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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"2015Inngår i: Mathematical Biosciences and Engineering, ISSN 1547-1063, E-ISSN 1551-0018, Vol. 12, nr 2Artikkel i tidsskrift (Fagfellevurdert)
• 2.
University of Louisiana at Lafayette, USA.
University of Brescia, Italy. Team ACUMES, INRIA, France. Leiden University, The Netherlands. Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap (from 2013).
Mathematical modeling with measures2019Inngår i: Nieuw Archief voor Wiskunde, ISSN 0028-9825, Vol. 20, nr September, s. 218-220Artikkel i tidsskrift (Fagfellevurdert)
• 3.
University of Louisiana at Lafayette, USA.
University of Brescia, Italy. Universite Côte d’Azur, France. Leiden University, Netherlands. Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap (from 2013).
Special issue: Mathematical modeling with measures2019Inngår i: Mathematical Biosciences and Engineering, ISSN 1547-1063, E-ISSN 1551-0018Artikkel i tidsskrift (Fagfellevurdert)
• 4. Aiki, T.
Technische Universiteit Eindhoven, Department of Mathematics and Computer Science, Eindhoven, Netherlands .
Preface2012Inngår i: Discrete and Continuous Dynamical Systems. Series S, ISSN 1937-1632, E-ISSN 1937-1179, discrete and cont, Vol. 5, nr 1, s. 1-Artikkel i tidsskrift (Fagfellevurdert)
• 5. 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 propagation2013Inngår i: Interfaces and free boundaries (Print), ISSN 1463-9963, E-ISSN 1463-9971, Vol. 15, nr 2, s. 167-180Artikkel i tidsskrift (Fagfellevurdert)
• 6. Aiki, T.
Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap.
Existence and uniqueness of solutions to a mathematical model predicting service life of concrete structures2009Inngår i: Advances in Mathematical Sciences and Applications, ISSN 1343-4373, Vol. 19, s. 119-129Artikkel i tidsskrift (Fagfellevurdert)
• 7.
Gifu University, Japan.
Eindhoven University Technology, Netherlands. Eindhoven University Technology, Netherlands.
On a one-dimensional shape-memory alloy model in its fast-temperature- activation limit2012Inngår i: Discrete and Continuous Dynamical Systems. Series S, ISSN 1937-1632, E-ISSN 1937-1179, Vol. 5, nr 1, s. 15-28Artikkel i tidsskrift (Fagfellevurdert)
• 8.
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 sciences2014Inngår i: Discrete and Continuous Dynamical Systems. Series S, ISSN 1937-1632, E-ISSN 1937-1179, Vol. 7, nr 1Artikkel i tidsskrift (Fagfellevurdert)
• 9.
Gifu University, Japan.
Eindhoven University of Technology.
Large time behavior of solutions to a moving-interface problem modeling concrete carbonation2010Inngår i: Communications on Pure and Applied Analysis, ISSN 1534-0392, E-ISSN 1553-5258, Vol. 9, nr 5, s. 1117-1129Artikkel i tidsskrift (Fagfellevurdert)
• 10.
Tokyo Womens University.
Netherlands.
Large-time asymptotics of moving-reaction interfaces involving nonlinear Henry’s law and time-dependent Dirichlet data2013Inngår i: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 93, s. 3-14Artikkel i tidsskrift (Fagfellevurdert)

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.

• 11. Aiki, Toyohiko
Eindhoven University of Technology.
Large-time behavior of a two-scale semilinear reaction-diffusion system for concrete sulfatation2014Inngår i: Mathematical methods in the applied sciences, ISSN 0170-4214, E-ISSN 1099-1476, Vol. 38, nr 7, s. 1451-1464Artikkel i tidsskrift (Fagfellevurdert)
• 12.
Japan.
Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap (from 2013).
Large-time behavior of solutions to a thermo-diffusion system with Smoluchowski interactions2017Inngår i: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 5, nr 5, s. 3009-3026Artikkel i tidsskrift (Fagfellevurdert)

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.

• 13.
Gifu University, Japan.
Eindhoven University of Technology.
On uniqueness of a weak solution of one-dimensional concrete carbonation problem2011Inngår i: Discrete and Continuous Dynamical Systems, ISSN 1078-0947, E-ISSN 1553-5231, Vol. 29, nr 4, s. 1345-1365Artikkel i tidsskrift (Fagfellevurdert)

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.

• 14.
Università di Roma La Sapienza.
Università di Roma La Sapienza. Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap. Eindhoven University of Technology.
Weak solutions to Allen-Cahn-like equations modelling consolidation of porous media2017Inngår i: IMA Journal of Applied Mathematics, ISSN 0272-4960, E-ISSN 1464-3634, Vol. 82, nr 1, s. 224-250Artikkel i tidsskrift (Fagfellevurdert)

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.

• 15.
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 soil2014Inngår i: Applied Mathematical Modelling, ISSN 0307-904X, E-ISSN 1872-8480, Vol. 38, nr 9-10, s. 2463-2475Artikkel i tidsskrift (Fagfellevurdert)

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.

• 16.
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 model2012Inngår i: Multiscale Mathematics: Hierarchy of Collective Phenomena and Interrelations between Hierarchical Structures, Kyushu University, Japan , 2012, Vol. 39, s. 22-31Konferansepaper (Fagfellevurdert)

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.

• 17.
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 convergence2012Inngår i: Japan journal of industrial and applied mathematics, ISSN 0916-7005, E-ISSN 1868-937X, Vol. 29, nr 2, s. 289-316Artikkel i tidsskrift (Fagfellevurdert)
• 18.
Sapienza Univ Roma, Dipartimento Sci Base & Applicate Ingn, Rome, Italy.
Sapienza Univ Roma, Dipartimento Sci Base & Applicate Ingn, Rome, Italy. Babes Bolyai Univ, Dept Psychol, Cluj, Romania Open Univ Netherlands, Dept Org, Heerlen, Netherlands. Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap (from 2013).
Free to move or trapped in your group: Mathematical modeling of information overload and coordination in crowded populations2018Inngår i: Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, Vol. 28, nr 9, s. 1831-1856Artikkel i tidsskrift (Fagfellevurdert)

We present modeling strategies that describe the motion and interaction of groups of pedestrians in obscured spaces. We start off with an approach based on balance equations in terms of measures and then we exploit the descriptive power of a probabilistic cellular automaton model. Based on a variation of the simple symmetric random walk on the square lattice, we test the interplay between population size and an interpersonal attraction parameter for the evacuation of confined and darkened spaces. We argue that information overload and coordination costs associated with information processing in small groups are two key processes that influence the evacuation rate. Our results show that substantial computational resources are necessary to compensate for incomplete information - the more individuals in (information processing) groups the higher the exit rate for low population size. For simple social systems, it is likely that the individual representations are not redundant and large group sizes ensure that this non-redundant information is actually available to a substantial number of individuals. For complex social systems, information redundancy makes information evaluation and transfer inefficient and, as such, group size becomes a drawback rather than a benefit. The effect of group sizes on outgoing fluxes, evacuation times and wall effects is carefully studied with a Monte Carlo framework accounting also for the presence of an internal obstacle.

• 19.
Sapienza University, Italy.
University of L’Aquila, Italy. Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap (from 2013). Gran Sasso Science Institute, Italy.
A lattice model for active–passive pedestrian dynamics: a quest for drafting effects2020Inngår i: Mathematical Biosciences and Engineering, ISSN 1547-1063, E-ISSN 1551-0018, Vol. 17, nr 1, s. 460-477Artikkel i tidsskrift (Fagfellevurdert)

We study the pedestrian escape from an obscure room using a lattice gas model with twospecies of particles. One species, called passive, performs a symmetric random walk on the lattice,whereas the second species, called active, is subject to a drift guiding the particles towards the exit.The drift mimics the awareness of some pedestrians of the geometry of the room and of the location ofthe exit. We provide numerical evidence that, in spite of the hard core interaction between particles –namely, there can be at most one particle of any species per site – adding a fraction of active particlesin the system enhances the evacuation rate of all particles from the room. A similar effect is alsoobserved when looking at the outgoing particle flux, when the system is in contact with an externalparticle reservoir that induces the onset of a steady state. We interpret this phenomenon as a discretespace counterpart of the drafting effect typically observed in a continuum set–up as the aerodynamicdrag experienced by pelotons of competing cyclists.

• 20.
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. Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap (from 2013). Eindhoven Univ Technol, Fac Chem Engn, ICMS, POB 513, NL-5600 MB Eindhoven, Netherlands.
Lattice model of reduced jamming by a barrier2016Inngår i: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 94, nr 4, artikkel-id 042115Artikkel i tidsskrift (Fagfellevurdert)
• 21. Cirillo, Emilio
Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap (from 2013).
Particle-based modeling of flow through obstacles2019Inngår i: Complexity science: An introduction / [ed] Mark A. Peletier, Rutger A. van Santen, World Scientific, 2019Kapittel i bok, del av antologi (Fagfellevurdert)

Particle diffusion is modified by the presence of barriers. In cells macro-molecules, behaving as obstacles, slow down the dynamics so that the mean-square displacement of molecules grows with time as a power law with exponent smaller than one. In different situations, such as grain and pedestrian dynamics, it can happen that an obstacle can accelerate the dynamics. In the framework of very basic models, we study the time needed by particles to cross a strip for different bulk dynamics and discuss the effect of obstacles. We find that in some regimes such a residence time is not monotonic with respect to the size and the position of the obstacles. We can then conclude that, even in very elementary systems where no interaction among particles is considered, obstacles can either slow down or accelerate the particle dynamics depending on their geometry and position.

• 22.
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. Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap (from 2013).
Blockage-induced condensation controlled by a local reaction2016Inngår i: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 94, nr 4Artikkel i tidsskrift (Fagfellevurdert)

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.

• 23.
Sapienza Universit`a di Roma.
Eindhoven University of Technology.
Can cooperation slow down emergency evacuations?2012Inngår i: Comptes rendus. Mecanique, ISSN 1631-0721, E-ISSN 1873-7234, Vol. 340, nr 9, s. 625-628Artikkel i tidsskrift (Fagfellevurdert)

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.

• 24.
Sapienza Universit`a di Roma, Italy.
Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för ingenjörsvetenskap och fysik (from 2013). Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap (from 2013). Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för ingenjörsvetenskap och fysik (from 2013). Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för ingenjörs- och kemivetenskaper (from 2013).
A lattice model approach to the morphology formation from ternary mixtures during the evaporation of one component2019Inngår i: The European Physical Journal Special Topics, ISSN 1951-6355, E-ISSN 1951-6401, Vol. 228, nr 1, s. 55-68Artikkel i tidsskrift (Fagfellevurdert)

Stimulated by experimental evidence in the field of solution-born thin films, we study the morphology formation in a three state lattice system subjected to the evaporation of one component. The practical problem that we address is the understanding of the parameters that govern morphology formation from a ternary mixture upon evaporation, as is the case in the fabrication of thin films from solution for organic photovoltaics. We use, as a tool, a generalized version of the Potts and Blume-Capel models in 2D, with the Monte Carlo Kawasaki-Metropolis algorithm, to simulate the phase behaviour of a ternary mixture upon evaporation of one of its components. The components with spin 1, −1 and 0 in the Blume-Capel dynamics correspond to the electron-acceptor, electron-donor and solvent molecules, respectively, in a ternary mixture used in the preparation of the active layer films in an organic solar cell. Furthermore, we introduce parameters that account for the relative composition of the mixture, temperature, and interaction between the species in the system. We identify the parameter regions that are prone to facilitate the phase separation. Furthermore, we study qualitatively the types of formed configurations. We show that even a relatively simple model, as the present one, can generate key morphological features, similar to those observed in experiments, which proves the method valuable for the study of complex systems.

• 25.
Università di Roma “La Sapienza”.
Gran Sasso Science Institute. Eindhoven University of Technology.
Does communication enhance pedestrians transport in the dark?2016Inngår i: Comptes rendus. Mecanique, ISSN 1631-0721, E-ISSN 1873-7234, Vol. 344, nr 1, s. 19-23Artikkel i tidsskrift (Fagfellevurdert)

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.

• 26.
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 approach2016Inngår i: Multiscale Modeling & simulation, ISSN 1540-3459, E-ISSN 1540-3467, Vol. 14, nr 2, s. 906-922Artikkel i tidsskrift (Fagfellevurdert)

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

• 27. Cirillo, Emilio N.M.
Eindhoven University of Technology.
Dynamics of pedestrians in regions with no visibility: A lattice model without exclusion2013Inngår i: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, Vol. 392, nr 17, s. 3578-3588Artikkel i tidsskrift (Fagfellevurdert)

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.

• 28. Cirillo, E,N.M
Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap.
Stationary currents in particle systems with constrained hopping rates2016Inngår i: Journal of Non-Equilibrium Thermodynamics, ISSN 0340-0204, E-ISSN 1437-4358, Vol. 41, nr 2, s. 99-106Artikkel i tidsskrift (Fagfellevurdert)
• 29.
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. Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap (from 2013).
Trapping in bottlenecks: Interplay between microscopic dynamics and large scale effects2017Inngår i: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 488, nr 11, s. 30-38Artikkel i tidsskrift (Fagfellevurdert)

We investigate the appearance of trapping states in pedestrian flows through bottlenecks as a result of the interplay between the geometry of the system and the microscopic stochastic dynamics. We model the flow through a bottleneck via a Zero Range Process on a one-dimensional periodic lattice. Particle are removed from the lattice sites with rates proportional to the local occupation numbers. The bottleneck is modeled by a particular site of the lattice whose updating rate saturates to a constant value as soon as the local occupation number exceeds a fixed threshold. We show that for any finite value of the threshold the stationary particle current saturates to the limiting bottleneck rate when the total particle density in the system exceeds a critical value corresponding to the bottleneck rate itself.

• 30.
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 strips2015Inngår i: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 442, s. 436-457Artikkel i tidsskrift (Fagfellevurdert)
• 31.
LAquila, Italy.
Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap (from 2013). Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap (from 2013). LAquila, Italy.
Modelling interactions between active and passive agents moving through heterogeneous environments2018Inngår i: Crowd Dynamics: volume 1 / [ed] Livio Gibelli, Nicola Bellomo, Basel: Springer , 2018, s. 211-257Kapittel i bok, del av antologi (Fagfellevurdert)

We study the dynamics of interacting agents from two distinct intermixed populations: one population includes active agents that follow a predetermined velocity field, while the second population contains exclusively passive agents, i.e., agents that have no preferred direction of motion. The orientation of their local velocity is affected by repulsive interactions with the neighboring agents and environment. We present two models that allow for a qualitative analysis of these mixed systems. We show that the residence times of this type of systems containing mixed populations is strongly affected by the interplay between these two populations. After showing our modelling and simulation results, we conclude with a couple of mathematical aspects concerning the well-posedness of our models.

• 32.
L.Aquila Italy.
Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap (from 2013). Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap (from 2013). L.Aquila Italy.
Modelling interactions between active and passive agents moving through heterogeneous environments2019Inngår i: Crowd Dynamics: Vol. 1: Theory, Models and Safety Problems / [ed] G. Libelli, N. Bellomo, Birkhäuser Verlag, 2019, s. 211-254Kapittel i bok, del av antologi (Fagfellevurdert)
• 33.
Eindhoven University of Technology.
California State University Long Beach. University of Rome Tor Vergata. Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap (from 2013). Eindhoven University of Technology.
Fluctuations around mean walking behaviors in diluted pedestrian flows2017Inngår i: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 95, nr 3Artikkel i tidsskrift (Fagfellevurdert)

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.

• 34.
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 method2015Inngår i: Mathematical Biosciences and Engineering, ISSN 1547-1063, E-ISSN 1551-0018, Vol. 12, nr 2, s. 337-356Artikkel i tidsskrift (Fagfellevurdert)

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.

• 35.
Tilburg University; Cognitrom.
Eindhoven University of Technology . Eindhoven University of Technology . Eindhoven University of Technology.
Cognitive distance, absorptive capacity and group rationality: A simulation study2014Inngår i: PLoS ONE, ISSN 1932-6203, E-ISSN 1932-6203, Vol. 9, nr 10Artikkel i tidsskrift (Fagfellevurdert)

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.

• 36.
Universitá Giustino Fortunato, Italy .
Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap (from 2013).
Existence of weak solutions to a nonlinear reaction-diffusion system with singular sources2017Inngår i: Electronic Journal of Differential Equations, ISSN 1550-6150, E-ISSN 1072-6691, Vol. 2017, nr 202, s. 1-16Artikkel i tidsskrift (Fagfellevurdert)

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.

• 37.
University of Warwick, UK.
Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap (from 2013). Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap (from 2013).
Discrete and continuum links to a nonlinear coupled transport problem of interacting populations2017Inngår i: The European Physical Journal Special Topics, ISSN 1951-6355, E-ISSN 1951-6401, Vol. 226, nr 10, s. 2345-2357Artikkel i tidsskrift (Fagfellevurdert)

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.

• 38.
University of Bremen, Germany.
Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap (from 2013).
Corrector estimates for the homogenization of a two-scale thermoelasticity problem with a priori known phase transformations2017Inngår i: Electronic Journal of Differential Equations, ISSN 1550-6150, E-ISSN 1072-6691, nr 57, s. 1-21Artikkel i tidsskrift (Fagfellevurdert)

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.

• 39.
University of Bremen.
Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap (from 2013).
Homogenization of a fully coupled thermoelasticity problem for a highly heterogeneous medium with a priori known phase transformations2017Inngår i: Mathematical methods in the applied sciences, ISSN 0170-4214, E-ISSN 1099-1476, Vol. 40, nr 11, s. 3955-3972Artikkel i tidsskrift (Fagfellevurdert)

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.

• 40.
University of Bergen, Norway.
Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap (from 2013). University of Bergen, Norway. Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap (from 2013). University of Hasselt, Belgium. University of Bergen, Norway. University of Bergen, Norway.
A pore-scale study of transport of inertial particles by water in porous media2019Inngår i: Chemical Engineering Science, ISSN 0009-2509, E-ISSN 1873-4405, Vol. 207, s. 397-409Artikkel i tidsskrift (Fagfellevurdert)

We study the transport of inertial particles in water flow in porous media. Our interest lies in understanding the accumulation of particles including the possibility of clogging. We propose that accumulation can be a result of hydrodynamic effects: the tortuous paths of the porous medium generate regions of dominating strain, which favour the accumulation of particles. Numerical simulations show that essentially two accumulation regimes are identified: for low and for high flow velocities. When particles accumulate at the entrance of a pore throat (high-velocity region), a clog is formed. This significantly modifies the flow, as the partial blockage of the pore causes a local redistribution of pressure, which diverts the upstream water flow into neighbouring pores. Moreover, we show that accumulation in high velocity regions occurs in heterogeneous media, but not in homogeneous media, where we refer to homogeneity with respect to the distribution of the pore throat diameters.

• 41.
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 approximation2012Inngår i: Multiscale Modeling & simulation, ISSN 1540-3459, E-ISSN 1540-3467, Vol. 10, nr 3, s. 874-905Artikkel i tidsskrift (Fagfellevurdert)
• 42.
Simon Fraser University, Canada; Dalhousie University, Canada; Eindhoven University of Technology, Netherlands.
Leiden University, Netherlands. Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap (from 2013).
Measure-valued mass evolution problems with flux boundary conditions and solution-dependent velocities2016Inngår i: SIAM Journal on Mathematical Analysis, ISSN 0036-1410, E-ISSN 1095-7154, Vol. 48, nr 3, s. 1929-1953Artikkel i tidsskrift (Fagfellevurdert)

In this paper we prove well-posedness for a measure-valued continuity equation with solution-dependent velocity and flux boundary conditions, posed on a bounded one-dimensional domain. We generalize the results of an earlier paper [J. Differential Equations, 259 (2015), pp. 10681097] to settings where the dynamics are driven by interactions. In a forward-Euler-like approach, we construct a time-discretized version of the original problem and employ those results as a building block within each subinterval. A limit solution is obtained as the mesh size of the time discretization goes to zero. Moreover, the limit is independent of the specific way of partitioning the time interval [0, T]. This paper is partially based on results presented in Chapter 5 of [Evolution Equations for Systems Governed by Social Interactions, Ph.D. thesis, Eindhoven University of Technology, 2015], while a number of issues that were still open there are now resolved.

• 43.
Eindhoven University of Technology.
Leiden University. Eindhoven University of Technology.
Modelling with measures: Approximation of a mass-emitting object by a point source2015Inngår i: Mathematical Biosciences and Engineering, ISSN 1547-1063, E-ISSN 1551-0018, Mathematical Biosciences and Engineering, Vol. 12, nr 2, s. 357-373Artikkel i tidsskrift (Fagfellevurdert)
• 44.
Eindoven University of Technology.
Eindoven University of Technology.
Modeling micro-macro pedestrian counter flow in heterogeneous domains2011Inngår i: Nonlinear Phenomena in Complex Systems, ISSN 1561-4085, E-ISSN 1817-2458, Vol. 14, nr 1, s. 27-37Artikkel i tidsskrift (Fagfellevurdert)

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.

• 45.
Netherlands.
Netherlands. Eindhoven University of Technology, The Netherlands.
Well-posedness and approximation of a measure-valued mass evolution problem with flux boundary conditions2014Inngår i: Comptes rendus. Mathematique, ISSN 1631-073X, E-ISSN 1778-3569, Vol. 352, nr 1, s. 51-54Artikkel i tidsskrift (Fagfellevurdert)

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.

• 46.
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 conditions2015Inngår i: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 259, nr 3, s. 1068-1097Artikkel i tidsskrift (Fagfellevurdert)

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.

• 47.
Eindhoven University of Technology.
Eindhoven University of Technology. Eindhoven University of Technology.
Crowds reaching targets by maximizing entropy: A Clausius-Duhem inequality approach2013Inngår i: Elsevier IFAC Publications / IFAC Proceedings series, ISSN 1474-6670, Vol. 46, nr 26, s. 263-268Artikkel i tidsskrift (Fagfellevurdert)

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.

• 48.
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 layers2014Inngår i: Networks and Heterogeneous Media, ISSN 1556-1801, E-ISSN 1556-181X, Vol. 9, nr 4, s. 709-737Artikkel i tidsskrift (Fagfellevurdert)

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.

• 49. Fatima, Tasnim
Technical University Eindhoven.
Sulfate attack in sewer pipes: Derivation of a concrete corrosion model via two-scale convergence2014Inngår i: Nonlinear Analysis, ISSN 1468-1218, Vol. 15, nr 1, s. 326-344Artikkel i tidsskrift (Fagfellevurdert)

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.

• 50.
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 study2012Inngår i: Advances in Mathematical Sciences and Applications, ISSN 1343-4373, Vol. 22, s. 295-318Artikkel i tidsskrift (Fagfellevurdert)
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