2023 Fiscal Year Annual Research Report
Understanding plasticity of metals through proving discrete-to-continuum limits of interacting particle systems
| Project/Area Number |
20K14358
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| Research Institution | Kanazawa University |
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Principal Investigator |
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| Project Period (FY) |
2020-04-01 – 2024-03-31
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| Keywords | discrete-to-continuum / interacting particles / dislocations / hydrodynamic limit |
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| Outline of Annual Research Achievements |
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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