| Title: | Some analysis of compressible fluids in multi-connected domains--- Part I |
| Time: | 15:00:00 - 16:00:00 |
| Place: | Room 501a, Academic Building No. 1, CUHK |
| Abstract: | This talk presents some results on the two-dimensional compressible Navier-Stokes equations and the Magnetohydrodynamic system in multi-connected domains. More precisely, we will talk about the global well-posedness and the large-time asymptotic behavior of the strong solutions, as well as some relevant div-curl type inequalities. The first part of the talk will showcase some known works, the peculiarity of the multi-connected domains, and the role of div-curl type inequalities. In the second part, we will mainly focus on various div-curl type inequalities. |
| Title: | Random Batch Methods for classical and quantum molecular dynamics |
| Time: | 15:00:00 - 16:00:00 |
| Place: | Room 501a, Academic Building No. 1 |
| Abstract: | Random batch methods were introduced for general interacting particle systems with a large number (N >> 1) of particles, with a linear complexity of O(N). We extend this method to molecular dynamics with Coulomb interactions, in the framework of Ewald summation. We will show its superior performance compared to the current state-of-the-art methods (for example, PPPM) for the corresponding problems, in both computational efficiency and parallelizability. We use it not only to reduce the cost of long-range interactions but also the short-range ones, and as a result, we are able to simulate 10 million molecules with just one GPU. We also extend it to quantum Monte Carlo simulation. |
| Title: | Some analysis of compressible fluids in multi-connected domains--- Part II |
| Time: | 15:00:00 - 16:00:00 |
| Place: | Room 501a, Academic Building No. 1, CUHK |
| Abstract: | This talk presents some results on the two-dimensional compressible Navier-Stokes equations and the Magnetohydrodynamic system in multi-connected domains. More precisely, we will talk about the global well-posedness and the large-time asymptotic behavior of the strong solutions, as well as some relevant div-curl type inequalities. The first part of the talk will showcase some known works, the peculiarity of the multi-connected domains, and the role of div-curl type inequalities. In the second part, we will mainly focus on various div-curl type inequalities. |