Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems I: The scalar case

We develop a one--parameter family of hp-version discontinuous Galerkin finite element methods for the numerical solution of quasilinear elliptic equations in divergence-form in a bounded Lipschitz domain. Using Brouwer's Fixed Point Theorem, we show existence and uniqueness of the solution. In addition, we derive an error bound in a broken energy norm which is optimal in h and mildly suboptimal in p

Resilience of Hierarchical Critical Infrastructure Networks

Concern over the resilience of critical infrastructure networks has increased dramatically over the last decade due to a number of well documented failures and the significant disruption associated with these. This has led to a large body of research that has adopted graph-theoretic based analysis in order to try and improve our understanding of infrastructure network resilience. Many studies have asserted that infrastructure networks possess a scale-free topology which is robust to random failures but sensitive to targeted attacks at highly connected hubs. However, many studies have ignored that many networks in addition to their topological connectivity may be organised either logically or spatially in a hierarchical system which may significantly change their response to perturbations. In this paper we explore if hierarchical network models exhibit significantly different higher-order topological characteristics compared to other network structures and how this impacts on their resilience to a number of different failure types. This is achieved by investigating a suite of synthetic networks as well as a suite of ‘real world’ spatial infrastructure networks

Measurement of σ(Hνeνeˉ)×BR(H→ZZ∗){\sigma(H\nu_e\bar{\nu_e})\times BR(H\rightarrow ZZ^\ast)} and Higgs production in ZZZZ fusion at a 1.4 TeV CLIC collider

This paper presents the potential measurement at 1.4 TeV CLIC of the cross-section (times branching ratio) of the Higgs production via $WW$ fusion with the Higgs subsequently decaying in $ZZ^\ast$, ${\sigma(H\nu_e\bar{\nu_e})\times BR(H\rightarrow ZZ^\ast)}$, and of the Higgs production via $ZZ$ fusion with the Higgs subsequently decaying in $b\bar{b}$, ${\sigma(He{^+}e{^-})\times BR(H\rightarrow b\bar{b})}$. For the $H\rightarrow ZZ^\ast$ decay the hadronic final state, ${ZZ^\ast\rightarrow q\bar{q}q\bar{q}}$, and the semi-leptonic final state, ${ZZ^\ast\rightarrow q\bar{q}l^+l^-}$, are considered. The results show that ${\sigma(H\nu_e\bar{\nu_e})\times BR(H\rightarrow ZZ^\ast)}$ can be measured with a precision of 18.3% and 6% for the hadronic and semi-leptonic channel, respectively. ${\sigma(He{^+}e{^-})\times BR(H\rightarrow b\bar{b})}$ can be measured with a precision of 1.7%. This measurement also contributes to the determination of the Higgs coupling to the $Z$ boson, $g_{H_{ZZ}}$.Comment: Talk presented at the International Workshop on Future Linear Colliders (LCWS14), Belgrade, Serbia, 6-10 October 201

Six Pillars of Social Policy: The State of Pensions and Health Care in Canada

William B.P. Robson, a co-author with David Slater of a series of papers on pension issues, has written an ambitious survey of the state of Canadian economic policy in the areas of pensions and health care. He argues that it is appropriate to tackle both issues in the same paper because they are both major spending programs strongly related to the life cycle of Canadians, and face challenges arising from the aging of the population. Robson notes that the pension debate uses the metaphor of three pillars to describe a comprehensive pension system: a safety net to guard against destitution in old age; a mandatory employment-related system to provide basic replacement income; and a voluntary system supported by provisions that reduce the double-taxation of saving. The main elements of public policy related to pensions in Canada cover these pillars. He recognizes that all three of the pillars cannot be directly applied to health care, but he argues that the three-pillar metaphor is still a fruitful perspective because it facilitates constructive responses to the pressures confronting Canada’s health system and illuminates interactions between the pension and health systems. Hence his title “six pillars of social policy”. Based on his examination of Canada’s pension and health-care systems, Robson makes a number of recommendations. First, he advocates more prefunding in both the pension and health areas to cover the future cost of the aging baby-boom cohort. Second, he recommends a gradual increase in the normal age of eligibility for pension benefits. Third, he recommends the creation of a second pillar, a mandatory contribution scheme in the health area as a way to avoid the development of a means-tested system that would exacerbate the disincentives to work and save. Fourth, he puts forward the idea of a new type of saving vehicle that provides tax-relief on distributions rather than on contributions so that Canadians can avoid the high marginal effective tax rates associated with means-tested programs.Health, Health Care, Health-care, Healthcare, Canada, Pensions, CPP, Retirement, Mandatory Contribution, Aging, Ageing

Remarks on separating words

The separating words problem asks for the size of the smallest DFA needed to distinguish between two words of length <= n (by accepting one and rejecting the other). In this paper we survey what is known and unknown about the problem, consider some variations, and prove several new results

Multi-waveband observations of colliding galaxies

Colliding galaxies represent a major challenge to both theorists and observers because of the large variety of phenomena which are expected to come into play during the interaction. Strong gravitational fluctuations may drive non-linear waves and instabilities throughout the stars and gas leading to enhanced star formation, nuclear activity and ultimately a mixing of the morphological components of the original galaxies. One relatively uncomplicated class of colliding galaxy where stellar waves play an important role in star formation are ring galaxies. Ring galaxies are probably formed when a companion galaxy passes through the center of a disk system driving circular waves through the disk (Lynds and Toomre 1976, Toomre 1978, Struck-Marcell 1990). Off-center collisions can generate non-circular waves and can be loosely described as banana-shaped although they may exhibit more complex forms as the waves expand into the disk. The propagation of such stellar and gaseous waves through the disk leads to enhanced star formation (e.g., Appleton and Struck-Marcell 1987a; Jeske 1986) and provides a unique probe of the response of the interstellar medium (ISM) to a propagating wave (see Appleton and Struck-Marcell 1987b). Here, the authors report results for 3 systems; the irregular ring Arp 143 (=VV 117); Wakamatsu's Seyfert ring (A0959-755; see Wakamatsu and Nishida 1987) and the brighter member of the pair of ring galaxies comprising of AM 1358-221. The most complete multi-wavelength data is for Arp 143. Optical charge coupled device (CCD) observations made with the 60 inch Palomar telescope at BV and r band, near-IR images at J (1.25 microns), H (1.65 microns) and k (2.2 microns) bands from the infrared camera (IRCAM) InSb array camera on the 3.8m United Kingdon Infrared Telescope (UKIRT) telescope and very large array (VLA) observations at 20cm in both the neutral hydrogen line and radio continuum are described. The observations of Wakamatsu's ring and AM 1358 were made only in the near-IR, and a comparison is made with available optical plate material

Is child weight status correctly reported to parents? Cross-sectional analysis of National Child Measurement Programme data using ethnic-specific BMI adjustments.

BACKGROUND: BMI underestimates and overestimates body fat in children from South Asian and Black ethnic groups, respectively. METHODS: We used cross-sectional NCMP data (2015-17) for 38 270 children in three inner-London local authorities: City & Hackney, Newham and Tower Hamlets (41% South Asian, 18.8% Black): 20 439 4-5 year-olds (48.9% girls) and 17 831 10-11 year-olds (49.1% girls). We estimated the proportion of parents who would have received different information about their child's weight status, and the area-level prevalence of obesity-defined as ≥98th centile-had ethnic-specific BMI adjustments been employed in the English National Child Measurement Programme (NCMP). RESULTS: Had ethnic-specific adjustment been employed, 19.7% (3112/15 830) of parents of children from South Asian backgrounds would have been informed that their child was in a heavier weight category, and 19.1% (1381/7217) of parents of children from Black backgrounds would have been informed that their child was in a lighter weight category. Ethnic-specific adjustment increased obesity prevalence from 7.9% (95% CI: 7.6, 8.3) to 9.1% (8.7, 9.5) amongst 4-5 year-olds and from 17.5% (16.9, 18.1) to 18.8% (18.2, 19.4) amongst 10-11 year-olds. CONCLUSIONS: Ethnic-specific adjustment in the NCMP would ensure equitable categorization of weight status, provide correct information to parents and support local service provision for families

Periodic electron structures in gases: a fluid model of the ‘‘window’’ phenomenon

Periodic electron spatial structures in gases occur within a window of voltages and pressures. Recent accurate solutions of Boltzmann’s equation portray this effect, but offer little physical insight into the causes of windowing. Here we show for the first time how such insight can be obtained using the fluid model established by Robson, White, and Petrović [Rev. Mod. Phys. 77, 1303 (2005)], with an appropriate generalization of the heat flux ansatz. Conversely, the success in portraying windowing itself becomes a stringent test of the integrity of this fluid model, which can then be applied to a wider range of problems