Agile thinking in motion graphics practice and its potential for design education

Motion Graphics is relatively new subject and its methodologies are still being developed. There are useful lessons to be learnt from the practice in early cinema from the 1890's to the 1930's where Agile thinking was used by a number of practitioners including Fritz Lang. Recent studies in MA Motion Graphics have accessed some of this thinking incorporating them in a series of Motion Graphic tests and experiments culminating in a two minute animation “1896 Olympic Marathon”. This paper demonstrates how the project and its design methodology can contribute new knowledge for the practice and teaching of this relatively new and expanding area of Motion Graphic Design. This would be not only invaluable to the International community of Motion Graphic practitioners, Educators and Researchers in their development of this maturing field. But also to the broader Multidisciplinary disciplines within Design Education. These methodologies have been arrived at by accessing the work of creative and reflective practice as defined by Carol Grey and Julian Marlin in Visualizing Research (2004) and reflective practice as defined by Donald Schon (1983). Central to the investigation has been the approach of Agile thinking from the methodology of "Bricolage" by Levi Strauss "The Savage Mind" (1966)

Iterated fibre sums of algebraic Lefschetz fibrations

Let M denote the total space of a Lefschetz fibration, obtained by blowing up a Lefschetz pencil on an algebraic surface. We consider the n-fold fibre sum M(n), generalizing the construction of the elliptic surfaces E(n). For a Lefschetz pencil on a simply-connected minimal surface of general type we partially calculate the Seiberg-Witten invariants of the fibre sum M(n) using a formula of Morgan-Szabo-Taubes. As an application we derive an obstruction for self-diffeomorphisms of the boundary of the tubular neighbourhood of a general fibre in M(n) to extend over the complement of the neighbourhood. Similar obstructions are known in the case of elliptic surfaces.Comment: 14 pages; to appear in Quart. J. Mat

Towards a general description of the interior structure of rotating black holes

The purpose of this paper is to present a number of proposals about the interior structure of a rotating black hole that is accreting slowly, but in an arbitrary time- and space-dependent fashion. The proposals could potentially be tested with numerical simulations. Outgoing and ingoing particles free-falling in the parent Kerr geometry become highly focused along the principal outgoing and ingoing null directions as they approach the inner horizon, triggering the mass inflation instability. The original arguments of Barrabes, Israel & Poisson (1990) regarding inflation in rotating black holes are reviewed, and shown to be based on Raychauduri's equation applied along the outgoing and ingoing null directions. It is argued that gravitational waves should behave in the geometric optics limit, and consequently that the spacetime should be almost shear-free. A full set of shear-free equations is derived. A specific line-element is proposed, which is argued should provide a satisfactory approximation during early inflation. Finally, it is argued that super-Planckian collisions between outgoing and ingoing particles will lead to entropy production, bringing inflation to an end, and precipitating collapse.Comment: 15 page

The interior structure of rotating black holes 3. Charged black holes

This paper extends to the case of charged rotating black holes the conformally stationary, axisymmetric, conformally separable solutions presented for uncharged rotating black holes in a companion paper. In the present paper, the collisionless fluid accreted by the black hole may be charged. The charge of the black hole is determined self-consistently by the charge accretion rate. As in the uncharged case, hyper-relativistc counter-streaming between ingoing and outgoing streams drives inflation at (just above) the inner horizon, followed by collapse. If both ingoing and outgoing streams are charged, then conformal separability holds during early inflation, but fails as inflation develops. If conformal separability is imposed throughout inflation and collapse, then only one of the ingoing and outgoing streams can be charged: the other must be neutral. Conformal separability prescribes a hierarchy of boundary conditions on the ingoing and outgoing streams incident on the inner horizon. The dominant radial boundary conditions require that the incident ingoing and outgoing number densities be uniform with latitude, but the charge per particle must vary with latitude such that the incident charge densities vary in proportion to the radial electric field. The sub-dominant angular boundary conditions require specific forms of the incident number- and charge-weighted angular motions. If the streams fall freely from outside the horizon, then the prescribed angular conditions can be achieved by the charged stream, but not by the neutral stream. Thus, as in the case of an uncharged black hole, the neutral stream must be considered to be delivered ad hoc to just above the inner horizon.Comment: Version 1: 12 pages, no figures. Version 2: Extensively revised, logic tightened, derivation more elegant. 18 pages, no figures. Version 3: Minor revisions to match published version. Mathematica notebook available at http://jila.colorado.edu/~ajsh/rotatinginflationary/rotatinginflationary.n

Cyclic group actions and embedded spheres in 4-manifolds

In this note we derive an upper bound on the number of 2-spheres in the fixed point set of a smooth and homologically trivial cyclic group action of prime order on a simply-connected 4-manifold. This improves the a priori bound which is given by one half of the Euler characteristic of the 4-manifold. The result also shows that in some cases the 4-manifold does not admit such actions of a certain order at all or that any such action has to be pseudofree.Comment: 13 pages; to appear in Proc. Amer. Math. So

Representing homology classes by symplectic surfaces

We derive an obstruction to representing a homology class of a symplectic 4-manifold by an embedded, possibly disconnected, symplectic surface.Comment: 5 page