4 citations · 4 across the 6 of their papers we have counts for
7 papers
Electric current dynamics in the stellarator coil winding surface model
Wadim Gerner, Anouk Nicolopoulos-Salle, Diego Pereira Botelho
In stellarator design, the coil winding surfaces support current distributions that shape the magnetic field. This work provides a theoretical framework e…
Inverse problems for quasi-linear elliptic systems modeling electrolysers
Giovanni S. Alberti, Wadim Gerner, Matteo Santacesaria
We investigate the electrochemical processes within an electrolyser cell, which are modelled by a coupled system of second-order quasi-linear elliptic PDEs. In this context, we stu…
Non-optimal domains for the helicity maximisation problem
Wadim Gerner
In [J. Cantarella, D. DeTurck, H. Gluck and M. Teytel, J. Math. Phys. 41:5615 (2000)] the helicity isoperimetric problem which asks to find a smooth domain of fixed volume which ma…
Quantitative Gaffney and Korn inequalities
Wadim Gerner
We prove a homogeneous, quantitative version of Ehrling's inequality for the function spaces , which reflects ge…
Kernel and image of the Biot-Savart operator and their applications in stellarator designs
Wadim Gerner
We consider the Biot-Savart operator acting on regular, div-free, surface currents \begin{gather} \nonumber \operatorname{BS}(j)(x)=\frac{1}{4π}\int_Σj(y)\…
Asymptotic windings, surface helicity and their applications in plasma physics
Wadim Gerner
In [J. Cantarella, J. Parsley, J. Geom. Phys. 60:1127 (2010)] Cantarella and Parsley introduced the notion of submanifold helicity. In the present paper we investigate properties o…
Properties of the Biot-Savart operator acting on surface currents
Wadim Gerner
We investigate properties of the image and kernel of the Biot-Savart operator in the context of stellarator designs for plasma fusion. We first show that for any given coil winding…