| 研究開始時の研究の概要 |
For a century engineers and physicists have tried to understand plastic deformation of metals. Plastic deformation is understood as the group behaviour of many crystallographic defects which move and interact on microscopic length- and time-scales. Due to the complexity of the motion of defects, there is a lot of ambiguity on models for their group behaviour. To work to solving this ambiguity, this research focuses on simplified models for defect dynamics, and aims to derive rigorously the group behaviour of the defects.
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| 研究実績の概要 |
Last fiscal year, within the scope of my research plan on understanding plasticity through the limit passage of microscopic particle systems (which consists of 3 parts: (A) convergence rates, (B) particle annihilation and (C) atomistic models), I got 3 papers published and 3 submitted; all of which to peer-reviewed journals.
4 out of these 6 papers contribute to part (B). The first develops a simple but accurate scheme for solving the nonlocal and nonlinear PDE for the particle density. The second provides a rigorous connection between the particle system and an underlying phase field model; both of which are used in the engineering literature. The third extends the previously obtained discrete-to-continuum limit result to a much larger class of particle systems, which includes models for dislocation structures rather than individual dislocations. The fourth proves the conjecture that the trajectories of the particles are Holder continuous, whereas before it was only known that these trajectories were continuous.
The 2 remaining papers out of the 6 papers mentioned above fit to part (C); both establish the continuum limit (hydrodynamic limit) of stochastic interacting particle systems. One describes annihilation and creation of particles, and the other describes collisions of particles.
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