On methods to determine bounds on the Q-factor for a given directivity

This paper revisit and extend the interesting case of bounds on the Q-factor for a given directivity for a small antenna of arbitrary shape. A higher directivity in a small antenna is closely connected with a narrow impedance bandwidth. The relation between bandwidth and a desired directivity is still not fully understood, not even for small antennas. Initial investigations in this direction has related the radius of a circumscribing sphere to the directivity, and bounds on the Q-factor has also been derived for a partial directivity in a given direction. In this paper we derive lower bounds on the Q-factor for a total desired directivity for an arbitrarily shaped antenna in a given direction as a convex problem using semi-definite relaxation techniques (SDR). We also show that the relaxed solution is also a solution of the original problem of determining the lower Q-factor bound for a total desired directivity. SDR can also be used to relax a class of other interesting non-convex constraints in antenna optimization such as tuning, losses, front-to-back ratio. We compare two different new methods to determine the lowest Q-factor for arbitrary shaped antennas for a given total directivity. We also compare our results with full EM-simulations of a parasitic element antenna with high directivity.Comment: Correct some minor typos in the previous versio

Critical exponents of the two-layer Ising model

The symmetric two-layer Ising model (TLIM) is studied by the corner transfer matrix renormalisation group method. The critical points and critical exponents are calculated. It is found that the TLIM belongs to the same universality class as the Ising model. The shift exponent is calculated to be 1.773, which is consistent with the theoretical prediction 1.75 with 1.3% deviation.Comment: 7 pages, with 10 figures include

System Size Stochastic Resonance: General Nonequilibrium Potential Framework

We study the phenomenon of system size stochastic resonance within the nonequilibrium potential's framework. We analyze three different cases of spatially extended systems, exploiting the knowledge of their nonequilibrium potential, showing that through the analysis of that potential we can obtain a clear physical interpretation of this phenomenon in wide classes of extended systems. Depending on the characteristics of the system, the phenomenon results to be associated to a breaking of the symmetry of the nonequilibrium potential or to a deepening of the potential minima yielding an effective scaling of the noise intensity with the system size.Comment: LaTex, 24 pages and 9 figures, submitted to Phys. Rev.

Wave nucleation rate in excitable systems in the low noise limit

Motivated by recent experiments on intracellular calcium dynamics, we study the general issue of fluctuation-induced nucleation of waves in excitable media. We utilize a stochastic Fitzhugh-Nagumo model for this study, a spatially-extended non-potential pair of equations driven by thermal (i.e. white) noise. The nucleation rate is determined by finding the most probable escape path via minimization of an action related to the deviation of the fields from their deterministic trajectories. Our results pave the way both for studies of more realistic models of calcium dynamics as well as of nucleation phenomena in other non-equilibrium pattern-forming processes

Prediction of infrared light emission from pi-conjugated polymers: a diagrammatic exciton basis valence bond theory

There is currently a great need for solid state lasers that emit in the infrared, as this is the operating wavelength regime for applications in telecommunications. Existing $\pi$--conjugated polymers all emit in the visible or ultraviolet, and whether or not $\pi$--conjugated polymers that emit in the infrared can be designed is an interesting challenge. On the one hand, the excited state ordering in trans-polyacetylene, the $\pi$--conjugated polymer with relatively small optical gap, is not conducive to light emission because of electron-electron interaction effects. On the other hand, excited state ordering opposite to that in trans-polyacetylene is usually obtained by chemical modification that increases the effective bond-alternation, which in turn increases the optical gap. We develop a theory of electron correlation effects in a model $\pi$-conjugated polymer that is obtained by replacing the hydrogen atoms of trans-polyacetylene with transverse conjugated groups, and show that the effective on-site correlation in this system is smaller than the bare correlation in the unsubstituted system. An optical gap in the infrared as well as excited state ordering conducive to light emission is thereby predicted upon similar structural modifications.Comment: 15 pages, 15 figures, 1 tabl