Kaon Weak Decays in Chiral Theories

The ten nonleptonic weak decays $K \to 2\pi$, $K \to 3\pi$, $K_L \to 2\gamma$, $K_S \to 2\gamma$, $K_L \to \pi^\circ 2\gamma$, are predicted for a chiral pole model based on the linear sigma model theory which automatically satisfies the partial conservation of axial current (PCAC) hypothesis. These predictions, agreeing with data to the 5% level and containing no or at most one free parameter, are compared with the results of chiral perturbation theory (ChPT). The latter ChPT approach to one-loop level is known to contain at least four free parameters and then predicts a $K_L \to \pi^\circ \gamma\gamma$ rate which is 60% shy of the experimental value. This suggests that ChPT is an unsatisfactory approach towards predicting kaon weak decays.Comment: 12 pages, 8 eps figure

Requirements Engineering as Creative Problem Solving: A Research Agenda for Idea Finding

This vision paper frames requirements engineering as a creative problem solving process. Its purpose is to enable requirements researchers and practitioners to recruit relevant theories, models, techniques and tools from creative problem solving to understand and support requirements processes more effectively. It uses 4 drivers to motivate the case for requirements engineering as a creative problem solving process. It then maps established requirements activities onto one of the longest-established creative problem solving processes, and uses these mappings to locate opportunities for the application of creative problem solving in requirements engineering. The second half of the paper describes selected creativity theories, techniques, software tools and training that can be adopted to improve requirements engineering research and practice. The focus is on support for problem and idea finding - two creative problem solving processes that our investigation revealed are poorly supported in requirements engineering. The paper ends with a research agenda to incorporate creative processes, techniques, training and tools in requirements projects

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

Family support and cardiac rehabilitation: A comparative study of the experiences of South Asian and White-European patients and their carer's living in the United Kingdom

Background: Effective lifestyle modification facilitated by cardiac rehabilitation is known to reduce the occurrence of adverse coronary events and mortality. South Asians have poorer outcomes after a myocardial infarction than the general UK population, but little is known about their experiences of family support, cardiac rehabilitation and lifestyle change. Aims: To explore the nature of family support available to a sample of South Asian and White-European cardiac patients and to highlight similarities and differences between these groups with regard to cardiac rehabilitation and lifestyle modification. Methods: Using a qualitative approach, semi-structured interviews (in 1 of 6 languages) were conducted by researchers with; 45 South Asian patients and 37 carers and 20 White-European patients and 17 carers. Interviews were conducted in a home setting, up to eighteen months after discharge from hospital following myocardial infarction, coronary artery bypass surgery or unstable angina. Results: The main themes that emerged related to the provision of advice and information, family support and burden, dietary change and exercise regimes. Conclusions: Several cultural and ethnic differences were identified between patients and their families alongside similarities, irrespective of ethnicity. These may represent generic characteristics of recovery after a cardiac event. Health professionals should develop a cultural repertoire to engage with diversity and difference. Not every difficulty a person encounters as they try to access appropriate service delivery can be attributed to ethnic background. By improving services generally, support for South Asian populations can be improved. The challenge is to know when ethnicity makes a difference and mediates a person's relationship with service support and when it does not. (C) 2007 European Society of Cardiology. Published by Elsevier B.V. All rights reserved

On the upstream mobility scheme for two-phase flow in porous media

When neglecting capillarity, two-phase incompressible flow in porous media is modelled as a scalar nonlinear hyperbolic conservation law. A change in the rock type results in a change of the flux function. Discretizing in one-dimensional with a finite volume method, we investigate two numerical fluxes, an extension of the Godunov flux and the upstream mobility flux, the latter being widely used in hydrogeology and petroleum engineering. Then, in the case of a changing rock type, one can give examples when the upstream mobility flux does not give the right answer.Comment: A preprint to be published in Computational Geoscience

Changes in growing season duration and productivity of northern vegetation inferred from long-term remote sensing data

Monitoring and understanding climate-induced changes in the boreal and arctic vegetation is critical to aid in prognosticating their future. Weused a 33 year (1982-2014) long record of satellite observations to robustly assess changes in metrics of growing season (onset: SOS, end: EOS and length: LOS) and seasonal total gross primary productivity. Particular attention was paid to evaluating the accuracy of these metrics by comparing them to multiple independent direct and indirect growing season and productivity measures. These comparisons reveal that the derived metrics capture the spatio-temporal variations and trends with acceptable significance level (generally p < 0.05). We find that LOS has lengthened by 2.60 d dec(-1) (p < 0.05) due to an earlier onset of SOS (-1.61 d dec(-1), p < 0.05) and a delayed EOS (0.67 d dec(-1), p < 0.1) at the circumpolar scale over the past three decades. Relatively greater rates of changes in growing season were observed in Eurasia (EA) and in boreal regions than in North America (NA) and the arctic regions. However, this tendency of earlier SOS and delayed EOS was prominent only during the earlier part of the data record (1982-1999). During the later part (2000-2014), this tendency was reversed, i.e. delayed SOS and earlier EOS. As for seasonal total productivity, we find that 42.0% of northern vegetation shows a statistically significant (p < 0.1) greening trend over the last three decades. This greening translates to a 20.9% gain in productivity since 1982. In contrast, only 2.5% of northern vegetation shows browning, or a 1.2% loss of productivity. These trends in productivity were continuous through the period of record, unlike changes in growing season metrics. Similarly, we find relatively greater increasing rates of productivity in EA and in arctic regions than in NA and the boreal regions. These results highlight spatially and temporally varying vegetation dynamics and are reflective of biome-specific responses of northern vegetation during last three decades

A theory of L1L^1-dissipative solvers for scalar conservation laws with discontinuous flux

We propose a general framework for the study of $L^1$ contractive semigroups of solutions to conservation laws with discontinuous flux. Developing the ideas of a number of preceding works we claim that the whole admissibility issue is reduced to the selection of a family of "elementary solutions", which are certain piecewise constant stationary weak solutions. We refer to such a family as a "germ". It is well known that (CL) admits many different $L^1$ contractive semigroups, some of which reflects different physical applications. We revisit a number of the existing admissibility (or entropy) conditions and identify the germs that underly these conditions. We devote specific attention to the anishing viscosity" germ, which is a way to express the "$\Gamma$-condition" of Diehl. For any given germ, we formulate "germ-based" admissibility conditions in the form of a trace condition on the flux discontinuity line $x=0$ (in the spirit of Vol'pert) and in the form of a family of global entropy inequalities (following Kruzhkov and Carrillo). We characterize those germs that lead to the $L^1$-contraction property for the associated admissible solutions. Our approach offers a streamlined and unifying perspective on many of the known entropy conditions, making it possible to recover earlier uniqueness results under weaker conditions than before, and to provide new results for other less studied problems. Several strategies for proving the existence of admissible solutions are discussed, and existence results are given for fluxes satisfying some additional conditions. These are based on convergence results either for the vanishing viscosity method (with standard viscosity or with specific viscosities "adapted" to the choice of a germ), or for specific germ-adapted finite volume schemes

CP Violation and ΔI=1/2\Delta I=1/2 Enhancement for K→ππK \to \pi\pi, K→ππγK \to \pi\pi\gamma Weak Decays

Data indicate that $\Delta I=1/2$ transitions account for 4.5-4.7% of both CP conserving and CP violating $K \to 2\pi$ decays, as well as CP conserving radiative $K \to \pi\pi\gamma$ processes. Observed $K \to \pi\pi\gamma/\pi\pi$ branching ratios are shown to scale near $\alpha/\pi$ or $\alpha/2\pi$. The $K_L$-$K_S$ mixing angle $\phi$ and the semileptonic weak-rate asymmetry $\delta$ are reviewed, and theory is shown to be consistent with data. Also, $K \to 2\pi$ $\Delta I=1/2$ dominance is studied in the context of the chiral constituent quark model, displaying again excellent agreement with data. Finally, indirect and direct kaon CP violation are successfully described in the framework of photon-mediated loop graphs. This suggests that kaon CPV can be understood via second-order weak transitions, radiatively corrected.Comment: Plain LaTeX, 12 pages, 4 EPS figures. PACS numbers: 11.30.Er, 12.15.Lk, 13.20.Eb, 13.40.Ks. Version 2: 14 pages, improved presentation, introductory and concluding remarks as well as references added; accepted for publication in Mod. Phys. Lett. A (2004

Fully adaptive multiresolution schemes for strongly degenerate parabolic equations with discontinuous flux

A fully adaptive finite volume multiresolution scheme for one-dimensional strongly degenerate parabolic equations with discontinuous flux is presented. The numerical scheme is based on a finite volume discretization using the Engquist--Osher approximation for the flux and explicit time--stepping. An adaptivemultiresolution scheme with cell averages is then used to speed up CPU time and meet memory requirements. A particular feature of our scheme is the storage of the multiresolution representation of the solution in a dynamic graded tree, for the sake of data compression and to facilitate navigation. Applications to traffic flow with driver reaction and a clarifier--thickener model illustrate the efficiency of this method

Hyperon Nonleptonic Weak Decays Revisited

We first review the current algebra - PCAC approach to nonleptonic octet baryon 14 weak decay B (\to) (B^{\prime})(\pi) amplitudes. The needed four parameters are independently determined by (\Omega \to \Xi \pi),(\Lambda K) and (\Xi ^{-}\to \Sigma ^{-}\gamma) weak decays in dispersion theory tree order. We also summarize the recent chiral perturbation theory (ChPT) version of the eight independent B (\to) (B^{\prime}\pi) weak (\Delta I) = 1/2 amplitudes containing considerably more than eight low-energy weak constants in one-loop order.Comment: 10 pages, RevTe