743 research outputs found
Profiles of inflated surfaces
We study the shape of inflated surfaces introduced in \cite{B1} and
\cite{P1}. More precisely, we analyze profiles of surfaces obtained by
inflating a convex polyhedron, or more generally an almost everywhere flat
surface, with a symmetry plane. We show that such profiles are in a
one-parameter family of curves which we describe explicitly as the solutions of
a certain differential equation.Comment: 13 pages, 2 figure
On Unconstrained SU(2) Gluodynamics with Theta Angle
The Hamiltonian reduction of classical SU(2) Yang-Mills field theory to the
equivalent unconstrained theory of gauge invariant local dynamical variables is
generalized to the case of nonvanishing theta angle. It is shown that for any
theta angle the elimination of the pure gauge degrees of freedom leads to a
corresponding unconstrained nonlocal theory of self-interacting second rank
symmetric tensor fields, and that the obtained classical unconstrained
gluodynamics with different theta angles are canonically equivalent as on the
original constrained level.Comment: 13 pages Revtex, no figures; several misprints corrected; version to
appear in Eur. Phys. J.
A new doubly discrete analogue of smoke ring flow and the real time simulation of fluid flow
Modelling incompressible ideal fluids as a finite collection of vortex
filaments is important in physics (super-fluidity, models for the onset of
turbulence) as well as for numerical algorithms used in computer graphics for
the real time simulation of smoke. Here we introduce a time-discrete evolution
equation for arbitrary closed polygons in 3-space that is a discretisation of
the localised induction approximation of filament motion. This discretisation
shares with its continuum limit the property that it is a completely integrable
system. We apply this polygon evolution to a significant improvement of the
numerical algorithms used in Computer Graphics.Comment: 15 pages, 3 figure
- …