Relative field-line helicity in bounded domains

Evolution of field line helicity during magnetic reconnection

Swarming in bounded domains

The Vicsek model is a prototype for the emergence of collective motion. In free space, it is characterized by a swarm of particles all moving in the same direction. Since this dynamic does not include attraction among particles, the swarm, while aligning in velocity space, has no spatial coherence. Adding specular reflection at the boundaries generates global spatial coherence of the swarms whi...

Bounded Domains and Unbounded Domains

First, notions of inside components and outside components are introduced for any subset of n-dimensional Euclid space. Next, notions of the bounded domain and the unbounded domain are defined using the above components. If the dimension is larger than 1, and if a subset is bounded, a unbounded domain of the subset coincides with an outside component (which is unique) of the subset. For a spher...

Helicity and the Electromagnetic Field

The structure of the Poincaré group gives, under all conditions, an equation of field helicity which reduces to the Maxwell equations and also gives cyclic relations between field components. If the underlying symmetry of special relativity is represented by the Poincaré group, it follows that the Maxwell equations and the cyclic equations are both products of special relativity itself, and bot...

Fractional Laplacian in bounded domains.

The fractional Laplacian operator -(-delta)(alpha/2) appears in a wide class of physical systems, including Lévy flights and stochastic interfaces. In this paper, we provide a discretized version of this operator which is well suited to deal with boundary conditions on a finite interval. The implementation of boundary conditions is justified by appealing to two physical models, namely, hopping ...