Understanding plasticity of metals through proving discrete-to-continuum limits of interacting particle systems
| Project/Area Number |
20K14358
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| Research Category |
Grant-in-Aid for Early-Career Scientists
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| Allocation Type | Multi-year Fund |
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| Review Section |
Basic Section 12040:Applied mathematics and statistics-related
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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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| Project Status |
Granted (Fiscal Year 2022)
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| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2023: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2022: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2021: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2020: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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| Keywords | discrete-to-continuum / interacting particles / dislocations / hydrodynamic limit / continuum limits / particle systems / Particle system |
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| Outline of Research at the Start |
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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| 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, 1 accepted and 2 submitted; all of which to highly respected peer-reviewed journals.
The first published paper completes part (B) in the one-dimensional case: it establishes the continuum limit for an interacting particle system in which particles of opposite sign can annihilate one another. It got published in one of the best journals in the field. The second published paper applies my previous achievements on (A) to obtain sharper estimates in approximation theory. One of the submitted papers reveals the connection between the particle system of this published paper and a quasi atomistic model (as in (C)).
Concerning the remaining four papers (one published, one accepted and two submitted), two of them establish the continuum limit (hydrodynamic limit) of stochastic interacting particle systems involving both annihilation and creation, which fits to (C). The accepted paper ensures local existence and uniqueness of certain singular ODEs with tools from dynamical systems, which provide a new framework for studying particle collisions in part (B) in higher dimensions.
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| Current Status of Research Progress |
Current Status of Research Progress
2: Research has progressed on the whole more than it was originally planned.
Reason
Half of the goals in the proposal have been completed in the published papers. These papers have sparked several follow-up problems related to projects (A), (B) and (C) in the proposal. I am currently working on 6 such problems.
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| Strategy for Future Research Activity |
I will continue the 6 problems mentioned in the "Current Status" section, and aim to submit 5 of them as papers to highly respected peer-reviewed journals during FY 2023. These papers will not reach all goals set out in projects (A), (B) and (C) in the proposal, but I believe that they make good progress towards them.
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Report
(3 results)
Research Products
(25 results)
