The discontinuous Galerkin method for fractional degenerate convection-diffusion equations

We propose and study discontinuous Galerkin methods for strongly degenerate convection-diffusion equations perturbed by a fractional diffusion (L\'evy) operator. We prove various stability estimates along with convergence results toward properly defined (entropy) solutions of linear and nonlinear equations. Finally, the qualitative behavior of solutions of such equations are illustrated through numerical experiments

Quantitative study of quasi-one-dimensional Bose gas experiments via the stochastic Gross-Pitaevskii equation

The stochastic Gross-Pitaevskii equation is shown to be an excellent model for quasi-one-dimensional Bose gas experiments, accurately reproducing the in situ density profiles recently obtained in the experiments of Trebbia et al. [Phys. Rev. Lett. 97, 250403 (2006)] and van Amerongen et al. [Phys. Rev. Lett. 100, 090402 (2008)], and the density fluctuation data reported by Armijo et al. [Phys. Rev. Lett. 105, 230402 (2010)]. To facilitate such agreement, we propose and implement a quasi-one-dimensional stochastic equation for the low-energy, axial modes, while atoms in excited transverse modes are treated as independent ideal Bose gases.Comment: 10 pages, 5 figures; updated figures with experimental dat

Tutorial on Hybridizable Discontinous Galerkin (HDG) for second-order elliptic problems

The HDG is a new class of discontinuous Galerkin (DG) methods that shares favorable properties with classical mixed methods such as the well known Raviart-Thomas methods. In particular, HDG provides optimal convergence of both the primal and the dual variables of the mixed formulation. This property enables the construction of superconvergent solutions, contrary to other popular DG methods. In addition, its reduced computational cost, compared to other DG methods, has made HDG an attractive alternative for solving problems governed by partial differential equations. A tutorial on HDG for the numerical solution of second-order elliptic problems is presented. Particular emphasis is placed on providing all the necessary details for the implementation of HDG methods.Peer ReviewedPreprin

A posteriori error analysis and adaptive non-intrusive numerical schemes for systems of random conservation laws

In this article we consider one-dimensional random systems of hyperbolic conservation laws. We first establish existence and uniqueness of random entropy admissible solutions for initial value problems of conservation laws which involve random initial data and random flux functions. Based on these results we present an a posteriori error analysis for a numerical approximation of the random entropy admissible solution. For the stochastic discretization, we consider a non-intrusive approach, the Stochastic Collocation method. The spatio-temporal discretization relies on the Runge--Kutta Discontinuous Galerkin method. We derive the a posteriori estimator using continuous reconstructions of the discrete solution. Combined with the relative entropy stability framework this yields computable error bounds for the entire space-stochastic discretization error. The estimator admits a splitting into a stochastic and a deterministic (space-time) part, allowing for a novel residual-based space-stochastic adaptive mesh refinement algorithm. We conclude with various numerical examples investigating the scaling properties of the residuals and illustrating the efficiency of the proposed adaptive algorithm

Empirical Investigation on Agile Methods Usage: Issues Identified from Early Adopters in Malaysia

Agile Methods are a set of software practices that can help to produce products faster and at the same time deliver what customers want. Despite the benefits that Agile methods can deliver, however, we found few studies from the Southeast Asia region, particularly Malaysia. As a result, less empirical evidence can be obtained in the country making its implementation harder. To use a new method, experience from other practitioners is critical, which describes what is important, what is possible and what is not possible concerning Agile. We conducted a qualitative study to understand the issues faced by early adopters in Malaysia where Agile methods are still relatively new. The initial study involves 13 participants including project managers, CEOs, founders and software developers from seven organisations. Our study has shown that social and human aspects are important when using Agile methods. While technical aspects have always been considered to exist in software development, we found these factors to be less important when using Agile methods. The results obtained can serve as guidelines to practitioners in the country and the neighbouring regions

A characteristic particle method for traffic flow simulations on highway networks

A characteristic particle method for the simulation of first order macroscopic traffic models on road networks is presented. The approach is based on the method "particleclaw", which solves scalar one dimensional hyperbolic conservations laws exactly, except for a small error right around shocks. The method is generalized to nonlinear network flows, where particle approximations on the edges are suitably coupled together at the network nodes. It is demonstrated in numerical examples that the resulting particle method can approximate traffic jams accurately, while only devoting a few degrees of freedom to each edge of the network.Comment: 15 pages, 5 figures. Accepted to the proceedings of the Sixth International Workshop Meshfree Methods for PDE 201

Achieving equity through 'gender autonomy': the challenges for VET policy and practice

This paper is based on research carried out in an EU Fifth Framework project on 'Gender and Qualification'. The research partners from five European countries investigated the impact of gender segregation in European labour markets on vocational education and training, with particular regard to competences and qualifications. The research explored the part played by gender in the vocational education and training experiences of (i) young adults entering specific occupations in child care, electrical engineering and food preparation/service (ii) adults changing occupations

Evidence of negative affective state in Cavalier King Charles Spaniels with syringomyelia

Syringomyelia is a common and chronic neurological disorder affecting Cavalier King Charles Spaniels. The condition is putatively painful, but evaluating the affective component of chronic pain in non-human animals is challenging. Here we employed two methods designed to assess animal affect – the judgement bias and reward loss sensitivity tests – to investigate whether Cavalier King Charles Spaniels with syringomyelia (exhibiting a fluid filled cavity (syrinx) in the spinal cord of ≥2mm diameter) were in a more negative affective state than those without the condition. Dogs with syringomyelia did not differ in age from those without the condition, but owners reported that they scratched more (P<0.05), in line with previous findings. They also showed a more negative judgement of ambiguous locations in the judgement bias task (P<0.05), indicating a more negative affective state, but did not show a greater sensitivity to loss of food rewards. These measures were unaffected by whether the dog was or was not receiving pain-relieving medication. Across all subjects, dogs whose owners reported high levels of scratching showed a positive judgement bias (P<0.05), indicating that scratching was not directly associated with a negative affective state. Tests of spontaneous behaviour (latency to jump up to or down from a 30cm high platform) and physiology (thermography of the eye) did not detect any differences. These results provide initial evidence from the judgement bias task that syringomyelia may be associated with negative affect in dogs, and open the way for further and larger studies to confirm findings and investigate the effects of medication in more detail

Fitness benefits of prolonged post-reproductive lifespan in women

Most animals reproduce until they die, but in humans, females can survive long after ceasing reproduction. In theory, a prolonged post-reproductive lifespan will evolve when females can gain greater fitness by increasing the success of their offspring than by continuing to breed themselves. Although reproductive success is known to decline in old age, it is unknown whether women gain fitness by prolonging lifespan post-reproduction. Using complete multi-generational demographic records, we show that women with a prolonged post-reproductive lifespan have more grandchildren, and hence greater fitness, in pre-modern populations of both Finns and Canadians. This fitness benefit arises because post-reproductive mothers enhance the lifetime reproductive success of their offspring by allowing them to breed earlier, more frequently and more successfully. Finally, the fitness benefits of prolonged lifespan diminish as the reproductive output of offspring declines. This suggests that in female humans, selection for deferred ageing should wane when one's own offspring become post-reproductive and, correspondingly, we show that rates of female mortality accelerate as their offspring terminate reproduction