You are here

  1. Home
  2. Dynamical Systems seminar - A computer-assisted proof of magnetic-field growth for the Stretch-Fold-Shear model of a kinematic dynamo

Dynamical Systems seminar - A computer-assisted proof of magnetic-field growth for the Stretch-Fold-Shear model of a kinematic dynamo

Dates
Wednesday, March 24, 2021 - 14:00 to 15:00

Speakers:Farhana Pramy and Ben Mestel (The Open University)

Title: A computer-assisted proof of magnetic-field growth for the Stretch-Fold-Shear model of a kinematic dynamo
The Stretch-Fold-Shear family $S_\alpha$ is a one-parameter family of linear operators acting on complex-valued functions $c(x)$, for $x \in [-1,1]$, and parametrised by a real parameter $\alpha \ge 0$. The family arises from a stylized model of magnetic field growth in kinematic dynamo theory that was developed by Andrew Gilbert and for which an eigenvalue of modulus greater than 1 corresponds to magnetic field growth. 
 In this talk we describe a computer-assisted proof of the existence of an eigenvalue of $S_\alpha$ of modulus greater than 1 for $\alpha$ in the range $\pi/2 < \alpha \le 5$, thereby partially proving a conjecture of Gilbert.