| 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. |
- Kronberg, Vi C. E., et al.
(författare)
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Numerical explorations of solvent borne adhesives : A lattice-based approach to morphology formation
- 2023
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Ingår i: Modelling and Simulation in Materials Science and Engineering. - : Institute of Physics (IOP). - 0965-0393 .- 1361-651X. ; 31:7
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Tidskriftsartikel (refereegranskat)abstract
- The internal structure of adhesive tapes determines the effective mechanicalproperties. This holds true especially for blended systems, here consisting ofacrylate and rubber phases. In this note, we propose a lattice-based modelto study numerically the formation of internal morphologies within a fourcomponent mixture (of discrete particles) where the solvent components evaporate. Mimicking numerically the interaction between rubber, acrylate, andtwo different types of solvents, relevant for the technology of adhesive tapes,we aim to obtain realistic distributions of rubber ball-shaped morphologies—they play a key role in the overall functionality of those special adhesives.Our model incorporates the evaporation of both solvents and allows for tuningthe strength of two essentially different solvent–solute interactions and of thetemperature of the system.
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| 3. |
- 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
-
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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| 4. |
- Muntean, Stela Andrea, et al.
(författare)
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Quantitative analysis of phase formation and growth in ternary mixtures upon evaporation of one component
- 2022
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Ingår i: Physical review. E. - : American Physical Society. - 2470-0045 .- 2470-0053. ; 106:2
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Tidskriftsartikel (refereegranskat)abstract
- We perform a quantitative analysis of Monte Carlo simulation results of phase separation in ternary blends upon evaporation of one component. Specifically, we calculate the average domain size and plot it as a function of simulation time to compute the exponent of the obtained power law. We compare and discuss results obtained by two different methods, for three different models: two-dimensional (2D) binary-state model (Ising model), 2D ternary-state model with and without evaporation. For the ternary-state models, we study additionally the dependence of the domain growth on concentration, temperature and initial composition. We reproduce the expected 1/3 exponent for the Ising model, while for the ternary-state model without evaporation and for the one with evaporation we obtain lower values of the exponent. It turns out that phase separation patterns that can form in this type of systems are complex. The obtained quantitative results give valuable insights towards devising computable theoretical estimations of size effects on morphologies as they occur in the context of organic solar cells.
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| 5. |
- 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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| 6. |
- 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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| 7. |
- 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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| 8. |
- Ackleh, Azmy S., et al.
(författare)
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Special issue: Mathematical modeling with measures
- 2020
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Ingår i: Mathematical Biosciences and Engineering. - : American Institute of Mathematical Sciences. - 1547-1063 .- 1551-0018. ; :3, s. 2451-2452
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Tidskriftsartikel (refereegranskat)
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| 9. |
- Acklehl, Azmy S., et al.
(författare)
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Special issue: Mathematical Modeling with Measures : Preface
- 2020
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Ingår i: Mathematical Biosciences and Engineering. - : American Institute of Mathematical Sciences. - 1547-1063 .- 1551-0018. ; 17:3, s. 2451-2452
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Tidskriftsartikel (övrigt vetenskapligt/konstnärligt)
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| 10. |
- Aiki, Toyohiko, et al.
(författare)
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A free boundary problem describing migration into rubbers : Quest of the large time behavior
- 2022
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Ingår i: Zeitschrift für angewandte Mathematik und Mechanik. - : John Wiley & Sons. - 0044-2267 .- 1521-4001. ; 102:7
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Tidskriftsartikel (refereegranskat)abstract
- In many industrial applications, rubber-based materials are routinely used in conjunction with various penetrants or diluents in gaseous or liquid form. It is of interest to estimate theoretically the penetration depth as well as the amount of diffusants stored inside the material. In this framework, we prove the global solvability and explore the large time-behavior of solutions to a one-phase free boundary problem with nonlinear kinetic condition that is able to describe the migration of diffusants into rubber. The key idea in the proof of the large time behavior is to benefit from a contradiction argument, since it is difficult to obtain uniform estimates for the growth rate of the free boundary due to the use of a Robin boundary condition posed at the fixed boundary.
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| 11. |
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| 12. |
- Aiki, Toyohiko, et al.
(författare)
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A macro-micro elasticity-diffusion system modeling absorption-induced swelling in rubber foams : Proof of the strong solvability
- 2021
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Ingår i: Quarterly of Applied Mathematics. - : American Mathematical Society (AMS). - 0033-569X .- 1552-4485. ; 79:3, s. 545-579
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Tidskriftsartikel (refereegranskat)abstract
- In this article, we propose a macro-micro (two-scale) mathematical model for describing the macroscopic swelling of a rubber foam caused by the microscopic absorption of some liquid. In our modeling approach, we suppose that the material occupies a one-dimensional domain which swells as described by the standard beam equation including an additional term determined by the liquid pressure. As special feature of our model, the absorption takes place inside the rubber foam via a lower length scale, which is assumed to be inherently present in such a structured material. The liquid's absorption and transport inside the material is modeled by means of a nonlinear parabolic equation derived from Darcy's law posed in a non-cylindrical domain defined by the macroscopic deformation (which is a solution of the beam equation). Under suitable assumptions, we establish the existence and uniqueness of a suitable class of solutions to our evolution system coupling the nonlinear parabolic equation posed on the microscopic non-cylindrical domain with the beam equation posed on the macroscopic cylindrical domain. In order to guarantee the regularity of the non-cylindrical domain, we impose a singularity to the elastic response function appearing in the beam equation.
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| 13. |
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| 14. |
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| 15. |
- Aiki, Toyohiko, et al.
(författare)
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Large-time asymptotics of moving-reaction interfaces involving nonlinear Henry’s law and time-dependent Dirichlet data
- 2013
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Ingår i: Nonlinear Analysis. - : Elsevier. - 0362-546X .- 1873-5215. ; 93, s. 3-14
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 16. |
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| 17. |
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| 18. |
- 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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| 19. |
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| 20. |
- Aiki, Toyohiko, et al.
(författare)
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On uniqueness of a weak solution of one-dimensional concrete carbonation problem
- 2011
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Ingår i: Discrete and Continuous Dynamical Systems. - : American Institute of Mathematical Sciences. - 1078-0947 .- 1553-5231. ; 29:4, s. 1345-1365
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Tidskriftsartikel (refereegranskat)abstract
- 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 class. Specifically, the uniqueness of weak solutions is proved by applying the dual equation method.
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| 21. |
- Aiki, T., et al.
(författare)
-
Preface
- 2012
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Ingår i: Discrete and Continuous Dynamical Systems. Series S. - : American Institute of Mathematical Sciences (AIMS). - 1937-1632 .- 1937-1179. ; 5:1, s. 1-
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Tidskriftsartikel (refereegranskat)
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| 22. |
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| 23. |
- 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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| 24. |
- Bourne, D., et al.
(författare)
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Is adding charcoal to soil a good method for CO2 sequestration? - : Modeling a spatially homogeneous soil
- 2014
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Ingår i: Applied Mathematical Modelling. - : Elsevier. - 0307-904X .- 1872-8480. ; 38:9-10, s. 2463-2475
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 25. |
- Chalupecky, Vladimir, et al.
(författare)
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Macroscopic corrosion front computations of sulfate attack in sewer pipes based on a micro-macro reaction-diffusion model
- 2012
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Ingår i: Multiscale Mathematics. - : Kyushu University, Japan. ; , s. 22-31
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Konferensbidrag (refereegranskat)abstract
- 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.
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| 26. |
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| 27. |
- 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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| 28. |
- Cirillo, Emilio, et al.
(författare)
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A lattice model for active–passive pedestrian dynamics : a quest for drafting effects
- 2020
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Ingår i: Mathematical Biosciences and Engineering. - : American Institute of Mathematical Sciences. - 1547-1063 .- 1551-0018. ; 17:1, s. 460-477
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 29. |
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| 30. |
- 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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| 31. |
- 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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| 32. |
- 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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| 33. |
- Cirillo, Emilio N.M., et al.
(författare)
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Deterministic reversible model of non-equilibrium phase transitions and stochastic counterpart
- 2020
-
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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| 34. |
- 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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| 35. |
- 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
-
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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| 36. |
- 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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| 37. |
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| 38. |
- 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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| 39. |
- Cirillo, E. N. M., et al.
(författare)
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Upscaling the interplay between diffusion and polynomial drifts through a composite thin strip with periodic microstructure
- 2020
-
Ingår i: Meccanica (Milano. Print). - : Springer. - 0025-6455 .- 1572-9648. ; 55:11, s. 2159-2179
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Tidskriftsartikel (refereegranskat)abstract
- We study the upscaling of a system of many interacting particles through a heterogenous thin elongated obstacle as modeled via a two-dimensional diffusion problem with a one-directional nonlinear convective drift. Assuming that the obstacle can be described well by a thin composite strip with periodically placed microstructures, we aim at deriving the upscaled model equations as well as the effective transport coefficients for suitable scalings in terms of both the inherent thickness at the strip and the typical length scales of the microscopic heterogeneities. Aiming at computable scenarios, we consider that the heterogeneity of the strip is made of an array of periodically arranged impenetrable solid rectangles and identify two scaling regimes what concerns the small asymptotics parameter for the upscaling procedure: the characteristic size of the microstructure is either significantly smaller than the thickness of the thin obstacle or it is of the same order of magnitude. We scale up the diffusion-polynomial drift model and list computable formulas for the effective diffusion and drift tensorial coefficients for both scaling regimes. Our upscaling procedure combines ideas of two-scale asymptotics homogenization with dimension reduction arguments. Consequences of these results for the construction of more general transmission boundary conditions are discussed. We illustrate numerically the concentration profile of the chemical species passing through the upscaled strip in the finite thickness regime and point out that trapping of concentration inside the strip is likely to occur in at least two conceptually different transport situations: (i) full diffusion/dispersion matrix and nonlinear horizontal drift, and (ii) diagonal diffusion matrix and oblique nonlinear drift.
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| 40. |
- 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
-
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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| 41. |
- 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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| 42. |
- Colangeli, Matteo, et al.
(författare)
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A reduction scheme for coupled Brownian harmonic oscillators
- 2022
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Ingår i: Journal of Physics A. - : Institute of Physics Publishing (IOPP). - 1751-8113 .- 1751-8121. ; 55:50
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Tidskriftsartikel (refereegranskat)abstract
- We propose a reduction scheme for a system constituted by two coupled harmonically-bound Brownian oscillators. We reduce the description by constructing a lower dimensional model which inherits some of the basic features of the original dynamics and is written in terms of suitable transport coefficients. The proposed procedure is twofold: while the deterministic component of the dynamics is obtained by a direct application of the invariant manifold method, the diffusion terms are determined via the fluctuation-dissipation theorem. We highlight the behavior of the coefficients up to a critical value of the coupling parameter, which marks the endpoint of the interval in which a contracted description is available. The study of the weak coupling regime is addressed and the commutativity of alternative reduction paths is also discussed.
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| 43. |
- Colangeli, Matteo, et al.
(författare)
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Model reduction of Brownian oscillators : Quantification of errors and long-time behaviour
- 2023
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Ingår i: Journal of Physics A. - : Institute of Physics (IOP). - 1751-8113 .- 1751-8121. ; 56
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Tidskriftsartikel (refereegranskat)abstract
- A procedure for model reduction of stochastic ordinary differential equations with additive noise was recently introduced in Colangeli et al (2022 J. Phys. A: Math. Theor.55 505002), based on the Invariant Manifold method and on the Fluctuation–Dissipation relation. A general question thus arises as to whether one can rigorously quantify the error entailed by the use of the reduced dynamics in place of the original one. In this work we provide explicit formulae and estimates of the error in terms of the Wasserstein distance, both in the presence or in the absence of a sharp time-scale separation between the variables to be retained or eliminated from the description, as well as in the long-time behavior.
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| 44. |
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| 45. |
- Colangeli, M., et al.
(författare)
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Reduced Markovian descriptions of Brownian dynamics : Toward an exact theory
- 2022
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Ingår i: Frontiers in Physics. - : Frontiers Media S.A.. - 2296-424X. ; 10
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Tidskriftsartikel (refereegranskat)abstract
- We outline a reduction scheme for a class of Brownian dynamics which leads to meaningful corrections to the Smoluchowski equation in the overdamped regime. The mobility coefficient of the reduced dynamics is obtained by exploiting the Dynamic Invariance principle, whereas the diffusion coefficient fulfils the Fluctuation-Dissipation theorem. Explicit calculations are carried out in the case of a harmonically bound particle. A quantitative pointwise representation of the reduction error is also provided and connections to both the Maximum Entropy method and the linear response theory are highlighted. Our study paves the way to the development of reduction procedures applicable to a wider class of diffusion processes.
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| 46. |
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| 47. |
- 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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| 48. |
- 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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| 49. |
- Curseu, Petru Lucian, et al.
(författare)
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Cognitive distance, absorptive capacity and group rationality : A simulation study
- 2014
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Ingår i: PLOS ONE. - San Fransisco : Public library science. - 1932-6203. ; 9:10
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Tidskriftsartikel (refereegranskat)abstract
- 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.
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| 50. |
- 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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