Towards an understanding of corporate web identity

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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

The Bell-Szekeres Solution and Related Solutions of the Einstein-Maxwell Equations

A novel technique for solving some head-on collisions of plane homogeneous light-like signals in Einstein-Maxwell theory is described. The technique is a by-product of a re-examination of the fundamental Bell-Szekeres solution in this field of study. Extensions of the Bell-Szekeres collision problem to include light-like shells and gravitational waves are described and a family of solutions having geometrical and topological properties in common with the Bell-Szekeres solution is derived.Comment: 18 pages, Latex fil

Variational data assimilation using targetted random walks

The variational approach to data assimilation is a widely used methodology for both online prediction and for reanalysis (offline hindcasting). In either of these scenarios it can be important to assess uncertainties in the assimilated state. Ideally it would be desirable to have complete information concerning the Bayesian posterior distribution for unknown state, given data. The purpose of this paper is to show that complete computational probing of this posterior distribution is now within reach in the offline situation. In this paper we will introduce an MCMC method which enables us to directly sample from the Bayesian\ud posterior distribution on the unknown functions of interest, given observations. Since we are aware that these\ud methods are currently too computationally expensive to consider using in an online filtering scenario, we frame this in the context of offline reanalysis. Using a simple random walk-type MCMC method, we are able to characterize the posterior distribution using only evaluations of the forward model of the problem, and of the model and data mismatch. No adjoint model is required for the method we use; however more sophisticated MCMC methods are available\ud which do exploit derivative information. For simplicity of exposition we consider the problem of assimilating data, either Eulerian or Lagrangian, into a low Reynolds number (Stokes flow) scenario in a two dimensional periodic geometry. We will show that in many cases it is possible to recover the initial condition and model error (which we describe as unknown forcing to the model) from data, and that with increasing amounts of informative data, the uncertainty in our estimations reduces

Do early-life exposures explain why more advantaged children get eczema? Findings from the U.K. Millennium Cohort Study

Background: Atopic dermatitis (eczema) in childhood is socially patterned, with higher incidence in more advantaged populations. However, it is unclear what factors explain the social differences. Objectives: To identify early-life risk factors for eczema, and to explore how early-life risk factors explain any differences in eczema. Methods: We estimated odds ratios (ORs) for ever having had eczema by age 5 years in 14 499 children from the U.K. Millennium Cohort Study (MCS), with a focus on maternal, antenatal and early-life risk factors and socioeconomic circumstances (SECs). Risk factors were explored to assess whether they attenuated associations between SECs and eczema. Results: Overall 35·1% of children had ever had eczema by age 5 years. Children of mothers with degree-level qualifications vs. no educational qualifications were more likely to have eczema (OR 1·52, 95% confidence interval 1·31–1·76), and there was a gradient across the socioeconomic spectrum. Maternal atopy, breastfeeding (1–6 weeks and ≥ 6 months), introduction of solids under 4 months or cow's milk under 9 months, antibiotic exposure in the first year of life and grime exposure were associated with an increased odds of having eczema. Female sex, Pakistani and Bangladeshi ethnicity, smoking during pregnancy, exposure to environmental tobacco smoke and having more siblings were associated with reduced odds for eczema. Controlling for maternal, antenatal and early-life characteristics (particularly maternal smoking during pregnancy, breastfeeding and number of siblings) reduced the OR for eczema to 1·26 (95% confidence interval 1·03–1·50) in the group with the highest educational qualifications compared with the least. Conclusions: In a representative U.K. child cohort, eczema was more common in more advantaged children. This was explained partially by early-life factors including not smoking during pregnancy, breastfeeding and having fewer siblings

Comparative analysis of techniques for evaluating the effectiveness of aircraft computing systems

Performability analysis is a technique developed for evaluating the effectiveness of fault-tolerant computing systems in multiphase missions. Performability was evaluated for its accuracy, practical usefulness, and relative cost. The evaluation was performed by applying performability and the fault tree method to a set of sample problems ranging from simple to moderately complex. The problems involved as many as five outcomes, two to five mission phases, permanent faults, and some functional dependencies. Transient faults and software errors were not considered. A different analyst was responsible for each technique. Significantly more time and effort were required to learn performability analysis than the fault tree method. Performability is inherently as accurate as fault tree analysis. For the sample problems, fault trees were more practical and less time consuming to apply, while performability required less ingenuity and was more checkable. Performability offers some advantages for evaluating very complex problems

Study of providing omnidirectional vibration isolation to entire space shuttle payload packages

Techniques to provide omnidirectional vibration isolation for a space shuttle payload package were investigated via a reduced-scale model. Development, design, fabrication, assembly and test evaluation of a 0.125-scale isolation model are described. Final drawings for fabricated mechanical components are identified, and prints of all drawings are included

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