When diffusion faces drift: Consequences of exclusion processes for bi-directional pedestrian flows

Cirillo, Emilio N. M.; Colangeli, Matteo; Muntean, Adrian; Thieu, T. K. Thoa

doi:10.1016/j.physd.2020.132651

Cited by 9 publications

(12 citation statements)

References 12 publications

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“…This numerical scheme has been studied in [19], where the authors implemented a version of KMC in the context of a lattice gas model with two species of particles. Further validation of the numerical methodology used here was reported in [20], based on a counterflow crowd dynamics model. The overall dynamics of our system is based on a continuous time Markov chain, i.e.…”

Section: Numerical Examplesmentioning

confidence: 99%

“…In particular, the larger ε of active particles the more patients need intensive care units (the more load will be placed on the intensive care unit). Note that our dynamics are incorporated in the continuous time Markov chain η(t) on Ω with rates c(η, η ′ ), for the detailed definitions of the rates c(η(t), η), see, e.g., [19,20].…”

Section: Numerical Examplesmentioning

confidence: 99%

“…Next, we select a configuration using the probability distribution c(η(t), η)/ ζ∈Ω c(η(t), ζ) and set η(t + τ ) = η (for the detailed definitions of the rates c(η(t), η), see e.g. [19,20]).…”

Section: Numerical Examplesmentioning

confidence: 99%

“…In the current version, we have improved the original simulations provided in [19,20] by creating the interaction among active and passive particles. We have each site on the lattice connected by edges.…”

Section: Numerical Examplesmentioning

confidence: 99%

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Combining Coupled Skorokhod SDE and Lattice Gas Frameworks for Multi-fidelity Modelling of Complex Behavioral Systems

Thieu¹,

Melnik²

2021

9th Edition of the International Conference on Computational Methods for Coupled Problems in Science and Engineering

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To model reliably behavioral systems with complex bio-social interactions, accounting for uncertainty quantification, is critical for many application areas. However, in terms of the mathematical formulation of the corresponding problems, one of the major challenges is coming from the fact that corresponding stochastic processes should, in most cases, be considered in bounded domains, possibly with obstacles. This has been known for a long time and yet, very little has been done for the quantification of uncertainties in modelling complex behavioral systems described by such stochastic processes. In this paper, we address this challenge by considering a coupled system of Skorokhodtype stochastic differential equations (SDEs) describing interactions between active and passive participants of a mixed-population group. In developing a multi-fidelity modelling methodology for such behavioral systems, we combine low-and high-fidelity results obtained from (a) the solution of the underlying coupled system of SDEs and (b) simulations with a statistical-mechanics-based lattice gas model, where we employ a kinetic Monte Carlo procedure. Furthermore, we provide representative numerical examples of healthcare systems, subject to an epidemic, where the main focus in our considerations is given to an interacting particle system of asymptomatic and susceptible populations.

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Section: Numerical Examplesmentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

Section: Numerical Examplesmentioning

confidence: 99%

See 2 more Smart Citations

Combining Coupled Skorokhod SDE and Lattice Gas Frameworks for Multi-fidelity Modelling of Complex Behavioral Systems

Thieu¹,

Melnik²

2021

9th Edition of the International Conference on Computational Methods for Coupled Problems in Science and Engineering

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“…[7,30,32,34,54,59,62]), but also active matter in a wider sense of agent systems like humans or robots (cf. [8,21,26,27,48,47,31]). In many of these systems a key issue is the interplay of the particles' own activity with crowding effects, which leads to the formation of complex and interesting patterns.…”

Section: Introductionmentioning

confidence: 99%

Active Crowds

Bruna¹,

Burger²,

Pietschmann³

et al. 2021

Preprint

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This chapter focuses on the mathematical modelling of active particles (or agents) in crowded environments. We discuss several microscopic models found in literature and the derivation of the respective macroscopic partial differential equations for the particle density. The macroscopic models share common features, such as cross diffusion or degenerate mobilities. We then take the diversity of macroscopic models to a uniform structure and work out potential similarities and differences. Moreover, we discuss boundary effects and possible applications in life and social sciences. This is complemented by numerical simulations that highlight the effects of different boundary conditions.

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Coupled stochastic systems of Skorokhod type: Well‐posedness of a mathematical model and its applications

Thieu

Muntean

Melnik

2022

Math Methods in App Sciences

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Population dynamics with complex biological interactions, accounting for uncertainty quantification, are critical for many application areas. However, due to the complexity of biological systems, the mathematical formulation of the corresponding problems faces the challenge that the corresponding stochastic processes should, in most cases, be considered in bounded domains. We propose a model based on a coupled system of reflecting Skorokhod‐type stochastic differential equations with jump‐like exit from a boundary. The setting describes the population dynamics of active and passive populations. As main working techniques, we use compactness methods and Skorokhod's representation of solutions to SDEs posed in bounded domains to prove the well‐posedness of the system. This functional setting is a new point of view in the field of modeling and simulation of population dynamics. We provide the details of the model, as well as representative numerical examples, and discuss the applications of a Wilson–Cowan‐type system, modeling the dynamics of two interacting populations of excitatory and inhibitory neurons. Furthermore, the presence of random input current, reflecting factors together with Poisson jumps, increases firing activity in neuronal systems.

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When diffusion faces drift: Consequences of exclusion processes for bi-directional pedestrian flows

Cited by 9 publications

References 12 publications

Combining Coupled Skorokhod SDE and Lattice Gas Frameworks for Multi-fidelity Modelling of Complex Behavioral Systems

Combining Coupled Skorokhod SDE and Lattice Gas Frameworks for Multi-fidelity Modelling of Complex Behavioral Systems

Active Crowds

Coupled stochastic systems of Skorokhod type: Well‐posedness of a mathematical model and its applications

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