The use of adaptive mesh refinement (AMR) techniques is crucial for accurate and efficient simulation of higher dimensional spacetimes. In this work we develop an adaptive algorithm tailored to the integration of finite difference discretizations of wave-like equations using characteristic coordinates. We demonstrate the algorithm by constructing a code implementing the Einstein-Klein-Gordon sy...

This paper introduces a number of refinements to the Parallel Coordinates visualisation metaphor for multidimensional data. Firstly, the traditional set of poly-lines are replaced with a collection of smooth curves across the attribute axes, allowing individual data elements to be traced under certain limitations; normally impossible due to the ‘crossing problem’. Then the notion of spreading o...

We construct explicit solutions of the Hermitian Yang-Mills equations on the noncommutative space C θ . In the commutative limit they coincide with the standard instantons on CP written in local coordinates.

Let M be a non-compact hyperbolic 3-manifold that has a triangulation by positively oriented ideal tetraedra. We explain how to produce local coordinates for the variety defined by the gluing equations for SL(3,C)representations. In particular we prove local rigidity of the “geometric” representation in SL(3,C), recovering a recent result of Menal-Ferrer and Porti. More generally we give a crit...

in this study, flow characteristics through symmetric stenosis artery are investigated. the shape of eccentricity for stenotic flows is limited by circular-cross sections and plaques are usually assumed as to be oriented concentrically. thegoverningequationsaretheusualnavier-stokesequationsandare numericallysolved by using finite volumemethod in arbitrary orthogonal curvilinear coordinates. in ad...