2014年度

2015.3.19 (木) 13:00〜16:00@中野キャンパス6階研究セミナー室3

第7-8回明治非線型数理セミナー

講演者1： Gadi Fibich (Tel Aviv University) 13:00〜

『Necklace solitary waves on bounded domains』

概要：In this talk I will present a new type of solitary waves of the two-dimensional cubic nonlinear Schrödinger equation on bounded domains. These multi-peak "necklace" solitary waves consist of several identical localized profiles ("pearls"), such that adjacent "pearls" have opposite signs. We observe numerically that necklace solitary waves on bounded domains such as rectangles, circles, and annuli, are stable at low powers, but become unstable at powers well below the critical power for collapse.

This is in contrast with the corresponding ground-state ("single-pearl") solitary waves, which are always stable. The necklace instability is excited by perturbations that break the antisymmetry between adjacent pearls, and thus lead to power transfer between pearls. In particular, necklace instability is unrelated to collapse. In order to compute numerically the profile of necklace solitary waves on bounded domains such as rectangles, circles, and annuli, we introduce a non-spectral variant of Petviashvili's renormalization method.

Joint work with Dima Shpigelman

講演者2： Olivier Pinaud (Colorado State University, U.S.) 14:30〜

『Recent results in the analysis of quantum hydrodynamical models』

概要：The motivation for this work is to lay the mathematical foundations of a formal theory introduced by P. Degond and C. Ringhofer in 2003 about quantum hydrodynamics. Their idea is to transpose to the quantum setting Levermore's closure strategy by entropy minimization for the derivation of hydrodynamical models. We will present two different types of results: the first ones concern the resolution of the so-called quantum moment problem, which is the first brick of the theory and a transposition to operators of the classical moment problem for measures. The second ones concern the dynamics of quantum states and their convergence to statistical equilibria.

2015.1.14 (水) 13:30〜14:30@中野キャンパス6階研究セミナー室3

第5回明治非線型数理セミナー・第8回自己組織化セミナー合同開催 (Poster)

講演者： Guy Theraulaz (Université Paul Sabatier, France)

『Secrets of swarm architecture: 3D stigmergic construction in ant colonies』

概要：One of the most famous feats of insect societies is their ability to build impressive nest architectures. The evolution of construction techniques used by ants, wasps, bees and termites has provided a whole set of innovations in terms of architectural designs that proved to be efficient to control nest temperature, to ensure gas exchanges with the outside environment or to adapt nest architecture to colony size. The big question is: how do insects interact to coordinate their building actions? To investigate these issues, we focused on the early stages of nest construction in the garden ant Lasius niger. We disentangled the coordinating mechanisms at work and then developed a 3D model implementing these mechanisms. Our model showed that the evaporation rate of a building pheromone was a highly influential parameter. The model also revealed that complex helicoidal structures connecting nearby chambers emerge from a constant remodeling process of the nest architecture.

2014.9.9 (火) 18:00〜19:00@生田キャンパス5号館5201室

第3回明治非線型数理セミナー

講演者： 長山雅晴 (北海道大学)

『自走粒子の集団運動に対する数理解析』

講演者は，8日〜11日まで，同部屋で理工学研究科の集中講義をおこなっています．

2014.6.2 (月) 17:30〜18:30@中野キャンパス6階603室(研究セミナー室3)

第1回明治非線型数理セミナー

講演者： 坂上貴之 (京都大学)『構造安定な二次元ハミルトンベクトル場の位相分類理論とその流体現象への応用』

概要：二次元の多重連結領域における構造安定なハミルトンベクトル場を考える．本講演では，そのハミルトニアンの等高線(流線)の位相構造の分類理論および，その位相構造に固有の「文字列」を割り当てる方法について解説する．また，本理論の流体現象への応用例も示す予定である．

流線の位相構造の文字列による流れの表現により，組み合わせ論的にすべての可能な流れを書き出すことが容易になるだけでなく，特定の流線の位相構造を特定の文字列によって表現できるため，流れ場構造の特徴づけの(分野横断を可能にする)共通言語としても利用できる．

また，このようなベクトル場は二次元非粘性・非圧縮流体の作る流れ場と対応しているので，この理論を使うと与えられた実験や数値計算で得られた流れ場の流線の構造の把握や時間発展を文字列で表現できるようになるなど応用上も新しい流体運動の記述を与える．

本研究は京都教育大学 横山知郎准教授との共同研究である．また，JST数学西浦領域におけるJST CREST「渦・境界相互作用が創出するパラダイムシフト」による支援により行われたものである．