70 citations · 433 across the 44 of their papers we have counts for
25 papers · 1 filter
Opinion Dynamics with Continuous Age Structure
Andrew Nugent, Susana N. Gomes, Marie-Therese Wolfram
We extend a classical model of continuous opinion formation to explicitly include an age-structured population. We begin by considering a stochastic differential equation model whi…
The mathematical theory of Hughes' model: a survey of results
Debora Amadori, Boris Andreianov, Marco Di Francesco +9
We provide an overview of the results on Hughes' model for pedestrian movements available in the literature. After the first successful approaches to solving a regularised version…
Steady states of an Elo-type rating model for players of varying strength
Bertram Düring, Josephine Evans, Marie-Therese Wolfram
In this paper we study the long-time behaviour of a kinetic formulation of an Elo-type rating model for a large number of interacting players with variable strength. The model resu…
A PDE model for unidirectional flows: stationary profiles and asymptotic behaviour
Annalisa Iuorio, Gaspard Jankowiak, Peter Szmolyan +1
In this paper, we investigate the stationary profiles of a convection-diffusion model for unidirectional pedestrian flows in domains with a single entrance and exit. The inflow and…
On anisotropic diffusion equations for label propagation
Lisa Maria Kreusser, Marie-Therese Wolfram
In many problems in data classification one wishes to assign labels to points in a point cloud with a certain number of them being already correctly labeled. In this paper, we prop…
Micro- and Macroscopic Modeling of Crowding and Pushing in Corridors
Michael Fischer, Gaspard Jankowiak, Marie-Therese Wolfram
Experiments with pedestrians revealed that the geometry of the domain, as well as the incentive of pedestrians to reach a target as fast as possible have a strong influence on the…
Trend to Equilibrium for Systems with Small Cross-Diffusion
Luca Alasio, Helene Ranetbauer, Markus Schmidtchen +1
This paper presents new analytical results for a class of nonlinear parabolic systems of partial different equations with small cross-diffusion which describe the macroscopic dynam…
Parameter estimation for macroscopic pedestrian dynamics models from microscopic data
Susana N. Gomes, Andrew M. Stuart, Marie-Therese Wolfram
In this paper we develop a framework for parameter estimation in macroscopic pedestrian models using individual trajectories -- microscopic data. We consider a unidirectional flow…
Mean field models for segregation dynamics
Martin Burger, Jan-Frederik Pietschmann, Helene Ranetbauer +2
In this paper we derive and analyse mean-field models for the dynamics of groups of individuals undergoing a random walk. The random motion of individuals is only influenced by the…
Asymptotic models for transport in large aspect ratio nanopores
B. Matejczyk, J. -F. Pietschmann, G. Richardson +1
Ion flow in charged nanopores is strongly influenced by the ratio of the Debye length to the pore radius. We investigate the asymptotic behaviour of solutions to the Poisson-Nernst…
Asymptotic gradient flow structures of a nonlinear Fokker-Planck equation
Maria Bruna, Martin Burger, Helene Ranetbauer +1
In this paper we consider a nonlinear Fokker-Planck equation with asymptotically small parameters. It describes the diffusion of finite-size particles in the presence of a fixed di…
Derivation and analysis of continuum models for crossing pedestrian traffic
Sabine Hittmeir, Helene Ranetbauer, Christian Schmeiser +1
In this paper we study hyperbolic and parabolic nonlinear partial differential equation models, which describe the evolution of two intersecting pedestrian flows. We assume that in…
Cross-diffusion systems with excluded volume effects and asymptotic gradient flows
Maria Bruna, Martin Burger, Helene Ranetbauer +1
In this paper we discuss the analysis of a cross-diffusion PDE system for a mixture of hard spheres, which was derived by Bruna and Chapman from a stochastic system of interacting…
Balanced growth path solutions of a Boltzmann mean field game model for knowledge growth
Martin Burger, Alexander Lorz, Marie-Therese Wolfram
In this paper we study balanced growth path solutions of a Boltzmann mean field game model proposed by Lucas et al [13] to model knowledge growth in an economy. Agents can either i…
Parabolic free boundary price formation models under market size fluctuations
Peter A. Markowich, Josef Teichmann, Marie-Therese Wolfram
In this paper we propose an extension of the Lasry-Lions price formation model which includes fluctuations of the numbers of buyers and vendors. We analyze the model in the case of…
Lane formation by side-stepping
Martin Burger, Sabine Hittmeir, Helene Ranetbauer +1
In this paper we study a system of nonlinear partial differential equations, which describes the evolution of two pedestrian groups moving in opposite direction. The pedestrian dyn…
On a Boltzmann mean field model for knowledge growth
Martin Burger, Alexander Lorz, Marie-Therese Wolfram
In this paper we analyze a Boltzmann type mean field game model for knowledge growth, which was proposed by Lucas and Moll. We discuss the underlying mathematical model, which cons…
A local version of the Hughes model for pedestrian flow
José A. Carrillo, Stephan Martin, Marie-Therese Wolfram
Roger Hughes proposed a macroscopic model for pedestrian dynamics, in which individuals seek to minimize their travel time but try to avoid regions of high density. One of the basi…
Dual two-state mean-field games
Diogo A. Gomes, Roberto M. Velho, Marie-Therese Wolfram
In this paper, we consider two-state mean-field games and its dual formulation. We then discuss numerical methods for these problems. Finally, we present various numerical experime…
Socio-economic applications of finite state mean field games
Diogo A. Gomes, Roberto M. Velho, Marie-Therese Wolfram
In this paper we present different applications of finite state mean field games to socio-economic sciences. Examples include paradigm shifts in the scientific community or the con…
On the asymptotic behavior of a Boltzmann-type price formation model
Martin Burger, Luis Caffarelli, Peter A. Markowich +1
In this paper we study the asymptotic behavior of a Boltzmann type price formation model, which describes the trading dynamics in a financial market. In many of these markets tradi…
Mean field games with nonlinear mobilities in pedestrian dynamics
Martin Burger, Marco Di Francesco, Peter Markowich +1
In this paper we present an optimal control approach modeling fast exit scenarios in pedestrian crowds. In particular we consider the case of a large human crowd trying to exit a r…
On a Boltzmann type price formation model
Martin Burger, Luis Caffarelli, Peter Markowich +1
In this paper we present a Boltzmann type price formation model, which is motivated by a parabolic free boundary model for the evolution of the prize presented by Lasry and Lions i…
A Drift-Diffusion-Reaction Model for Excitonic Photovoltaic Bilayers: Asymptotic Analysis and A 2-D HDG Finite-Element Scheme
Daniel Brinkman, Klemens Fellner, Peter A. Markowich +1
We present and discuss a mathematical model for the operation of bilayer organic photovoltaic devices. Our model couples drift-diffusion-recombination equations for the charge carr…