| 1. |
- 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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| 2. |
- 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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| 3. |
- 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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| 4. |
- 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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| 5. |
- 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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