開催日：2026/02/24～2026/02/26
Finite Element solver for kinematically incompatible non-simply connected Föppl-von Kármán plates②｜2025a033
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開催概要
- 開催方法：オンライン開催
- 主要言語：英語
- 主催：九州大学マス・フォア・インダストリ研究所
- 種別・種目： 一般研究-短期共同研究
- 研究計画題目：Finite Element solver for kinematically incompatible non-simply connected Föppl-von Kármán plates
- 研究代表者：Fabbrini Edoardo（京都大学）
- 研究実施期間：2025年4月21日(月) ～ 2025年5月3日(土),
2026年2月24日(火) ～ 2026年2月26日(木) - 公開期間：2025年4月28日(月),
2026年2月24日(火) ～ 2026年2月26日(木) - 研究計画詳細：https://joint2.imi.kyushu-u.ac.jp/research_chooses/view/2025a033
プログラム
2月24日（火）,25（水）,26日（木）
15：00-16：00(45-minute lecture followed by 15 minutes of Q&A)
Marco MORANDOTTI（Politecnico di Torino）
Multi-agent dynamics with labels and their continuum limit
Three 45-minute lessons.
Many complex systems arising from the modeling of natural or artificial phenomena, even social sciences, involve many particles, or agents whose evolution might be affected by the choice of a strategy, or as a consequence of belonging to a certain subgroup of agents, identified by a label. Studying these systems can help us understand these phenomena, make prediction and even account for rather general degrees of stochasticity.
In this course, we will set up a powerful analytical framework to study these systems and see a few examples. This framework will allow us to perform the limit as the number of agents diverges to infinity, thus passing from the discrete, Lagrangian description to that of the density of agents with strategies. The advantage of this approach is to describing the evolution of a single quantity through a PDE, rather than following those of the individual agents. The typical limit PDE is a continuity equation for deterministic dynamics and a Fokker—Planck equation in case stochasticity is accounted for.
The plan of the classes is the following:
- Introduction, setting of the problem, and standing hypotheses on the velocity vector fields for the agent variable (a point in the Euclidean space) and for the label variable (a probability measure). Typical dynamics included in this setting: deterministic vs stochastic, through the addition of the Brownian motion.
- A case study from evolutionary game theory: the spatially inhomogeneous replicator equation. Introduction to the classical replicator equation; addition of the spatial dependence; mean-field limit.
- Derivation of the replicator equation from the Moran process. Introduction to the Moran process; extension to multiple strategies; limit to the replicator equation in the weak selection regime.
References
Ambrosio, Fornasier, Morandotti, and Savaré: Spatially Inhomogeneous Evolutionary Games, CPAM, 2021.
Hofbauer and Sigmund: Evolutionary games and population dynamics. Cambridge University Press 1998.
Morandotti and Orlando: Replicator dynamics as the large population limit of a discrete Moran process in the weak selection regime: A proof via Eulerian specification. ESAIM:COCV, 2025.
Nowak: Evolutionary Dynamics: Exploring the Equations of Life. Belknap Press (2006).
申込方法
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