Equation of state of hard oblate ellipsoids by replica exchange Monte Carlo

We implemented the replica exchange Monte Carlo technique to produce the equation of state of hard 1:5 aspect-ratio oblate ellipsoids for a wide density range. For this purpose, we considered the analytical approximation of the overlap distance given by Bern and Pechukas and the exact numerical solution given by Perram and Wertheim. For both cases we capture the expected isotropic-nematic transition at low densities and a nematic-crystal transition at larger densities. For the exact case, these transitions occur at the volume fraction 0.341, and in the interval $0.584-0.605$, respectively.Comment: 4 pages, 2 figure

Nariai--Bertotti--Robinson spacetimes as a building material for one-way wormholes with horizons, but without singularity

We discuss the problem of wormholes from the viewpoint of gluing together two Reissner--Nordstr\"om-type universes while putting between them a segment of the Nariai-type world (in both cases there are also present electromagnetic fields as well as the cosmological constant). Such a toy wormhole represents an example of one-way topological communication free from causal paradoxes, though involving a travel to next spacetime sheet since one has to cross at least a pair of horizons through which the spacetimes' junction occurs. We also consider the use of thin shells in these constructions. Such a ``material'' for wormholes we choose taking into account specific properties of the Nariai--Bertotti--Robinson spacetimes.Comment: 5 pages, a talk delivered at the 11th Marcel Grossmann Meeting (2006

Bifurcation analysis of a normal form for excitable media: Are stable dynamical alternans on a ring possible?

We present a bifurcation analysis of a normal form for travelling waves in one-dimensional excitable media. The normal form which has been recently proposed on phenomenological grounds is given in form of a differential delay equation. The normal form exhibits a symmetry preserving Hopf bifurcation which may coalesce with a saddle-node in a Bogdanov-Takens point, and a symmetry breaking spatially inhomogeneous pitchfork bifurcation. We study here the Hopf bifurcation for the propagation of a single pulse in a ring by means of a center manifold reduction, and for a wave train by means of a multiscale analysis leading to a real Ginzburg-Landau equation as the corresponding amplitude equation. Both, the center manifold reduction and the multiscale analysis show that the Hopf bifurcation is always subcritical independent of the parameters. This may have links to cardiac alternans which have so far been believed to be stable oscillations emanating from a supercritical bifurcation. We discuss the implications for cardiac alternans and revisit the instability in some excitable media where the oscillations had been believed to be stable. In particular, we show that our condition for the onset of the Hopf bifurcation coincides with the well known restitution condition for cardiac alternans.Comment: to be published in Chao

Electronic transport through a parallel--coupled triple quantum dot molecule: Fano resonances and bound states in the continuum

The electronic transport through a triple quantum dot molecule attached in parallel to leads in presence of a magnetic flux is studied. Analytical expressions of the linear conductance and density of states for the molecule in equilibrium at zero temperature are obtained. As a consequence of quantum interference, the conductance exhibits in general a Breit--Wigner and two Fano resonances, the positions and widths of which are controlled by the magnetic field. Every two flux quanta, there is an inversion of roles of the bonding and antibonding states. For particular values of the magnetic flux and dot-lead couplings, one or even both Fano resonances collapse and bound states in the continuum (BIC's) are formed. The line broadenings of the molecular states are examined as a function of the Aharonov--Bohm phase around the condition for the formation of BIC's, finding resonances extremely narrow and robust against variations of the magnetic field.Comment: 15 pages, 7 figure