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  • 1.
    Aiki, Toyohiko
    et al.
    Gifu University, Japan.
    Anthonissen, Martijn
    Eindhoven University Technology, Netherlands.
    Muntean, Adrian
    Eindhoven University Technology, Netherlands.
    On a one-dimensional shape-memory alloy model in its fast-temperature- activation limit2012In: Discrete and Continuous Dynamical Systems. Series S, ISSN 1937-1632, E-ISSN 1937-1179, Vol. 5, no 1, p. 15-28Article in journal (Refereed)
  • 2.
    Bernhoff, Niclas
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Discrete Velocity Models for Polyatomic Molecules Without Nonphysical Collision Invariants2018In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 172, no 3, p. 742-761Article in journal (Refereed)
    Abstract [en]

    An important aspect of constructing discrete velocity models (DVMs) for the Boltzmann equation is to obtain the right number of collision invariants. Unlike for the Boltzmann equation, for DVMs there can appear extra collision invariants, so called spurious collision invariants, in plus to the physical ones. A DVM with only physical collision invariants, and hence, without spurious ones, is called normal. The construction of such normal DVMs has been studied a lot in the literature for single species, but also for binary mixtures and recently extensively for multicomponent mixtures. In this paper, we address ways of constructing normal DVMs for polyatomic molecules (here represented by that each molecule has an internal energy, to account for non-translational energies, which can change during collisions), under the assumption that the set of allowed internal energies are finite. We present general algorithms for constructing such models, but we also give concrete examples of such constructions. This approach can also be combined with similar constructions of multicomponent mixtures to obtain multicomponent mixtures with polyatomic molecules, which is also briefly outlined. Then also, chemical reactions can be added.

  • 3.
    Bogers, J.
    et al.
    TU Eindhoven, The Netherlands.
    Kumar, Kundan
    TU Eindhoven, The Netherlands.
    Notten, P. H. L.
    TU Eindhoven, The Netherlands.
    Oudenhoven, J. F. M.
    TU Eindhoven, The Netherlands.
    Pop, I. S.
    TU Eindhoven, The Netherlands.
    A multiscale domain decomposition approach for chemical vapor deposition2013In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 246, p. 65-73Article in journal (Refereed)
    Abstract [en]

    We consider the process of chemical vapor deposition on a trenched Si substrate. To understand the process (including e.g. the layer conformality) at the trench scale (microscale), we need solutions at both the trench and reactor scales (macroscale). Due to the huge difference in size of these scales, straightforward numerical computations are very challenging. To overcome this difficulty, we consider a multiscale approach by introducing an intermediate scale (the mesoscale). We start with a time-continuous model describing the transport processes and then perform time discretization. At each time step, using the ideas of domain decomposition inspired from Lions (1988) [4], we provide iterative coupling conditions for these three different scales. Using a weak formulation for the time-discrete equations, we prove the convergence of this iterative scheme at each time step. The approach also provides an alternative proof for the existence of the solutions for the time-discrete formulation. (C) 2012 Elsevier B.V. All rights reserved.

  • 4.
    Both, Jakub Wiktor
    et al.
    University of Bergen, Bergen, Norway.
    Borregales, Manuel
    University of Bergen, Bergen, Norway.
    Nordbotten, Jan Martin
    University of Bergen, Bergen, Norway; Princeton University, Princeton, NJ, USA.
    Kumar, Kundan
    University of Bergen, Bergen, Norway.
    Radu, Florin Adrian
    University of Bergen, Bergen, Norway.
    Robust fixed stress splitting for Biot’s equations in heterogeneous media2017In: Applied Mathematics Letters, ISSN 0893-9659, E-ISSN 1873-5452, Vol. 68, p. 101-108Article in journal (Refereed)
    Abstract [en]

    We study the iterative solution of coupled flow and geomechanics in heterogeneous porous media, modeled by a three-field formulation of the linearized Biot's equations. We propose and analyze a variant of the widely used Fixed Stress Splitting method applied to heterogeneous media. As spatial discretization, we employ linear Galerkin finite elements for mechanics and mixed finite elements (lowest order Raviart Thomas elements) for flow. Additionally, we use implicit Euler time discretization. The proposed scheme is shown to be globally convergent with optimal theoretical convergence rates. The convergence is rigorously shown in energy norms employing a new technique. Furthermore, numerical results demonstrate robust iteration counts with respect to the full range of Lame parameters for homogeneous and heterogeneous media. Being in accordance with the theoretical results, the iteration count is hardly influenced by the degree of heterogeneities.

  • 5.
    Bourne, D.
    et al.
    Univ Glasgow, Sch Math & Stat, Glasgow.
    Fatima, T.
    Eindhoven Univ Technol, Dept Math & Comp Sci, NL.
    van Meurs, P.
    Eindhoven Univ Technol, Dept Math & Comp Sci, NL.
    Muntean, Adrian
    Eindhoven University of Technology,.
    Is adding charcoal to soil a good method for CO2 sequestration? -: Modeling a spatially homogeneous soil2014In: Applied Mathematical Modelling, ISSN 0307-904X, E-ISSN 1872-8480, Vol. 38, no 9-10, p. 2463-2475Article in journal (Refereed)
    Abstract [en]

    Carbon sequestration is the process of capture and long-term storage of atmospheric carbon dioxide (CO2) with the aim to avoid dangerous climate change. In this paper, we propose a simple mathematical model (a coupled system of nonlinear ODEs) to capture some of the dynamical effects produced by adding charcoal to fertile soils. The main goal is to understand to which extent charcoal is able to lock up carbon in soils. Our results are preliminary in the sense that we do not solve the CO2 sequestration problem. Instead, we do set up a flexible modeling framework in which the interaction between charcoal and soil can be tackled by means of mathematical tools.We show that our model is well-posed and has interesting large-time behaviour. Depending on the reference parameter range (e.g., type of soil) and chosen time scale, numerical simulations suggest that adding charcoal typically postpones the release of CO2. © 2013 Elsevier Inc.

  • 6.
    Chalupecky, Vladimir
    et al.
    Kyushu University, Japan.
    Fatima, Tasnim
    Eindhoven University of Technology, The Netherlands.
    Kruschwitz, Jens
    Strassen.NRW, Gelsenkirchen, Germany.
    Muntean, Adrian
    Eindhoven University of Technology, The Netherland.
    Macroscopic corrosion front computations of sulfate attack in sewer pipes based on a micro-macro reaction-diffusion model2012In: Multiscale Mathematics: Hierarchy of Collective Phenomena and Interrelations between Hierarchical Structures, Kyushu University, Japan , 2012, Vol. 39, p. 22-31Conference paper (Refereed)
    Abstract [en]

    We consider a two-scale reaction diffusion system able to capture the corrosion of concrete with sulfates. Our aim here is to define and compute two macroscopic corrosion indicators: typical pH drop and gypsum profiles. Mathematically, the system is coupled, endowed with micro-macro transmission conditions, and posed on two different spatially-separated scales: one microscopic (pore scale) and one macroscopic (sewer pipe scale). We use a logarithmic expression to compute values of pH from the volume averaged concentration of sulfuric acid which is obtained by resolving numerically the two-scale system (microscopic equations with direct feedback with the macroscopic diffusion of one of the reactants). Furthermore, we also evaluate the content of the main sulfatation reaction (corrosion) product---the gypsum---and point out numerically a persistent kink in gypsum's concentration profile. Finally, we illustrate numerically the position of the free boundary separating corroded from not-yet-corroded regions.

  • 7.
    Chalupecky, Vladimir
    et al.
    Kyushu Univ, Inst Math Ind, Nishi Ku, Fukuoka 8190395, Japan.
    Muntean, Adrian
    Eindhoven University of Technology.
    Semi-discrete finite difference multiscale scheme for a concrete corrosion model: A priori estimates and convergence2012In: Japan journal of industrial and applied mathematics, ISSN 0916-7005, E-ISSN 1868-937X, Vol. 29, no 2, p. 289-316Article in journal (Refereed)
  • 8.
    Cirillo, Emilio N.M.
    et al.
    Università di Roma “La Sapienza”.
    Colangeli, Matteo
    Gran Sasso Science Institute.
    Muntean, Adrian
    Eindhoven University of Technology.
    Does communication enhance pedestrians transport in the dark?2016In: Comptes rendus. Mecanique, ISSN 1631-0721, E-ISSN 1873-7234, Vol. 344, no 1, p. 19-23Article in journal (Refereed)
    Abstract [en]

    We study the motion of pedestrians through an obscure tunnel where the lack of visibility hides the exits. Using a lattice model, we explore the effects of communication on the effective transport properties of the crowd of pedestrians. More precisely, we study the effect of two thresholds on the structure of the effective nonlinear diffusion coefficient. One threshold models pedestrian communication efficiency in the dark, while the other one describes the tunnel capacity. Essentially, we note that if the evacuees show a maximum trust (leading to a fast communication), they tend to quickly find the exit and hence the collective action tends to prevent the occurrence of disasters.

  • 9.
    Curseu, Petru Lucian
    et al.
    Tilburg University; Cognitrom.
    Krehel, Oleh
    Eindhoven University of Technology .
    Evers, Joep H. M.
    Eindhoven University of Technology .
    Muntean, Adrian
    Eindhoven University of Technology.
    Cognitive distance, absorptive capacity and group rationality: A simulation study2014In: PLoS ONE, ISSN 1932-6203, E-ISSN 1932-6203, Vol. 9, no 10Article in journal (Refereed)
    Abstract [en]

    We report the results of a simulation study in which we explore the joint effect of group absorptive capacity (as the average individual rationality of the group members) and cognitive distance (as the distance between the most rational group member and the rest of the group) on the emergence of collective rationality in groups. We start from empirical results reported in the literature on group rationality as collective group level competence and use data on real-life groups of four and five to validate a mathematical model. We then use this mathematical model to predict group level scores from a variety of possible group configurations (varying both in cognitive distance and average individual rationality). Our results show that both group competence and cognitive distance are necessary conditions for emergent group rationality. Group configurations, in which the groups become more rational than the most rational group member, are groups scoring low on cognitive distance and scoring high on absorptive capacity.

  • 10.
    Evers, Joep H.
    et al.
    Eindoven University of Technology.
    Muntean, Adrian
    Eindoven University of Technology.
    Modeling micro-macro pedestrian counter flow in heterogeneous domains2011In: Nonlinear Phenomena in Complex Systems, ISSN 1561-4085, E-ISSN 1817-2458, Vol. 14, no 1, p. 27-37Article in journal (Refereed)
    Abstract [en]

    We present a micro-macro strategy able to describe the dynamics of crowds in heterogeneous spatial domains. Herein we focus on the example of pedestrian counter flow. The main working tools include the use of mass and porosity measures together with their transport as well as suitable application of a version of Radon-Nikodym Theorem formulated for finite measures. Finally, we illustrate numerically our microscopic model and emphasize the effects produced by an implicitly defined social velocity.

  • 11.
    Evers, Joep
    et al.
    Eindhoven University of Technology.
    Muntean, Adrian
    Eindhoven University of Technology.
    van de Ven, Fons
    Eindhoven University of Technology.
    Crowds reaching targets by maximizing entropy: A Clausius-Duhem inequality approach2013In: Elsevier IFAC Publications / IFAC Proceedings series, ISSN 1474-6670, Vol. 46, no 26, p. 263-268Article in journal (Refereed)
    Abstract [en]

    In this paper we propose the use of concepts from thermodynamics in the study of crowd dynamics. Our continuous model consists of the continuity equation for the density of the crowd and a kinetic equation for the velocity field. The latter includes a nonlocal term that models interactions between individuals. To support our modelling assumptions, we introduce an inequality that resembles the Second Law of Thermodynamics, containing an entropy-like functional. We show that its time derivative equals a positive dissipation term minus a corrector term. The latter term should be small for the time derivative of the entropy to be positive. In case of isotropic interactions the corrector term is absent. For the anisotropic case, we support the claim that the corrector term is small by simulations for the corresponding particle system. They reveal that this term is sufficiently small for the entropy still to increase. Moreover, we show that the entropy converges in time towards a limit value.

  • 12. Gulikers, Lennart
    et al.
    Evers, Joep
    Muntean, Adrian
    Eindhoven University of Technology.
    Lyulin, Alexey
    The effect of perception anisotropy on particle systems describing pedestrian flows in corridors2013In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, Vol. 2013, no 4Article in journal (Refereed)
    Abstract [en]

    We consider a microscopic model (a system of self-propelled particles) to study the behaviour of a large group of pedestrians walking in a corridor. Our point of interest is the effect of anisotropic interactions on the global behaviour of the crowd. The anisotropy we have in mind reflects the fact that people do not perceive (i.e. see, hear, feel or smell) their environment equally well in all directions. The dynamics of the individuals in our model follow from a system of Newton-like equations in the overdamped limit. The instantaneous velocity is modelled in such a way that it accounts for the angle at which an individual perceives another individual. We investigate the effects of this perception anisotropy by means of simulations, very much in the spirit of molecular dynamics. We define a number of characteristic quantifiers (including the polarization index and Morisita index) that serve as measures, for example, for organization and clustering, and we use these indices to investigate the influence of anisotropy on the global behaviour of the crowd. The goal of the paper is to investigate the potential of this model; extensive statistical analysis of simulation data and reproducing any specific real-life situation are beyond its scope.

  • 13.
    Ijioma, Ekeoma Rowland
    et al.
    Meiji University, 4-21-1 Nakano, Nakano-ku, Tokyo, Japan.
    Muntean, Adrian
    Eindhoven University of Technology, P.O. Box 513, MB Eindhoven, Netherlands.
    Ogawa, Toshiyuki
    Meiji University, 4-21-1 Nakano, Nakano-ku, Tokyo, Japan.
    Effect of material anisotropy on the fingering instability in reverse smoldering combustion2015In: International Journal of Heat and Mass Transfer, ISSN 0017-9310, E-ISSN 1879-2189, Vol. 81, p. 924-938Article in journal (Refereed)
  • 14.
    Ijioma, Ekeoma Rowland
    et al.
    Meiji University,Tokyo, Japan.
    Muntean, Adrian
    Eindhoven University of Technology.
    Ogawa, Toshiyuki
    Meiji University, Tokyo, Japan.
    Pattern formation in reverse smouldering combustion: A homogenisation approach2013In: Combustion theory and modelling, ISSN 1364-7830, E-ISSN 1741-3559, Vol. 17, no 2, p. 185-223Article in journal (Refereed)
    Abstract [en]

    The development of fingering char patterns on the surface of porous thin materials has been investigated in the framework of reverse combustion. This macroscopic characteristic feature of combustible media has also been studied experimentally and through the use of phenomenological models. However, not much attention has been given to the behaviour of the emerging patterns based on characteristic material properties. Starting from a microscopic description of the combustion process, macroscopic models of reverse combustion that are derived by the application of the homogenisation technique are presented. Using proper scaling by means of a small scale parameter E, the results of the formal asymptotic procedure are justified by qualitative multiscale numerical simulations at the microscopic and macroscopic levels. We consider two equilibrium models that are based on effective conductivity contrasts, in a simple adiabatic situation, to investigate the formation of unstable fingering patterns on the surface of a charred material. The behaviour of the emerging patterns is analysed using primarily the Peclet and Lewis numbers as control parameters.

  • 15. Ijioma, E.R.
    et al.
    Muntean, Adrian
    Eindhoven Univ Technol, Ctr Anal Sci Comp & Applicat,.
    Ogawa, T.
    Corrigendum to "Pattern formation in reverse smouldering combustion: A homogenisation approach" (vol 17, pg 185, 2013)2013In: Combustion theory and modelling, ISSN 1364-7830, E-ISSN 1741-3559, Vol. 17, no 3, p. 577-Article in journal (Refereed)
  • 16.
    Karlsson, Christian
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics (from 2013).
    Regression Models of 3D Wakes for Propellers2018Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    In this work, regression models for the wake field entering a propeller at certain axial andnominal position have been proposed. Wakes are non-uniform flows following a body immersedin a viscous fluid. We have proposed models for the axial and tangential velocity distribution asfunctions of ship hull and propeller measures. The regression models were modelled using Fourierseries and parameter estimations based on skewed-Gaussian and sine functions. The wake fieldis an important parameter in propeller design. The regression models are based on experimentaldata provided by the Rolls-Royce Hydrodynamic Research Center in Kristinehamn. Also we havestudied the flow in the axial velocity distribution in the propeller plane using the coherent structurecoloring method. The coherent structure coloring is used to study coherent patterns by looking atfluid particle kinematics. Using this type of analysis, we observed that the velocity distributionbehaves kinematically similar in the different regions of the wake distribution, which according tothe coherent structure coloring indicate coherence.

  • 17.
    Kotik, Nikolai
    Karlstad University, Faculty of Technology and Science.
    Solution to boundary-contact problems of elasticity in mathematical models of the printing-plate contact system for flexographic printing2007Doctoral thesis, monograph (Other scientific)
    Abstract [en]

    Boundary-contact problems (BCPs) are studied within the frames of

    classical mathematical theory of elasticity and plasticity

    elaborated by Landau, Kupradze, Timoshenko, Goodier, Fichera and

    many others on the basis of analysis of two- and three-dimensional

    boundary value problems for linear partial differential equations.

    A great attention is traditionally paid both to theoretical

    investigations using variational methods and boundary singular

    integral equations (Muskhelishvili) and construction of solutions

    in the form that admit efficient numerical evaluation (Kupradze).

    A special family of BCPs considered by Shtaerman, Vorovich,

    Alblas, Nowell, and others arises within the frames of the models

    of squeezing thin multilayer elastic sheets. We show that

    mathematical models based on the analysis of BCPs can be also

    applied to modeling of the clich\'{e}-surface printing contacts

    and paper surface compressibility in flexographic printing.

    The main result of this work is formulation and complete

    investigation of BCPs in layered structures, which includes both

    the theoretical (statement of the problems, solvability and

    uniqueness) and applied parts (approximate and numerical

    solutions, codes, simulation).

    We elaborate a mathematical model of squeezing a thin elastic

    sheet placed on a stiff base without friction by weak loads

    through several openings on one of its boundary surfaces. We

    formulate and consider the corresponding BCPs in two- and

    three-dimensional bands, prove the existence and uniqueness of

    solutions, and investigate their smoothness including the behavior

    at infinity and in the vicinity of critical points. The BCP in a

    two-dimensional band is reduced to a Fredholm integral equation

    (IE) with a logarithmic singularity of the kernel. The theory of

    logarithmic IEs developed in the study includes the analysis of

    solvability and development of solution techniques when the set of

    integration consists of several intervals. The IE associated with

    the BCP is solved by three methods based on the use of

    Fourier-Chebyshev series, matrix-algebraic determination of the

    entries in the resulting infinite system matrix, and

    semi-inversion. An asymptotic theory for the BCP is developed and

    the solutions are obtained as asymptotic series in powers of the

    characteristic small parameter.

    We propose and justify a technique for the solution of BCPs and

    boundary value problems with boundary conditions of mixed type

    called the approximate decomposition method (ADM). The main idea

    of ADM is simplifying general BCPs and reducing them to a chain

    of auxiliary problems for 'shifted' Laplacian in long rectangles

    or parallelepipeds and then to a sequence of iterative problems

    such that each of them can be solved (explicitly) by the Fourier

    method. The solution to the initial BCP is then obtained as a

    limit using a contraction operator, which constitutes in

    particular an independent proof of the BCP unique solvability.

    We elaborate a numerical method and algorithms based on the

    approximate decomposition and the computer codes and perform

    comprehensive numerical analysis of the BCPs including the

    simulation for problems of practical interest. A variety of

    computational results are presented and discussed which form the

    basis for further applications for the modeling and simulation of

    printing-plate contact systems and other structures of

    flexographic printing. A comparison with finite-element solution

    is performed.

  • 18.
    Krehel, O.
    et al.
    Eindhoven Univ Technol, Dept Math & Comp Sci, MB Eindhoven.
    Muntean, Adrian
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Knabner, P.
    Univ Erlangen Nurnberg, Dept Math, Erlangen, Germany.
    Multiscale modeling of colloidal dynamics in porous media including aggregation and deposition2015In: Advances in Water Resources, ISSN 0309-1708, E-ISSN 1872-9657, Vol. 86, p. 209-216Article in journal (Refereed)
  • 19.
    Kumar, Kundan
    et al.
    Technische Universiteit Eindhoven.
    Pisarenco, Maxim
    Technische Universiteit Eindhoven.
    Rudnaya, Maria
    Technische Universiteit Eindhoven.
    Savcenco, Valeriu
    Technische Universiteit Eindhoven.
    A note on analysis and numerics of algae growth2014In: Nonlinear Analysis, ISSN 1468-1218, Vol. 15, p. 392-403Article in journal (Refereed)
  • 20.
    Kumar, Kundan
    et al.
    University of Texas at Austin, Austin, USA.
    Pop, I. S.
    Eindhoven University of TechnologyEindhovenThe Netherlands; University of Bergen, Bergen, Norway.
    Radu, F. A.
    University of Bergen, Bergen, Norway.
    Convergence analysis for a conformal discretization of a model for precipitation and dissolution in porous media2014In: Numerische Mathematik, ISSN 0029-599X, E-ISSN 0945-3245, Vol. 127, no 4, p. 715-749Article in journal (Refereed)
    Abstract [en]

    In this paper we discuss the numerical analysis of an upscaled (core scale) model describing the transport, precipitation and dissolution of solutes in a porous medium. The particularity lies in the modeling of the reaction term, especially the dissolution term, which has a multivalued character. We consider the weak formulation for the upscaled equation and provide rigorous stability and convergence results for both the semi-discrete (time discretization) and the fully discrete schemes. In doing so, compactness arguments are employed.

  • 21. Kumar, Kundan
    et al.
    Pop, I. S.
    Radu, F. A.
    Convergence analysis of mixed numerical schemes for reactive flow in a porous medium2013In: SIAM Journal on Numerical Analysis, ISSN 0036-1429, E-ISSN 1095-7170, Vol. 51, no 4, p. 2283-2308Article in journal (Refereed)
  • 22. Kumar, Kundan
    et al.
    Pop, I. S.
    Radu, F. A.
    Numerical analysis for an upscaled model for dissolution and precipitation in porous media2013In: Numerical mathematics and advanced applications 2011: Proceedings of ENUMATH 2011, the 9th European Conference on Numerical Mathematics and Advanced Applications, Leicester, September 2011 / [ed] Herausgeber: Cangiani, A., Davidchack, R.L., Georgoulis, E.H., Gorban, A.N., Levesley, J., Tretyakov, M.V, Springer Berlin/Heidelberg, 2013, p. 703-711Chapter in book (Other academic)
  • 23.
    Kumar, Kundan
    et al.
    Center for Subsurface Modeling, The Uni versity of Texas at Austin, USA.
    van Helvoort, M.
    Supply Chain Development, Jumbo Supermarkten B.V., The Netherlands.
    Pop, I. S.
    Department of Mathematics and Computer Sciences, Eindhoven University of Technology, The Netherlands & Institute of Mathematics, University of Bergen, Bergen, Norway.
    Rigorous upscaling of rough boundaries for reactive flows2014In: Zeitschrift für angewandte Mathematik und Mechanik, ISSN 0044-2267, E-ISSN 1521-4001, Vol. 94, no 7-8, p. 623-644Article in journal (Refereed)
    Abstract [en]

    We consider a mathematical model for reactive flow in a channel having a rough (periodically oscillating) boundary with both period and amplitude ε. The ions are being transported by the convection and diffusion processes. These ions can react at the rough boundaries and get attached to form the crystal (precipitation) and become immobile. The reverse process of dissolution is also possible. The model involves non‐linear and multi‐valued rates and is posed in a fixed geometry with rough boundaries. We provide a rigorous justification for the upscaling process in which we define an upscaled problem defined in a simpler domain with flat boundaries. To this aim, we use periodic unfolding techniques combined with translation estimates. Numerical experiments confirm the theoretical predictions and illustrate a practical application of this upscaling process.

  • 24.
    Kumar, Kundan
    et al.
    Eindhoven University of Technology, Netherlands.
    van Noorden, T. L.
    Eindhoven University of Technology, Netherlands.
    Pop, I. S.
    Eindhoven University of Technology, Netherlands.
    Effective dispersion equations for reactive flows involving free boundaries at the microscale2011In: Multiscale Modeling & simulation, ISSN 1540-3459, E-ISSN 1540-3467, Vol. 9, no 1, p. 29-58Article in journal (Refereed)
    Abstract [en]

    We consider a pore-scale model for reactive flow in a thin two-dimensional strip, where the convective transport dominates the diffusion. Reactions take place at the lateral boundaries of the strip (the walls), where the reaction product can deposit in a layer with a nonnegligible thickness compared to the width of the strip. This leads to a free boundary problem, in which the moving interface between the fluid and the deposited (solid) layer is explicitly taken into account. Using asymptotic expansion methods, we derive an upscaled, one-dimensional model by averaging in the transversal direction. The result is consistent with (Taylor dispersion) models obtained previously for a constant geometry. Finally, numerical computations are presented to compare the outcome of the effective (upscaled) model with the transversally averaged, two-dimensional solution.

  • 25. Kumar, Kundan
    et al.
    van Noorden, Tycho L.
    Wheeler, Mary F.
    Wick, Thomas
    An ALE-based method for reaction-induced boundary movement towards clogging2015In: Numerical mathematics and advanced applications—ENUMATH 2013: Proceedings of ENUMATH 2013, the 10th European Conference on Numerical Mathematics and Advanced Applications, Lausanne, August 2013 / [ed] Abdulle, A., Deparis, S., Kressner, D., Nobile, F., Picasso, M., Springer, 2015, Vol. 103, p. 633-641Chapter in book (Other academic)
  • 26.
    Lakkis, Omar
    et al.
    Netherlands.
    A. Madzvamuse, A.
    Netherlands.
    Muntean, Adrian
    Netherlands.
    Venkataraman, C.
    Netherlands.
    Reaction–diffusion systems on evolving domains: The fishy story of Turing patterns2014In: Oberwolfach Report No. 43/2014: Reactive Flows in Deformable, Complex Media / [ed] Margot Gerritsen et al., European Mathematical Society Publishing House, 2014Conference paper (Refereed)
  • 27.
    Lundin, Lukas
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics.
    Tip vortex cavitation and diffused vorticity of propeller profiles: a modelling approach: Investigation of an implemented TVI model, and  implementation and investigation of a DVH model2017Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    To predict fluid properties and interactions is an important task for the industry. It is plagued, however, by being close to impossible to predict analytically. Hence, it is customary to turn to numerical solutions. This in itself comes with many different methods and approaches suitable for different needs. This work focuses on two methods: Tip Vortex Index (TVI) and Diffused Vortex Hydrodynamics (DVH). TVI is a method to predict when a marine propeller will experience cavitation of tip vortices and is based on calculations from a Boundary Element Method (BEM). DVH is a particle method for simulating the circulation of a fluid in two dimensions and three dimensions. The aim is to investigate an implemented TVI model based on MPUF-3A for different marine propeller series, with different sub-designs for a total of 28 unique propellers, and implement the DVH method and test it for 3 different bodies. The results of this thesis show that the implemented TVI model is non-functional for the 28 different propellers, but the DVH method is successfully implemented and able to handle 2 different bodies.

  • 28.
    Muntean, Adrian
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science. Technical University of Eindhoven.
    Error bounds on semi-discrete finite element approximations of a moving-boundary system arising in concrete corrosion2008In: International Journal of Numerical Analysis & Modeling, ISSN 1705-5105, Vol. 5, no 3, p. 353-372Article in journal (Refereed)
    Abstract [en]

    Finite element approximations of positive weak solutions to a onephase unidimensional moving-boundary system with kinetic condition describing the penetration of a sharp-reaction interface in concrete are considered. A priori and a posteriori error estimates for the semi-discrete fields of active concentrations and for the position of the moving interface are obtained. The important feature of the system of partial differential equations is that the nonlinear coupling occurs due to the presence of both the moving boundary and the non-linearities of localized sinks and sources by reaction.

  • 29.
    Muntean, Adrian
    et al.
    Tech Univ Eindhoven, CASA Ctr Anal Sci Comp & Applicat.
    Böhm, M. A.
    Univ Bremen, ZeTeM Ctr Ind Math, Bremen, Germany.
    Kropp, J.
    Univ Appl Sci, Lab Baustofftechnol, Bremen, Germany.
    Moving carbonation fronts in concrete: A moving-sharp-interface approach2011In: Chemical Engineering Science, ISSN 0009-2509, E-ISSN 1873-4405, Vol. 66, no 3, p. 538-547Article in journal (Refereed)
  • 30.
    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.

  • 31.
    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)
  • 32.
    Nyflött, Åsa
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Chemical Sciences (from 2013).
    Structure-Performance Relations of Oxygen Barriers for Food Packaging2017Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Food packaging should ensure the safety and quality of food, minimize spoilage and provide an easy way of storing and handling it. Barrier coatings are generally used to meet the demands placed on fibre-based food packages, as these have the ability to regulate the amount of gases that can enter them. Some gases are detrimental to food quality: oxygen, for example, initiates lipid oxidation in fatty foods. Using both experimental data and computer modelling, this thesis explains some aspects of how the structure of barrier coatings influences the mass transport of oxygen with the aim of obtaining essential knowledge that can be used to optimize the performance of barriers.

    Barrier coatings are produced from polyvinyl alcohol and kaolin blends that are coated onto a polymeric support. The chemical and physical structures of these barriers were characterized according to their influence on permeability in various climates. At a low concentration of kaolin, the crystallinity of polyvinyl alcohol decreased; in the thinner films, the kaolin particles were orientated in the basal plane of the barrier coating. The experimental results indicated a complex interplay between the polymer and the filler with respect to permeability.

    A computer model for permeability incorporating theories for the filled polymeric layer to include the polymer crystallinity, addition of filler, filler aspect ratio and surrounding moisture was developed. The model shows that mass transport was affected by the aspect ratio of the clay in combination with the clay concentration, as well as the polymer crystallinity. The combined model agreed with the experiments, showing that it is possible to combine different theories into one model that can be used to predict the mass transport.

    Four barrier coatings: polyethylene, ethylene vinyl alcohol + kaolin, latex + kaolin and starch were evaluated using the parameters of greenhouse gas emissions and product costs. After the production of the barrier material, the coating process and the end-of-life handling scenarios were analysed, it emerged that starch had the lowest environmental impact and latex + kaolin had the highest.

  • 33.
    Radu, Florin A.
    et al.
    University of Bergen, Norway.
    Kumar, Kundan
    University of Bergen, Norway.
    Nordbotten, Jan M.
    University of Bergen, Norway.
    Pop, Iuliu S.
    University of Bergen, Norway; Hasselt University, Belgium.
    A robust, mass conservative scheme for two-phase flow in porous media including Hölder continuous nonlinearities2018In: IMA Journal of Numerical Analysis, ISSN 0272-4979, E-ISSN 1464-3642, Vol. 38, no 2, p. 884-920Article in journal (Refereed)
  • 34.
    Radu, Florin A.
    et al.
    University of Bergen, P. O. Box 7800, N-5020 Bergen, Norway.
    Muntean, Adrian
    Eindhoven University of Technology, P. O. Box 513, 5600 MB Eindhoven, The Netherlands.
    Pop, I.S.
    University of Bergen, P. O. Box 7800, N-5020 Bergen, Norway.
    Suciu, N.
    University of Erlangen-Nuremberg, Cauerstr. 11, D-91058 Erlangen, Germany.
    Kloditz, O.
    UFZ-Helmholtz Center for Environmental Research, Permoserstr. 15, D-04318 Leipzig, Germany.
    A mixed finite element discretization scheme for a concrete carbonation model with concentration-dependent porosity2013In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 246, p. 74-85Article in journal (Other academic)
  • 35.
    Richardson, Omar
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Mathematical analysis and approximation of a multiscale elliptic-parabolic system2018Licentiate thesis, monograph (Other academic)
    Abstract [en]

    We study a two-scale coupled system consisting of a macroscopic elliptic equation and a microscopic parabolic equation. This system models the interplay between a gas and liquid close to equilibrium within a porous medium with distributed microstructures. We use formal homogenization arguments to derive the target system. We start by proving well-posedness and inverse estimates for the two-scale system. We follow up by proposing a Galerkin scheme which is continuous in time and discrete in space, for which we obtain well-posedness, a priori error estimates and convergence rates. Finally, we propose a numerical error reduction strategy by refining the grid based on residual error estimators.

  • 36.
    Shestopalov, Yury
    Karlstad University.
    Collective decisions: some problem statements and mathematical methods2011In: Proceedings of XVIII International Conference Problems of Decision Making under Uncertainties (PDMU-2011), September 19-23, 2011. Yalta, Ukraine, Kyiv, 2011, p. 33-34Conference paper (Refereed)
  • 37.
    Unosson, Ida
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013).
    Andersson, Matilda
    Karlstad University, Faculty of Health, Science and Technology (starting 2013).
    Matematikundervisning i förskoleklass och årskurs 1: Lärare berättar om subtraktionsundervisning2019Independent thesis Advanced level (professional degree), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    The purpose of this qualitative study was to investigate how the progression appears in the teaching of subtraction between preschool class and grade 1. What was examined was whether the teaching in subtraction is interrelated be- tween these grades or whether it differs completely. In order to find this out, interviews were conducted with employed qualified teachers in pre-school class and grade 1. Through these interviews we got to learn about the teachers' stories about how they work and what influences their choices in their work on subtraction. A teaching media analysis was also carried out on the teaching materials that teachers stated they used in the teaching of subtraction. The re- sults show that teachers in pre-school class work very much with laboratory teaching materials in their teaching as well as in whole class or smaller groups, while teachers in grade 1 work less in whole class/groups but more with indi- vidual work. The work in grade 1 proves to be more focused on the fact that teachers want something to assess the students compared to the preschool class' work where much of the learning is done through play. The results show that preschool teachers work either very little with subtraction or not at all com- pared to primary school teachers in grade 1 where subtraction is practiced on a regular basis. In preschool the terminology that is used is both formal and informal, however, overall more informal words are used compared to grade 1 where more formal words are used. The results also show that preschool teach- ers prepare the subtraction strategy step-by-step calculations. In grade 1 the strategy step-by-step calculations are used as well as the numerical calculations strategy.

  • 38.
    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.

  • 39.
    Windfäll, Åsa
    Karlstad University, Faculty of Technology and Science, Department of Mathematics.
    Some Problems in Kinetic Theory and Applications2011Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    This thesis consists of four papers. the first is devoted to discrete velocity models, the second to hydrodynamic equation beyond Navier-Stokes level, the third to a multi-linear Maxwell model for economic or social dynamics and the fourth is devoted to a function related to the Riemann zeta-function.

    In Paper 1, we consider the general problem of construction and classification of normal, i.e. without spurious invariants, discrete velocity models (DVM) of the classical Boltzman equation. We explain in detail how this problem can be solved and present a complete classification of normal plane DVMs with relatively small number n of velocities (n≤10). Some results for models with larger number of velocities are also presented.

    In Paper 2, we discuss hydrodynamics at the Burnett level. Since the Burnett equations are ill-posed, we describe how to make a regularization of these. We derive the well-posed generalized Burnett equations (GBEs) and discuss briefly an optimal choice of free parameters and consider a specific version of these equations. Finally we prove linear stability for GBE and present some numerical result on the sound propagationbased on GBEs.

    In Paper 3, we study a Maxwell kinetic model of socio-economic behavior. The model can predict a time dependent distribution of wealth among the participants in economic games with an arbitrary, but sufficiently large, number of players. The model depends on three different positive parameters {γ,q,s} where s and q are fixed by market conditions and γ is a control parameter. In particular, we investigate the efficiency of control. Some exact solutions and numerical examples are presented.

    In Paper 4, we study a special function u(s,x), closely connected to the Riemann zeta-function ζ(s), where s is a complex number. We study in detail the properties of u(s,x) and in particular the location of its zeros s(x), for various x≥0. For x=0 the zeros s(0) coincide with non-trivial zeros of ζ(s). We perform a detailed numerical study of trajectories of various zeros s(x) of u(s,x).

  • 40.
    Zhang, Y.
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Chemical Sciences (from 2013).
    Forssén, Patrik
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Chemical Sciences (from 2013).
    Fornstedt, Torgny
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Chemical Sciences (from 2013).
    Gulliksson, M.
    Orebrov Univ, Sch Sci & Technol, Dept Math, Orebro, Sweden.
    Dai, X.
    Zhejiang Univ, City Coll, Sch Comp Sci, Hangzhou, Zhejiang, Peoples R China.
    An adaptive regularization algorithm for recovering the rate constant distribution from biosensor data2018In: Inverse Problems in Science and Engineering, ISSN 1741-5977, E-ISSN 1741-5985, Vol. 26, no 10, p. 1464-1489Article in journal (Refereed)
    Abstract [en]

    We present here the theoretical results and numerical analysis of a regularization method for the inverse problem of determining the rate constant distribution from biosensor data. The rate constant distribution method is a modern technique to study binding equilibrium and kinetics for chemical reactions. Finding a rate constant distribution from biosensor data can be described as a multidimensional Fredholm integral equation of the first kind, which is a typical ill-posed problem in the sense of J. Hadamard. By combining regularization theory and the goal-oriented adaptive discretization technique, we develop an Adaptive Interaction Distribution Algorithm (AIDA) for the reconstruction of rate constant distributions. The mesh refinement criteria are proposed based on the a posteriori error estimation of the finite element approximation. The stability of the obtained approximate solution with respect to data noise is proven. Finally, numerical tests for both synthetic and real data are given to show the robustness of the AIDA.

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