An Introduction to Conformal Ricci Flow

We introduce a variation of the classical Ricci flow equation that modifies the unit volume constraint of that equation to a scalar curvature constraint. The resulting equations are named the Conformal Ricci Flow Equations because of the role that conformal geometry plays in constraining the scalar curvature. These equations are analogous to the incompressible Navier-Stokes equations of fluid mechanics inasmuch as a conformal pressure arises as a Lagrange multiplier to conformally deform the metric flow so as to maintain the scalar curvature constraint. The equilibrium points are Einstein metrics with a negative Einstein constant and the conformal pressue is shown to be zero at an equilibrium point and strictly positive otherwise. The geometry of the conformal Ricci flow is discussed as well as the remarkable analytic fact that the constraint force does not lose derivatives and thus analytically the conformal Ricci equation is a bounded perturbation of the classical unnormalized Ricci equation. That the constraint force does not lose derivatives is exactly analogous to the fact that the real physical pressure force that occurs in the Navier-Stokes equations is a bounded function of the velocity. Using a nonlinear Trotter product formula, existence and uniqueness of solutions to the conformal Ricci flow equations is proven. Lastly, we discuss potential applications to Perelman's proposed implementation of Hamilton's program to prove Thurston's 3-manifold geometrization conjectures.Comment: 52 pages, 1 figur

Infrared Behaviour and Running Couplings in Interpolating Gauges in QCD

We consider the class of gauges that interpolates between Landau- and Coulomb-gauge QCD, and show the non-renormalisation of the two independent ghost-gluon vertices. This implies the existence of two RG-invariant running couplings, one of which is interpreted as an RG-invariant gauge parameter. We also present the asymptotic infrared limit of solutions of the Dyson-Schwinger equations in interpolating gauges. The infrared critical exponents of these solutions as well as the resulting infrared fixed point of one of the couplings are independent of the gauge parameter. This coupling also has a fixed point in the Coulomb gauge limit and constitutes a second invariant charge besides the well known colour-Coulomb potential.Comment: 8 pages, 2 figures; v2: minor changes, version published in PR

Emissivity measurements of reflective surfaces at near-millimeter wavelengths

We have developed an instrument for directly measuring the emissivity of reflective surfaces at near-millimeter wavelengths. The thermal emission of a test sample is compared with that of a reference surface, allowing the emissivity of the sample to be determined without heating. The emissivity of the reference surface is determined by one’s heating the reference surface and measuring the increase in emission. The instrument has an absolute accuracy of Δe = 5 x 10^-4 and can reproducibly measure a difference in emissivity as small as Δe = 10^-4 between flat reflective samples. We have used the instrument to measure the emissivity of metal films evaporated on glass and carbon fiber-reinforced plastic composite surfaces. We measure an emissivity of (2.15 ± 0.4) x 10^-3 for gold evaporated on glass and (2.65 ± 0.5) x 10^-3 for aluminum evaporated on carbon fiber-reinforced plastic composite

Barriers in the p-spin interacting spin-glass model. The dynamical approach

We investigate the barriers separating metastable states in the spherical p-spin glass model using the instanton method. We show that the problem of finding the barrier heights can be reduced to the causal two-real-replica dynamics. We find the probability for the system to escape one of the highest energy metastable states and the energy barrier corresponding to this process.Comment: 4 pages, 1 figur

Age, growth, mortality, and radiometric age validation of gray snapper (Lutjanus griseus) from Louisiana

The gray snapper (Lutjanus griseus) is a temperate and tropical reef fish that is found along the Gulf of Mexico and Atlantic coasts of the southeastern United States. The recreational fishery for gray snapper has developed rapidly in south Louisiana with the advent of harvest and seasonal restrictions on the established red snapper (L. campechanus) fishery. We examined the age and growth of gray snapper in Louisiana with the use of cross-sectioned sagittae. A total of 833 specimens, (441 males, 387 females, and 5 of unknown sex) were opportunistically sampled from the recreational fishery from August 1998 to August 2002. Males ranged in size from 222 to 732 mm total length (TL) and from 280 g to 5700 g total weight (TW) and females ranged from 254 to 756 mm TL and from 340 g to 5800 g TW. Both edge analysis and bomb radiocarbon analyses were used to validate otolith-based age estimates. Ages were estimated for 718 individuals; both males and females ranged from 1 to 28 years. The von Bertalanffy growth models derived from TL at age were Lt = 655.4{1–e[–0.23(t)]} for males, Lt = 657.3{1–e[– 0.21(t)]} for females, and L t = 656.4{1–e[– 0.22 (t)]} for all specimens of known sex. Catch curves were used to produce a total mortality (Z) estimate of 0.17. Estimates of M calculated with various methods ranged from 0.15 to 0.50; however we felt that M= 0.15 was the most appropriate estimate based on our estimate of Z. Full recruitment to the gray snapper recreational fishery began at age 4, was completed by age 8, and there was no discernible peak in the catch curve dome