Abstract : Emergent structures are patterns arising via collective actions of many individual entities. In the context of life sciences, they range from the subatomic level to the entire anthropo- and biosphere. The main objective of this minisymposium is to bring together experts working in diverse areas of modeling of collective behavior and emergent phenomena, employing ordinary, stochastic, partial and functional differential equations. Applications include self-organizing systems of interacting agents, flocking and swarming, pedestrian dynamics, and network dynamics. The minisymposium will cover mathematical modeling, analytical and numerical results, focusing on applications and gaining new insights into the principles of emergence and self-organization.
00068 (1/2) : 2D @G501 [Chair: Lisa Maria Kreusser]
[03562] Emergence of Biological Transportation Networks as a Self-Regulated Process
Format : Talk at Waseda University
Author(s) :
Simone Portaro (KAUST)
Abstract : Our purpose is to investigate self-regulating processes modeling biological transportation networks by writing formal $L^2$-gradient flow for a tensor valued diffusivity $D$. We will explore a broad class of entropy dissipations associated with a purely diffusive model and investigate the formal $L^2$-gradient flow of the Fokker-Planck equation. It derives an integral formula for the second variation of the dissipation functional, proving convexity, and couples the Poisson equation for electric potential obtaining the Poisson-Nernst-Planck system. Numerical results are also presented.
[03929] Bifurcations in collective dynamics: ordered and disordered behaviour
Format : Talk at Waseda University
Author(s) :
Sara Merino-Aceituno (University of Vienna)
Raphael Winter (University of Vienna)
Christian Schmeiser (University of Vienna)
Pierre Degond (University of Toulouse)
Abstract : In this talk, I will review some questions that arise around the classical Vicsek model - which is a model for collective dynamics where agents move at a constant speed while trying to adopt the averaged orientation of their neighbours, up
to some noise. I will discuss the emergence of bifurcations leading to disordered and ordered motion, depending on the local density of the agents.
This is a very interesting phenomenon: it showcases how two completely different observed behaviours can appear simultaneously from agents that interact following the same rules.
[04259] A new approach to upscaling of KTEs modelling cell migration
Format : Talk at Waseda University
Author(s) :
Anna Zhigun (Queen’s University Belfast)
Christina Surulescu (University of Kaiserslautern-Landau)
Abstract : A new approach to upscaling of a class of kinetic transport equations that can, e.g. model cell migration in a fibrous environment under the influence of attractants will be presented. It doesn’t rely on a Hilbert space setting and provides a unified and transparent way of obtaining both parabolic and hyperbolic scalings. Formal computations are mimicked by rigorous operations with Radon measures. A key tool is a PDE that connects zero and second order moments.
[04922] Asymptotic limits of transient patterns in a continuous-space interacting particle system.
Format : Talk at Waseda University
Author(s) :
Dietmar B Oelz (University of Queensland)
Cecilia Gonzalez Tokman (University of Queensland)
Abstract : We study a discrete-time interacting particle system with continuous state space. The process has applications in the modeling of actin filament turnover in biological cells through branching and subsequent rapid debranching. In continuous phase space, it can be interpreted as a voter model and as a step-wise mutation model. Its solutions are characterized by transient clusters reminiscent of either actin filament assemblies in the cell cortex or of the formation of opinion clusters.
We reformulate the process in terms of the inter-particle distances and focus on their marginal and joint distributions. We construct a recurrence relation for the associated characteristic functions and pass to the large population limit reminiscent of the Fleming-Viot super-processes. The precise characterization of all marginal distributions established in this work opens the way to a detailed analysis of cluster dynamics. We also obtain a recurrence relation which enables us to compute the moments of the asymptotic single particle distribution characterizing the transient aggregates. Our results indicate that aggregates have a fat-tailed distribution.
[04504] Model Reduction and Coarse-Graining of Complex Systems
Format : Online Talk on Zoom
Author(s) :
Hong Duong (University of Birmingham)
Abstract : Complex systems in nature and in applications (such as molecular systems, crowd dynamics, swarming, opinion formation, just to name a few) are often described by systems of stochastic differential equations (SDEs) and partial differential equations (PDEs). It is often analytically impossible or computationally prohibitively expensive to deal with the full models due to their high dimensionality (degrees of freedom, number of involved parameters, etc.). It is thus of great importance to approximate such large and complex systems by simpler and lower dimensional ones, while still preserving the essential information from the original model. This procedure is referred to as model reduction or coarse-graining in the literature. In this talk, I will present methods for qualitative and quantitative coarse-graining of several SDEs and PDEs, in the presence or absence of a scale-separation.
[05047] Splitting methods for optimal control
Format : Online Talk on Zoom
Author(s) :
David Goodwin (Aarhaus University)
Mohammadali Foroozandeh (Zurich Instruments)
Pranav Singh (University of Bath)
Abstract : The optimal control of a physical system requires efficient numerical solvers for computing dynamics, accurate gradients, and efficient optimization routines.
Of particular interest in this talk are quantum systems such as spins and electrons under the influence of external time-dependent controls such as lasers and magnetic fields. In this talk I will present a highly efficient optimal control procedure called QOALA which adaptively switches splitting based solvers and utilizes exact gradients.
[05107] Nonlocal Cross-interaction Systems on Graphs: Energy Landscape and Dynamics
Format : Online Talk on Zoom
Author(s) :
Jan-Frederik Pietschmann (University of Augsburg)
Markus Schmidtchen (Technische Universität Dresden)
Georg Heinze (University of Augsburg)
Abstract : We explore the dynamical behavior and energetic properties of a model of two species that interact nonlocally on finite graphs. We introduce the setting of nonquadratic Finslerian gradient flows on generalized graphs featuring nonlinear mobilities. In a continuous and local setting, this class of systems exhibits a wide variety of patterns, including mixing of the two species, partial engulfment, or phase separation. We showcase how this rich behavior carries over to the graph structure. We present analytical and numerical evidence thereof.
