Meiji University Center for Mathematical Modeling and Applications

第30回明治非線型数理セミナーとの合同開催

Filament and Membrane Hole Dynamics in
Fluid Flow
（流体中のフィラメントと膜小孔のダイナミクス）

講演日時：

2025年2月28日（金） 15:00～16:30

講演会場：

明治大学中野キャンパス 高層棟6階 603教室（対面開催）

講演者　：

森 洋一朗 氏　ペンシルベニア大学

概要

　Systems in which elastic structures interact with the surrounding fluid abound in biophysics. Here, we will focus on problems in which a one-dimensional structure interacts with the surrounding 3D fluid. In contrast to problems in which 2D surfaces interact with a 3D fluid, there are significant analytical and computational issues that have not yet been resolved. First, we discuss slender body theory, which concerns the dynamics of thin filaments in 3D Stokes flow. We formulate a novel boundary value problem for thin filaments and prove the validity and demonstrate limitations of slender body approximation, a commonly used method for the study of such problems. As a second problem, we discuss the problem of open membrane dynamics. We formulate the equations and develop a numerical method when the membrane geometry is axisymmetric. Grid refinement is used near the membrane edge to capture the singularity in the stress. The simulated dynamics of membrane hole closure is compared with simpler ODE models.

第29回明治非線型数理セミナーとの合同開催

Generation and motion of interfaces in a mass-conserving reaction-diffusion system

講演日時：

2025年2月20日（木） 15:30～16:30

講演会場：

明治大学中野キャンパス 高層棟6階 603教室（対面開催）

講演者　：

Cyrill Muratov 氏　University of Pisa

概要

　Reaction-diffusion models with nonlocal constraints naturally arise as limiting cases of coupled bulk-surface models of intracellular signaling. In this talk, I will present a minimal, mass-conserving model of cell-polarization on a curved membrane in the limit of slow surface diffusion. Using the tools of formal asymptotics and calculus of variations, we study the characteristic wave-pinning behavior of this system on three dynamical timescales. On the short timescale, generation of an interface separating high- and low-concentration domains is established under suitable conditions. Intermediate timescale dynamics is shown to lead to a uniform growth or shrinking of these domains to sizes which are fixed by global parameters. Finally, the long time dynamics reduces to area-preserving geodesic curvature flow that may lead to multi-interface steady state solutions. These results provide a foundation for studying cell polarization and related phenomena in biologically relevant geometries.

第28回明治非線型数理セミナーおよびCNRS東京ラボ FJ-LMI* との合同開催

Diffusion law and the growth of the reaction term select the boundary condition

講演日時：

2025年2月10日（月） 15:30～16:30

講演会場：

明治大学中野キャンパス 高層棟6階 603教室（対面開催）

講演者　：

Danielle Hilhorst 氏　CNRS, Université de Paris-Saclay

概要

　We consider a one-dimensional non-Fickian diffusion equation and show how either a homogeneous Dirichlet boundary condition or a homogeneous Neumann boundary condition appears along the boundary of an inner domain when the diffusivity in the outer domain tends to zero. This is joint work with Seungmin Kang, Hoyoun Kim and Yong Jung Kim.

* FJ-LMI: https://fj-lmi.cnrs.fr/about-fj-lmi/

主催

明治大学先端数理科学インスティテュート (MIMS)
共同利用・共同研究拠点「現象数理学研究拠点」

＊本講演会は、明治非線型数理セミナーとの合同開催です

明治非線型数理セミナー

コーディネーター

俣野博（明治大学）

問い合わせ先