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

Photonic realization of the relativistic Kronig-Penney model and relativistic Tamm surface states

Photonic analogues of the relativistic Kronig-Penney model and of relativistic surface Tamm states are proposed for light propagation in fibre Bragg gratings (FBGs) with phase defects. A periodic sequence of phase slips in the FBG realizes the relativistic Kronig-Penney model, the band structure of which being mapped into the spectral response of the FBG. For the semi-infinite FBG Tamm surface states can appear and can be visualized as narrow resonance peaks in the transmission spectrum of the grating

Purity-bounded uncertainty relations in multidimensional space -- generalized purity

Uncertainty relations for mixed quantum states (precisely, purity-bounded position-momentum relations, developed by Bastiaans and then by Man'ko and Dodonov) are studied in general multi-dimensional case. An expression for family of mixed states at the lower bound of uncertainty relation is obtained. It is shown, that in case of entropy-bounded uncertainty relations, lower-bound state is thermal, and a transition from one-dimensional problem to multi-dimensional one is trivial. Results of numerical calculation of the relation lower bound for different types of generalized purity are presented. Analytical expressions for general purity-bounded relations for highly mixed states are obtained.Comment: 12 pages, 2 figures. draft version, to appear in J. Phys. A Partially based on a poster "Multidimensional uncertainty relations for states with given generalized purity" presented on X Intl. Conf. on Quantum Optics'2004 (Minsk, Belarus, May 30 -- June 3, 2004) More actual report is to be presented on ICSSUR-2005, Besan\c{c}on, France and on EQEC'05, Munich. V. 5: amended article after referees' remark