研究集会

URL:https://tinyurl.com/tkwjom4


※ 本ワークショップは以下の支援を受けて開催されます．
Italian Embassy’s program: ”Japan meets Italian Scientists”
JSPS科研費 新学術領域研究 課題番号:19H05131 (研究代表者:Cesana Pierluigi)


プログラム

13:00 - 14:00
講演者 : Marco Morandotti (Technical University of Turin, IT)
講演タイトル : Variational models for dislocations: dynamics and upscaling
Abstract:
In this seminar, I will present a semi-discrete model for screw dislocation in an elastic solid undergoing anti-plane deformations. An amenable variational setting is proposed to study equilibrium configuration by energy minimisation principles. The dissipative dynamics of screw dislocations is studied rigorously as the gradient flow of the renormalised energy. Finally, I will address upscaling problems in one and two dimensions, showing how plasticity can be recovered when the number of dislocations grows to infinity.

14:00 - 14:40
講演者 : Masatoshi Mitsuhara (Kyushu University)
講演タイトル : Microscopic observation of formation process of kink bands in Mg-Zn-Y alloy with LPSO phase
Abstract:
The formation process of the kink bands in Mg-6%Zn-9%Y alloy was investigated in detail by in-situ analysis by SEM, and it succeeded in capturing the microstruc-tural change with no surface relief which should be called as the incipient kink bands (IKBs). Using TEM, it clearly founded that the IKBs involve the terminated-subgrain-boundaries which consists of edge dislocation arrays.
Authors: Masatoshi Mitsuhara (Kyushu University,), Shigeto Yamasaki (Kyushu University), Hideharu Nakashima (Kyushu University), Koji Hagihara (Osaka Uni-versity), Toshiyuki Fujii (Tokyo Institute of Technology).

14:40 - 15:00 休憩

15:00 - 15:40
講演者 : Pierluigi Cesana (Kyushu University)
講演タイトル : Mathematical models and ideas for disclinations
Abstract:
We present some recent results on the modeling of rotational mismatches and frustrations at the level of a crystal lattice. We introduce an energy functional defined over a triangular lattice accounting for nearest-neighbor interactions. We design special rotational type boundary value problems on the lattice so that the minimizers necessarily exhibit non-homogeneous rotations. We are interested in the asymptotics of the energy minima and minimizers as the lattice spacing van-ishes which we compute exactly with Gamma-convergence. We perform some nu-merical calculations for the discrete model and show that both the shape of the solutions as well as the values of the energies are in agreement with classical re-sults for positive and negative disclinations. This is a collaboration with P. van Meurs (Kanazawa).

15:40 - 16:20
講演者 : Kenji Kajiwara (Kyushu University)
講演タイトル : Log-aesthetic Curves in Industrial Design as Similarity Geometric Analogue of Euler’s Elasticae
Abstract:
We consider the log-aesthetic curves (LAC) which is the family of the planar curves developed in the industrial design as the shape elements with built-in aes-thetic character. We show that LAC can be formulated by the traveling wave solu-tions of the integrable deformation equation of the planar curves in the similarity geometry, as well as the variational principle with respect to the ”fairing energy”. This implies that LAC can be regarded as the similarity geometric analogue of the Euler’s elasticae. Based on this observation, we extend LAC to the space curves and surfaces.

組織委員：
Pierluigi Cesana (Kyushu University), cesana(at)imi.kyushu-u.ac.jp
Marco Morandotti (Technical University of Turin, IT)