Properties of derivative expansion approximations to the renormalization group

Approximation only by derivative (or more generally momentum) expansions, combined with reparametrization invariance, turns the continuous renormalization group for quantum field theory into a set of partial differential equations which at fixed points become non-linear eigenvalue equations for the anomalous scaling dimension $\eta$. We review how these equations provide a powerful and robust means of discovering and approximating non-perturbative continuum limits. Gauge fields are briefly discussed. Particular emphasis is placed on the r\^ole of reparametrization invariance, and the convergence of the derivative expansion is addressed.Comment: (Minor touch ups of the lingo.) Invited talk at RG96, Dubna, Russia; 14 pages including 2 eps figures; uses LaTeX, epsf and sprocl.st

Excitation of the molecular gas in the nuclear region of M82

We present high-resolution HIFI spectroscopy of the nucleus of the archetypical starburst galaxy M 82. Six ^(12)CO lines, 2 ^(13)CO lines and 4 fine-structure lines have been detected. Besides showing the effects of the overall velocity structure of the nuclear region, the line profiles also indicate the presence of multiple components with different optical depths, temperatures, and densities in the observing beam. The data have been interpreted using a grid of PDR models. It is found that the majority of the molecular gas is in low density (n = 10^(3.5) cm^(-3)) clouds, with column densities of N_H = 10^(21.5) cm^(-2) and a relatively low UV radiation field (G_0 = 10^2). The remaining gas is predominantly found in clouds with higher densities (n = 10^5 cm^(-3)) and radiation fields (G_0 = 10^(2.75)), but somewhat lower column densities (N_H = 10^(21.2) cm^(-2)). The highest J CO lines are dominated by a small (1% relative surface filling) component, with an even higher density (n = 10^6 cm^(-3)) and UV field (G_0 = 10^(3.25)). These results show the strength of multi-component modelling for interpretating the integrated properties of galaxies

Computer program to generate attitude error equations for a gimballed platform

Computer program for solving attitude error equations related to gimballed platform is described. Program generates matrix elements of attitude error equations when initial matrices and trigonometric identities have been defined. Program is written for IBM 360 computer

Varieties of cheese

While Cheddar cheese is by far the main type as far as English speaking countries are concerned, it is only one of a large number of varieties of cheese which are becoming more universal in production and consumption. In other than English speaking countries Cheddar cheese is almost unknown and yet the consumption of cheese in some of these countries is very much greater. The naming of cheese types has usually been a result of the use of the name of the place where the cheese was first made. Thus cheeses of similar type but produced in a different locality or country, were given different names. While small differences may occur between cheese produced in different localities these differences are not sufficient to warrant the naming of the cheese as distinct types. For example, Cheddar cheeses produced in different localities sometimes have slight differences which an experienced cheese grader can readily detect but all cheese would still be regarded as Cheddar type. With a very large number of named cheeses to consider it is necessary to find some basis for dividing the cheese into groups and thus a study of the group will cover the main features of the many named cheeses which might be included in that group.https://researchlibrary.agric.wa.gov.au/bulletins/1256/thumbnail.jp

Gauged Dimension Bubbles

Some of the peculiar electrodynamical effects associated with gauged ``dimension bubbles'' are presented. Such bubbles, which effectively enclose a region of 5d spacetime, can arise from a 5d theory with a compact extra dimension. Bubbles with thin domain walls can be stabilized against total collapse by the entrapment of light charged scalar bosons inside the bubble, extending the idea of a neutral dimension bubble to accommodate the case of a gauged U(1) symmetry. Using a dielectric approach to the 4d dilaton-Maxwell theory, it is seen that the bubble wall is almost totally opaque to photons, leading to a new stabilization mechanism due to trapped photons. Photon dominated bubbles very slowly shrink, resulting in a temperature increase inside the bubble. At some critical temperature, however, these bubbles explode, with a release of radiation.Comment: 14 pages, no figures; to appear in Phys.Rev.