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  • 1.
    Ackleh, Azmy S.
    et al.
    University of Louisiana at Lafayette, USA.
    Lyons, Rainey
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Saintier, Nicolas
    Universidad de Buenos Aires, Argentina.
    High resolution finite difference schemes for a size structured coagulation-fragmentation model in the space of radon measures2023In: Mathematical Biosciences and Engineering, ISSN 1547-1063, E-ISSN 1551-0018, Vol. 20, no 7, p. 11805-11820Article in journal (Refereed)
    Abstract [en]

    In this paper, we develop explicit and semi-implicit second-order high-resolution finite difference schemes for a structured coagulation-fragmentation model formulated on the space of Radon measures. We prove the convergence of each of the two schemes to the unique weak solution of the model. We perform numerical simulations to demonstrate that the second order accuracy in the Bounded-Lipschitz norm is achieved by both schemes.

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  • 2.
    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)
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  • 3.
    Alho, Artur
    et al.
    Universidade de Lisboa, Portugal.
    Lim, Woei Chet
    University of Waikato, New Zealand.
    Uggla, Claes
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics (from 2013).
    Cosmological global dynamical systems analysis2022In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 39, no 14, p. 1-14, article id 145010Article in journal (Refereed)
    Abstract [en]

    We consider a dynamical systems formulation for models with an exponential scalar field and matter with a linear equation of state in a spatially flat and isotropic spacetime. In contrast to earlier work, which only considered linear hyperbolic fixed point analysis, we do a center manifold analysis of the non-hyperbolic fixed points associated with bifurcations. More importantly though, we construct monotonic functions and a Dulac function. Together with the complete local fixed point analysis this leads to proofs that describe the entire global dynamics of these models, thereby complementing previous local results in the literature. 

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  • 4.
    Araújo C., Juan C.
    et al.
    Umeå University.
    Engström, Christian
    Linnaeus University.
    Wadbro, Eddie
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). Umeå University.
    Shape optimization for the strong routing of light in periodic diffraction gratings2023In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 472, article id 111684Article in journal (Refereed)
    Abstract [en]

    In the quest for the development of faster and more reliable technologies, the ability to control the propagation, confinement, and emission of light has become crucial. The design of guide mode resonators and perfect absorbers has proven to be of fundamental importance. In this project, we consider the shape optimization of a periodic dielectric slab aiming at efficient directional routing of light to reproduce similar features of a guide mode resonator. For this, the design objective is to maximize the routing efficiency of an incoming wave. That is, the goal is to promote wave propagation along the periodic slab. A Helmholtz problem with a piecewise constant and periodic refractive index medium models the wave propagation, and an accurate Robin-to-Robin map models an exterior domain. We propose an optimal design strategy that consists of representing the dielectric interface by a finite Fourier formula and using its coefficients as the design variables. Moreover, we use a high order finite element (FE) discretization combined with a bilinear Transfinite Interpolation formula. This setting admits explicit differentiation with respect to the design variables, from where an exact discrete adjoint method computes the sensitivities. We show in detail how the sensitivities are obtained in the quasi-periodic discrete setting. The design strategy employs gradient-based numerical optimization, which consists of a BFGS quasi-Newton method with backtracking line search. As a test case example, we present results for the optimization of a so-called single port perfect absorber. We test our strategy for a variety of incoming wave angles and different polarizations. In all cases, we efficiently reach designs featuring high routing efficiencies that satisfy the required criteria. 

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  • 5.
    Araújo, Juan C.
    et al.
    Umeå University.
    Wadbro, Eddie
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). Umeå University.
    Shape optimization for the strong directional scattering of dielectric nanorods2021In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 122, no 8, p. 3683-3704Article in journal (Refereed)
    Abstract [en]

    In this project, we consider the shape optimization of a dielectric scatterer aiming at efficient directional routing of light. In the studied setting, light interacts with a penetrable scatterer with dimension comparable to the wavelength of an incoming planar wave. The design objective is to maximize the scattering efficiency inside a target angle window. For this, a Helmholtz problem with a piecewise constant refractive index medium models the wave propagation, and an accurate Dirichlet-to-Neumann map models an exterior domain. The strategy consists of using a high-order finite element (FE) discretization combined with gradient-based numerical optimization. The latter consists of a quasi-Newton (BFGS) with backtracking line search. A discrete adjoint method is used to compute the sensitivities with respect to the design variables. Particularly, for the FE representation of the curved shape, we use a bilinear transfinite interpolation formula, which admits explicit differentiation with respect to the design variables. We exploit this fact and show in detail how sensitivities are obtained in the discrete setting. We test our strategy for a variety of target angles, different wave frequencies, and refractive indexes. In all cases, we efficiently reach designs featuring high scattering efficiencies that satisfy the required criteria.

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  • 6.
    Barua, Arnab
    et al.
    Helmholtz Centre for Infection Research, DEU; Center for Information Services and High Performance Computing, DEU.
    Syga, Simon
    Center for Information Services and High Performance Computing, DEU.
    Mascheroni, Pietro
    Centre for Infection Research, DEU.
    Kavallaris, Nikos I.
    University of Chester, GBR.
    Meyer-Hermann, Michael
    Centre for Infection Research, DEU; Technische Universität Braunschweig, DEU.
    Deutsch, Andreas
    Center for Information Services and High Performance Computing, DEU.
    Hatzikirou, Haralampos
    Braunschweig Integrated Centre of Systems Biology, DEU; Center for Information Services and High Performance Computing, DEU; Khalifa University, ARE.
    Entropy-driven cell decision-making predicts ‘fluid-to-solid’ transition in multicellular systems2020In: New Journal of Physics, E-ISSN 1367-2630, Vol. 22, no 12, p. 123034-123034Article in journal (Refereed)
    Abstract [en]

    Cellular decision making allows cells to assume functionally different phenotypes in response to microenvironmental cues, with or without genetic change. It is an open question, how individual cell decisions influence the dynamics at the tissue level. Here, we study spatio-temporal pattern formation in a population of cells exhibiting phenotypic plasticity, which is a paradigm of cell decision making. We focus on the migration/resting and the migration/proliferation plasticity which underly the epithelial-mesenchymal transition and the go or grow dichotomy. We assume that cells change their phenotype in order to minimize their microenvironmental entropy following the LEUP (Least microEnvironmental Uncertainty Principle) hypothesis. In turn, we study the impact of the LEUP-driven migration/resting and migration/proliferation plasticity on the corresponding multicellular spatio-temporal dynamics with a stochastic cell-based mathematical model for the spatio-temporal dynamics of the cell phenotypes. In the case of the go or rest plasticity, a corresponding mean-field approximation allows to identify a bistable switching mechanism between a diffusive (fluid) and an epithelial (solid) tissue phase which depends on the sensitivity of the phenotypes to the environment. For the go or grow plasticity, we show the possibility of Turing pattern formation for the ‘solid’ tissue phase and its relation with the parameters of the LEUP-driven cell decisions.

  • 7.
    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.

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  • 8.
    Bernhoff, Niclas
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Linearized Boltzmann Collision Operator: I. Polyatomic Molecules Modeled by a Discrete Internal Energy Variable and Multicomponent Mixtures2023In: Acta Applicandae Mathematicae - An International Survey Journal on Applying Mathematics and Mathematical Applications, ISSN 0167-8019, E-ISSN 1572-9036, Vol. 183, no 1, p. 1-45, article id 3Article in journal (Refereed)
    Abstract [en]

    The linearized Boltzmann collision operator appears in many important applications of the Boltzmann equation. Therefore, knowing its main properties is of great interest. This work extends some classical results for the linearized Boltzmann collision operator for monatomic single species to the case of polyatomic single species, while also reviewing corresponding results for multicomponent mixtures of monatomic species. The polyatomicity is modeled by a discrete internal energy variable, that can take a finite number of (given) different values. Results concerning the linearized Boltzmann collision operator being a nonnegative symmetric operator with a finite-dimensional kernel are reviewed. A compactness result, saying that the linearized operator can be decomposed into a sum of a positive multiplication operator, the collision frequency, and a compact operator, bringing e.g., self-adjointness, is extended from the classical result for monatomic single species, under reasonable assumptions on the collision kernel. With a probabilistic formulation of the collision operator as a starting point, the compactness property is shown by a splitting, such that the terms can be shown to be, or be the uniform limit of, Hilbert-Schmidt integral operators and as such being compact operators. Moreover, bounds on - including coercivity of - the collision frequency are obtained for a hard sphere like model, from which Fredholmness of the linearized collision operator follows, as well as its domain. 

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  • 9.
    Bernhoff, Niclas
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Linearized Boltzmann collision operator: II. Polyatomic molecules modeled by a continuous internal energy variable2023In: Kinetic and Related Models, ISSN 1937-5093, E-ISSN 1937-5077, Vol. 16, no 6, p. 828-849Article in journal (Refereed)
    Abstract [en]

    The linearized collision operator of the Boltzmann equation can in a natural way be written as a sum of a positive multiplication operator, the collision frequency, and an integral operator. Compactness of the integral operator for monatomic single species is a classical result, while corresponding results for mixtures and polyatomic single species where the polyatomicity is modeled by a discrete internal energy variable, are more recently obtained. In this work the compactness of the integral operator for polyatomic single species, for which the number of internal degrees of freedom is greater or equal to two and the polyatomicity is modeled by a continuous internal energy variable, is studied. Compactness of the integral operator is obtained by proving that its terms are, or, at least, can be approximated by, Hilbert-Schmidt integral operators, under some assumptions on the collision kernel. Self-adjointness of the linearized collision operator follows. Moreover, bounds on -including coercivity of -the collision frequency, are obtained for some particular collision kernels -corresponding to hard sphere like models, but also hard potential with cut-off like models. Then it follows that the linearized collision operator is a Fredholm operator.

  • 10.
    Bernland, Anders
    et al.
    Umeå universitet, Institutionen för datavetenskap.
    Wadbro, Eddie
    Umeå universitet, Institutionen för datavetenskap.
    Berggren, Martin
    Umeå universitet, Institutionen för datavetenskap.
    Acoustic shape optimization using cut finite elements2018In: International Journal for Numerical Methods in Engineering, ISSN 0029-5981, E-ISSN 1097-0207, Vol. 113, no 3, p. 432-449Article in journal (Refereed)
    Abstract [en]

    Fictitious domain methods are attractive for shape optimization applications, since they do not require deformed or regenerated meshes. A recently developed such method is the CutFEM approach, which allows crisp boundary representations and for which uniformly well-conditioned system matrices can be guaranteed. Here, we investigate the use of the CutFEM approach for acoustic shape optimization, using as test problem the design of an acoustic horn for favorable impedance-matching properties. The CutFEM approach is used to solve the Helmholtz equation, and the geometry of the horn is implicitly described by a level-set function. To promote smooth algorithmic updates of the geometry, we propose to use the nodal values of the Laplacian of the level-set function as design variables. This strategy also improves the algorithm's convergence rate, counteracts mesh dependence, and, in combination with Tikhonov regularization, controls small details in the optimized designs. An advantage with the proposed method is that the exact derivatives of the discrete objective function can be expressed as boundary integrals, as opposed to when using a traditional method that uses mesh deformations. The resulting horns possess excellent impedance-matching properties and exhibit surprising subwavelength structures, not previously seen, which are possible to capture due to the fixed mesh approach.

  • 11.
    Bernland, Anders
    et al.
    Umeå universitet, Institutionen för datavetenskap.
    Wadbro, Eddie
    Umeå universitet, Institutionen för datavetenskap.
    Berggren, Martin
    Umeå universitet, Institutionen för datavetenskap.
    SHAPE OPTIMIZATION OF A COMPRESSION DRIVER PHASE PLUG2019In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 41, no 1, p. B181-B204Article in journal (Refereed)
    Abstract [en]

    A compression driver is an electro-acoustic transducer with considerably higher efficiency than direct radiating loudspeakers, thanks to the increased radiation resistance caused by a large vibrating diaphragm placed in a compression chamber with small openings. The transition section between compression chamber and output waveguide, the phase plug, must be carefully designed to avoid irregularities in the output sound pressure level (SPL) as a function of frequency. Here we present a shape optimization method based on an implicit level-set description and adjoint sensitivity analysis, which enables a large number of design parameters and vast design freedom. The CutFEM approach, a fictitious domain finite element method, removes the need for mesh updates and makes the method robust and computationally inexpensive. Numerical experiments for a generic annular diaphragm compression driver are presented, with optimized designs showing only minor frequency irregularities. Two different objective functions are considered: one for maximum SPL and one where the SPL is fitted to that of a hypothetical ideal design; the latter approach is found to be more effective in reducing irregularities. Visco-thermal boundary-layer losses are included in a post-processing step, and, though the influence of losses is clearly noticeable, the overall performance is similar and the optimized designs still outperform the original design.

  • 12.
    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.

  • 13.
    Bokhari, Ahmad H.
    et al.
    Umeå University, Sweden.
    Berggren, Martin
    Umeå University, Sweden.
    Noreland, Daniel
    Uppsala Science Park, Sweden; Umeå University, Sweden.
    Wadbro, Eddie
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). Umeå University, Sweden.
    Loudspeaker cabinet design by topology optimization2023In: Scientific Reports, E-ISSN 2045-2322, Vol. 13, no 1, article id 21248Article in journal (Refereed)
    Abstract [en]

    Using material distribution-based topology optimization, we optimize the bandpass design of a loudspeaker cabinet targeting low frequencies. The objective is to maximize the loudspeaker’s output power for a single frequency as well as a range of frequencies. To model the loudspeaker’s performance, we combine a linear electromechanical transducer model with a computationally efficient hybrid 2D–3D model for sound propagation. The adjoint variable approach computes the gradients of the objective function with respect to the design variables, and the Method of Moving Asymptotes (MMA) solves the topology optimization problem. To manage intermediate values of the material indicator function, a quadratic penalty is added to the objective function, and a non-linear filter is used to obtain a mesh independent design. By carefully selecting the target frequency range, we can guide the optimization algorithm to successfully generate a loudspeaker design with the required bandpass character. To the best of our knowledge, this study constitutes the first successful attempt to design the interior structure of a loudspeaker cabinet using topology optimization.

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  • 14.
    Bokhari, Ahmad H.
    et al.
    Umeå universitet, Sverige.
    Hassan, Emadeldeen
    Umeå universitet, Sverige; Menoufia University, Egypt.
    Wadbro, Eddie
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). Umeå universitet, Sverige.
    Topology optimization of microwave frequency dividing multiplexers2023In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 66, no 5, article id 106Article in journal (Refereed)
    Abstract [en]

    We use material-distribution-based topology optimization to design a three-port frequency dividing multiplexer at microwave frequencies. That is, by placing a good electric conductor inside the design domain, we aim to design a passive device that splits the incoming signal’s frequencies into two frequency bands and transmits them to their respective output ports. The Helmholtz equation models the time-harmonic wave propagation problem. We solve the governing equation using the finite element method. The adjoint variable method provides the required gradients, and we solve the topology optimization problem using Svanberg’s MMA algorithm. In this study, we present a technique for modeling the distribution of a good electric conductor within the design domain. In addition, we derive a power balance expression, which aids in formulating a series of three objective functions. In each successive objective function, we add more information and evaluate its impact on the results. The results show that by selecting a suitable objective function, we achieve more than 93.7% transmission for both the frequency bands. Moreover, the numerical experiments suggest that the optimization problem is self penalized and is sensitive to the initial design. 

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  • 15.
    Bokhari, Ahmad Hasnain
    et al.
    Umeå universitet, Institutionen för datavetenskap.
    Berggren, Martin
    Umeå universitet, Institutionen för datavetenskap.
    Noreland, Daniel
    Umeå universitet, Institutionen för datavetenskap.
    Wadbro, Eddie
    Umeå universitet, Institutionen för datavetenskap.
    A computationally efficient hybrid 2D–3D subwoofer model2021In: Scientific Reports, E-ISSN 2045-2322, Vol. 11, article id 255Article in journal (Refereed)
    Abstract [en]

    A subwoofer generates the lowest frequency range in loudspeaker systems. Subwoofers are used in audio systems for live concerts, movie theatres, home theatres, gaming consoles, cars, etc. During the last decades, numerical simulations have emerged as a cost- and time-efficient complement to traditional experiments in the design process of different products. The aim of this study is to reduce the computational time of simulating the average response for a given subwoofer design. To this end, we propose a hybrid 2D–3D model that reduces the computational time significantly compared to a full 3D model. The hybrid model describes the interaction between different subwoofer components as interacting modules whose acoustic properties can partly be pre-computed. This allows us to efficiently compute the performance of different subwoofer design layouts. The results of the hybrid model are validated against both a lumped element model and a full 3D model over a frequency band of interest. The hybrid model is found to be both accurate and computationally efficient.

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  • 16.
    Bokhari, Ahmad Hasnain
    et al.
    Umeå universitet.
    Mousavi, Abbas
    Umeå universitet.
    Niu, Bin
    Dalian University of Technology, CHN.
    Wadbro, Eddie
    Umeå universitet.
    Topology optimization of an acoustic diode?2021In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 63, no 6, p. 2739-2749Article in journal (Refereed)
    Abstract [en]

    By using topology optimization, we consider the problem of designing a passive acoustic device that allows for one-way flow of sound waves; such a device is often colloquially referred to as an acoustic diode. The Helmholtz equation is used to model the time harmonic linear wave propagation together with a Dirichlet-to-Neumann (DtN) type boundary condition, and the finite element method is used for discretization. The objective of this study is to maximize the wave propagation in one direction (from left to right) and minimize the wave propagation in the reverse direction (from right to left) for planar incoming waves. The method of moving asymptotes (MMA) solves the optimization problem, and a continuation approach is used for the penalizing intermediate design variables. The results for the optimized waveguide show that more than 99.8% of the power of planar incoming waves get transmitted from left to right while less than 0.3% gets transmitted in the reverse direction for planar incoming waves in the specified frequency range. Since a true diode is a non-reciprocal device and here we used a linear acoustic wave model, which is basically reciprocal, we discuss details about how it appears to be possible to obtain a one-way waveguiding effect using this linear model.

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  • 17.
    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.

  • 18.
    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.

  • 19.
    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.

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  • 20.
    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)
  • 21.
    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.

  • 22.
    Colangeli, M.
    et al.
    Univ Laquila, Italy.
    Muntean, Adrian
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Reduced Markovian descriptions of Brownian dynamics: Toward an exact theory2022In: Frontiers in Physics, E-ISSN 2296-424X, Vol. 10, article id 903030Article in journal (Refereed)
    Abstract [en]

    We outline a reduction scheme for a class of Brownian dynamics which leads to meaningful corrections to the Smoluchowski equation in the overdamped regime. The mobility coefficient of the reduced dynamics is obtained by exploiting the Dynamic Invariance principle, whereas the diffusion coefficient fulfils the Fluctuation-Dissipation theorem. Explicit calculations are carried out in the case of a harmonically bound particle. A quantitative pointwise representation of the reduction error is also provided and connections to both the Maximum Entropy method and the linear response theory are highlighted. Our study paves the way to the development of reduction procedures applicable to a wider class of diffusion processes.

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  • 23.
    Colangeli, Matteo
    et al.
    University of L'Aquila, Italy.
    Duong, Manh Hong
    University of Birmingham, United Kingdom.
    Muntean, Adrian
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). Karlstad University, Faculty of Arts and Social Sciences (starting 2013), Center for Societal Risk Research, CSR (from 2020).
    Model reduction of Brownian oscillators: Quantification of errors and long-time behaviour2023In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, E-ISSN 1751-8121, Vol. 56, article id 345003Article in journal (Refereed)
    Abstract [en]

    A procedure for model reduction of stochastic ordinary differential equations with additive noise was recently introduced in Colangeli et al (2022 J. Phys. A: Math. Theor.55 505002), based on the Invariant Manifold method and on the Fluctuation–Dissipation relation. A general question thus arises as to whether one can rigorously quantify the error entailed by the use of the reduced dynamics in place of the original one. In this work we provide explicit formulae and estimates of the error in terms of the Wasserstein distance, both in the presence or in the absence of a sharp time-scale separation between the variables to be retained or eliminated from the description, as well as in the long-time behavior.

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  • 24.
    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, 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.

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  • 25.
    Eden, Michael
    et al.
    Zentrum für Technomathematik, Department of Mathematics and Computer Science, University of Bremen, Germany.
    Nikolopoulos, Christos
    Department of Mathematics, School of Sciences, University of the Aegean, Greece.
    Muntean, Adrian
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    A multiscale quasilinear system for colloids deposition in porous media: Weak solvability and numerical simulation of a near-clogging scenario2022In: Nonlinear Analysis: Real World Applications, ISSN 1468-1218, Vol. 63, article id 103408Article in journal (Refereed)
    Abstract [en]

    We study the weak solvability of a macroscopic, quasilinear reaction–diffusion system posed in a 2D porous medium which undergoes microstructural problems. The solid matrix of this porous medium is assumed to be made out of circles of not-necessarily uniform radius. The growth or shrinkage of these circles, which are governed by an ODE, has direct feedback to the macroscopic diffusivity via an additional elliptic cell problem. The reaction–diffusion system describes the macroscopic diffusion, aggregation, and deposition of populations of colloidal particles of various sizes inside a porous media made of prescribed arrangement of balls. The mathematical analysis of this two-scale problem relies on a suitable application of Schauder's fixed point theorem which also provides a convergent algorithm for an iteration method to compute finite difference approximations of smooth solutions to our multiscale model. Numerical simulations illustrate the behavior of the local concentration of the colloidal populations close to clogging situations.

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  • 26.
    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.

  • 27.
    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.

  • 28.
    Fuhrmann, Jürgen
    et al.
    Weierstrass Institute, DEU.
    Hai Doan, Duy
    m4sim GmbH, DEU.
    Glitzky, Annegret
    Weierstrass Institute, DEU.
    Liero, Matthias
    Weierstrass Institute, DEU.
    Nika, Grigor
    Weierstrass Institute, DEU.
    Unipolar Drift-Diffusion Simulation of S-Shaped Current-Voltage Relations for Organic Semiconductor Devices2020In: Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples. FVCA 2020: Methods, Theoretical Aspects, Examples. FVCA 2020 / [ed] R. Klöfkorn ; E. Keilegavlen ; F.A. Radu ; J. Fuhrmann, Springer, 2020, p. 625-633Chapter in book (Refereed)
    Abstract [en]

    We discretize a unipolar electrothermal drift-diffusion model for organic semiconductor devices with Gauss–Fermi statistics and charge carrier mobilities having positive temperature feedback. We apply temperature dependent Ohmic contact boundary conditions for the electrostatic potential and use a finite volume based generalized Scharfetter-Gummel scheme. Applying path-following techniques we demonstrate that the model exhibits S-shaped current-voltage curves with regions of negative differential resistance, only recently observed experimentally.

  • 29.
    Grützner, Simon
    et al.
    University of Bremen, DEU.
    Muntean, Adrian
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Identifying processes governing damage evolution in quasi-static elasticity.: Part 2 - Numerical simulations2022In: Advances in Mathematical Sciences and Applications, E-ISSN 1343-4373, Vol. 31, no 1, p. 147-173Article in journal (Refereed)
    Abstract [en]

    We investigate numerically a quasi-static elasticity system of Kachanov-type. To do so we propose an Euler time discretization combined with a suitable finite elements scheme (FEM) to handle the discretization is space. We use ODE-type arguments to prove the consistency of the scheme as well as its convergence rate. We rely on the computational platform FEniCS© to perform the FEM discretizations in space needed to compute the model output. The simulation results show a good agreement with both the physics of the problem and with our previous qualitative mathematical analysis results obtained for precisely the same problem setting. Furthermore, our implementation recovers nicely the theoretically expected convergence rate. This is a preliminary study preparing the framework for the rigorous numerical identification of the damage process in Kachanovtype models.

  • 30. 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.

  • 31.
    Hosseini, Ahmad
    et al.
    Umea University, Sweden; University of Nova Gorica, Slovenia.
    Wadbro, Eddie
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). Umea University, Sweden.
    Ngoc Do, Dung
    Umea University, Sweden.
    Lindroos, Ola
    wedish University of Agricultural Sciences, Sweden.
    A scenario-based metaheuristic and optimization framework for cost-effective machine-trail network design in forestry2023In: Computers and Electronics in Agriculture, ISSN 0168-1699, E-ISSN 1872-7107, Vol. 212, article id 108059Article in journal (Refereed)
    Abstract [en]

    Designing an optimal machine trail network is a complex locational problem that requires an understanding of different machines’ operations and terrain features as well as the trade-offs between various objectives. With the overall goal to minimize the operational costs of the logging operation, this paper proposes a mathematical optimization model for the trail network design problem and a greedy heuristic method based on different randomized search scenarios aiming to find the optimal location of machine trails —with potential to reduce negative environmental impact. The network is designed so that all trees can be reached and adapted to how the machines can maneuver while considering the terrain elevation’s influence. To examine the effectiveness and practical performance of the heuristic and the optimization model, it was applied in a case study on four harvest units with different topologies and shapes. The computational experiments show that the heuristic can generate solutions that outperform the solutions corresponding to conventional, manual designs within practical time limits for operational planning. Moreover, to highlight certain features of the heuristic and the parameter settings’ effect on its performance, we present an extensive computational sensitivity analysis. 

  • 32.
    Hägg, Linus
    et al.
    Umeå University.
    Wadbro, Eddie
    Umeå University.
    Nonlinear filters in topology optimization: existence of solutions and efficient implementation for minimum compliance problems2017In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 55, no 3, p. 1017-1028Article in journal (Refereed)
    Abstract [en]

    Material distribution topology optimization problems are generally ill-posed if no restriction or regularization method is used. To deal with these issues, filtering procedures are routinely applied. In a recent paper, we presented a framework that encompasses the vast majority of currently available density filters. In this paper, we show that these nonlinear filters ensure existence of solutions to a continuous version of the minimum compliance problem. In addition, we provide a detailed description on how to efficiently compute sensitivities for the case when multiple of these nonlinear filters are applied in sequence. Finally, we present large-scale numerical experiments illustrating some characteristics of these cascaded nonlinear filters.

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  • 33.
    Hägg, Linus
    et al.
    Umeå universitet.
    Wadbro, Eddie
    Umeå universitet.
    On minimum length scale control in density based topology optimization2018In: Structural and multidisciplinary optimization (Print), ISSN 1615-147X, E-ISSN 1615-1488, Vol. 58, no 3, p. 1015-1032Article in journal (Refereed)
    Abstract [en]

    The archetypical topology optimization problem concerns designing the layout of material within a given region of space so that some performance measure is extremized. To improve manufacturability and reduce manufacturing costs, restrictions on the possible layouts may be imposed. Among such restrictions, constraining the minimum length scales of different regions of the design has a significant place. Within the density filter based topology optimization framework the most commonly used definition is that a region has a minimum length scale not less than D if any point within that region lies within a sphere with diameter D > 0 that is completely contained in the region. In this paper, we propose a variant of this minimum length scale definition for subsets of a convex (possibly bounded) domain We show that sets with positive minimum length scale are characterized as being morphologically open. As a corollary, we find that sets where both the interior and the exterior have positive minimum length scales are characterized as being simultaneously morphologically open and (essentially) morphologically closed. For binary designs in the discretized setting, the latter translates to that the opening of the design should equal the closing of the design. To demonstrate the capability of the developed theory, we devise a method that heuristically promotes designs that are binary and have positive minimum length scales (possibly measured in different norms) on both phases for minimum compliance problems. The obtained designs are almost binary and possess minimum length scales on both phases.

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  • 34.
    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)
  • 35.
    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.

  • 36. 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)
  • 37.
    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.

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  • 38.
    Kavallaris, Nikos I.
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Nikolopoulos, Christos V.
    University of Aegean, Greece.
    Yannacopoulos, Athanasios N.
    Athens University of Economics and Business, Greece; Athens University of Economics and Business, Greece.
    On the impact of noise on quenching for a nonlocal diffusion model driven by a mixture of Brownian and fractional Brownian motions2023In: Discrete and Continuous Dynamical Systems. Series S, ISSN 1937-1632, E-ISSN 1937-1179Article in journal (Refereed)
    Abstract [en]

    In this paper, we study a stochastic parabolic problem involving anonlocal diffusion operator associated with nonlocal Robin-type boundary conditions. The stochastic dynamics under consideration is driven by a mixtureof a classical Brownian and a fractional Brownian motion with Hurst indexH ∈ (1/2, 1). We first establish local in time existence results and then exploreconditions under which the resulting SPDE exhibits finite-time quenching. Using results on the probability distribution of perpetual integral functionals ofBrownian motion as well as tail estimates for the fractional Brownian motionwe provide analytic estimates for certain quantities of interest, such as upperbounds for quenching times and the corresponding quenching probabilities.The existence of global in time solutions is also investigated and as a consequence a lower estimate of the quenching time is also derived. Our analyticalresults demonstrate the non-trivial impact of the noise on the dynamics ofthe system. The analytic results are complemented with a detailed numericalstudy of the model under Dirichlet boundary conditions. A possible application concerning MEMS technology is considered and the implications of theresults in this context are commented upon.

  • 39.
    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.

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  • 40.
    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)
  • 41.
    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: Real World Applications, ISSN 1468-1218, Vol. 15, p. 392-403Article in journal (Refereed)
  • 42.
    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.

  • 43.
    Kumar, Kundan
    et al.
    Tech Univ Eindhoven, Eindhoven, Netherlands.
    Pop, I. S.
    Tech Univ Eindhoven, Eindhoven, Netherlands; Univ Bergen, Bergen, Norway.
    Radu, F. A.
    Univ Bergen, Bergen, Norway.
    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)
  • 44. 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)
  • 45.
    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.

  • 46.
    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.

  • 47. 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)
  • 48.
    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)
  • 49.
    Lindström, M.
    et al.
    Åbo Akademi University, Finland.
    Miihkinen, Santeri
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Norrbo, D.
    Åbo Akademi University, Finland.
    Exact essential norm of generalized Hilbert matrix operators on classical analytic function spaces2022In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 408, article id 108598Article in journal (Refereed)
    Abstract [en]

    We compute the exact value of the essential norm of ageneralized Hilbert matrix operator acting on weightedBergman spaces Apv and weighted Banach spaces H∞v ofanalytic functions, where v is a general radial weight. Inparticular, we obtain the exact value of the essential normof the classical Hilbert matrix operator on standard weightedBergman spaces Apα for p > 2 + α, α ≥ 0, and on Korenblumspaces H∞α for 0 < α < 1. We also cover the Hardy spaceHp, 1 < p < ∞, case. In the weighted Bergman space case, theessential norm of the Hilbert matrix is equal to the conjecturedvalue of its operator norm and similarly in the Hardy spacecase the essential norm and the operator norm coincide. Wealso compute the exact value of the norm of the Hilbert matrixon H∞wα with weights wα(z) = (1 − |z|)α for all 0 < α < 1. Also in this case, the values of the norm and essential normcoincide.

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    fulltext
  • 50.
    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.

    Download full text (pdf)
    KAU_LL_TVI_AND_DVH
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