425, Vol. 24, no 5, p. 657-677Article in journal (Refereed)
    Abstract [en]

    We prove an upper bound for the convergence rate of the homogenization limit epsilon -> 0 for a linear transmission problem for a advection-diffusion(-reaction) system posed in areas with low and high diffusivity, where epsilon is a suitable scale parameter. In this way we rigorously justify the formal homogenization asymptotics obtained in [37] (van Noorden, T. and Muntean, A. (2011) Homogenization of a locally-periodic medium with areas of low and high diffusivity. Eur. J. Appl. Math. 22, 493-516). We do this by providing a corrector estimate. The main ingredients for the proof of the correctors include integral estimates for rapidly oscillating functions with prescribed average, properties of the macroscopic reconstruction operators, energy bounds, and extra two-scale regularity estimates. The whole procedure essentially relies on a good understanding of the analysis of the limit two-scale problem.

  • 62.
    Peter, M. A.
    et al.
    University of Bremen, Postfach 330 440, 28334 Bremen, Germany.
    Muntean, Adrian
    University of Bremen, Postfach 330 440, 28334 Bremen, Germany.
    Meier, S. A.
    University of Bremen, Postfach 330 440, 28334 Bremen, Germany.
    Böhm, M.
    University of Bremen, Postfach 330 440, 28334 Bremen, Germany.
    Competition of several carbonation reactions in concrete: A parametric study2008In: Cement and Concrete Research, ISSN 0008-8846, E-ISSN 1873-3948, Vol. 38, no 12, p. 1385-1393Article in journal (Refereed)
  • 63.
    Ray, N.
    et al.
    Friedrich-Alexander University of Erlangen-Nuremberg, Cauerstraße 11, 91058 Erlangen, Germany.
    Muntean, Adrian
    Technical University Eindhoven, Eindhoven, Netherlands.
    Knabner, P.
    Friedrich-Alexander University of Erlangen-Nuremberg, Cauerstraße 11, 91058 Erlangen, Germany.
    Rigorous homogenization of a Stokes-Nernst-Planck-Poisson system2012In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 390, no 1, p. 374-393Article in journal (Refereed)
  • 64.
    Roos Johansson, Sara
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Analysverktyg för digitala matematiska spel: Etnografisk innehållsanalys av digitala matematiska spel för undervisande lärare i årskurs 1 - 32017Independent thesis Advanced level (degree of Master (One Year)), 20 credits / 30 HE creditsStudent thesis
    Abstract [sv]

    Syftet med studien var att utveckla samt pröva ett analysverktyg för att se vilka matematiska förmågor fem olika matematiska digitala spel faktiskt erbjöd eleverna. Analysverktyget måste vara förenligt med kursplanen i matematik, för årskurs 1–3, och taluppfattning. Analysverktyget var baserat på Mathematical Competency Research Framework (MCRF) (Lithner et al., 2010). Vidare inkluderades relevanta förmågor från kursplanen i matematik och taluppfattning. En kodningsmanual samt ett kodningsschema användes i datainsamlingen. Kodningsmanualen innehåller 2–3 frågor formulerade från analysverktyget. Resultatet visar att analysverktyget behöver utveckla resonemangsförmågan samt kommunikationsförmågan. Två av de digitala spelen erbjöd begreppsförmågan, procedurförmågan samt kommunikationsförmågan. De andra tre erbjöd problemlösning, begreppsförmågan, procedurförmågan samt kommunikationsförmågan. För lärare innebär resultatet att analysverktyget kan användas för att undersöka vad de digitala spelen tillför undervisningen samt eleverna.

  • 65.
    Samokhin, Alexander
    et al.
    Moscow State Tech Univ Radio Engn & Automat, Moscow 117648, Russia..
    Shestopalov, Youri
    Karlstad University, Division for Engineering Sciences, Physics and Mathematics.
    Kobayashi, Kazuya
    Chuo Univ, Bunkyo Ku, Tokyo 1128551, Japan.
    Stationary iteration methods for solving 3D electromagnetic scattering problems2013In: Applied Mathematics and Computation, ISSN 0096-3003, E-ISSN 1873-5649, Vol. 222, p. 107-122Article in journal (Refereed)
    Abstract [en]

    Generalized Chebyshev iteration (GCI) applied for solving linear equations with nonselfadjoint operators is considered. Sufficient conditions providing the convergence of iterations imposed on the domain of localization of the spectrum on the complex plane are obtained. A minimax problem for the determination of optimal complex iteration parameters is formulated. An algorithm of finding an optimal iteration parameter in the case of arbitrary location of the operator spectrum on the complex plane is constructed for the generalized simple iteration method. The results are applied to numerical solution of volume singular integral equations (VSIEs) associated with the problems of the mathematical theory of wave diffraction by 3D dielectric bodies. In particular, the domain of the spectrum location is described explicitly for low-frequency scattering problems and in the general case. The obtained results are discussed and recommendations concerning their applications are given. (C) 2013 Elsevier Inc. All rights reserved.

  • 66.
    Stenberg, David
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Matematikintresse: Finns det?2012Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
  • 67.
    van Lith, B. S.
    et al.
    Eindhoven University of Technology - P. O. Box 513, NL-5600 MB Eindhoven, The Netherlands.
    Muntean, Adrian
    Eindhoven University of Technology - P. O. Box 513, NL-5600 MB Eindhoven, The Netherlands.
    Storm, C.
    Eindhoven University of Technology - P. O. Box 513, NL-5600 MB Eindhoven, The Netherlands.
    A continuum model for hierarchical fibril assembly2014In: Europhysics letters, ISSN 0295-5075, E-ISSN 1286-4854, Vol. 106, no 6Article in journal (Refereed)
    Abstract [en]

    Most of the biological polymers that make up our cells and tissues are hierarchically structured. For biopolymers ranging from collagen, to actin, to fibrin and amyloid fibrils this hierarchy provides vitally important versatility. The structural hierarchy must be encoded in the self-assembly process, from the earliest stages onward, in order to produce the appropriate substructures. In this letter, we explore the kinetics of multistage self-assembly processes in a model system which allows comparison to bulk probes such as light scattering. We apply our model to recent turbidimetry data on the self-assembly of collagen fibrils. Our analysis suggests a connection between diffusion-limited aggregation kinetics and fibril growth, supported by slow, power-law growth at very long time scales.

  • 68.
    van Meurs, Patrick
    et al.
    Eindhoven University of Technology.
    Muntean, Adrian
    Eindhoven University of Technology.
    Upscaling of the dynamics of dislocation walls2014In: Advances in Mathematical Sciences and Applications, ISSN 1343-4373, Vol. 24, no 2, p. 401-414Article in journal (Refereed)
    Abstract [en]

    We perform the discrete-to-continuum limit passage for a microscopic model describing the time evolution of dislocations in a one dimensional setting. This answers the related open question raised by Geers et al. in [GPPS13]. The proof of the upscaling procedure (i.e. the discrete-to-continuum passage) relies on the gradient flow structure of both the discrete and continuous energies of dislocations set in a suitable evolutionary variational inequality framework. Moreover, the convexity and Γ-convergence of the respective energies are properties of paramount importance for our arguments.

  • 69.
    van Meurs, Patrick
    et al.
    Eindhoven University of Technology, Netherlands.
    Muntean, Adrian
    Eindhoven University of Technology, Netherlands .
    Peletier, M.A.
    Eindhoven University of Technology, Netherlands.
    Upscaling of dislocation walls in finite domains2014In: European journal of applied mathematics (Print), ISSN 0956-7925, E-ISSN 1469-4425, Vol. 25, no 6, p. 749-781Article in journal (Refereed)
    Abstract [en]

    We wish to understand the macroscopic plastic behaviour of metals by upscaling the micromechanics of dislocations. We consider a highly simplified dislocation network, which allows our discrete model to be a one dimensional particle system, in which the interactions between the particles (dislocation walls) are singular and non-local. As a first step towards treating realistic geometries, we focus on finite-size effects rather than considering an infinite domain as typically discussed in the literature. We derive effective equations for the dislocation density by means of Gamma-convergence on the space of probability measures. Our analysis yields a classification of macroscopic models, in which the size of the domain plays a key role.

  • 70.
    van Noorden, T.L.
    et al.
    Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The Netherlands.
    Muntean, Adrian
    Technische Universiteit Eindhoven, P.O. Box 513, 5600 MB Eindhoven, The Netherlands.
    Homogenisation of a locally periodic medium with areas of low and high diffusivity2011In: European journal of applied mathematics (Print), ISSN 0956-7925, E-ISSN 1469-4425, Vol. 22, no 5, p. 493-516Article in journal (Refereed)
  • 71.
    Vromans, Arthur
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). Centre for Analysis, Computer Science and Applications (CASA), Department of Mathematics and Computers Science, Eindhoven University of Technology, Eindhoven, the Netherlands.
    A pseudoparabolic reaction-diffusion-mechanics system: Modeling, analysis and simulation2018Licentiate thesis, monograph (Other academic)
    Abstract [en]

    In this thesis, parabolic-pseudoparabolic equations are derived coupling chemical reactions, diffusion, flow and mechanics in a heterogeneous medium using the framework of mixture theory. The weak solvability in 1-D of the obtained models is studied. Furthermore, it is numerically illustrated that approximate solutions according to the Rothe method exhibit expected realistic behaviour. For a simpler model formulation, the periodic homogenization in higher space dimensions is performed.

  • 72.
    Wigren, Thomas
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    The Cauchy-Schwarz inequality: Proofs and applications in various spaces2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    We give some background information about the Cauchy-Schwarz inequality including its history. We then continue by providing a number of proofs for the inequality in its classical form using various proof techniques, including proofs without words. Next we build up the theory of inner product spaces from metric and normed spaces and show applications of the Cauchy-Schwarz inequality in each content, including the triangle inequality, Minkowski's inequality and Hölder's inequality. In the final part we present a few problems with solutions, some proved by the author and some by others.

  • 73.
    Zemskov, E. P.
    et al.
    Brandeis Univ, Dept Chem, Waltham, MA 02454 USA; Russian Acad Sci, Ctr Comp, Moscow 119333, Russia.
    Epstein, I. R.
    Brandeis Univ, Dept Chem, Waltham, MA 02454 USA; Russian Acad Sci, Ctr Comp, Moscow 119333, Russia.
    Muntean, Adrian
    Technische Universiteit Eindhoven.
    Oscillatory pulses in FitzHugh-Nagumo type systems with cross-diffusion2011In: Mathematical Medicine and Biology, ISSN 1477-8599, E-ISSN 1477-8602, Vol. 28, no 2, p. 217-226Article in journal (Refereed)
12 51 - 73 of 73
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