Carbonation caused by atmospheric carbon dioxide is one of the major physicochemical processes which can compromise the service life of reinforced concrete structures. While the bulk of the carbonation reaction is that of calcium hydroxide, other constituents of the porous matrix can also carbonate and compete with calcium hydroxide for carbon dioxide. Particularly the carbonation of calcium-silicate hydrates and unhydrated constituents are neglected by most authors in carbonation prediction models. In this paper, a mathematical model of carbonation is extended to include additional carbonation and hydration reactions. The competition of the several reactions and their effect on the carbonation depth is investigated by dimensional analysis and numerical simulations. A parameter study emphasises that multiple internal reaction layers appear. Their position and speed essentially depend on the strength of the different reactions. It is also observed that, for a wide range of parameters, the effect of some of the additional reactions on the carbonation depth is small. In particular, a comparison with data from laboratory experiments justifies the neglect of the carbonation of the unhydrated constituents in prediction models. (M. A. Peter), a.muntean@tue.nl (A. Muntean), sebam@math.uni-bremen.de (S. A. Meier), mbohm@math.unibremen.de (M. Böhm).

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.

Understanding and modeling the dynamics of pedestrian crowds can help with designing and increasing the safety of civil facilities. A key feature of crowds is its intrinsic stochasticity, appearing even under very diluted conditions, due to the variability in individual behaviours. Individual stochasticity becomes even more important under densely crowded conditions, since it can be nonlinearly magnified and may lead to potentially dangerous collective behaviours. 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 year-long 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 TM 3D-range sensor and automatic headtracking algorithms. The temporal homogeneity of our large database of trajectories allows us to robustly define and separate average walking behaviours 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 direction. 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 novel model for the dynamics of undisturbed pedestrians, based on stochastic differential equations, that provides a good agreement with our experimental observations, including the occurrence of rare events.

Understanding the complex behavior of pedestrians walking in crowds is a challenge for both science and technology. In particular, obtaining reliable models for crowd dynamics, capable of exhibiting qualitatively and quantitatively the observed emergent features of pedestrian flows, may have a remarkable impact for matters as security, comfort and structural serviceability. Aiming at a quantitative understanding of basic aspects of pedestrian dynamics, extensive and high-accuracy measurements of pedestrian trajectories have been performed. More than 100.000 reallife, time-resolved trajectories of people walking along a trafficked corridor in a building of the Eindhoven University of Technology, The Netherlands, have been recorded. A measurement strategy based on Microsoft Kinect TM has been used; the trajectories of pedestrians have been analyzed as ensemble data. The main result consists of a statistical descriptions of

Carbonation is the reaction of environmental carbon dioxide with alkaline species in concrete. It is one of the major degradation mechanisms affecting the durability of reinforced concrete structures. In this paper, a mathematical model of the carbonation process is formulated and simulated using the finite-element method. Nonlinear reaction rates, Robin boundary conditions and a decrease of the concrete porosity in time are taken into account. A dimensional analysis based on a nondimensionalisation of the entire model is introduced to identify the key parameters and the different characteristic time and length scales of the whole process. Numerical simulations show the occurrence of an internal reaction layer travelling through the material. The speed and the width of the layer are rigorously defined via dimensionless quantities. A parameter study shows that the speed and the width are strongly related to the size of the Thiele modulus which is typically large. The relevance of other parameters is also investigated. The model is validated for accelerated and natural carbonation settings.