Infrared Magnitude-Redshift Relations for Luminous Radio Galaxies

Infrared magnitude-redshift relations for the 3CR and 6C samples of radio galaxies are presented for a wide range of plausible cosmological models, including those with non-zero cosmological constant OmegaLambda. Variations in the galaxy formation redshift, metallicity and star formation history are also considered. The results of the modelling are displayed in terms of magnitude differences between the models and no-evolution tracks, illustrating the amount of K-band evolution necessary to account for the observational data. Given a number of plausible assumptions, the results of these analyses suggest that: (i) cosmologies which predict T_0xH_0>1 (where T_0 denotes the current age of the universe) can be excluded; (ii) the star formation redshift should lie in the redshift interval 5evolution, the high redshift radio galaxies are more luminous (ie. more massive) than those nearby in models with finite OmegaLambda, including the favoured model with Omega=0.3, OmegaLambda=0.7. For cosmological models with larger values of T_0xH_0, the conclusions are the same regardless of whether any adjustments are made or not. The implications of these results for cosmology and models of galaxy formation are discussed.

Nucleated polymerization with secondary pathways. I. Time evolution of the principal moments.

Self-assembly processes resulting in linear structures are often observed in molecular biology, and include the formation of functional filaments such as actin and tubulin, as well as generally dysfunctional ones such as amyloid aggregates. Although the basic kinetic equations describing these phenomena are well-established, it has proved to be challenging, due to their non-linear nature, to derive solutions to these equations except for special cases. The availability of general analytical solutions provides a route for determining the rates of molecular level processes from the analysis of macroscopic experimental measurements of the growth kinetics, in addition to the phenomenological parameters, such as lag times and maximal growth rates that are already obtainable from standard fitting procedures. We describe here an analytical approach based on fixed-point analysis, which provides self-consistent solutions for the growth of filamentous structures that can, in addition to elongation, undergo internal fracturing and monomer-dependent nucleation as mechanisms for generating new free ends acting as growth sites. Our results generalise the analytical expression for sigmoidal growth kinetics from the Oosawa theory for nucleated polymerisation to the case of fragmenting filaments. We determine the corresponding growth laws in closed form and derive from first principles a number of relationships which have been empirically established for the kinetics of the self-assembly of amyloid fibrils.