Page 532 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 532
PDE MODELS IN LIFE AND SOCIAL SCIENCES (MS-71)
Pedestrian Models with Congestion Effects
Rafael Bailo, rafael.bailo@univ-lille.fr
Université de Lille, France
Coauthors: Pedro Aceves-Sanchez, Pierre Degond, Zoé Mercier
We propose a macroscopic model for pedestrian dynamics with a congestion effect. Said effect
is achieved through the introduction of a singular pseudo-pressure term in the hydrodynamic
formulation of the model, resulting in an asymptotic transition between two different dynamics.
To handle the numerical simulation of the model, we adapt an implicit, asymptotic-preserving
scheme that has proven successful in dealing with Euler system with capacity constraints. We
present numerical examples and discuss their validity with respect to the microscopic setting.
Phase separation in active Brownian particles
Maria Bruna, bruna@maths.cam.ac.uk
University of Cambridge, United Kingdom
In this talk, I will discuss models for active matter systems consisting of many self-propelled
particles. These can be used to describe biological systems such as bird flocks, fish schools,
and bacterial suspensions. In contrast to passive particles, these systems can undergo phase
separation without any attractive interactions, a mechanism known as motility-induced phase
separation. Starting with a microscopic model for active Brownian particles with repulsive
interactions, I will discuss four possible macroscopic PDEs (ranging from a nonlocal model
to a local cross-diffusion system). I will discuss work in progress concerning the stability and
analysis of such models.
Linking graph Allen–Cahn and MBO with fidelity, towards applications
in classification and imaging
Jeremy Budd, j.m.budd-1@tudelft.nl
TU Delft, Netherlands
Coauthor: Yves van Gennip
An emerging technique in clustering, segmentation and classification problems is to consider the
dynamics of flows defined on finite graphs. In particular Bertozzi and co-authors considered dy-
namics related to Allen–Cahn flow (Bertozzi, Flenner, 2012) and the MBO algorithm (Merkur-
jev, Kostic, Bertozzi, 2013) for this purpose. In (Budd, Van Gennip, 2019, arxiv preprint)
the authors showed that the MBO algorithm is a special case of a "semi-discrete" scheme for
Allen–Cahn flow.
In this talk, we extend this semi-discrete link to the case with fidelity forcing. Furthermore,
this semi-discrete scheme yields a family of MBO-like schemes for classification applications,
which we shall explore as alternatives to the original MBO scheme.
530
Pedestrian Models with Congestion Effects
Rafael Bailo, rafael.bailo@univ-lille.fr
Université de Lille, France
Coauthors: Pedro Aceves-Sanchez, Pierre Degond, Zoé Mercier
We propose a macroscopic model for pedestrian dynamics with a congestion effect. Said effect
is achieved through the introduction of a singular pseudo-pressure term in the hydrodynamic
formulation of the model, resulting in an asymptotic transition between two different dynamics.
To handle the numerical simulation of the model, we adapt an implicit, asymptotic-preserving
scheme that has proven successful in dealing with Euler system with capacity constraints. We
present numerical examples and discuss their validity with respect to the microscopic setting.
Phase separation in active Brownian particles
Maria Bruna, bruna@maths.cam.ac.uk
University of Cambridge, United Kingdom
In this talk, I will discuss models for active matter systems consisting of many self-propelled
particles. These can be used to describe biological systems such as bird flocks, fish schools,
and bacterial suspensions. In contrast to passive particles, these systems can undergo phase
separation without any attractive interactions, a mechanism known as motility-induced phase
separation. Starting with a microscopic model for active Brownian particles with repulsive
interactions, I will discuss four possible macroscopic PDEs (ranging from a nonlocal model
to a local cross-diffusion system). I will discuss work in progress concerning the stability and
analysis of such models.
Linking graph Allen–Cahn and MBO with fidelity, towards applications
in classification and imaging
Jeremy Budd, j.m.budd-1@tudelft.nl
TU Delft, Netherlands
Coauthor: Yves van Gennip
An emerging technique in clustering, segmentation and classification problems is to consider the
dynamics of flows defined on finite graphs. In particular Bertozzi and co-authors considered dy-
namics related to Allen–Cahn flow (Bertozzi, Flenner, 2012) and the MBO algorithm (Merkur-
jev, Kostic, Bertozzi, 2013) for this purpose. In (Budd, Van Gennip, 2019, arxiv preprint)
the authors showed that the MBO algorithm is a special case of a "semi-discrete" scheme for
Allen–Cahn flow.
In this talk, we extend this semi-discrete link to the case with fidelity forcing. Furthermore,
this semi-discrete scheme yields a family of MBO-like schemes for classification applications,
which we shall explore as alternatives to the original MBO scheme.
530
