A presentation for doctoral qualifying exam of our team member, Hansol Park, was held on May 8th, 2020.
A presentation of doctoral dissertation of our team member,
Woojoo Shim will be held on April 17th, 2020.
Date: April 17th (Fri) 11:00a.m.~12:00p.m.
Title: On the emergent behaviors of stochastic flocking models.
Abstract: We study stochastic alignment of the Justh-Krishnaprasad(J-K) model under the additive and multiplicative noises. Justh and Krishnaprasad proposed a planar Newtonian particle model for an ensemble of flocking agents moving with a unit speed, where the dynamics of the heading angles (of velocities) is governed by a generalized Kuramoto-type model with a communication weight. In this paper, we are interested in the random perturbation of the communication weight, which is represented by the additive and multiplicative noises.
There will be an invited talk.
Title: Regularity and Long-Time Behavior for Hydrodynamic Flocking Models
Speaker: Prof. Trevor Leslie (Univ. of Wisconsin-Madison)
Time: 2020 March 10th, 04:00pm~05:00pm
We consider the Euler Alignment model, a hydrodynamic analog of the discrete Cucker-Smale flocking ODE system. The salient feature of the Cucker-Smale model is the interaction of agents through a so-called “communication protocol” that tends to align the velocities of the agents; this alignment mechanism also drives the Euler Alignment PDEs. We discuss several of the different communication protocols treated in the literature and the corresponding wellposedness theory for the Euler Alignment model in each case. In the case of smooth, bounded protocols in one space dimension, it is possible to completely characterize the initial data leading to the existence of regular solutions, in terms of a certain pointwise balance between the initial velocity and the “total influence” from the density profile. This balance is captured by the sign of a certain quantity that we denote by e. Under the additional assumption of periodicity, a quantity closely related to e determines the long-time distortion of the density profile away from its average value.
The following is the information for our weekly seminar in this semester.
Date : March 13th, 2020 ~ (every Friday)
Time: 09:00am ~ 12:00pm
Text: “A Course on Rough Paths” by Peter K. Friz and Martin Hairer
Schedule for presentations
3/13: Linglong Du (Ch 1)
3/20: Bora Moon (Ch 2)
3/27: So Young Park (Ch 3)
4/3: Min-Jun Choi (Ch 4)
4/10: Hyun Jin An (Ch 5)
4/17: Presentation of Doctoral Dissertation by Woojoo Shim
4/24: Myeongju Kang (Ch 6)
5/1: Hangjun Jo (Ch 7)
5/8: Doctoral qualifying exam of Hansol Park
5/15: Woojoo Shim (Ch 8)
5/22: Hansol Park (Ch 9)
If you want to join our seminar, please contact Myeongju Kang: email@example.com