Complementary therapies for labour and birth: A randomized controlled trial of antenatal integrative medicine for pain management in labour

Objective: To evaluate the effect of an antenatal integrative medicine education programme in addition to usual care for nulliparous women on intrapartum epidural use. Design: Open-label, assessor blind, randomized controlled trial. Setting: 2 public hospitals in Sydney, Australia. Population: 176 nulliparous women with low-risk pregnancies, attending hospital-based antenatal clinics. Methods and intervention: The Complementary Therapies for Labour and Birth protocol, based on the She Births and acupressure for labour and birth courses, incorporated 6 evidence-based complementary medicine techniques: acupressure, visualisation and relaxation, breathing, massage, yoga techniques, and facilitated partner support. Randomisation occurred at 24–36 weeks’ gestation, and participants attended a 2-day antenatal education programme plus standard care, or standard care alone. Main outcome measures: Rate of analgesic epidural use. Secondary: onset of labour, augmentation, mode of birth, newborn outcomes. Results:There was a significant difference in epidural use between the 2 groups: study group (23.9%) standard care (68.7%; risk ratio (RR) 0.37 (95% CI 0.25 to 0.55), p≤0.001). The study group participants reported a reduced rate of augmentation (RR=0.54 (95% CI 0.38 to 0.77), p Conclusions: The Complementary Therapies for Labour and Birth study protocol significantly reduced epidural use and caesarean section. This study provides evidence for integrative medicine as an effective adjunct to antenatal education, and contributes to the body of best practice evidence

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

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

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

Interference phenomena in scalar transport induced by a noise finite correlation time

The role played on the scalar transport by a finite, not small, correlation time, $\tau_u$, for the noise velocity is investigated, both analytically and numerically. For small $\tau_u$'s a mechanism leading to enhancement of transport has recently been identified and shown to be dominating for any type of flow. For finite non-vanishing $\tau_u$'s we recognize the existence of a further mechanism associated with regions of anticorrelation of the Lagrangian advecting velocity. Depending on the extension of the anticorrelated regions, either an enhancement (corresponding to constructive interference) or a depletion (corresponding to destructive interference) in the turbulent transport now takes place.Comment: 8 pages, 3 figure

Bloch Approximation in Homogenization and Applications

The classical problem of homogenization of elliptic operators with periodically oscillating coefficients is revisited in this paper. As is well known, the homogenization process in a classical framework is concerned with the study of asymptotic behavior of solutions $u^\varepsilon$ of boundary value problems associated with such operators when the period $\varepsilon>0$ of the coefficients is small. In a previous work by C. Conca and M. Vanninathan [SIAM J. Appl. Math., 57 (1997), pp. 1639--1659], a new proof of weak convergence as $\varepsilon\to 0$ towards the homogenized solution was furnished using Bloch wave decomposition. Following the same approach here, we go further and introduce what we call Bloch approximation, which will provide energy norm approximation for the solution $u^\varepsilon$. We develop several of its main features. As a simple application of this new object, we show that it contains both the first and second order correctors. Necessarily, the Bloch approximation will have to capture the oscillations of the solution in a sharper way. The present approach sheds new light and offers an alternative for viewing classical results

The Neumann problem in thin domains with very highly oscillatory boundaries

In this paper we analyze the behavior of solutions of the Neumann problem posed in a thin domain of the type $R^\epsilon = \{(x_1,x_2) \in \R^2 \; | \; x_1 \in (0,1), \, - \, \epsilon \, b(x_1) < x_2 < \epsilon \, G(x_1, x_1/\epsilon^\alpha) \}$ with $\alpha>1$ and $\epsilon > 0$, defined by smooth functions $b(x)$ and $G(x,y)$, where the function $G$ is supposed to be $l(x)$-periodic in the second variable $y$. The condition $\alpha > 1$ implies that the upper boundary of this thin domain presents a very high oscillatory behavior. Indeed, we have that the order of its oscillations is larger than the order of the amplitude and height of $R^\epsilon$ given by the small parameter $\epsilon$. We also consider more general and complicated geometries for thin domains which are not given as the graph of certain smooth functions, but rather more comb-like domains.Comment: 20 pages, 4 figure

Necessary Optimality Conditions for a Dead Oil Isotherm Optimal Control Problem

We study a system of nonlinear partial differential equations resulting from the traditional modelling of oil engineering within the framework of the mechanics of a continuous medium. Recent results on the problem provide existence, uniqueness and regularity of the optimal solution. Here we obtain the first necessary optimality conditions.Comment: 9 page

Quasivariational solutions for first order quasilinear equations with gradient constraint

We prove the existence of solutions for an evolution quasi-variational inequality with a first order quasilinear operator and a variable convex set, which is characterized by a constraint on the absolute value of the gradient that depends on the solution itself. The only required assumption on the nonlinearity of this constraint is its continuity and positivity. The method relies on an appropriate parabolic regularization and suitable {\em a priori} estimates. We obtain also the existence of stationary solutions, by studying the asymptotic behaviour in time. In the variational case, corresponding to a constraint independent of the solution, we also give uniqueness results