非線形解析セミナーの記録（2023年度）

日時 2月22日(木)　　13時00分〜
場所 矢上キャンパス14棟733室
講演者 Gabriela Planas 氏 (Universidade Estadual de Campinas)
講演題目 Some existence results for Cell-fluid Navier-Stokes Equations
講演要旨 In this talk, we consider a general Cell-fluid Navier-Stokes Model with the inclusion of Chemotaxis. This general model relays on a mixture theory multiphase formulation. It consists of two mass balance equations and two general momentum balance equations, for the cell and fluid phase combined with a convection-diffusion-reaction equation for oxygen. We will discuss some recent results on the existence of weak and strong solutions in a two or three-dimensional bounded domain when the fluids are assumed to be incompressible with constant volume fraction.

日時 12月15日(金)　　16時45分〜
場所 矢上キャンパス14棟733室
講演者 須田颯 氏 (慶應義塾大学)
講演題目 Derivation of fractional diffusion equations from stochastic harmonic chains
講演要旨 In this talk, we will consider the problem of deriving macroscopic dynamics (PDE) from a microscopic interacting system (stochastic systems on lattice). In particular, we will derive a phenomenon called “anomalous heat transport” as a fractional diffusion equation from “stochastic harmonic chain (SHC)”. Anomalous heat transport (violation of Fourier’s law) has been observed in numerical simulations for one-dimensional nonlinear Hamiltonian systems (anharmonic chains). Since rigorous analysis of deterministic nonlinear systems is difficult, models in which nonlinear effects are approximated by stochastic perturbations have been studied. First, I will briefly explain the framework for deriving PDEs from microscopic systems. Then, I will present previous results on deriving fractional diffusion equations from SHCs and my results.

日時 11月24日(金)　　10時00分〜
場所 矢上キャンパス14棟733室
講演者 Lorenzo Cavallina 氏 (東北大学)
Patrick van Meurs 氏 (金沢大学)
Norbert Požár 氏 (金沢大学)
講演題目 Cavallina 氏
Face 2-phase: how much overdetermination is enough to get symmetry in multi-phase problems
van Meurs 氏
Convergence of a phases-field model to a system of moving particles (P) in 1D with collisions
Požár 氏
A rate-independent model of droplet evolution
講演要旨 講演要旨およびプログラムはこちらのPDFをご覧下さい

日時 6月23日(月)　１7時００分〜
場所 矢上キャンパス14棟733室
講演者 小池開 氏 (東京工業大学)
講演題目 Space-Time Pointwise asymptotic expansion for 1D viscous compressible flow
講演要旨 We consider solutions to 1D barotropic Navier−Stokes equations and construct their time-asymptotic expansions. Time-asymptotic expansion for solutions to NS equations are previously constructed by van Baalen, Popović, and Wayne (SIAM J. Math. Anal., ’08) in an L^2 framework. In this talk, we construct a similar expansion for which we can also obtain space-time pointwise estimates for the remainder. This in particular implies that the expansion is valid in L^1(\mathbb{R}).

日時 ４月１０日(月)　１４時００分〜１５時３０分
場所 矢上キャンパス12棟208室
講演者 Professor Dieter Bothe (Technical University of Darmstadt)
講演題目 Mass transfer across actual fluid interfaces - modeling and simulation
講演要旨 Fluid interfaces, such as bubbles, droplets, and liquid films that are out of chemical equilibrium irreversibly exchange mass. These interfaces, as part of real-world multiphase fluid systems, feature many complexities that make them challenging to study. Firstly, the fluid interface is a free, moving, and deformable phase boundary, making the problem inherently nonlinear and geometrically difficult. Introducing surface tension and the related pressure jump, the fluid interface renders the numerical treatment non-trivial even for pure fluids, especially if high density and/or viscosity ratios are present. If the fluid interface carries adsorbed molecules, the resulting Marangoni stresses add further nonlinearities to the system, resulting for instance in non-monotonic rise behavior.
　The bulk phases can also lead to complications. For example, in the case of gas bubbles, the ambient liquid is often a multicomponent mixture containing ionic constituents in polar liquids such as water, resulting in intrinsic electrical effects and/or non-Newtonian rheological behavior due to dissolved macromolecules such as polymers. The diffusive transport of solutes is characterized by high Schmidt numbers, often resulting in large Péclet numbers at moderate to large Reynolds numbers. This leads to extremely fine concentration boundary layers, of a thickness possibly down to the Bachelor length scale, requiring specific techniques for accurate numerical treatment, a challenge further tightened if fast chemical reactions occur.
　For complex liquids with, say, viscoelastic behavior, the interaction between the fluid interface, acting as an obstacle for the flow kinematics, with the liquid elasticity leads to surprising phenomena like negative wakes, cusp formation, and the well-known velocity jump discontinuity. In comparison to this, the gas phase description is not too involved with possible cross-diffusion and, more demanding, compressibility effects during longer bubble rise. Coming back to contamination by surfactants, the adsorption of surfactant strongly influences local mass transfer rates of, e.g., gaseous components into a liquid phase. Even for stagnant fluids, the partial coverage of the interface with surfactant molecules constitutes a barrier to mass transfer.
　The talk will provide an in-depth survey of the state of the art of local mass transfer modeling and computation at actual fluid interfaces, with a focus on recent work on subgrid-scale modeling and the interplay of surfactants and interfacial mass transfer.

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