2014 Fiscal Year Final Research Report
Dynamical feature of mathematically obtained m-point blow-up solution in mean field equation for two-dimensional point vortex system
| Project/Area Number |
24540400
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Mathematical physics/Fundamental condensed matter physics
|
|---|
| Research Institution | Shizuoka University |
|---|
Principal Investigator |
|
|---|
| Co-Investigator(Renkei-kenkyūsha) |
HATORI Tadatsugu 神奈川大学, 理学部, 非常勤講師 (80023729)
YANAGISAWA Taku 奈良女子大学, 理学部, 教授 (30192389)
OHTSUKA Hiroshi 金沢大学, 数物科学系, 教授 (20342470)
|
|---|
| Project Period (FY) |
2012-04-01 – 2015-03-31
|
| Keywords | 自己組織化 / 2次元点渦系 / 絶対負温度 / Onsager理論 / インバースカスケード |
|---|
| Outline of Final Research Achievements |
It is mathematically anticipated by Nagasaki and Suzuki that in the two-dimensional point vortex system there is an equilibrium singular solution diverging at m points whose inverse temperature is given by β = -8πm. Our final goal is to understand the solution dynamically.
The following notations are used here: u velocity field, ω vorticity, ψ stream function. The point vortex system relaxes violently by the second term div(uω) in the Euler equation. After the violent relaxation, the system reaches a state characterized by div(uω)=0. In this state there are many small regions with different temperature and in each region, the collisional effect vanishes. The small diffusive effect remains due to the interaction between small regions with different beta. This is the main mechanism of the slow relaxation in the point vortex system.
|
| Free Research Field |
数値流体力学
|
