Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Complete solvability of the inertial spin model with an averaged spin


Authors: Hyungjin Huh and Dohyun Kim
Journal: Quart. Appl. Math.
MSC (2020): Primary 34C15; Secondary 34D06, 34C40
DOI: https://doi.org/10.1090/qam/1601
Published electronically: October 14, 2021
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We study the inertial spin model which consists of two variables: velocity as a mechanical observable and spin as an internal variable. In this paper, we slightly modified the original inertial spin model where the spin in the dynamics of the velocity is replaced by the average of spins. Moreover, by introducing two external control functions (rotation control and alignment control), we show the emergence of velocity and spin alignments mainly depends on these control functions. Finally, we perform numerical simulations that support and complement our theoretical results.


References [Enhancements On Off] (What's this?)

References

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC (2020): 34C15, 34D06, 34C40

Retrieve articles in all journals with MSC (2020): 34C15, 34D06, 34C40


Additional Information

Hyungjin Huh
Affiliation: Department of Mathematics, Chung-Ang University, Seoul 06974, Republic of Korea
MR Author ID: 725994
ORCID: 0000-0001-9844-845X
Email: huh@cau.ac.kr

Dohyun Kim
Affiliation: School of Mathematics, Statistics and Data Science, Sungshin Women’s University, Seoul 02844, Republic of Korea
MR Author ID: 858181
Email: dohyunkim@sungshin.ac.kr

Keywords: Cucker-Smale model, flocking, inertial spin model, swarm sphere model, synchronization
Received by editor(s): March 28, 2021
Received by editor(s) in revised form: September 5, 2021
Published electronically: October 14, 2021
Additional Notes: The first author was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government (MSIT) (2020R1F1A1A01072197)
The work of the second author was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No.2021R1F1A1055929) and the Sungshin Women’s University Research Grant H20210070.
Article copyright: © Copyright 2021 Brown University