Sharp measure contraction property for generalized H-type Carnot groups

We prove that H-type Carnot groups of rank $k$ and dimension $n$ satisfy the $\mathrm{MCP}(K,N)$ if and only if $K\leq 0$ and $N \geq k+3(n-k)$. The latter integer coincides with the geodesic dimension of the Carnot group. The same result holds true for the larger class of generalized H-type Carnot groups introduced in this paper, and for which we compute explicitly the optimal synthesis. This constitutes the largest class of Carnot groups for which the curvature exponent coincides with the geodesic dimension. We stress that generalized H-type Carnot groups have step 2, include all corank 1 groups and, in general, admit abnormal minimizing curves. As a corollary, we prove the absolute continuity of the Wasserstein geodesics for the quadratic cost on all generalized H-type Carnot groups.Comment: 18 pages. This article extends the results of arXiv:1510.05960. v2: revised and improved version. v3: final version, to appear in Commun. Contemp. Mat

The role of fundamental solution in Potential and Regularity Theory for subelliptic PDE

In this survey we consider a general Hormander type operator, represented as a sum of squares of vector fields plus a drift and we outline the central role of the fundamental solution in developing Potential and Regularity Theory for solutions of related PDEs. After recalling the Gaussian behavior at infinity of the kernel, we show some mean value formulas on the level sets of the fundamental solution, which are the starting point to obtain a comprehensive parallel of the classical Potential Theory. Then we show that a precise knowledge of the fundamental solution leads to global regularity results, namely estimates at the boundary or on the whole space. Finally in the problem of regularity of non linear differential equations we need an ad hoc modification of the parametrix method, based on the properties of the fundamental solution of an approximating problem

Approximations of Sobolev norms in Carnot groups

This paper deals with a notion of Sobolev space $W^{1,p}$ introduced by J.Bourgain, H.Brezis and P.Mironescu by means of a seminorm involving local averages of finite differences. This seminorm was subsequently used by A.Ponce to obtain a Poincar\'e-type inequality. The main results that we present are a generalization of these two works to a non-Euclidean setting, namely that of Carnot groups. We show that the seminorm expressd in terms of the intrinsic distance is equivalent to the $L^p$ norm of the intrinsic gradient, and provide a Poincar\'e-type inequality on Carnot groups by means of a constructive approach which relies on one-dimensional estimates. Self-improving properties are also studied for some cases of interest

On the Hausdorff volume in sub-Riemannian geometry

For a regular sub-Riemannian manifold we study the Radon-Nikodym derivative of the spherical Hausdorff measure with respect to a smooth volume. We prove that this is the volume of the unit ball in the nilpotent approximation and it is always a continuous function. We then prove that up to dimension 4 it is smooth, while starting from dimension 5, in corank 1 case, it is C^3 (and C^4 on every smooth curve) but in general not C^5. These results answer to a question addressed by Montgomery about the relation between two intrinsic volumes that can be defined in a sub-Riemannian manifold, namely the Popp and the Hausdorff volume. If the nilpotent approximation depends on the point (that may happen starting from dimension 5), then they are not proportional, in general.Comment: Accepted on Calculus and Variations and PD

An embedded shock-fitting technique on unstructured dynamic grids

In this paper, a new shock-fitting technique based on unstructured dynamic grids is proposed to improve the performances of the unstructured “boundary” shock-fitting technique developed by Liu and co-workers in [1, 2]. The main feature of this new technique, which we call the “embedded” shock-fitting technique, is its capability to insert or remove shocks or parts thereof during the calculation. This capability is enabled by defining subsets of grid-points (mutually connected by lines) which behave as either “common”- or “shock”-points, shock-waves being made of an ordered collection of shock-points. Two different sets of flow variables, corresponding to the upstream and downstream sides of the shocks, are assigned to the shock-points, which may be switched to common- and back to shock-points, a feature that allows to vary the length of the existing shocks and/or make new shock-branches appear. This paper illustrates the algorithmic features of this new technique and presents the results obtained when simulating both steady and un-steady, two-dimensional flows

Talking about a nanny nation: investigating the rhetoric framing public health debates in Australian news media

Objectives and importance of study: News media portrayal of public health issues influences public opinion, policy action and decision making. This study aimed to analyse the use of 'nanny state' frames in Australian news media coverage; identify the stakeholders invoking this frame; determine which public health-related policies attract such framing; and investigate whether 'nanny state' framing is directly challenged in news coverage. STUDY TYPE: A qualitative framing analysis. METHODS: Articles featuring the term 'nanny state' that were published in Australian print newspapers during matched periods between March and September in 2017 and 2018 were sourced through Factiva, coded and analysed for content and 'nanny state' framing. Content analysis was used to identify any public health-related issues that the terminology nanny state was applied to, and who was portrayed as imposing the nanny state. Frame analysis was used to analyse what meanings are co-presented with the phrase nanny state. RESULTS: Out of 81 print newspaper articles that included the term 'nanny state', 19% linked the term to restricting personal choice or creating dissatisfaction with too many health-related rules and regulations broadly, across a range of issues, including: bike helmets, e-cigarettes, firearm restrictions, seatbelts, pool fences and smoking bans. The next most frequent links were to regulations on alcohol (17%), road safety (14%), obesity-related issues (7%) and tobacco control (6%). Of the 81 articles, 53% appeared in news publications owned by News Corporation Australia, 20% in Fairfax Media (Nine Entertainment) publications, 17% in Daily Mail and General Trust and 10% in publications owned by other organisations. Governments were the entity most frequently framed as imposing the nanny state. Most nanny state framings (73%) were negative towards public health controls and focused on policies and regulations. Nanny state was portrayed as an assault on freedom and choice (14%) and used to attack proponents of nanny state controls (11%), while few articles framed the nanny state (7%) in a favourable light. CONCLUSIONS: 'Nanny state' is a rhetorical device commonly used in Australian news media that may contribute to discrediting of the regulation of a range of health-related issues. News Corp publications are a major propagator of nanny state rhetoric in Australian newspaper media. Public health advocates are not commonly represented within nanny state debates within the news media

Extrapolated shock fitting for two-dimensional flows on structured grids

Over the years the development of structured-grid shock-fitting techniques faced two main problems: the handling of a moving discontinuity on a fixed background grid and the capability of simulating complex flow configurations. In the proposed work, the authors present a new shock-fitting technique for structured-grid solvers that is capable of overcoming the limitations that affected the different approaches originally developed. The technique presented here removes the tight link between grid topology and shock topology, which characterizes previous shock fitting as well as front tracking methods. This significantly simplifies their implementation and more importantly reduces the computational overhead related to these geometrical manipulations. Interacting discontinuities and shocks interacting with a solid boundary are discussed and analyzed. Finally, a quantitative investigation of the error reduction obtained with the approach proposed via a global grid convergence analysis is presented

Utilization of a population health survey in policy and practice: a case study

BackgroundThere is growing interest by funding bodies and researchers in assessing the impact of research on real world policy and practice. Population health monitoring surveys provide an important source of data on the prevalence and patterns of health problems, but few empirical studies have explored if and how such data is used to influence policy or practice decisions. Here we provide a case study analysis of how the findings from an Australian population monitoring survey series of children&rsquo;s weight and weight-related behaviors (Schools Physical Activity and Nutrition Survey (SPANS)) have been used, and the key facilitators and barriers to their utilization.MethodsData collection included semi-structured interviews with the chief investigators (n = 3) and end-users (n = 9) of SPANS data to explore if, how and under what circumstances the survey findings had been used, bibliometric analysis and verification using documentary evidence. Data analysis involved thematic coding of interview data and triangulation with other data sources to produce case summaries of policy and practice impacts for each of the three survey years (1997, 2004, 2010). Case summaries were then reviewed and discussed by the authors to distil key themes on if, how and why the SPANS findings had been used to guide policy and practice.ResultsWe found that the survey findings were used for agenda setting (raising awareness of issues), identifying areas and target groups for interventions, informing new policies, and supporting and justifying existing policies and programs across a range of sectors. Reported factors influencing use of the findings were: i) the perceived credibility of survey findings; ii) dissemination strategies used; and, iii) a range of contextual factors.ConclusionsUsing a novel approach, our case study provides important new insights into how and under what circumstances population health monitoring data can be used to influence real world policy and practice. The findings highlight the importance of population monitoring programs being conducted by independent credible agencies, researchers engaging end-users from the inception of survey programs and utilizing existing policy networks and structures, and using a range of strategies to disseminate the findings that go beyond traditional peer review publications.<br /

Widening the debate about conflict of interest: addressing relationships between journalists and the pharmaceutical industry

The phone-hacking scandal that led to the closure of the News of the World newspaper in Britain has prompted international debate about media practices and regulation. It is timely to broaden the discussion about journalistic ethics and conduct to include consideration of the impact of media practices upon the population’s health. Many commercial organizations cultivate relationships with journalists and news organizations with the aim of influencing the content of health-related news and information communicated through the media. Given the significant influence of the media on the health of individuals and populations, we should be alert to the potential impact of industry-journalist relationships on health care, health policy and public health. The approach taken by the medical profession to its interactions with the pharmaceutical industry provides a useful model for management of industry influence. Keywords Journalism, mass media, pharmaceutical industry, conflict of interest, ethics, media regulationNHMR

A new computational technique for re-entry flow calculations based upon a shock-fitting technique for unstructured grids

An in-house developed, 2D/3D unstructured CFD solver has been extended to deal with a mixture of thermally perfect gases in chemical non-equilibrium. The Euler equations have been coupled with a state-to-state kinetic model for argon plasma. The spatial discretization uses compact stencil Residual Distribution Schemes and shock waves can be modelled using either shock-capturing or shock-fitting. Promising results have been obtained using the shock-fitting approach for a 2D hypersonic flow past the fore-body of a circular cylinder