Partial regularity for a surface growth model

We prove two partial regularity results for the scalar equation $u_t+u_{xxxx}+\partial_{xx}u_x^2=0$, a model of surface growth arising from the physical process of molecular epitaxy. We show that the set of space-time singularities has (upper) box-counting dimension no larger than $7/6$ and $1$-dimensional (parabolic) Hausdorff measure zero. These parallel the results available for the three-dimensional Navier--Stokes equations. In fact the mathematical theory of the surface growth model is known to share a number of striking similarities with the Navier--Stokes equations, and the partial regularity results are the next step towards understanding this remarkable similarity. As far as we know the surface growth model is the only lower-dimensional "mini-model" of the Navier--Stokes equations for which such an analogue of the partial regularity theory has been proved. In the course of our proof, which is inspired by the rescaling analysis of Lin (1998) and Ladyzhenskaya & Seregin (1999), we develop certain nonlinear parabolic Poincar\'e inequality, which is a concept of independent interest. We believe that similar inequalities could be applicable in other parabolic equations.Comment: 29 page

AOIPS 3 User's guide. Volume 1: Overview and software utilization

This is Volume I of the Atmospheric and Oceanographic Information Processing System (AOIPS) User's Guide. AOIPS 3 is the version of the AOIPS software as of April 1989. The AOIPS software was developed jointly by the Goddard Space Flight Center and General Sciences Corporation. Volume 1 is intended to provide the user with an overall guide to the AOIPS system. It introduces the user to AOIPS system concepts, explains how programs are related and the necessary order of program execution, and provides brief descriptions derived from on-line help for every AOIPS program. It is intended to serve as a reference for information such as: program function, inmput/output variable descriptions, program limitations, etc. AOIPS is an interactive meteorological processing system with capabilities to ingest and analyze the many types of meteorological data. AOIPS includes several applications in areas of relevance to meteorological research. AOIPS is partitioned into four applications components: satellite data analysis, radar data analysis, aircraft data analysis, and utilities

The star-formation history of the universe - an infrared perspective

A simple and versatile parameterized approach to the star formation history allows a quantitative investigation of the constraints from far infrared and submillimetre counts and background intensity measurements. The models include four spectral components: infrared cirrus (emission from interstellar dust), an M82-like starburst, an Arp220-like starburst and an AGN dust torus. The 60 $\mu$m luminosity function is determined for each chosen rate of evolution using the PSCz redshift data for 15000 galaxies. The proportions of each spectral type as a function of 60 $\mu$m luminosity are chosen for consistency with IRAS and SCUBA colour-luminosity relations, and with the fraction of AGN as a function of luminosity found in 12 $\mu$m samples. The luminosity function for each component at any wavelength can then be calculated from the assumed spectral energy distributions. With assumptions about the optical seds corresponding to each component and, for the AGN component, the optical and near infrared counts can be accurately modelled. A good fit to the observed counts at 0.44, 2.2, 15, 60, 90, 175 and 850 $\mu$m can be found with pure luminosity evolution in all 3 cosmological models investigated: $\Omega_o$ = 1, $\Omega_o$ = 0.3 ($\Lambda$ = 0), and $\Omega_o$ = 0.3, $\Lambda$ = 0.7. All 3 models also give an acceptable fit to the integrated background spectrum. Selected predictions of the models, for example redshift distributions for each component at selected wavelengths and fluxes, are shown. The total mass-density of stars generated is consistent with that observed, in all 3 cosmological models.Comment: 20 pages, 25 figures. Accepted for publication in ApJ. Full details of models can be found at http://astro.ic.ac.uk/~mrr/countmodel

A Tension Shell Structure for Application to Entry Vehicles

The shape of a shell of revolution designed t o have only tensile stresses under axisymmetric aerodynamic loadings has been derived on the basis of linear membrane theory. values of circumferential tension is also given. The results of this paper indicate that the design of an entry vehicle based on the tension shell concept leads to desirable aerodynamic and structural characteristics, namely, high drag and low weight

The Gravitational Hamiltonian in the Presence of Non-Orthogonal Boundaries

This paper generalizes earlier work on Hamiltonian boundary terms by omitting the requirement that the spacelike hypersurfaces $\Sigma_t$ intersect the timelike boundary $\cal B$ orthogonally. The expressions for the action and Hamiltonian are calculated and the required subtraction of a background contribution is discussed. The new features of a Hamiltonian formulation with non-orthogonal boundaries are then illustrated in two examples.Comment: 23 pages, 1 figure, LaTeX. The action is altered to include a corner term which results in a different value for the non-orthogonal term. An additional appendix with Euclidean results is included. To appear in Class. Quant. Gra

The arch truss girder again.—More upon the new system

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Summary of progress and plans for penguin-related analyses, with reference to comments made on previous submissions

Modelling of penguin dynamics, including of their interaction with pelagic fish abundance, by MARAM scientists is taking place on three fronts: I) Models of the possible impact of fishing in the vicinity of penguin colonies II) Models of the impact of the total pelagic catch on penguin dynamics III) Models of Robben Island penguin dynamics using tag-recapture data. This paper summarises the current situation, offering an understanding of recent debates on certain aspects of earlier analyses, and indicates plans for future analyses on all three fronts. It should be noted that progress on I) is linked to the initiatives of the ICTT (Island Closure Task Team) of the PWG. Furthermore note that it is planned to submit results from the analyses planned for review at the annual international assessment review workshop scheduled to be held over 29 November to 3 December later this year, so that results therefrom can inform the PWG deliberations later in December from which recommendations for management of the Pelagic Fishery for 2011 will be developed

The Power Spectrum of the PSC Redshift Survey

We measure the redshift-space power spectrum P(k) for the recently completed IRAS Point Source Catalogue (PSC) redshift survey, which contains 14500 galaxies over 84% of the sky with 60 micron flux >= 0.6 Jansky. Comparison with simulations shows that our estimated errors on P(k) are realistic, and that systematic errors due to the finite survey volume are small for wavenumbers k >~ 0.03 h Mpc^-1. At large scales our power spectrum is intermediate between those of the earlier QDOT and 1.2 Jansky surveys, but with considerably smaller error bars; it falls slightly more steeply to smaller scales. We have fitted families of CDM-like models using the Peacock-Dodds formula for non-linear evolution; the results are somewhat sensitive to the assumed small-scale velocity dispersion \sigma_V. Assuming a realistic \sigma_V \approx 300 km/s yields a shape parameter \Gamma ~ 0.25 and normalisation b \sigma_8 ~ 0.75; if \sigma_V is as high as 600 km/s then \Gamma = 0.5 is only marginally excluded. There is little evidence for any `preferred scale' in the power spectrum or non-Gaussian behaviour in the distribution of large-scale power.Comment: Latex, uses mn.sty, 14 pages including 11 Postscript figures. Accepted by MNRA