- 日時：2024年11月5日（火） 16:30-17:30
- 場所：京都大学 吉田キャンパス本部構内 総合校舎111講義室（mapの53番）
- 講師：Dr. Jan Haskovec (King Abdullah University of Science and Technology, The Computer, Electrical and Mathematical Science and Engineering division)
- 題目：Delay differential equations in models of collective motion
- 要旨：I will give an overview of recent results for models of collective behavior governed by functional differential equations with non-Markovian structure. The talk will focus on models of interacting agents with applications in biology (flocking, swarming), social sciences (opinion formation) and engineering (swarm robotics), where latency (delay) plays a significant role. I will characterize two main sources of delay - inter-agent communications ("transmission delay") and information processing ("reaction delay") - and discuss their impacts on the group dynamics. I will give an ovierview of analytical methods for studying the asymptotic behavior of the models in question and their mean-field limits. In particular, I will show that the transmission vs. reaction delay leads to fundamentally different mathematical structures and requires appropriate choice of analytical tools. Finally, motivated by situations where finite speed of information propagation is significant, I will introduce an interesting class of problems where the delay depends nontrivially and nonlinearly on the state of the system, and discuss the available analytical results and open problems here.
[1] J. Haskovec: Graph limit of the consensus model with self-delay. J. Phys. A: Math. Theor. 57 (2024), 345203.
[2] J. Haskovec: Direct proof of unconditional asymptotic consensus in the Hegselmann-Krause model with transmission-type delay. Bull. London Math. Soc. 53 (2021), pp. 1312-1323.
[3] J. Haskovec: Flocking in the Cucker-Smale model with self-delay and nonsymmetric interaction weights. J. Math. Anal. Appl. 514 (2022), 126261.
- 日時：2024年8月8日（火） 15:00-16:30
- 場所：京都大学 吉田キャンパス本部構内 総合研究7号館情報１講義室（キャンパスマップ68の建物，1階107）
- 講師：Prof. Vladimir Latocha (the University of Lorraine, Institut Elie Cartan de Lorraine)
- 題目：Improving solution manufacturing for highly anisotropic elliptic problems
- 要旨：In plasma physics, the electric field in a magnetised cavity is given as the solution to an anisotropic elliptic problem. When the intensity of the magnetic field is high, the situation becomes demanding, as the charged particles are nearly trapped along the magnetic field lines. From a numerical point of view, this leads to mixing different scales, damaging the numercial accuracy of the computations. However, separating scales and using differential geometry techniques allowed us to provide a reliable solution to a problem of interest, opening the way to developing reliable methods for solving theses problems.
- 日時：2024年7月30日（火） 15:00-16:00
- 場所：京都大学 吉田キャンパス本部構内 工学部総合校舎111
- 講師：Dr. Nico C. X. Stuhlmüller (Debye Institute for Nanomaterials Science, Utrecht University, Netherlands)
- 題目：Unconventional computers build from colloids and microfluidic channels
- 要旨：The energy consumption of machine learning is doubling every 4 months. This growth is projected to outpace the global energy production by 2040. The main bottleneck to more energy efficient machine learning is the von Neumann architecture, on which our computers are build. Novel unconventional compute architectures are promising to overcome this bottleneck. In this talk I present two different approaches.
1) Topological protection ensures stability of information and particle transport against perturbations. We explore experimentally and computationally the topologically protected transport of magnetic colloids above spatially inhomogeneous magnetic patterns, revealing that transport complexity can be encoded in both the driving loop and the pattern. Complex patterns support intricate transport modes when the microparticles are subjected to simple time-periodic loops of a uniform magnetic field. Using simple patterns and complex loops, we simultaneously and independently control the motion of several identical microparticles differing only in their positions above the pattern. Combining complex patterns and complex loops we transport microparticles from unknown locations to predefined positions and then force them to follow arbitrarily complex trajectories concurrently [1].
2) Memristive crossbar arrays have been used to massively reduce the energy consumption in feed forward machine learning networks. However, the training of networks, which usually consumes orders of magnitude more energy, is still done in conventional computers. As a first proof of concept we study in simulation NAND-gates build from microfluidic conical channels that act as memristors. Additionally we show simple learning procedures that can be implemented fully in hardware. These will open a way to enable the training as well as the inference to be done in memristive crossbar arrays, thereby massively reducing energy costs.
[1] Nico C. X. Stuhlmüller, et al., Nat. Commun. 14, 7517 (2023) https://doi.org/10.1038/s41467-023-43390-0
- 日時：2024年5月14日（火） 15:00-16:00
- 場所：京都大学 吉田キャンパス本部構内 総合研究8号館 講義室4（キャンパスマップ 59番）
- 講師：Prof. Ansgar Jüngel (Institute of Analysis and Scientific Computing, Technische Universität Wien, Austria)
- 題目：Emerging network structures: from biological vessel formation to neuromorphic computing
- 要旨：The understanding of the emergence of network structures is fundamental to describe biological networks like blood vessels and interconnected neuron systems. The vision is to develop biology-influenced computer devices whose design is inspired by the neural networks of the brain. Compared to artificial intelligence that relies on algorithms to process information, neuromorphic computing uses hardware that mimics the function of the brain. In this talk, we present diffusion-type models describing phenomena from cell biology, which may lead to biological or artificial networks. We report on some models, explain their key features, and present first numerical simulations.
- 第 1 回流体コロキウム
- 日時：3月19日（火）14:00-17:30
- 場所：京都大学（工学部総合校舎２１３）
- 発表者
田口智清（京大大学・情報学研究科）
奥田 尚（京都大学・数理解析研究所）
蛭田佳樹（京都大学・数理解析研究所）
富田卓磨（京大大学・情報学研究科） - プログラム
- Japan-France Joint Workshop: Interacting Particle Systems and Fluid Mechanics: Theory and Applications
- Date：Nov. 2 (Wed.) 14:00-18:50(JST)
- Venue：Institut Français du Japon-Kansai（アンスティチュ・フランセ関西）
- Speakers：
François Golse (Ecole Polytechnique)Yasunori Maekawa (Kyoto University)Ayman Moussa (Sorbonne Université & Ecole Normale Supérieure)Takaaki Nishida (Kyoto University)Francesco Salvarani (De Vinci Research Center & University of Pavia)Satoshi Taguchi (Kyoto University)
Tetsuro Tsuji (Kyoto University)
Shugo Yasuda (University of Hyogo) - Timetable (PDF)
- 日時：2022年10月28日（金） 16:30-17:30
- 場所：京都大学 吉田キャンパス本部構内 工学部総合校舎 111講義室（キャンパスマップ 53番）
- 講師：Prof. Francesco Salvarani (Pôle Universitaire Léonard de Vinci, France & Dipartimento di Matematica, Università di Pavia, Italy)
- 題目：Kinetic description of polyatomic gases undergoing resonant collisions
- 要旨：This talk is devoted to the study of a kinetic model describing a polyatomic gas in which the microscopic internal and kinetic energies are separately conserved during a collision process (resonant collisions). This behaviour has been observed in some physical phenomena, for example in the collisions between selectively excited CO_2 molecules. After describing the model itself, we prove the related H-theorem and show that, at the equilibrium, two temperatures are expected. We moreover prove a compactness property of the corresponding linearized Boltzmann operator. The peculiar structure of resonant collision rules allows to tensorize the problem and separately treat the internal energy contributions. We also propose a geometric variant of Grad's proof of the compactness property in the monatomic case.
- 本セミナーは、日本航空宇宙学会関西支部分科会「非平衡流体への運動学的アプローチ」（第8回）として開催されます。
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- 日時：
2020年3月11日（水）2020年3月30日（月）15:00-17:00
※新型コロナウイルス感染症の拡大防止のため，上記の通り開催日が変更されました．
COVID-19に関する現状を鑑み一旦中止とします．ご予定頂いていた方にはご不便，ご迷惑をおかけしますが，ご了解のほどよろしくおねがい申し上げます． - 場所：京都大学 吉田キャンパス本部構内 工学部総合校舎 213室（キャンパスマップ 53番）
- （第１部：15:00-16:00）講師：小池開 （慶應義塾大学理工学研究科）
- 題目：希薄気体力学における移動境界問題の数学解析について
- 要旨：希薄気体力学における移動境界問題について，講演者の成果を中心に，数学的な研究をいくつか紹介する．とくに，圧縮性粘性流体中を運動する物体の長時間挙動に関する講演者の結果を重点的に説明する．この結果は，BGK気体中を運動する物体の長時間挙動に関する数値計算結果 [Tsuji & Aoki, J. Comput. Phys. 250, 574–600 (2013)]にある程度の数学的な説明を与えるものである．また，講演者が抱えている今後の課題についても説明し，討論の種にできればと考えている．
- （第２部：16:00-17:00）講師：千葉逸人 （東北大学材料科学高等研究所）
- 題目：ネットワーク上の蔵本モデル
- 要旨：蔵本モデルは同期現象の標準的な数理モデルである。ここでは一般のネットワーク上で与えられた蔵本モデルのダイナミクスを一般化スペクトル理論を用いて解析し、同期が起こる条件とネットワーク構造の関係を明らかにする。
- 本セミナーは，二国間交流事業SAKURAプログラム「自己組織化する粒子集団に対する運動論的アプローチの開拓」の一環として行われます．
- 日時：2019年11月1日（金） 16:30-17:30
- 場所：京都大学 吉田キャンパス本部構内 工学部総合校舎 111講義室（キャンパスマップ 53番）
- 講師：Prof. Francesco Salvarani (Dipartimento di Matematica, Università di Pavia, Italy)
- 題目：On the homogenization problem for the linear Boltzmann equation
- 要旨：In this talk, we study the homogenization problem for the linear Boltzmann equation when the optical parameters are highly heterogeneous in the energy variable. We employ the method of two-scale convergence to arrive at the homogenization result. In doing so, we show the induction of a memory effect in the homogenization limit and we discuss its link with the self-shielding effect in nuclear reactor physics. The results presented here have been obtained in collaboration with Harsha Hutridurga and Olga Mula.
- 本セミナーは，日本航空宇宙学会関西支部分科会主催の「運動論方程式，流体力学とその周辺」（第10回）となります．
- 日時：2018年12月28日（金） 15:30-16:30
- 場所：京都大学 吉田キャンパス本部構内 工学部総合校舎 111講義室（キャンパスマップ 53番）
- 講師：Prof. Shih-Hsien Yu (Department of Mathematics, National University of Singapore, Singapore)
- 題目：Green's functions and Compressible Navier-Stokes equation
- 要旨：A class of decomposition of Green's functions for the compressible Navier-Stokes
linearized around a constant state is introduced. The singular structures of the Green's functions
are developed as essential devices to use the nonlinearity directly to covert the
2nd order quasi-linear PDE into a system of zero-th order integral equation with regular
integral kernels. The system of integrable equations allows a wider class of functions such as BV solutions.
We have shown global existence and well-posedness of the compressible Navier-Stokes
equation for isentropic gas with the gas constant $\gamma \in (0,e)$ in the Lagrangian
coordinate for the class of the BV functions and point wise $L^\infty$ around a constant state; and the
underline pointwise structure of the solutions is constructed.
- 日時：2018年9月7日（金） 15:00-16:00
- 場所：京都大学 吉田キャンパス本部構内 工学部総合校舎 213講義室（キャンパスマップ 53番）
- 講師：Prof. Ansgar Jüngel (Institute for Analysis and Scientific Computing, Vienna University of Technology, Austria)
- 題目：Multicomponent fluids: thermodynamic structure and structure-preserving numerical discretization
- 要旨：Multicomponent fluids can be modeled by parabolic cross-diffusion systems with fluxes which depend on the density gradients of all species. These systems possess a thermodynamic structure that can be translated into a mathematical formulation with nice properties like positivity of the diffusion matrix and boundedness of the mass fractions. For numerical discretizations, it is important to preserve these properties. In this talk, we present structure-preserving finite-volume and finite-element approximations modeling Stefan-Maxwell flows and ion transport through membranes.
