| 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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Anticipation decides on lane formation in pedestrian counterflow - a simulation study
- 2020
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Ingår i: Advances in Mathematical Sciences and Applications. - Tokyo, Japan : Gakko Tosho. - 1343-4373. ; 29:1, s. 171-185
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Tidskriftsartikel (refereegranskat)abstract
- Human crowds base most of their behavioral decisions upon anticipated states oftheir walking environment. We explore a minimal version of a lattice model to study lanesformation in pedestrian counterow. Using the concept of horizon depth, our simulationresults suggest that the anticipation eect together with the presence of a small backgroundnoise play an important role in promoting collective behaviors in a counterow setup. Theseingredients facilitate the formation of seemingly stable lanes and ensure the ergodicity of the system.
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| 4. |
- 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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| 5. |
- Cirillo, Emilio N. M., et al.
(författare)
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Can cooperation slow down emergency evacuations?
- 2012
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Ingår i: Comptes rendus. Mecanique. - : Elsevier. - 1631-0721 .- 1873-7234. ; 340:9, s. 625-628
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 6. |
- Cirillo, Emilio N.M., et al.
(författare)
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Deterministic reversible model of non-equilibrium phase transitions and stochastic counterpart
- 2020
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Ingår i: Journal of Physics A. - : Institute of Physics (IOP). - 1751-8113 .- 1751-8121. ; 53:30
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Tidskriftsartikel (refereegranskat)abstract
- Npoint particles move within a billiard table made of two circular cavities connected by a straight channel. The usual billiard dynamics is modified so that it remains deterministic, phase space volumes preserving and time reversal invariant. Particles move in straight lines and are elastically reflected at the boundary of the table, as usual, but those in a channel that are moving away from a cavity invert their motion (rebound), if their number exceeds a given thresholdT. When the geometrical parameters of the billiard table are fixed, this mechanism gives rise to non-equilibrium phase transitions in the largeNlimit: lettingT/Ndecrease, the homogeneous particle distribution abruptly turns into a stationary inhomogeneous one. The equivalence with a modified Ehrenfest two urn model, motivated by the ergodicity of the billiard with no rebound, allows us to obtain analytical results that accurately describe the numerical billiard simulation results. Thus, a stochastic exactly solvable model that exhibits non-equilibrium phase transitions is also introduced.
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| 7. |
- 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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| 8. |
- Cirillo, Emilio N.M., et al.
(författare)
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Dynamics of pedestrians in regions with no visibility : A lattice model without exclusion
- 2013
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Ingår i: Physica A: Statistical Mechanics and its Applications. - : Elsevier. - 0378-4371. ; 392:17, s. 3578-3588
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 9. |
- 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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| 10. |
- Cirillo, Emilio N.M., et al.
(författare)
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When diffusion faces drift : consequences of exclusion processes for bi–directional pedestrian flows
- 2020
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Ingår i: Physica D. - : Elsevier. - 0167-2789 .- 1872-8022. ; 413
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Tidskriftsartikel (refereegranskat)abstract
- Stochastic particle-based models are useful tools for describing the collective movement of large crowds of pedestrians in crowded confined environments. Using descriptions based on the simple exclusion process, two populations of particles, mimicking pedestrians walking in a built environment, enter a room from two opposite sides. One population is passive - being unaware of the local environment; particles belonging to this group perform a symmetric random walk. The other population has information on the local geometry in the sense that as soon as particles enter a visibility zone, a drift activates them. Their self-propulsion leads them towards the exit. This second type of species is referred here as active. The assumed crowdedness corresponds to a near-jammed scenario. The main question we ask in this paper is: Can we induce modifications of the dynamics of the active particles to improve the outgoing current of the passive particles? To address this question, we compute occupation number profiles and currents for both populations in selected parameter ranges. Besides observing the more classical faster-is-slower effect, new features appear as prominent like the non-monotonicity of currents, self-induced phase separation within the active population, as well as acceleration of passive particles for large-drift regimes of active particles.
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| 11. |
- Lyons, Rainey, et al.
(författare)
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A Continuum Model for Morphology Formation from Interacting Ternary Mixtures : Simulation Study of the Formation and Growth of Patterns
- 2023
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Ingår i: Physica D. - : Elsevier. - 0167-2789 .- 1872-8022. ; 453
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Tidskriftsartikel (refereegranskat)abstract
- Our interest lies in exploring the ability of a coupled nonlocal system of two quasilinear parabolic partial differential equations to produce phase separation patterns. The obtained patterns are referred here as morphologies. Our target system is derived in the literature as the rigorous hydrodynamic limit of a suitably scaled interacting particle system of Blume–Capel–type driven by Kawasaki dynamics. The system describes in a rather implicit way the interaction within a ternary mixture that is the macroscopic counterpart of a mix of two populations of interacting solutes in the presence of a background solvent. Our discussion is based on the qualitative behavior of numerical simulations of finite volume approximations of smooth solutions to our system and their quantitative postprocessing in terms of two indicators (correlation and structure factor calculations). Our results show many similar qualitative features (e.g. general shape and approximate coarsening rates) which have been observed in previous works on the stochastic Blume–Capel dynamics with three interacting species. The properties of the obtained morphologies (shape, connectivity, and so on) can play a key role in, e.g., the design of the active layer for efficient organic solar cells.
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| 12. |
- Lyons, Rainey, et al.
(författare)
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Phase separation and morphology formation in interacting ternarymixtures under evaporation : Well-posedness and numerical simulation of a non-local evolution system
- 2024
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Ingår i: Nonlinear Analysis. - : Elsevier. - 1468-1218. ; 77
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Tidskriftsartikel (refereegranskat)abstract
- We study a nonlinear coupled parabolic system with non-local drift terms modeling at the continuum level the inter-species interaction within a ternary mixture that allows the evaporation of one of the species. In the absence of evaporation, the proposed system coincides with the hydrodynamic limit of a stochastic interacting particle system of Blume–Capel-type driven by the Kawasaki dynamics. Similar governing dynamics are found in models used to study morphology formation in the design of organic solar cells, thin adhesive bands, and other applications. We investigate the well-posedness of the target system and present preliminary numerical simulations which incorporate ‘from the top’ evaporation into the model. We employ a finite volumes scheme to construct approximations of the weak solution and illustrate how the evaporation process can affect the shape and connectivity of the evolving-in-time morphologies
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| 13. |
- Raveendran, Vishnu, et al.
(författare)
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Homogenization of a reaction-diffusion problem with large nonlinear drift and Robin boundary data
- 2024
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Ingår i: Quarterly of Applied Mathematics. - : American Mathematical Society (AMS). - 0033-569X .- 1552-4485.
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Tidskriftsartikel (refereegranskat)abstract
- We study the periodic homogenization of a reaction-diffusion problem with large nonlinear drift and Robin boundary condition posed in an unbounded perforated domain. The nonlinear problem is associated with the hydrodynamic limit of a totally asymmetric simple exclusion process (TASEP) governing a population of interacting particles crossing a domain with obstacle. We are interested in deriving rigorously the upscaled model equations and the corresponding effective coefficients for the case when the microscopic dynamics are linked to a particular choice of characteristic length and time scales that lead to an exploding nonlinear drift. The main mathematical difficulty lies in proving the two-scale compactness and strong convergence results needed for the passage to the homogenization limit. To cope with the situation, we use the concept of two-scale compactness with drift, which is similar to the more classical two-scale compactness result but it is defined now in moving coordinates. We provide as well a strong convergence result for the corrector function, starting this way the search for the order of the convergence rate of the homogenization process for our target nonlinear drift problem.
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| 14. |
- Raveendran, Vishnu
(författare)
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Homogenization of reaction-diffusion problems with nonlinear drift in thin structures
- 2022
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- We study the question of periodic homogenization of a variably scaled reaction-diffusion equation with non-linear drift of polynomial type. The non-linear drift was derived as hydrodynamic limit of a totally asymmetric simple exclusion process (TASEP) for a population of interacting particles crossing a domain with obstacle. We consider three different geometries: (i) Bounded domain crossed by a finitely thin flat composite layer; (ii) Bounded domain crossed by an infinitely thin flat composite layer; (iii) Unbounded composite domain.\end{itemize} For the thin layer cases, we consider our reaction-diffusion problem endowed with slow or moderate drift. Using energy-type estimates as well as concepts like thin-layer convergence and two-scale convergence, we derive homogenized evolution equations and the corresponding effective model parameters. Special attention is paid to the derivation of the effective transmission conditions across the separating limit interfaces. As a special scaling, the problem with large drift is treated separately for an unbounded composite domain. Because of the imposed large drift, this nonlinearity is expected to explode in the limit of a vanishing scaling parameter. To deal with this special case, we employ two-scale formal homogenization asymptotics with drift to derive the corresponding upscaled model equations as well as the structure of the effective transport tensors. Finally, we use Schauder's fixed point Theorem as well as monotonicity arguments to study the weak solvability of the upscaled model posed in the unbounded domain. This study wants to contribute with theoretical understanding needed when designing thin composite materials which are resistant to slow, moderate, and high velocity impacts.
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| 15. |
- Raveendran, Vishnu, et al.
(författare)
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Upscaling of a reaction-diffusion-convection problem with exploding non-linear drift
- 2022
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Ingår i: Quarterly of Applied Mathematics. - : American Mathematical Society (AMS). - 0033-569X .- 1552-4485. ; 80:4, s. 641-667
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Tidskriftsartikel (refereegranskat)abstract
- We study a reaction-diffusion-convection problem with non-linear drift posed in a domain with periodically arranged obstacles. The non-linearity in the drift is linked to the hydrodynamic limit of a totally asymmetric simple exclusion process (TASEP) governing a population of interacting particles crossing a domain with obstacle. Because of the imposed large drift scaling, this non-linearity is expected to explode in the limit of a vanishing scaling parameter. As main working techniques, we employ twoscale formal homogenization asymptotics with drift to derive the corresponding upscaled model equations as well as the structure of the effective transport tensors. Finally, we use Schauder???s fixed point theorem as well as monotonicity arguments to study the weak solvability of the upscaled model posed in an unbounded domain. This study wants to contribute with theoretical understanding needed when designing thin composite materials that are resistant to high velocity impacts.
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| 16. |
- Setta, Mario, et al.
(författare)
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A mesoscopic lattice model for morphology formation in ternary mixtures with evaporation
- 2023
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Ingår i: Communications in nonlinear science & numerical simulation. - : Elsevier. - 1007-5704 .- 1878-7274. ; 119
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Tidskriftsartikel (refereegranskat)abstract
- We develop a mesoscopic lattice model to study the morphology formation in inter-acting ternary mixtures with the evaporation of one component. As concrete potentialapplication of our model, we wish to capture morphologies as they are typically arisingduring the fabrication of organic solar cells. In this context, we consider an evaporatingsolvent into which two other components are dissolved, as a model for a 2-componentcoating solution that is drying on a substrate. We propose a 3-spins dynamics to describethe evolution of the three interacting species. As main tool, we use a Monte CarloMetropolis-based algorithm, with the possibility of varying the system’s temperature,mixture composition, interaction strengths, and evaporation kinetics. The main novelty isthe structure of the mesoscopic model – a bi-dimensional lattice with periodic boundaryconditions, divided into square cells to encode a mesoscopic range interaction amongthe units. We investigate the effect of the model parameters on the structure of theresulting morphologies. Finally, we compare the results obtained with the mesoscopicmodel with corresponding ones based on an analogous lattice model with a short rangeinteraction among the units, i.e. when the mesoscopic length scale coincides with themicroscopic length scale of the lattice.
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