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

Distribution of lactic acid between plasma and red cells during work and recovery

Lactic acid concentrations in plasma and red cells during work and recover

Creative approaches to emotional expression animation

In facial expression research, it is well established that certain emotional expressions are universally recognized. Studies into observer perception of expressions have built upon this research by highlighting the importance of particular facial regions, actions, and movements to the recognition of emotions. In many studies, the stimuli for such studies have been generated through posing by non-experts or performances by trained actors. However, character animators are required to craft recognizable, believable emotional facial expressions as a part of their profession. In this poster, the authors discuss some of the creative processes employed in their research into emotional expressions, and how practice-led research into expression animation might offer a new perspective on the generation of believable emotional expressions

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

Considerations for believable emotional facial expression animation

Facial expressions can be used to communicate emotional states through the use of universal signifiers within key regions of the face. Psychology research has identified what these signifiers are and how different combinations and variations can be interpreted. Research into expressions has informed animation practice, but as yet very little is known about the movement within and between emotional expressions. A better understanding of sequence, timing, and duration could better inform the production of believable animation. This paper introduces the idea of expression choreography, and how tests of observer perception might enhance our understanding of moving emotional expressions

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

Full major-shell calculation for states that were degenerate in a single-j-shell calculation

A full fp calculation is performed for states which were degenerate in a single-j-shell calculation in which isospin-zero two-body matrix elements were set to zero energy. Most of the splitting in a complete shell calculation (but not all) comes from the T=0 part of the interaction.Comment: 5 pages, RevTeX4. Submitted to Physical Review

Investigating facial animation production through artistic inquiry

Studies into dynamic facial expressions tend to make use of experimental methods based on objectively manipulated stimuli. New techniques for displaying increasingly realistic facial movement and methods of measuring observer responses are typical of computer animation and psychology facial expression research. However, few projects focus on the artistic nature of performance production. Instead, most concentrate on the naturalistic appearance of posed or acted expressions. In this paper, the authors discuss a method for exploring the creative process of emotional facial expression animation, and ask whether anything can be learned about authentic dynamic expressions through artistic inquiry