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• 1. Ackelh, A.S.
Institute for Complex Molecular Systems & Centre for Analysis, Scientific computing and Applications, Eindhoven University of Technology.
Preface to "modeling with measures"2015In: Mathematical Biosciences and Engineering, ISSN 1547-1063, E-ISSN 1551-0018, Vol. 12, no 2Article in journal (Refereed)
• 2. Aiki, T.
Technische Universiteit Eindhoven, Department of Mathematics and Computer Science, Eindhoven, Netherlands .
Preface2012In: Discrete and Continuous Dynamical Systems. Series S, ISSN 1937-1632, E-ISSN 1937-1179, discrete and cont, Vol. 5, no 1, 1- p.Article in journal (Refereed)
• 3.
Japan Womens Univ, Fac Sci, Dept Math, Bunkyo Ku, Tokyo.
Vrije Univ Amsterdam, Fac Sci, Dept Math, Amsterdam, Netherlands. Bukkyo Univ, Sch Educ Math, Kita Ku, Kyoto. Eindhoven Univ Technol, Dept Math & Comp Sci,.
Analysis of non-equilibrium evolution problems: Selected topics in material and life sciences2014In: Discrete and Continuous Dynamical Systems. Series S, ISSN 1937-1632, E-ISSN 1937-1179, Vol. 7, no 1Article in journal (Refereed)
• 4. Aiki, T.
Eindhoven Univ Technol, Dept Math & Comp Sci.
A free-boundary problem for concrete carbonation: Front nucleation and rigorous justification of the root t-law of propagation2013In: Interfaces and free boundaries (Print), ISSN 1463-9963, E-ISSN 1463-9971, Vol. 15, no 2, 167-180 p.Article in journal (Refereed)
• 5. Aiki, T.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
Existence and uniqueness of solutions to a mathematical model predicting service life of concrete structures2009In: Advances in Mathematical Sciences and Applications, ISSN 1343-4373, Vol. 19, 119-129 p.Article in journal (Refereed)
• 6.
Gifu University, Japan.
Eindhoven University Technology, Netherlands. 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, 15-28 p.Article in journal (Refereed)
• 7.
Gifu University, Japan.
Eindhoven University of Technology.
Large time behavior of solutions to a moving-interface problem modeling concrete carbonation2010In: Communications on Pure and Applied Analysis, ISSN 1534-0392, E-ISSN 1553-5258, Vol. 9, no 5, 1117-1129 p.Article in journal (Refereed)
• 8.
Tokyo Womens University.
Netherlands.
Large-time asymptotics of moving-reaction interfaces involving nonlinear Henry’s law and time-dependent Dirichlet data2013In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 93, 3-14 p.Article in journal (Refereed)

We study the large-time behavior of the free boundary position capturing the one-dimensional motion of the carbonation reaction front in concrete-based materials. We extend here our rigorous justification of the t-behavior of reaction penetration depths by including nonlinear effects due to deviations from the classical Henry's law and time-dependent Dirichlet data.

• 9. Aiki, Toyohiko
Eindhoven University of Technology.
Large-time behavior of a two-scale semilinear reaction-diffusion system for concrete sulfatation2014In: Mathematical methods in the applied sciences, ISSN 0170-4214, E-ISSN 1099-1476, Vol. 38, no 7, 1451-1464 p.Article in journal (Refereed)
• 10.
Japan.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
Large-time behavior of solutions to a thermo-diffusion system with Smoluchowski interactions2017In: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 5, no 5, 3009-3026 p.Article in journal (Refereed)

We prove the large time behavior of solutions to a coupled thermo-diffusion arising in the modeling of the motion of hot colloidal particles in porous media. Additionally, we also ensure the uniqueness of solutions of the target problem. The main mathematical difficulty is due to the presence in the right-hand side of the equations of products between temperature and concentration gradients. Such terms mimic the so-called thermodynamic Soret and Dufour effects. These are cross-coupling terms emphasizing in this context a strong interplay between heat conduction and molecular diffusion.

The full text will be freely available from 2018-05-30 15:04
• 11.
Gifu University, Japan.
Eindhoven University of Technology.
On uniqueness of a weak solution of one-dimensional concrete carbonation problem2011In: Discrete and Continuous Dynamical Systems, ISSN 1078-0947, E-ISSN 1553-5231, Vol. 29, no 4, 1345-1365 p.Article in journal (Refereed)

In our previous works we studied a one-dimensional free-boundary model related to the aggressive penetration of gaseous carbon dioxide in unsaturated concrete. Essentially, global existence and uniqueness of weak solutions to the model were obtained when the initial functions are bounded on the domain. In this paper we investigate the well-posedness of the problem for the case when the initial functions belong to a $\displaystyle{{L}}^{{2}}-$ class. Specifically, the uniqueness of weak solutions is proved by applying the dual equation method.

• 12.
Università di Roma La Sapienza.
Università di Roma La Sapienza. Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science. Eindhoven University of Technology.
Weak solutions to Allen-Cahn-like equations modelling consolidation of porous media2017In: IMA Journal of Applied Mathematics, ISSN 0272-4960, E-ISSN 1464-3634, Vol. 82, no 1, 224-250 p.Article in journal (Refereed)

We study the weak solvability of a system of coupled Allen–Cahn-like equations resembling cross-diffusion which arises as a model for the consolidation of saturated porous media. Besides using energy-like estimates, we cast the special structure of the system in the framework of the Leray–Schauder fixed-point principle and ensure in this way the local existence of strong solutions to a regularized version of our system. Furthermore, weak convergence techniques ensure the existence of weak solutions to the original consolidation problem. The uniqueness of global-in-time solutions is guaranteed in a particular case. Moreover, we use a finite difference scheme to show the negativity of the vector of solutions.

• 13.
Univ Glasgow, Sch Math & Stat, Glasgow.
Eindhoven Univ Technol, Dept Math & Comp Sci, NL. Eindhoven Univ Technol, Dept Math & Comp Sci, NL. 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, 2463-2475 p.Article in journal (Refereed)
• 14.
Kyushu University, Japan.
Eindhoven University of Technology, The Netherlands. Strassen.NRW, Gelsenkirchen, Germany. 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, 22-31 p.Conference paper (Refereed)

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.

• 15.
Kyushu Univ, Inst Math Ind, Nishi Ku, Fukuoka 8190395, Japan.
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, 289-316 p.Article in journal (Refereed)
• 16.
Sapienza Univ Roma, Dipartimento Sci Base & Appl Ingn, Via A Scarpa 16, I-00161 Rome, Italy.
Eindhoven Univ Technol, ICMS, Dept Math & Comp Sci, POB 513, NL-5600 MB Eindhoven, Netherlands. Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science. Eindhoven Univ Technol, Fac Chem Engn, ICMS, POB 513, NL-5600 MB Eindhoven, Netherlands.
Lattice model of reduced jamming by a barrier2016In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 94, no 4, 042115Article in journal (Refereed)
• 17.
Sapienza Univ Roma, Dipartimento Sci Base & Appl Ingn, Via A Scarpa 16, I-00161 Rome, Italy.
Gran Sasso Sci Inst, Viale F Crispi 7, I-00167 Laquila, Italy. Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
Blockage-induced condensation controlled by a local reaction2016In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 94, no 4Article in journal (Refereed)

We consider the setup of stationary zero range models and discuss the onset of condensation induced by a local blockage on the lattice. We show that the introduction of a local feedback on the hopping rates allows us to control the particle fraction in the condensed phase. This phenomenon results in a current versus blockage parameter curve characterized by two nonanalyticity points.

• 18.
Sapienza Universit`a di Roma.
Eindhoven University of Technology.
Can cooperation slow down emergency evacuations?2012In: Comptes rendus. Mecanique, ISSN 1631-0721, E-ISSN 1873-7234, Vol. 340, no 9, 625-628 p.Article in journal (Refereed)

We study the motion of pedestrians through obscure corridors where the lack of visibility hides the precise position of the exits. Using a lattice model, we explore the effects of cooperation on the overall exit flux (evacuation rate). More precisely, we study the effect of the buddying threshold (of no–exclusion per site) on the dynamics of the crowd. In some cases, we note that if the evacuees tend to cooperate and act altruistically, then their collective action tends to favor the occurrence of disasters.

• 19.
Università di Roma “La Sapienza”.
Gran Sasso Science Institute. 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, 19-23 p.Article in journal (Refereed)

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.

• 20.
Sapienza Universit`a di Roma.
Gran Sasso Science Institute. Eindhoven University of Technology.
Effects of communication efficiency and exit capacity on fundamental diagrams for pedestrian motion in an obscure tunnel: a particle system approach2016In: Multiscale Modeling & simulation, ISSN 1540-3459, E-ISSN 1540-3467, Vol. 14, no 2, 906-922 p.Article in journal (Refereed)

Fundamental diagrams describing the relation between pedestrians' speed and density are key points in understanding pedestrian dynamics. Experimental data evidence the onset of complex behaviors in which the velocity decreases with the density, and different logistic regimes are identified. This paper addresses the issue of pedestrian transport and of fundamental diagrams for a scenario involving the motion of pedestrians escaping from an obscure tunnel. We capture the effects of communication efficiency and exit capacity by means of two thresholds controlling the rate at which particles (walkers, pedestrians) move on the lattice. Using a particle system model, we show that in the absence of limitation in communication among pedestrians, we reproduce with good accuracy the standard fundamental diagrams, whose basic behaviors can be interpreted in terms of exit capacity limitation. When the effect of limited communication ability is considered, then interesting nonintuitive phenomena occur. In particular, we shed light on the loss of monotonicity of the typical speed-density curves, revealing the existence of a pedestrian density optimizing the escape. We study both the discrete particle dynamics and the corresponding hydrodynamic limit (a porous medium equation and a transport (continuity) equation). We also point out the dependence of the effective transport coefficients on the two thresholds---the essence of the microstructure information.Read More: http://epubs.siam.org/doi/10.1137/15M1030960

• 21. Cirillo, Emilio N.M.
Eindhoven University of Technology.
Dynamics of pedestrians in regions with no visibility: A lattice model without exclusion2013In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, Vol. 392, no 17, 3578-3588 p.Article in journal (Refereed)

We investigate the motion of pedestrians through obscure corridors where the lack of visibility (due to smoke, fog, darkness, etc.) hides the precise position of the exits. We focus our attention on a set of basic mechanisms, which we assume to be governing the dynamics at the individual level. Using a lattice model, we explore the effects of non-exclusion on the overall exit flux (evacuation rate). More precisely, we study the effect of the buddying threshold (of no-exclusion per site) on the dynamics of the crowd and investigate to which extent our model confirms the following pattern revealed by investigations on real emergencies: If the evacuees tend to cooperate and act altruistically, then their collective action tends to favor the occurrence of disasters. The research reported here opens many fundamental questions and should be seen therefore as a preliminary investigation of the very complex behavior of the people and their motion in dark regions.

• 22. Cirillo, E,N.M
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
Stationary currents in particle systems with constrained hopping rates2016In: Journal of Non-Equilibrium Thermodynamics, ISSN 0340-0204, E-ISSN 1437-4358, Vol. 41, no 2, 99-106 p.Article in journal (Refereed)
• 23.
Dipartimento di Scienze di Base e Applicate per l’Ingegneria, Sapienza Università di Roma, Via A. Scarpa 16, I–00161, Roma, Italy.
Dipartimento di Ingegneria e Scienze dell’Informazione e Matematica, Università degli Studi dell’Aquila, Via Vetoio, 67100 L’Aquila, Italy. Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
Trapping in bottlenecks: interplay between microscopic dynamics and large scale effects2017In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, Vol. 488, no 11, 30-38 p.Article in journal (Refereed)
• 24.
Univ Roma La Sapienza, Dipartimento Sci Base & Applicate Ingn, Rome, Italy.
Eindhoven Univ Technol, Inst Complex Mol Syst, Eindhoven, Netherlands. Eindhoven Univ Technol, Inst Complex Mol Syst. Eindhoven Univ Technol, Inst Complex Mol Syst, Eindhoven, Netherlands. Indian Inst Technol Delhi, Delhi, India.
Residence time estimates for asymmetric simple exclusion dynamics on strips2015In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 442, 436-457 p.Article in journal (Refereed)
• 25.
Eindhoven University of Technology.
California State University Long Beach. University of Rome Tor Vergata. Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science. Eindhoven University of Technology.
Fluctuations around mean walking behaviors in diluted pedestrian flows2017In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 95, no 3Article in journal (Refereed)

Understanding and modeling the dynamics of pedestrian crowds can help with designing and increasing the safety of civil facilities. A key feature of a crowd is its intrinsic stochasticity, appearing even under very diluted conditions, due to the variability in individual behaviors. Individual stochasticity becomes even more important under densely crowded conditions, since it can be nonlinearly magnified and may lead to potentially dangerous collective behaviors. To understand quantitatively crowd stochasticity, we study the real-life dynamics of a large ensemble of pedestrians walking undisturbed, and we perform a statistical analysis of the fully resolved pedestrian trajectories obtained by a yearlong high-resolution measurement campaign. Our measurements have been carried out in a corridor of the Eindhoven University of Technology via a combination of Microsoft Kinect 3D range sensor and automatic head-tracking algorithms. The temporal homogeneity of our large database of trajectories allows us to robustly define and separate average walking behaviors from fluctuations parallel and orthogonal with respect to the average walking path. Fluctuations include rare events when individuals suddenly change their minds and invert their walking directions. Such tendency to invert direction has been poorly studied so far, even if it may have important implications on the functioning and safety of facilities. We propose a model for the dynamics of undisturbed pedestrians, based on stochastic differential equations, that provides a good agreement with our field observations, including the occurrence of rare events.

• 26.
Eindhoven University of Technolology; Politecnio di Torino.
Eindhoven University of Technolology. Eindhoven University of Technolology.
Parameter estimation of social forces in pedestrian dynamics models via a probabilistic method2015In: Mathematical Biosciences and Engineering, ISSN 1547-1063, E-ISSN 1551-0018, Vol. 12, no 2, 337-356 p.Article in journal (Refereed)

Focusing on a specific crowd dynamics situation, including real life experiments and measurements, our paper targets a twofold aim: (1) we present a Bayesian probabilistic method to estimate the value and the uncertainty (in the form of a probability density function) of parameters in crowd dynamic models from the experimental data; and (2) we introduce a fitness measure for the models to classify a couple of model structures (forces) according to their fitness to the experimental data, preparing the stage for a more general model-selection and validation strategy inspired by probabilistic data analysis. Finally, we review the essential aspects of our experimental setup and measurement technique.

• 27.
Tilburg University; Cognitrom.
Eindhoven University of Technology . Eindhoven University of Technology . 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)

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.

• 28.
Universitá Giustino Fortunato, Italy .
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
Existence of weak solutions to a nonlinear reaction-diffusion system with singular sources2017In: Electronic Journal of Differential Equations, ISSN 1550-6150, E-ISSN 1072-6691, Vol. 2017, no 202, 1-16 p.Article in journal (Refereed)

We discuss the existence of a class of weak solutions to a nonlinear parabolic system of reaction-diffusion type endowed with singular production terms by reaction. The singularity is due to a potential occurrence of quenching localized to the domain boundary. The kind of quenching we have in mind is due to a twofold contribution: (i) the choice of boundary conditions, modeling in our case the contact with an infinite reservoir filled with ready-to-react chemicals and (ii) the use of a particular nonlinear, non-Lipschitz structure of the reaction kinetics. Our working techniques use fine energy estimates for approximating non-singular problems and uniform control on the set where singularities are localizing.

• 29.
University of Warwick, UK.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science. Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
Discrete and continuum links to a nonlinear coupled transport problem of interacting populations2017In: The European Physical Journal Special Topics, ISSN 1951-6355, E-ISSN 1951-6401, Vol. 226, no 10, 2345-2357 p.Article in journal (Refereed)

We are interested in exploring interacting particle systemsthat can be seen as microscopic models for a particular structure ofcoupled transport flux arising when different populations are jointlyevolving. The scenarios we have in mind are inspired by the dynamicsof pedestrian flows in open spaces and are intimately connectedto cross-diffusion and thermo-diffusion problems holding a variationalstructure. The tools we use include a suitable structure of the relativeentropy controlling TV-norms, the construction of Lyapunov functionalsand particular closed-form solutions to nonlinear transport equations,a hydrodynamics limiting procedure due to Philipowski, as wellas the construction of numerical approximates to both the continuumlimit problem in 2D and to the original interacting particle systems.

• 30.
University of Bremen.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
Corrector estimates for the homogenization of a two-scale thermoelasticity problem with a priori known phase transformations2017In: Electronic Journal of Differential Equations, ISSN 1550-6150, E-ISSN 1072-6691, no 57, 1-21 p.Article in journal (Refereed)

We investigate corrector estimates for the solutions of a thermoelasticity problem posed in a highly heterogeneous two-phase medium and its corresponding two-scale thermoelasticity model which was derived in [11] by two-scale convergence arguments. The medium in question consists of a connected matrix with disconnected, initially periodically distributed inclusions separated by a sharp interface undergoing a priori known phase transformations. While such estimates seem not to be obtainable in the fully coupled setting, we show that for some simplified scenarios optimal convergence rates can be proven rigorously. The main technique for the proofs are energy estimates using special reconstructions of two-scale functions and particular operator estimates for periodic functions with zero average. Here, additional regularity results for the involved functions are necessary.

• 31.
University of Bremen.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
Homogenization of a fully coupled thermoelasticity problem for a highly heterogeneous medium with a priori known phase transformations2016In: Mathematical methods in the applied sciences, ISSN 0170-4214, E-ISSN 1099-1476Article in journal (Refereed)

We investigate a linear, fully coupled thermoelasticity problem for a highly heterogeneous, two-phase medium. The medium in question consists of a connected matrix with disconnected, initially periodically distributed inclusions separated by a sharp interface undergoing an a prioriknown interface movement because of phase transformations. After transforming the moving geometry to an ϵ-periodic, fixed reference domain, we establish the well-posedness of the model and derive a number of ϵ-independent a priori estimates. Via a two-scale convergence argument, we then show that the ϵ-dependent solutions converge to solutions of a corresponding upscaled model with distributed time-dependent microstructures.

• 32.
Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon, England.
Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon, England. Eindhoven University of Technology.
Single and two-scale sharp-interface models for concrete carbonation - Asymptotics and numerical approximation2012In: Multiscale Modeling & simulation, ISSN 1540-3459, E-ISSN 1540-3467, Vol. 10, no 3, 874-905 p.Article in journal (Refereed)
• 33.
Eindhoven University of Technology.
Leiden University. Eindhoven University of Technology.
Modelling with measures: Approximation of a mass-emitting object by a point source2015In: Mathematical Biosciences and Engineering, ISSN 1547-1063, E-ISSN 1551-0018, Mathematical Biosciences and Engineering, Vol. 12, no 2, 357-373 p.Article in journal (Refereed)
• 34.
Eindoven University of Technology.
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, 27-37 p.Article in journal (Refereed)

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.

• 35.
Netherlands.
Netherlands. Eindhoven University of Technology, The Netherlands.
Well-posedness and approximation of a measure-valued mass evolution problem with flux boundary conditions2014In: Comptes rendus. Mathematique, ISSN 1631-073X, E-ISSN 1778-3569, Vol. 352, no 1, 51-54 p.Article in journal (Refereed)

This Note deals with imposing a flux boundary condition on a non-conservative measure-valued mass evolution problem posed on a bounded interval. To establish the wellposedness of the problem, we exploit particle system approximations of the mass accumulation in a thin layer near the active boundary. We derive the convergence rate for the approximation procedure as well as the structure of the flux boundary condition in the limit problem.

• 36.
Eindhoven University of Technology, Netherlands.
Leiden University, Netherlands. Eindhoven University of Technology, Netherlands.
Mild solutions to a measure-valued mass evolution problem with flux boundary conditions2015In: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 259, no 3, 1068-1097 p.Article in journal (Refereed)

We investigate the well-posedness and approximation of mild solutions to a class of linear transport equations on the unit interval [0, 1] endowed with a linear discontinuous production term, formulated in the space M([0, 1]) of finite Borel measures. Our working technique includes a detailed boundary layer analysis in terms of a semigroup representation of solutions in spaces of measures able to cope with the passage to the singular limit where thickness of the layer vanishes. We obtain not only a suitable concept of solutions to the chosen measure-valued evolution problem, but also derive convergence rates for the approximation procedure and get insight in the structure of flux boundary conditions for the limit problem.

• 37.
Eindhoven University of Technology.
Eindhoven University of Technology. 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, 263-268 p.Article in journal (Refereed)

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.

• 38.
Eindhoven University of Technology, Netherlands.
Meiji University, Tokyo. Meiji University, Tokyo. Eindhoven University of Technology, Netherlands.
Homogenization and dimension reduction of filtration combustion in heterogeneous thin layers2014In: Networks and Heterogeneous Media, ISSN 1556-1801, E-ISSN 1556-181X, Vol. 9, no 4, 709-737 p.Article in journal (Refereed)

We study the homogenization of a reaction-diffusion-convection system posed in an epsilon-periodic delta-thin layer made of a two-component (solid-air) composite material. The microscopic system includes heat flow, diffusion and convection coupled with a nonlinear surface chemical reaction. We treat two distinct asymptotic scenarios: (1) For a fixed width delta > 0 of the thin layer, we homogenize the presence of the microstructures (the classical periodic homogenization limit epsilon --> 0); (2) In the homogenized problem, we pass to delta --> 0 (the vanishing limit of the layer's width). In this way, we are preparing the stage for the simultaneous homogenization (epsilon --> 0) and dimension reduction limit (delta --> 0) with delta = delta (epsilon). We recover the reduced macroscopic equations from [25] with precise formulas for the effective transport and reaction coefficients. We complement the analytical results with a few simulations of a case study in smoldering combustion. The chosen multiscale scenario is relevant for a large variety of practical applications ranging from the forecast of the response to fire of refractory concrete, the microstructure design of resistance-to-heat ceramic-based materials for engines, to the smoldering combustion of thin porous samples under microgravity conditions.

• 39. Fatima, Tasnim
Technical University Eindhoven.
Sulfate attack in sewer pipes: Derivation of a concrete corrosion model via two-scale convergence2014In: Nonlinear Analysis, ISSN 1468-1218, Vol. 15, no 1, 326-344 p.Article in journal (Refereed)

We explore the homogenization limit and rigorously derive upscaled equations for a microscopic reaction-diffusion system modeling sulfate corrosion in sewer pipes made of concrete. The system, defined in a periodically-perforated domain, is semi-linear, partially dissipative and weakly coupled via a non-linear ordinary differential equation posed on the solid-water interface at the pore level. First, we show the well-posedness of the microscopic model. We then apply homogenization techniques based on two-scale convergence for a uniformly periodic domain and derive upscaled equations together with explicit formulas for the effective diffusion coefficients and reaction constants. We use a boundary unfolding method to pass to the homogenization limit in the non-linear ordinary differential equation. Finally, we give the strong formulation of the upscaled system.

• 40.
Eindhoven University of Technology.
Eindhoven University of Technology. Gifu University Yanagido.
Distributed space scales in a semilinear reaction-diffusion system including parabolic variational inequality: a well-posedness study2012In: Advances in Mathematical Sciences and Applications, ISSN 1343-4373, Vol. 22, 295-318 p.Article in journal (Refereed)
• 41.
Eindhoven Univ Technol, Ctr Anal Sci Comp & Applicat, Dept Math & Comp Sci, NL-5600 MB Eindhoven, Netherlands.
Eindhoven University of Technology. Univ Dundee, Div Math, Dundee DD1 4HN, Scotland.
Unfolding-based corrector estimates for a reaction-diffusion system predicting concrete corrosion2012In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 91, no 6, 1129-1154 p.Article in journal (Refereed)
• 42.
Technical University Eindhoven, The Netherlands.
Technical University Eindhoven, The Netherlands. Computing Centre of the Russian Academy of Sciences, Moscow, Russia. Technical University Eindhoven, The Netherlands.
Homogenization of a reaction-diffusion system modeling sulfate corrosion of concrete in locally periodic perforated domains2011In: Journal of Engineering Mathematics, ISSN 0022-0833, E-ISSN 1573-2703, Vol. 69, no 2, 261-276 p.Article in journal (Refereed)
• 43. Gruetzner, S
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
Brief Introduction to Damage Mechanics and its Relation to Deformations2017In: Mathematical Analysis of Continuum Mechanics and Industrial Applications II: Proceedings of the International Conference ComFos16, Springer, 2017Chapter in book (Refereed)
• 44. Gulikers, Lennart
Eindhoven University of Technology.
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)

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.

• 45.
Meiji University, 4-21-1 Nakano, Nakano-ku, Tokyo, Japan.
Eindhoven University of Technology, P.O. Box 513, MB Eindhoven, Netherlands. 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, 924-938 p.Article in journal (Refereed)
• 46.
Meiji University,Tokyo, Japan.
Eindhoven University of Technology. 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, 185-223 p.Article in journal (Refereed)

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.

• 47. Ijioma, E.R.
Eindhoven Univ Technol, Ctr Anal Sci Comp & Applicat,.
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, 577- p.Article in journal (Refereed)
• 48.
Gran Sasso Sci Inst, Math & Comp Sci Div, Laquila, Italy..
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
Asymptotic analysis of a semi-linear elliptic system in perforated domains: Well-posedness and correctors for the homogenization limit2016In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 439, no 1, 271-295 p.Article in journal (Refereed)

In this study, we prove results on the weak solvability and homogenization of a microscopic semi-linear elliptic system posed in perforated media. The model presented here explores the interplay between stationary diffusion and both surface and volume chemical reactions in porous media. Our interest lies in deriving homogenization limits (upscaling) for alike systems and particularly in justifying rigorously the obtained averaged descriptions. Essentially, we prove the well-posedness of the microscopic problem ensuring also the positivity and boundedness of the involved concentrations and then use the structure of the two scale expansions to derive corrector estimates delimitating this way the convergence rate of the asymptotic approximates to the macroscopic limit concentrations. Our techniques include Moser-like iteration techniques, a variational formulation, two scale asymptotic expansions as well as energy-like estimates.

• 49.
Eindhoven Univ Technol, Dept Math & Comp Sci, MB Eindhoven.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science. 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, 209-216 p.Article in journal (Refereed)
• 50.
Eindhoven University of Technology, Netherlands.
Japan Women's University, Japan. Eindhoven University of Technology, Netherlands.
Homogenization of a thermo-diffusion system with smoluchowski interactions2014In: Networks and Heterogeneous Media, ISSN 1556-1801, E-ISSN 1556-181X, Vol. 9, no 4, 739-762 p.Article in journal (Refereed)

We study the solvability and homogenization of a thermal-diffusion reaction problem posed in a periodically perforated domain. The system describes the motion of populations of hot colloidal particles interacting together via Smoluchowski production terms. The upscaled system, obtained via two-scale convergence techniques, allows the investigation of deposition effects in porous materials in the presence of thermal gradients.

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