三好 建正 チームリーダ（理化学研究所，計算科学研究機構）
「Chaos, Predictability, and Data Assimilation」
概要： Data assimilation is a cross-disciplinary science to synergize numerical simulations and observational data, using statistical methods and applied mathematics. As computers become more powerful and enable more precise simulations, it will become more important to compare the simulation with actual observations. Data assimilation is also considered as chaos synchronization, a science field investigating synchronization of two chaotic dynamical systems through a limited exchange of information. In this presentation, I will introduce essential ideas of data assimilation for chaotic dynamical systems to maximize the predicting capability.
村主 崇行 助教（京都大学，白眉センター）
「Automated Generation and Optimization of PDE solvers」
概要： I am Takayuki Muranushi, an astrophysicist. My approach is to design
and implement new programming languages for astrophysical simulations.
Paraiso is a domain specific language embedded in functional programming language Haskell, for automated tuning of explicit solvers of partial differential equations (PDEs) on Graphic Processing Units (GPUs) as well as multicore CPUs. In Paraiso, one can describe PDE solving algorithms succinctly using tensor equations notation. Hydrodynamic properties, interpolation methods and other building blocks are described in abstract, modular, re-usable and combinable forms, which lets us generate versatile solvers from little set of Paraiso source codes.
A Navier-Stokes solver has been implemented and tested by Paraiso. A single source code less than 500 lines can be used to generate solvers of arbitrary dimensions, for both multicore CPUs and GPUs. We demonstrate both manual annotation based tuning and evolutionary computing based automated tuning of the program, that provides faster-than-hand-tuned codes on CPUs and an order of magnitude faster code on GPUs.
Recently, I've been trying to solve problems with such long timescales that explicit methods are not applicative. Also explicit solvers of PDEs, especially when combined with phenomenological models, tend to develop pathologically small timesteps or NaNs. As an alternative, I've been trying to formulate PDE solving methods methods as optimization problems on f(t,x) thus eliminating needs of causal time integral. I'm looking forward to the discussion with applied mathematicians!
郡 宏 准教授（お茶の水大学，大学院人間文化創成科学研究科）
「Novel dynamical behavior and coarse-grained description in oscillator networks」
概要： Oscillator networks exhibit a rich variety of dynamical behavior, including synchronization, clustering, waves, and spatio-temporal chaos. In this talk, I will present our recent studies on novel
dynamical behavior in coupled and forced oscillators: (i) Synchronization-chaos transition in oscillator networks, (ii)
instability due to interplay between noise and nonlinearity, (iii) common-noise-induced synchronization in an infinite number of globally coupled oscillators (i.e., the Kuramoto model). Finally, I will talk
about a new method for the coarse-grained description of oscillator networks.
備考: いつもと開催曜日と時刻が違うことにご注意下さい．また， 本セミナーは坂上クレスト連携セミナーとしても共催されます．
Elliott Ginder 助教（北海道大学，電子科学研究所）
「Interfacial dynamics and free boundary problems for oscillating membrane motions」
概要： We will present results on a model equation
related to droplet and bubble motions. The target equation is
a hyperbolic free boundary problem with volume and contact
angle constraints. By constructing a minimizing movement,
we are able to approximate the evolution and we show how
to obtain the convergence to a weak solution in the
one-dimensional (spatial) setting.
A different approach is needed for the case of "overhanging" contact angles, and so we have developed an approximation method, using thresholding dynamics, for computing motion by multiphase, volume preserving, mean curvature flow (with prescribed contact angles). Since this approach only specifies the velocity of the interface, we will also consider the case where the interface is allowed to oscillate.
The numerical methods for our approximation schemes have also been constructed and we would also like to show the numerical results of their implementation.
This is joint work with K. Svadlenka.
Pinaki Chakraborty 准教授(沖縄科学技術大学院大学)
「The Spectral Link in Turbulent Frictional Drag and Turbulent Mean Velocity Profile」