Asymptotic limits of a self-dual Ginzburg-Landau functional in bounded domains

In the author's joint paper [HJS] with Jest and Struwe, we discuss asymtotic limits of a self-dual Ginzburg-Landau functional involving a section of a line bundle over a closed Riemann surface and a connection on this bundle. In this paper, the author generalizes the above results [HJS] to the case of bounded domains.

Two estimates concerning asymptotics of the minimizations of a Ginzburg-Landau functional

We prove two asymptotical estimates for minimizers of a Ginzburg-Landau functional of the form integral(Omega) [1/2 \del u\(2) + 1/4 epsilon(2) (1 - \u\(2))(2) W (x)] dx.

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.

The effectiveness of commercially available sports drinks

The purpose of this review is to evaluate the effectiveness of commercially available sports drinks by answering the questions: (i) will consuming a sports drink be beneficial to performance? and (ii) do different sports drinks vary in their effectiveness? To answer these questions we have considered the composition of commercially available sports drinks, examined the rationale for using them, and critically reviewed the vast number of studies that have investigated the effectiveness of sports drinks on performance. The focus is on the drinks that contain low carbohydrate concentrations (10%, which are intended for carbohydrate loading, Our conclusions are 3-fold. First, because of variations in drink composition and research design, much of the sports drinks research from the past cannot be applied direct Iv to the effectiveness of currently available sports drinks. Secondly, in studies where a practical protocol has been used along with a currently available sports beverage, there is evidence to suggest that consuming a sports drinks will improve performance compared with consuming a placebo beverage. Finally, there is little evidence that any one sports drink is superior to any of the other beverages on the market.

On the effect of tracer density on axial dispersion in a batch oscillatory baffled column

In this paper, we report our modelling evaluation on the effect of tracer density on axial dispersion in a batch oscillatory baffled column (OBC). Tracer solution of potassium nitrite, its specific density ranged from 1.0 to 1.5, was used in the study, and was injected to the vertical column from either the top or bottom. Local concentration profiles are measured using conductivity probes at two locations along the height of the column. Using the experimental measured concentration profiles together with both 'Tank-in-Series' and 'Plug Flow with Axial Dispersion' models, axial dispersion coefficients were determined and used to describe the effect of specific tracer density on mixing in the OBC. The results showed that the axial dispersion coefficients evaluated by the two models are very similar in both magnitudes and trends, and the range of variations in such coefficients is generally larger for the bottom injection than for the top one. Empirical correlations linking the mechanical energy for mixing, the specific density of tracer and axial dispersion coefficient were established. Using these correlations, we identified the enhancements of up to 269% on axial dispersion for various specific tracer densities. (C) 2002 Elsevier Science B.V. All rights reserved.

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.