A widely used prototype phase model to describe the synchronous behavior of weakly coupled limit-cycle oscillators is the Kuramoto model whose dynamics for sufficiently large ensemble of oscillators can be effectively approximated by the corresponding mean-field equation ’the Kuramoto Sakaguchi Equation’. In the recent past, it has been extensively studied to analyze the phase transition of...
The classical Nernst-Planck model suffers from its inability to accurately resolve boundary layers where locally large ion concentrations and pronounced voltage differences occur. In nanofluidic applications like nanopores with charged pore walls,
one spatial dimension is in the order of the Debye length which corresponds to the boundary layer width.
Improved models, in particular models that...
To model hybrid resonances in fusion plasma, Maxwell’s equations feature a sign changing permittivity tensor. The problem can be expressed as a degenerate elliptic PDE. There is no uniqueness of the solution, and the solutions admit a singularity inside the domain.
A small regularizing viscosity parameter can be introduced, but the problem is still numerically challenging because of the...
We consider the sedimentation of N identical spherical particles in a uniform gravitational field. Particle rotation is included in the model while inertia is neglected.
In the dilute case, the result in [5] shows that the particles do not get closer in finite time. The rigorous convergence of the dynamics to the solution of a Vlasov-Stokes equation is proven in [4] in a certain averaged...
