Forces on a magnet moving past figure-eight coils

Eccentric figure-eight coils for transcranial magnetic stimulation.

Previously we proposed an eccentric figure-eight coil that can cause threshold stimulation in the brain at lower driving currents. In this study, we performed numerical simulations and magnetic stimulations to healthy subjects for evaluating the advantages of the eccentric coil. The simulations were performed using a simplified spherical brain model and a realistic human brain model. We found t...

Brownian Motion on the Figure Eight

In an interval containing the origin we study a Brownian motion which returns to zero as soon as it reaches the boundary. We determine explicitly its transition probability, prove it is ergodic and calculate the decay rate to equilibrium. It is shown that the process solves the martingale problem for certain asymmetric boundary conditions and can be regarded as a diffusion on an eight shaped do...

Intraoperative MRI: a moving magnet.

Hyperbolic Geometry on the Figure-Eight Knot Complement

The exact relationship between knot theory and non-euclidean geometry was a puzzle that survived more than 100 years. The histories of the two subjects were clearly intertwined; Carl Friedrich Gauss was a pioneer and did much to popularize both fields. After Gauss their two histories diverge a little, although taken together the list of luminaries in the two fields reads like a mathematical and...

Coils, Currents and Forces: Ampère’s Experiments on Electromagnetism

The focus of my paper lies on the discussion of some experiments that are to be implemented in the website of the STeT-project. In this discussion, several experiments described by André-Marie Ampère will play a central role. He is one of the researchers whose names are inseparably connected with electromagnetism. It was his experimental work after Hans Christian Ørsted’s discovery of electroma...