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| The 21st Century COE Program | ||
| Center of Excellence for Research and Education on Complex Functional Mechanical Systems | ||
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| The 21st Century COE Program | ||
| Center of Excellence for Research and Education on Complex Functional Mechanical Systems | ||
| 日時： | 2008年03月19日（水） 14:00〜 |
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| 場所： | 京都大学 工学部11号館 2階 会議室 |
| 講演者： | Prof. Reinhard Illner (Department of Mathematics and Statistics, University of Victoria, Canada) |
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| 講演題目： | Kinetic and fluid flow models for traffic flows |
| 講演要旨： | The management of traffic on modern expressways requires reasonable theoretical explanations of the origin of emergent phenomena (like traffic synchronization, the observation of multiple equilibria flows for certain densities, and the formation and propagation of stop-and-go waves for high densities). This talk will be an introduction to modern kinetic and fluid flow models of traffic flow, and how these models are related. A key feature of the modeling is the incorporation of the nonlocality in traffic (the fact that drivers will react to what they see at a location ahead, and at a distance depending on their speed). I will show how this is easily implemented into kinetic models of Fokker-Planck type, how one obtains unusual partial differential equations from these kinetic models, and how these partial differential equations depict stop-and-go waves in traffic as special solutions. |
| 講演者： | Prof. Irene M. Gamba (Department of Mathematics, University of Texas at Austin, USA) |
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| 講演題目： | Analysis and spectral-Lagrangian solvers for general non-linear Boltzmann type Equations |
| 講演要旨： |
We study long time dynamics to solutions of initial value problems to rather general Boltzmann kinetic models may describe qualitatively different processes in applications, but have many features in common. In particular we focus in the existence, uniqueness and asymptotics to dynamical scaling (self-similar) solutions and connections to stable laws for non-Gaussian states. In addition we present a deterministic spectral solver for the non-linear Boltzmann Transport Equation (energy conservative and non-conservative) for rather general collision kernels. The computation of the non-linear Boltzmann Collision integral and the lack of appropriate conservation properties due to spectral methods has been taken care by framing the conservation properties in the form of a constrained minimization problem which is solved easily using a Lagrange multiplier method. We benchmark our code with several examples of models for Maxwell type of interactions, (elastic or inelastic) for which explicit solution formulas are known. The numerical moments are compared with exact moments formulas and the numerical non-equilibrium probability distributions functions are compared to the general asymptotic results. The numerical method also produces accurate results in the case of inelastic hard-sphere interactions. Finally we show some preliminary calculations space inhomogeneous boundary value problems. |
| 京都大学大学院 | 工学研究科 | 機械理工学専攻 | マイクロエンジニアリング専攻 | 航空宇宙工学専攻 |
| 情報学研究科 | 複雑系科学専攻 | |||
| 京都大学 | 国際融合創造センター | |||
| 拠点リーダー | 椹木哲夫（工学研究科・機械理工学専攻） | |||