Numerical relativity with characteristic evolution, using six angular patches

The characteristic approach to numerical relativity is a useful tool in evolving gravitational systems. In the past this has been implemented using two patches of stereographic angular coordinates. In other applications, a six-patch angular coordinate system has proved effective. Here we investigate the use of a six-patch system in characteristic numerical relativity, by comparing an existing two-patch implementation (using second-order finite differencing throughout) with a new six-patch implementation (using either second- or fourth-order finite differencing for the angular derivatives). We compare these different codes by monitoring the Einstein constraint equations, numerically evaluated independently from the evolution. We find that, compared to the (second-order) two-patch code at equivalent resolutions, the errors of the second-order six-patch code are smaller by a factor of about 2, and the errors of the fourth-order six-patch code are smaller by a factor of nearly 50.Comment: 12 pages, 5 figures, submitted to CQG (special NFNR issue

Znajek-Damour Horizon Boundary Conditions with Born-Infeld Electrodynamics

In this work, the interaction of electromagnetic fields with a rotating (Kerr) black hole is explored in the context of Born-Infeld (BI) theory of electromagnetism instead of standard Maxwell theory and particularly BI theory versions of the four horizon boundary conditions of Znajek and Damour are derived. Naturally, an issue to be addressed is then whether they would change from the ones given in Maxwell theory context and if they would, how. Interestingly enough, as long as one employs the same local null tetrad frame as the one adopted in the works by Damour and by Znajek to read out physical values of electromagnetic fields and fictitious surface charge and currents on the horizon, it turns out that one ends up with exactly the same four horizon boundary conditions despite the shift of the electrodynamics theory from a linear Maxwell one to a highly non-linear BI one. Close inspection reveals that this curious and unexpected result can be attributed to the fact that the concrete structure of BI equations happens to be such that it is indistinguishable at the horizon to a local observer, say, in Damour's local tetrad frame from that of standard Maxwell theory.Comment: 38 pages, Revtex, typos corrected, accepted for publication in Phys. Rev.

A Formal Approach to Model Emotional Agents Behaviour in Disaster Management Situations

Abstract. Emotions in Agent and Multi-Agent Systems change their behaviour to a more ’natural ’ way of performing tasks thus increasing believability. This has various implications on the overall performance of a system. In particular in situations where emotions play an important role, such as disaster management, it is a challenge to infuse artificial emotions into agents, especially when a plethora of emotion theories are yet to be fully accepted. In this work, we develop a formal model for agents demonstrating emotional behaviour in emergency evacuation. We use state-based formal methods to define agent behaviour in two lay-ers; one that deals with non-emotional and one dealing with emotional behaviour. The emotional level takes into account emotions structures, personality traits and emotion contagion models. A complete formal def-inition of the evacuee agent is given followed by a short discussion on visual simulation and results to demonstrate the refinement of the for-mal model into code