Stochastic Hybrid Control

The objective of this paper is to study the stochastic version of a previous paper of the authors, in which hybrid control for deterministic systems was considered. The modelling is quite similar to the deterministic case. We have a system whose state is composed of a continuous part and a discrete part. They are affected by a continuous type control and an impulse control. The dynamics is moreover perturbed by noise, also a continuous and a discrete noise process. The Markovian character of the state process is preserved. We develop the model and show how the dynamic programming approach leads to some involved quasi-variational inequality

An interpretive review of consensus statements on clinical guideline development and their application in the field of traditional and complementary medicine

© 2017 The Author(s). Background: Despite ongoing consumer demand and an emerging scientific evidence-base for traditional and complementary medicine (T&CM), there remains a paucity of reliable information in standard clinical guidelines about their use. Often T&CM interventions are not mentioned, or the recommendations arising from these guidelines are unhelpful to end-users (i.e. patients, practitioners and policy makers). Insufficient evidence of efficacy may be a contributing factor however, often informative recommendations could still be made by drawing on relevant information from other avenues. In light of this, the aim of this research was to review national and internationally endorsed consensus statements for clinical guideline developers, and to interpret how to apply these methods when making recommendations regarding the use of T&CM. Method: The critical interpretive review method was used to identify and appraise relevant consensus statements published between 1995 and 2015. The statements were identified using a purposive sampling technique until data saturation was reached. The most recent edition of a statement was included in the analysis. The content, scope and themes of the statements were compared and interpreted within the context of the T&CM setting; including history, regulation, use, emerging scientific evidence-base and existing guidelines. Results: Eight consensus statements were included in the interpretive review. Searching stopped at this stage as no new major themes were identified. The five themes relevant to the challenges of developing T&CM guidelines were: (1) framing the question; (2) the limitations of using an evidence hierarchy; (3) strategies for dealing with insufficient, high quality evidence; (4) the importance of qualifying a recommendation; and (5) the need for structured consensus development. Conclusion: Evidence regarding safety, efficacy and cost effectiveness are not the only information required to make recommendations for clinical guidelines. Modifying factors such as burden of disease, magnitude of effect, current use, demand, equity and ease of integration should also be considered. Uptake of the recommendations arising from this review are expected to result in the development of higher quality clinical guidelines that offer greater assistance to those seeking answers about the appropriate use of T&CM

Homogenization of Maxwell's equations in periodic composites

We consider the problem of homogenizing the Maxwell equations for periodic composites. The analysis is based on Bloch-Floquet theory. We calculate explicitly the reflection coefficient for a half-space, and derive and implement a computationally-efficient continued-fraction expansion for the effective permittivity. Our results are illustrated by numerical computations for the case of two-dimensional systems. The homogenization theory of this paper is designed to predict various physically-measurable quantities rather than to simply approximate certain coefficients in a PDE.Comment: Significantly expanded compared to v1. Accepted to Phys.Rev.E. Some color figures in this preprint may be easier to read because here we utilize solid color lines, which are indistinguishable in black-and-white printin

Asymptotics for metamaterials and photonic crystals

Metamaterial and photonic crystal structures are central to modern optics and are typically created from multiple elementary repeating cells. We demonstrate how one replaces such structures asymptotically by a continuum, and therefore by a set of equations, that captures the behaviour of potentially high-frequency waves propagating through a periodic medium. The high-frequency homogenization that we use recovers the classical homogenization coefficients in the low-frequency long-wavelength limit. The theory is specifically developed in electromagnetics for two-dimensional square lattices where every cell contains an arbitrary hole with Neumann boundary conditions at its surface and implemented numerically for cylinders and split-ring resonators. Illustrative numerical examples include lensing via all-angle negative refraction, as well as omni-directive antenna, endoscope and cloaking effects. We also highlight the importance of choosing the correct Brillouin zone and the potential of missing interesting physical effects depending upon the path chosen

Mathematical formulation of a dynamical system with dry friction subjected to external forces

We consider the response of a one-dimensional system with friction. S.W. Shaw (Journal of Sound and Vibration, 1986) introduced the set up of different coefficients for the static and dynamic phases (also called stick and slip phases). He constructs a step by step solution, corresponding to an harmonic forcing. In this paper, we show that the theory of variational inequalities provides an elegant and synthetic approach to obtain the existence and uniqueness of the solution, avoiding the step by step construction. We then apply the theory to a real structure with real data and show that the model is quite accurate. In our case, the forcing motion comes from dilatation, due to temperature

On the terminal velocity of sedimenting particles in a flowing fluid

The influence of an underlying carrier flow on the terminal velocity of sedimenting particles is investigated both analytically and numerically. Our theoretical framework works for a general class of (laminar or turbulent) velocity fields and, by means of an ordinary perturbation expansion at small Stokes number, leads to closed partial differential equations (PDE) whose solutions contain all relevant information on the sedimentation process. The set of PDE's are solved by means of direct numerical simulations for a class of 2D cellular flows (static and time dependent) and the resulting phenomenology is analysed and discussed.Comment: 13 pages, 2 figures, submitted to JP

Social and Cultural Factors Affecting Complementary and Alternative Medicine (CAM) Use during Menopause in Sydney and Bologna

Background. Previous surveys found CAM use during menopause to be popular. This paper compares the results from two surveys (Sydney and Bologna) to examine factors that determine the extent and pattern of CAM use to alleviate menopausal symptoms. Methods. Women, aged 45–65 years, who were symptomatic when transitioning through menopause or asymptomatic but taking menopause-specific treatments, were recruited in Sydney (n=1,296) and Bologna (n=1,106) to complete the same voluntary, anonymous, and self-administered questionnaire. The results were reanalysed using stratified analyses to determine similarities and differences. Results. Demographics of the two cohorts differed significantly. CAM was more popular in Sydney. The most significant determinants of CAM use were the use of CAM for other conditions besides menopause and the severity of vasomotor symptoms. Occupational status was a determinant of CAM use amongst Bologna respondents only. In order to relieve symptoms, Australian and Italian women used different CAM modalities whose effectiveness was generally perceived as good. Conclusion. CAM use is popular amongst menopausal women from Sydney and Bologna. Differences in the patterns of CAM use seem to depend on CAM availability and on the educational level and professional status of users. The complex interaction between market, social, and cultural factors of CAM use seems to be more influential on women’s choice of CAM than the available evidence of their effectiveness

Convergence of the Generalized Volume Averaging Method on a Convection-Diffusion Problem: A Spectral Perspective

A mixed formulation is proposed and analyzed mathematically for coupled convection-diffusion in heterogeneous medias. Transfer in solid parts driven by pure diffusion is coupled with convection-diffusion transfer in fluid parts. This study is carried out for translation-invariant geometries (general infinite cylinders) and unidirectional flows. This formulation brings to the fore a new convection-diffusion operator, the properties of which are mathematically studied: its symmetry is first shown using a suitable scalar product. It is proved to be self-adjoint with compact resolvent on a simple Hilbert space. Its spectrum is characterized as being composed of a double set of eigenvalues: one converging towards −∞ and the other towards +∞, thus resulting in a nonsectorial operator. The decomposition of the convection-diffusion problem into a generalized eigenvalue problem permits the reduction of the original three-dimensional problem into a two-dimensional one. Despite the operator being nonsectorial, a complete solution on the infinite cylinder, associated to a step change of the wall temperature at the origin, is exhibited with the help of the operator’s two sets of eigenvalues/eigenfunctions. On the computational point of view, a mixed variational formulation is naturally associated to the eigenvalue problem. Numerical illustrations are provided for axisymmetrical situations, the convergence of which is found to be consistent with the numerical discretization