Partial regularity of weak solutions of the liquid crystal equilibrium system

For a parameter, we consider the modified relaxed energy of the liquid crystal system. Each minimizer of the modified relaxed energy is a weak solution to the liquid crystal equilibrium system. We prove the partial regularity of minimizers of the modified relaxed energy. We also prove the existence of infinitely many weak solutions for the special boundary value x.

Regularity and relaxed problems of minimizing biharmonic maps into spheres

For n >= 5 and k >= 4, we show that any minimizing biharmonic map from Omega subset of R-n to S-k is smooth off a closed set whose Hausdorff dimension is at most n - 5. When n = 5 and k = 4, for a parameter lambda is an element of [0, 1] we introduce lambda-relaxed energy H-lambda of the Hessian energy for maps in W-2,W-2 (Omega; S-4) so that each minimizer u(lambda) of H-lambda is also a biharmonic map. We also establish the existence and partial regularity of a minimizer of H-lambda for lambda is an element of [0, 1).

Positive solutions of a Neumann problem with competing critical nonlinearities

We present existence results for a Neumann problem involving critical Sobolev nonlinearities both on the right hand side of the equation and at the boundary condition.. Positive solutions are obtained through constrained minimization on the Nehari manifold. Our approach is based on the concentration 'compactness principle of P. L. Lions and M. Struwe.

Rapid screening of 4000 individuals for germ-line variations in the BRAF gene

Background: The BRAF gene is frequently somatically altered in malignant melanoma. A majority of variations are at the valine 600 residue leading to a V600E substitution that constitutively activates the kinase. We screened 4000 patient and control DNAs for germ-line variations at the valine 600 residue. Methods: We developed a novel assay by adapting single-base variation assays and software for MALDI-TOF (matrix-assisted laser desorption/ionization time-of-flight) mass spectrometry to screen for all 5 reported variants at codon 600 of the BRAF gene. We screened a case-control collection comprising samples from 1082 melanoma patients and 154 of their unaffected relatives from 1278 families and from 2744 individuals from 659 unselected twin families with no history of melanoma. A panel of 66 melanoma cell lines was used for variation-positive controls. Results: All melanoma cell lines that we had found previously to carry a codon 600 variation were verified in this study. Three of the 4 possible variants (V600E n = 47, V600K n = 2, V600R n = 1) were detected, but no case of V600D was available. No germ-line variants were found in the samples from the 3980 melanoma patients or from the control individuals. Conclusions: This new assay is a high-throughput, automated alternative to standard sequencing and can be used as a rapid initial screen for somatic variants associated with melanoma. Germ-line variants at valine 600 are unlikely to exist and do not contribute to the reported role of the BRAF gene in melanoma predisposition. (c) 2006 American Association for Clinical Chemistry.

Functional-structural plant modelling using a combination of architectural analysis, L-systems and a canonical model of function

This paper presents a new method for producing a functional-structural plant model that simulates response to different growth conditions, yet does not require detailed knowledge of underlying physiology. The example used to present this method is the modelling of the mountain birch tree. This new functional-structural modelling approach is based on linking an L-system representation of the dynamic structure of the plant with a canonical mathematical model of plant function. Growth indicated by the canonical model is allocated to the structural model according to probabilistic growth rules, such as rules for the placement and length of new shoots, which were derived from an analysis of architectural data. The main advantage of the approach is that it is relatively simple compared to the prevalent process-based functional-structural plant models and does not require a detailed understanding of underlying physiological processes, yet it is able to capture important aspects of plant function and adaptability, unlike simple empirical models. This approach, combining canonical modelling, architectural analysis and L-systems, thus fills the important role of providing an intermediate level of abstraction between the two extremes of deeply mechanistic process-based modelling and purely empirical modelling. We also investigated the relative importance of various aspects of this integrated modelling approach by analysing the sensitivity of the standard birch model to a number of variations in its parameters, functions and algorithms. The results show that using light as the sole factor determining the structural location of new growth gives satisfactory results. Including the influence of additional regulating factors made little difference to global characteristics of the emergent architecture. Changing the form of the probability functions and using alternative methods for choosing the sites of new growth also had little effect. (c) 2004 Elsevier B.V. All rights reserved.

The influence of pressure during solidification of high pressure die cast aluminium telecommunications components

The effects of process variables on the quality of high-pressure die cast components was determined with the aid of in-cavity pressure sensors. In particular, the effects of set intensification pressure, delay time, and casting velocity have been investigated. The in-cavity pressure sensor has been used to determine how conditions within the die-cavity are related to the process parameters regulated by the die casting machine, and in turn the effect of variations in these parameters on the integrity of the final part. Porosity was found to decrease with increasing intensification pressure and increase with increasing casting velocity. The delay time before the application of the intensification pressure was not observed to have a significant effect on porosity levels. (c) 2006 Elsevier B.V. All rights reserved.

The role of migration in urban transition : studies of the relationship between migration and modernisation for Brisbane and Stockholm

Wilbur Zelinsky formulated a Hypothesis of Mobility Transition in 1971,in which he tried to relate all aspects of mobility to the Demographic Transition and modernisation. This dissertation applies the theoretical framework, proposed by Zelinsky and extended to encompass a family of transitions, to understand migration patterns of city regions. The two city regions, Brisbane and Stockholm, are selected as case studies, representing important city regions of similar size, but drawn from contrasting historical settings. A comparison of the case studies with the theoretical framework aims to determine how the relative contributions of net migration, the source areas of migrants, and the migration intensity change with modernisation. In addition, the research also aims to identify aspects of modernisation affecting migration. These aspects of migration are analysed with a "historical approach" and a "multivariate approach". An extensive investigation into the city regions' historical background provides the source, from which evidence for a relationship between migration and modernisation is extracted. With this historical approach, similarities and differences in migration patterns are identified. The other research approach analyse multivariate data, from the last two decades, on migration flows and modernisation. Correlations between migration and key aspects of modernisation are tested with multivariate regression, based on an alternative version of a spatial interaction model. The project demonstrates that the changing functions of cities and the structural modernisation are influential on migration. Similar patterns are found, regarding the relative contributions of net migration and natural increase to population growth. The research finds links between these changes in the relative contribution of net migration and demographic modernisation. The findings on variations in urban and rural source areas of migrants to city regions do not contradict the expected pattern, but data limitations prevent definite conclusion to be drawn. The assessment of variations in migration intensity resulted in the expected pattern not being supported. Based on Swedish data, the hypothesised increase in migration intensity is rejected. Interactional migration data also show patterns different from those derived from the theoretical framework. The findings, from both research approaches, suggested that structural modernisation affected migration flows more than demographic modernisation. The findings lead to a formulation of hypothesised patterns for migration to city regions. The study provides an important research contribution by applying the two research approaches to city regions. It also combines the study of internal and international migration to address the research objectives within a framework of transitional change.

Australia's relationship with the United States: The case for greater independence

A number of recent events-especially attempts to negotiate a bilateral trade agreement and Australia's participation in the conflicts in Afghanistan and Iraq(1)-have thrown Australia's relationship with the United States into sharp relief. While this relationship has historically enjoyed strong bilateral endorsement, such uncritical support is beginning to unravel. At the very least, the relationship is being subjected to a renewed, more critical scrutiny. This paper argues that a dispassionate analysis of the relationship is appropriate and overdue. Not only are the benefits that accrue to 'Australia' from the relationship debateable, even when judged within the limited calculus of the 'national interest', but Australia's uncritical support for US foreign policy is also helping to entrench potentially damaging aspects of American foreign policy and somewhat ironically-undermining the legitimacy of its pre-eminent 'hegemonic' position.

Information, Wildlife Valuation, Conservation: Experiments and Policy

The authors use experimental surveys to investigate the association between individuals' knowledge of particular wildlife species and their stated willingness to allocate funds to conserve each. The nature of variations in these allocations between species (e.g., their dispersion) as participants' knowledge increases is examined. Factors influencing these changes are suggested. Willingness-to-pay allocations are found not to measure the economic value of species, but are shown to be policy relevant. The results indicate that poorly known species, e.g., in remote areas, may obtain relatively less conservation support than they deserve. (JEL Q51, Q57, Q58)

Slurry flow in mills with TCPL - An efficient pulp lifter for ag/sag mills

The difficulties associated with slurry transportation in autogenous (ag) and semi-autogenous (sag) grinding mills have become more apparent in recent years with the increasing trend to build larger diameter mills for grinding high tonnages. This is particularly noticeable when ag/sag mills are run in closed circuit with classifiers such as fine screens/cyclones. Extensive test work carried out on slurry removal mechanism in grate discharge mills (ag/sag) has shown that the conventional pulp lifters (radial and curved) have inherent drawbacks. They allow short-circuiting of the slurry from pulp lifters into the grinding chamber leading to slurry pool formation. Slurry pool absorbs part of the impact thus inhibiting the grinding process. Twin Chamber Pulp Lifter (TCPL) - an efficient design of pulp lifter developed by the authors overcomes the inherent drawbacks of the conventional pulp lifters. Extensive testing in both laboratory and pilot scale mills has shown that the TCPL completely blocks the flow-back process, thus allowing the mill to operate close to their design flow capacity. The TCPL performance is also found to be independent of variations in charge volume and grate design, whereas they significantly affect the performance of conventional pulp lifters (radial and curved). (c) 2006 Elsevier B.V. All rights reserved.