| 1. |
- Cirillo, Emilio N.M., et al.
(författare)
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A lattice model approach to the morphology formation from ternary mixtures during the evaporation of one component
- 2019
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Ingår i: The European Physical Journal Special Topics. - : Springer. - 1951-6355 .- 1951-6401. ; 228:1, s. 55-68
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 2. |
- Ackelh, A.S., et al.
(författare)
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Preface to "modeling with measures"
- 2015
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Ingår i: Mathematical Biosciences and Engineering. - : American Institute of Mathematical Sciences (AIMS). - 1547-1063 .- 1551-0018. ; 12:2
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Tidskriftsartikel (refereegranskat)
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| 3. |
- Ackleh, Azmy S., et al.
(författare)
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Mathematical modeling with measures
- 2019
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Ingår i: Nieuw Archief voor Wiskunde. - Leiden : Koninklijk Wiskundig Genootschap. - 0028-9825. ; 20:September, s. 218-220
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Tidskriftsartikel (refereegranskat)
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| 4. |
- Aiki, Toyohiko, et al.
(författare)
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Large-time behavior of solutions to a thermo-diffusion system with Smoluchowski interactions
- 2017
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Ingår i: Journal of Differential Equations. - : Elsevier. - 0022-0396 .- 1090-2732. ; 5:5, s. 3009-3026
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 5. |
- Artale Harris, Pietro, et al.
(författare)
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Weak solutions to Allen-Cahn-like equations modelling consolidation of porous media
- 2017
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Ingår i: IMA Journal of Applied Mathematics. - : Oxford University Press. - 0272-4960 .- 1464-3634. ; 82:1, s. 224-250
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 6. |
- Ciallellla, Alessandro, et al.
(författare)
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Free to move or trapped in your group : Mathematical modeling of information overload and coordination in crowded populations
- 2018
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Ingår i: Mathematical Models and Methods in Applied Sciences. - Singapore : World Scientific. - 0218-2025. ; 28:9, s. 1831-1856
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 7. |
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| 8. |
- Cirillo, Emilio N. M., et al.
(författare)
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Blockage-induced condensation controlled by a local reaction
- 2016
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Ingår i: Physical review. E. - 2470-0045 .- 2470-0053. ; 94:4
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 9. |
- Cirillo, Emilio N.M., et al.
(författare)
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Does communication enhance pedestrians transport in the dark?
- 2016
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Ingår i: Comptes rendus. Mecanique. - : Elsevier. - 1631-0721 .- 1873-7234. ; 344:1, s. 19-23
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 10. |
- Cirillo, Emilio N.M., et al.
(författare)
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Effects of communication efficiency and exit capacity on fundamental diagrams for pedestrian motion in an obscure tunnel : a particle system approach
- 2016
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Ingår i: Multiscale Modeling & simulation. - : Siam publications. - 1540-3459 .- 1540-3467. ; 14:2, s. 906-922
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Tidskriftsartikel (refereegranskat)abstract
- 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
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| 11. |
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| 12. |
- Cirillo, E.N.M., et al.
(författare)
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Trapping in bottlenecks : Interplay between microscopic dynamics and large scale effects
- 2017
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Ingår i: Physica A. - : Elsevier. - 0378-4371 .- 1873-2119. ; 488:11, s. 30-38
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 13. |
- Cirillo, Emilio, et al.
(författare)
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Particle-based modeling of flow through obstacles
- 2019
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Ingår i: Complexity science. - : World Scientific. - 9789813239593 - 9789813239616
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Bokkapitel (refereegranskat)abstract
- 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.
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| 14. |
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| 15. |
- Corbetta, Alessandro, et al.
(författare)
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Fluctuations around mean walking behaviors in diluted pedestrian flows
- 2017
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Ingår i: Physical review. E. - : American Physical Society. - 2470-0045 .- 2470-0053. ; 95:3
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 16. |
- Corbetta, Alessandro, et al.
(författare)
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Parameter estimation of social forces in pedestrian dynamics models via a probabilistic method
- 2015
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Ingår i: Mathematical Biosciences and Engineering. - : American Institute of Mathematical Sciences. - 1547-1063 .- 1551-0018. ; 12:2, s. 337-356
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 17. |
- de Bonis, Ida, et al.
(författare)
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Existence of weak solutions to a nonlinear reaction-diffusion system with singular sources
- 2017
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Ingår i: Electronic Journal of Differential Equations. - San Marcos : Texas State University. - 1550-6150 .- 1072-6691. ; 2017:202, s. 1-16
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 18. |
- Duong, M. H., et al.
(författare)
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Discrete and continuum links to a nonlinear coupled transport problem of interacting populations
- 2017
-
Ingår i: The European Physical Journal Special Topics. - : Springer. - 1951-6355 .- 1951-6401. ; 226:10, s. 2345-2357
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 19. |
- Eden, Michael, 1987-, et al.
(författare)
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Corrector estimates for the homogenization of a two-scale thermoelasticity problem with a priori known phase transformations
- 2017
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Ingår i: Electronic Journal of Differential Equations. - : TEXAS STATE UNIVERSITY, USA. - 1550-6150 .- 1072-6691. ; :57, s. 1-21
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 20. |
- Eden, Michael, 1987-, et al.
(författare)
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Homogenization of a fully coupled thermoelasticity problem for a highly heterogeneous medium with a priori known phase transformations
- 2017
-
Ingår i: Mathematical methods in the applied sciences. - : John Wiley & Sons. - 0170-4214 .- 1099-1476. ; 40:11, s. 3955-3972
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 21. |
- Endo Kokubun, M. A., et al.
(författare)
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A pore-scale study of transport of inertial particles by water in porous media
- 2019
-
Ingår i: Chemical Engineering Science. - : Elsevier. - 0009-2509 .- 1873-4405. ; 207, s. 397-409
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 22. |
- Evers, J. H. M., et al.
(författare)
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Measure-valued mass evolution problems with flux boundary conditions and solution-dependent velocities
- 2016
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Ingår i: SIAM Journal on Mathematical Analysis. - : SIAM Publications. - 0036-1410 .- 1095-7154. ; 48:3, s. 1929-1953
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 23. |
- Evers, Joep H.M., et al.
(författare)
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Mild solutions to a measure-valued mass evolution problem with flux boundary conditions
- 2015
-
Ingår i: Journal of Differential Equations. - : Elsevier. - 0022-0396 .- 1090-2732. ; 259:3, s. 1068-1097
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 24. |
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| 25. |
- Gruetzner, Simon, et al.
(författare)
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Brief Introduction to Damage Mechanics and its Relation to Deformations
- 2018
-
Ingår i: Mathematical Analysis of Continuum Mechanics and Industrial Applications II. - : Springer. - 9789811062834 ; , s. 115-124
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Konferensbidrag (refereegranskat)abstract
- We discuss some principle concepts of damage mechanics and outline a possibility to address the open question of the damage-to-deformation relation by suggesting a parameter identification setting. To this end, we introduce a variable motivated by the physical damage phenomenon and comment on its accessibility through measurements. We give an extensive survey on analytic results and present an isotropic irreversible partial damage model in a dynamic mechanical setting in form of a second order hyperbolic equation coupled with an ordinary differential equation for the damage evolution. We end with a note on a possible parameter identification setting.
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| 26. |
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| 27. |
- Ijioma, Ekeoma R., et al.
(författare)
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Fast Drift Effects In The Averaging Of A Filtration Combustion System : A Periodic Homogenization Approach
- 2019
-
Ingår i: Quarterly of Applied Mathematics. - : Brown University Boston. - 0033-569X .- 1552-4485. ; 77:1, s. 71-104
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Tidskriftsartikel (refereegranskat)abstract
- We target the periodic homogenization of a semi-linear reaction-diffusion-convection system describing filtration combustion, where fast drifts are triggered by the competition between heat and mass transfer processes in an asymptotic regime of dominant convection. In addition, we consider the interplay between surface nonlinear chemical reactions and transport processes. To handle the oscillations occurring due to the heterogeneity of the medium, we rely on the concept of two-scale convergence with drift to obtain, for suitably scaled model parameters, the upscaled system of equations together with effective transport parameters. The main difficulty is to treat the case of a coupled multi-physics problem. We proceed by extending the results reported by G. Allaire et al. and other related papers in this context to the case of a coupled system of evolution equations pertinent to filtration combustion.
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| 28. |
- Kimura, Masato, et al.
(författare)
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Analysis of a projection method for the Stokes problem using an ε-Stokes approach
- 2019
-
Ingår i: Japan journal of industrial and applied mathematics. - : Springer. - 0916-7005 .- 1868-937X. ; 36:3, s. 959-985
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Tidskriftsartikel (refereegranskat)abstract
- We generalize pressure boundary conditions of an ε-Stokes problem. Our ε-Stokes problem connects the classical Stokes problem and the corresponding pressure-Poisson equation using one parameter ε>0. For the Dirichlet boundary condition, it is proven in Matsui and Muntean (Adv Math Sci Appl, 27:181–191,2018) that the solution for the ε-Stokes problem converges to the one for the Stokes problem as ε tends to 0, and to the one for the pressure-Poisson problem as εtends to ∞. Here, we extend these results to the Neumann and mixed boundary conditions. We also establis herror estimates in suitable norms between the solutions to the ε-Stokes problem, the pressure-Poisson problem and the Stokes problem, respectively. Several numerical examples are provided to show that several such error estimates are optimal in ε. Our error estimates are improved if one uses the Neumann boundary conditions. In addition, we show that the solution to the ε-Stokes problem has a nice asymptotic structure.
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| 29. |
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| 30. |
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| 31. |
- Kruschwitz, Jens, et al.
(författare)
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Modelling, simulation and parameter identification of active pollution reduction with photocatalytic asphalt
- 2019
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Ingår i: Acta Polytechnica. - Prague : Czech Technical University in Prague. - 1210-2709 .- 1805-2363. ; 59:1, s. 51-58
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Tidskriftsartikel (refereegranskat)abstract
- We develop and implement a numerical model to simulate the effect of photocatalytic asphalt on reducing the concentration of nitrogen monoxide (NO) due to the presence of heavy traffic in an urban environment. The contributions in this paper are threefold: we model and simulate the spread and breakdown of pollution in an urban environment, we provide a parameter estimation process that can be used to find missing parameters, and finally, we train and compare this simulation with different data sets. We analyse the results and provide an outlook on further research.
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| 32. |
- Kumazaki, Kota, et al.
(författare)
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Local weak solvability of a moving boundary problem describing swelling along a halfline
- 2019
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Ingår i: Networks and Heterogeneous Media. - : American Institute of Mathematical Sciences. - 1556-1801 .- 1556-181X. ; 14:3, s. 445-469
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Tidskriftsartikel (refereegranskat)abstract
- We obtain the local well-posedness of a moving boundary problem that describes the swelling of a pocket of water within an infinitely thin elongated pore (i.e. on [a, +∞), a > 0). Our result involves fine a priori estimates of the moving boundary evolution, Banach fixed point arguments as well as an application of the general theory of evolution equations governed by subdifferentials.
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| 33. |
- Lind, Martin, 1985-, et al.
(författare)
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A Priori Feedback Estimates for Multiscale Reaction-Diffusion Systems
- 2018
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Ingår i: Numerical Functional Analysis and Optimization. - : Taylor & Francis. - 0163-0563 .- 1532-2467. ; 39:4, s. 413-437
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Tidskriftsartikel (refereegranskat)abstract
- We study the approximation of a multiscale reaction–diusion system posed on both macroscopic and microscopic space scales. The coupling between the scales is done through micro– macro ux conditions. Our target system has a typical structure for reaction–diusion ow problems in media with distributed microstructures (also called, double porosity materials). Besides ensuring basic estimates for the convergence of two-scale semidiscrete Galerkin approximations, we provide a set of a priori feedback estimates and a local feedback error estimator that help in designing a distributed-high-errors strategy to allow for a computationally ecient zooming in and out from microscopic structures. The error control on the feedback estimates relies on two-scale-energy, regularity, and interpolation estimates as well as on a ne bookeeping of the sources responsible with the propagation of the (multiscale) approximation errors. The working technique based on a priori feedback estimates is in principle applicable to a large class of systems of PDEs with dual structure admitting strong solutions. A
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| 34. |
- Lind, Martin, 1985-, et al.
(författare)
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Well-posedness and inverse Robin estimate for a multiscale elliptic/parabolic system
- 2018
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Ingår i: Applicable Analysis. - : Taylor & Francis. - 0003-6811 .- 1563-504X. ; 97:1, s. 89-106
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Tidskriftsartikel (refereegranskat)abstract
- We establish the well-posedness of a coupled micro–macro parabolic– elliptic system modeling the interplay between two pressures in a gas–liquid mixture close to equilibrium that is filling a porous media with distributed microstructures. Additionally, we prove a local stability estimate for the inverse micro–macro Robin problem, potentially useful in identifying quantitatively a micro–macro interfacial Robin transfer coefficient given microscopic measurements on accessible fixed interfaces. To tackle the solvability issue we use two-scale energy estimates and twoscale regularity/compactness arguments cast in the Schauder’s fixed point theorem. A number of auxiliary problems, regularity, and scaling arguments are used in ensuring the suitable Fréchet differentiability of the solution and the structure of the inverse stability estimate.
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| 35. |
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| 36. |
- Matsui, Kazunori, et al.
(författare)
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Asymptotic analysis of an ε-Stokes problem connecting Stokes and pressure-Poisson problems
- 2018
-
Ingår i: Advances in Mathematical Sciences and Applications. - Tokyo, Japan : Gakkotosho. - 1343-4373. ; 27:1, s. 181-191
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Tidskriftsartikel (refereegranskat)abstract
- In this Note, we prepare an ε-Stokes problem connecting the Stokes problem and the corresponding pressure-Poisson equation using one parameter ε > 0. We prove that the solution to the ε-Stokes problem, convergences as ε tends to 0 or ∞ to the Stokes and pressure-Poisson problem, respectively.
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| 37. |
- Muntean, Adrian, 1974-, et al.
(författare)
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Asymptotics of diffusion-limited fast reactions
- 2018
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Ingår i: Quarterly of Applied Mathematics. - : American Mathematical Society (AMS). - 0033-569X .- 1552-4485. ; 76, s. 199-213
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Tidskriftsartikel (refereegranskat)abstract
- We are concerned with the fast-reaction asymptotics λ → ∞ for a semi-linear coupled diffusion-limited reaction system in contact with infinite reservoirs of reactants. We derive the system of limit equations and prove the uniqueness of its solutions for equal diffusion coefficients. Additionally, we emphasize the structure of the limit free boundary problem. The key tools of our analysis include (uniform with respect to λ) L 1 -estimates for both fluxes and products of reaction and a balanced formulation, where combinations of the original components which balance the fast reaction are used.
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| 38. |
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| 39. |
- Muntean, Adrian, 1974-, et al.
(författare)
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Corrector estimates for a thermo-diffusion model with weak thermal coupling
- 2016
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- The present work deals with the derivation of corrector estimates for the two-scale homogenization of a thermo-diffusion model with weak thermal coupling posed in a heterogeneous medium endowed with periodically arranged high-contrast microstructures. The terminology “weak thermal coupling” refers here to the variable scaling in terms of the small homogenization parameter ε of the heat conductiondiffusion interaction terms, while the “high-contrast” is thought particularly in terms of the heat conduction properties of the composite material. As main target, we justify the first-order terms of the multiscale asymptotic expansions in the presence of coupled fluxes, induced by the joint contribution of Sorret and Dufour-like effects. The contrasting heat conduction combined with cross coupling lead to the main mathematical difficulty in the system. Our approach relies on the method of periodic unfolding combined with ε-independent estimates for the thermal and concentration fields and for their coupled fluxes.
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| 40. |
- Muntean, Adrian, 1974-, et al.
(författare)
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Corrector estimates for a thermo-diffusion model with weak thermal coupling
- 2018
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Ingår i: Multiscale Modeling & simulation. - : Society for Industrial and Applied Mathematics. - 1540-3459 .- 1540-3467. ; 16:2, s. 807-832
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Tidskriftsartikel (refereegranskat)abstract
- The present work deals with the derivation of corrector estimates for the two-scale homogenization of a thermodiffusion model with weak thermal coupling posed in a heterogeneous medium endowed with periodically arranged high-contrast microstructures. The term “weak thermal coupling” refers here to the variable scaling in terms of the small homogenization parameter $\varepsilon$ of the heat conduction-diffusion interaction terms, while the “high-contrast” is considered particularly in terms of the heat conduction properties of the composite material. As a main target, we justify the first-order terms of the multiscale asymptotic expansions in the presence of coupled fluxes, induced by the joint contribution of Sorret and Dufour-like effects. The contrasting heat conduction combined with cross coupling leads to the main mathematical difficulty in the system. Our approach relies on the method of periodic unfolding combined with $\varepsilon$-independent estimates for the thermal and concentration fields and for their coupled fluxes.
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| 41. |
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| 42. |
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| 43. |
- Muntean, Adrian, 1974-
(författare)
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Preface
- 2018
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Ingår i: Applicable Analysis. - : Taylor & Francis. - 0003-6811 .- 1563-504X. ; 97:1, s. 1-2
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Tidskriftsartikel (refereegranskat)
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| 44. |
- Richardson, Omar, et al.
(författare)
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Effects of Environment Knowledge in Evacuation Scenarios Involving Fire and Smoke : A Multiscale Modelling and Simulation Approach
- 2018
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Ingår i: Fire technology. - : Springer. - 0015-2684 .- 1572-8099. ; 55:2, s. 415-436
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Tidskriftsartikel (refereegranskat)abstract
- We study the evacuation dynamics of a crowd evacuating from a complex geometry in the presence of a fire as well as of a slowly spreading smoke curtain.The crowd is composed of two kinds of individuals: those who know the layout of the building, and those who do not and rely exclusively on potentially informed neighbors to identify a path towards the exit. We aim to capture the effect the knowledge of the environment has on the interaction between evacuees and their residence time in the presence of fire and evolving smoke. Our approach is genuinely multiscale—we employ a two-scale model that is able to distinguish between compressible and incompressible pedestrian flow regimes and allows for micro and macro pedestrian dynamics. Simulations illustrate the expected qualitative behavior of the model. We finish with observations on how mixing evacuees with different levels of knowledge impacts important evacuation aspects.
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| 45. |
- Richardson, Omar
(författare)
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Mathematical analysis and approximation of a multiscale elliptic-parabolic system
- 2018
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- We study a two-scale coupled system consisting of a macroscopic elliptic equation and a microscopic parabolic equation. This system models the interplay between a gas and liquid close to equilibrium within a porous medium with distributed microstructures. We use formal homogenization arguments to derive the target system. We start by proving well-posedness and inverse estimates for the two-scale system. We follow up by proposing a Galerkin scheme which is continuous in time and discrete in space, for which we obtain well-posedness, a priori error estimates and convergence rates. Finally, we propose a numerical error reduction strategy by refining the grid based on residual error estimators.
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| 46. |
- Thoa Thieu, T.K., et al.
(författare)
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Weak solvability of a fluid-like driven system for active-passive pedestrian dynamics
- 2019
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Ingår i: Nonlinear Studies. - : I&S publishers. - 1359-8678. ; 26:4, s. 991-1006
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Tidskriftsartikel (refereegranskat)abstract
- We study the question of weak solvability for a nonlinear coupled parabolic system thatmodels the evolution of a complex pedestrian flow. The main feature is that the flow is composed ofa mix of densities of active and passive pedestrians that are moving with different velocities. We relyon special energy estimates and on the use a Schauder’s fixed point argument to tackle the existenceof solutions to our evolution problem.
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| 47. |
- Vo Anh, Khoa, et al.
(författare)
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A Note on Iterations-based Derivations of High-order Homogenization Correctors for Multiscale Semi-linear Elliptic Equations
- 2016
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Ingår i: Applied Mathematics Letters. - : Elsevier BV. - 0893-9659 .- 1873-5452. ; 58, s. 103-109
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Tidskriftsartikel (refereegranskat)abstract
- This Note aims at presenting a simple and efficient procedure to derive the structure of high-order corrector estimates for the homogenization limit applied to a semi-linear elliptic equation posed in perforated domains. Our working technique relies on monotone iterations combined with formal two-scale homogenization asymptotics. It can be adapted to handle more complex scenarios including for instance nonlinearities posed at the boundary of perforations and the vectorial case, when the model equations are coupled only through the nonlinear production terms.
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| 48. |
- Vo Anh, Khoa, et al.
(författare)
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Corrector homogenization estimates for a non-stationary Stokes-Nernst-Planck-Poisson system in perforated domains
- 2019
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Ingår i: Communications in Mathematical Sciences. - : INT PRESS BOSTON. - 1539-6746 .- 1945-0796. ; 17:3, s. 705-738
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Tidskriftsartikel (refereegranskat)abstract
- We consider a non-stationary Stokes-Nernst-Planck-Poisson system posed in perforated domains. Our aim is to justify rigorously the homogenization limit for the upscaled system derived by means of two-scale convergence in [N. Ray, A. Muntean, and P. Knabner, J. Math. Anal. Appl., 390(1):374-393, 2012]. In other words, we wish to obtain the so-called corrector homogenization estimates that specify the error obtained when upscaling the microscopic equations. Essentially, we control in terms of suitable norms differences between the micro-and macro-concentrations and between the corresponding micro- and macro-concentration gradients. The major challenges that we face are the coupled flux structure of the system, the nonlinear drift terms and the presence of the microstructures. Employing various energy-like estimates, we discuss several scalings choices and boundary conditions.
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| 49. |
- Vromans, Arthur, 1989-, et al.
(författare)
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A mixture theory-based concrete corrosion model coupling chemical reactions, diffusion and mechanics
- 2018
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Ingår i: PACIFIC JOURNAL OF MATHEMATICS FOR INDUSTRY. - London, UK : Springer. - 2198-4115. ; 10
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Tidskriftsartikel (refereegranskat)abstract
- A 3-D continuum mixture model describing the corrosion of concrete with sulfuric acid is built. Essentially, the chemical reaction transforms slaked lime (calcium hydroxide) and sulfuric acid into gypsum releasing water. The model incorporates the evolution of chemical reaction, diffusion of species within the porous material and mechanical deformations. This model is applied to a 1-D problem of a plate-layer between concrete and sewer air. The influx of slaked lime from the concrete and sulfuric acid from the sewer air sustains a gypsum creating chemical reaction (sulfatation or sulfate attack). The combination of the influx of matter and the chemical reaction causes a net growth in the thickness of the gypsum layer on top of the concrete base. The model allows for the determination of the plate layer thickness h = h(t) as function of time, which indicates both the amount of gypsum being created due to concrete corrosion and the amount of slaked lime and sulfuric acid in the material. The existence of a parameter regime for which the model yields a non-decreasing plate layer thickness h(t) is identified numerically. The robustness of the model with respect to changes in the model parameters is also investigated.
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| 50. |
- Vromans, Arthur J., 1989-, et al.
(författare)
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Homogenization of a pseudo-parabolic system via a spatial-temporal decoupling : Upscaling and corrector estimates for perforated domains
- 2019
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Ingår i: Mathematics in Engineering. - : AIMS Press. - 2640-3501. ; 1:3, s. 548-582
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Tidskriftsartikel (refereegranskat)abstract
- We determine corrector estimates quantifying the convergence speed of the upscaling of a pseudo-parabolic system containing drift terms incorporating the separation of length scales with relative size 1. To achieve this goal, we exploit a natural spatial-temporal decomposition, which splits the pseudo-parabolic system into an elliptic partial differential equation and an ordinary differential equation coupled together. We obtain upscaled model equations, explicit formulas for effective transport coefficients, as well as corrector estimates delimitating the quality of the upscaling. Finally, for special cases we show convergence speeds for global times, i.e., t ∈ R+, by using time intervals expanding to the whole R+ simultaneously with passing to the homogenization limit ↓ 0.
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