Banca de DEFESA: Marina Costa Merch dos Santos
Uma banca de DEFESA de MESTRADO foi cadastrada pelo programa.STUDENT : Marina Costa Merch dos Santos
DATE: 03/02/2023
TIME: 10:00
LOCAL: Departamento de Matemática
TITLE:
Bifurcations in the Interaction of Two Dipoles in the Presence of an External Magnetic FieldKEY WORDS:
PAGES: 82
BIG AREA: Ciências Exatas e da Terra
AREA: Matemática
SUMMARY:
Consider two magnetic dipoles fixed in the plane, free to spin, separated by a distance r, subjected to a homogenous external magnetic field applied with a certain orientation. This system is a non-linear dynamical system and the goal of this work is to determine and classify its equilibrium points and the bifurcations suffered by the system caused by the changes of the applied fields. The equations of the motion of the dipoles are obtained from Newton’s second law in angular terms considering the torques that each of the dipoles undergoes due to the presence of the other and due to rotational friction. We show that only two of the eight equilibrium points, obtained in the absence of an external magnetic field, are stable. Their basins of attraction were built using the Runge-Kutta method. As the intensity and orientation of the applied external field are varied, the system can undergo five different types of bifurcations that can destroy, create and change the stability of these equilibrium points. For high intensities, we observe that only four equilibrium points remain, and only one is stable. The results of this analysis were obtained from the application of a combination of the Continuation Method, the Newton-Raphson Method and the Runge-Kutta Method.
BANKING MEMBERS:
Presidente - 1700664 - YURI DUMARESQ SOBRAL
Interno - 1702477 - LUCAS CONQUE SECO FERREIRA
Interno - 2185886 - PAULO HENRIQUE PEREIRA DA COSTA
Externo ao Programa - 3228575 - JORGE CARLOS LUCERO
Externo à Instituição - RUDIMAR LUIZ NOS - UTFPR