In this comment we demonstrate that the example of a DC conducting wire of finite length as and example for the application of the Biot-Savart Law is flawed due to the non-conservation of electric charge for such an unphysical setting. The implications drawn in [1] on the restrictions of Ampère’s Circuital Law in integral form are unnecessary as long as only physically realizable situations obe...

This paper is devoted to a phenomenon in hyperbolic balance laws, first described by Fiedler and Liebscher [2], which is similar in spirit to the Turing instability. The combination of two individually stabilising effects can lead to quite rich dynamical behaviour, like instabilities, oscillations, or pattern formation. Our problem is composed of two ingredients. First, we have a strictly hyper...

Presented is a numerical model for solving the nonlinear dynamics of Alfvén eigenmodes and energetic ions self-consistently. The model is an extension of a previous bump-on-tail model [1, 2], taking into account particle orbits and wave fields in realistic toroidal geometries. The model can be used in conjunction with an orbit averaged Monte Carlo code that handles heating and current drive (si...

In one space dimension the standard conservation law has the form A class of high resolution multidimensional wave-propagation algorithms is described for general time-dependent hyperbolic systems. The methods are based on solving Riemann problems and qt 1 f(q)x 5 0, (1) applying limiter functions to the resulting waves, which are then propagated in a multidimensional manner. For nonlinear syst...

Applying the variational method, the spinless reduced Bethe-Salpeter (RBS) equation is solved for the mesonic systems, and the mass spectra are obtained. The method is applied to the Hamiltonian with the Gaussian and hydrogen-type trial wave functions, and different potential models are examined. The results for the different potentials are in challenge in light mesons, while they are consisten...

Non{strictly-hyperbolic and mixed-type conservation laws pose a challenge to computational methods. Speciically, the computation of transitional shock waves, which are dependent on the parabolic regularization of the conservation laws, is sensitive to the numerical viscosity. In this paper, we propose a front tracking algorithm that treats transitional shock waves correctly. The algorithm inclu...