Golden Ratio Controlled Chaos in Supersymmetric Dynamics

We construct supersymmetric Lagrangians for the recently constructed off-shell worldline N=3 supermultiplet $Y_I/(i D_I X)$ for I=1,2,3, where $Y_I$ and $X$ are standard, Salam-Strathdee superfields: $Y_I$ fermionic and $X$ bosonic. Already the Lagrangian bilinear in component fields exhibits a total of thirteen free parameters, seven of which specify Zeeman-like coupling to external (magnetic) fluxes. All but special subsets of this parameter space describe aperiodic oscillatory response, some of which are controlled by the "golden ratio," $\varphi\approx1.61803$. We also show that all of these Lagrangians admit an $N=3\to 4$ supersymmetry extension, while a subset admits two inequivalent such extensions

An enamel-painted glass bottle from a “Turkish pit” in Buda

The fragments of a high quality, enamel painted, blue glass bottle with the date 1671 on its shoulder were found in the Castle District of Buda, in a huge pit dated to the period of the Ottoman occupation. The shape of the object shows eastern influences, while its decoration is clearly western. The origin of the bottle is probably Transylvanian, based on its characteristics and a small group of parallels

Periodic forcing in viscous fingering of a nematic liquid crystal

We study viscous fingering of an air-nematic interface in a radial Hele-Shaw cell when periodically switching on and off an electric field, which reorients the nematic and thus changes its viscosity, as well as the surface tension and its anisotropy (mainly enforced by a single groove in the cell). We observe undulations at the sides of the fingers which correlate with the switching frequency and with tip oscillations which give maximal velocity to smallest curvatures. These lateral undulations appear to be decoupled from spontaneous (noise-induced) side branching. We conclude that the lateral undulations are generated by successive relaxations between two limiting finger widths. The change between these two selected pattern scales is mainly due to the change in the anisotropy. This scenario is confirmed by numerical simulations in the channel geometry, using a phase-field model for anisotropic viscous fingering.Comment: completely rewritten version, more clear exposition of results (14 pages in Revtex + 7 eps figures

Centrosymmetric graphs and a lower bound for graph energy of fullerenes

The energy of a molecular graph G is defined as the summation of the absolute values of the eigenvalues of adjacency matrix of a graph G. In this paper, an infinite class of fullerene graphs with 10n vertices, n ≥ 2, is considered. By proving centrosymmetricity of the adjacency matrix of these fullerene graphs, a lower bound for its energy is given. Our method is general and can be extended to other class of fullerene graphs