Instantons for Vacuum Decay at Finite Temperature in the Thin Wall Limit

In $N+1$ dimensions, false vacuum decay at zero temperature is dominated by the $O(N+1)$ symmetric instanton, a sphere of radius $R_0$, whereas at temperatures $T>>R_0^{-1}$, the decay is dominated by a `cylindrical' (static) $O(N)$ symmetric instanton. We study the transition between these two regimes in the thin wall approximation. Taking an $O(N)$ symmetric ansatz for the instantons, we show that for $N=2$ and $N=3$ new periodic solutions exist in a finite temperature range in the neighborhood of $T\sim R_0^{-1}$. However, these solutions have higher action than the spherical or the cylindrical one. This suggests that there is a sudden change (a first order transition) in the derivative of the nucleation rate at a certain temperature $T_*$, when the static instanton starts dominating. For $N=1$, on the other hand, the new solutions are dominant and they smoothly interpolate between the zero temperature instanton and the high temperature one, so the transition is of second order. The determinantal prefactors corresponding to the `cylindrical' instantons are discussed, and it is pointed out that the entropic contributions from massless excitations corresponding to deformations of the domain wall give rise to an exponential enhancement of the nucleation rate for $T>>R_0^{-1}$.Comment: 24 pages, 7 figures available upon request, DAMTP-R-94/

Geographic Information Systems (GIS) in Assessing Dental Health

The present study investigated the distribution profile of dental caries and its association with areas of social deprivation at the individual and contextual level. The cluster sample consisted of 1,002 12-year-old schoolchildren from Piracicaba, SP, Brazil. The DMFT Index was used for dental caries and the Care Index was used to determine access to dental services. On the individual level, variables were associated with a better oral status. On the contextual level, areas were not associated with oral status. However, maps enabled determining that the central districts have better social and oral conditions than the deprived outlying districts