G. H. M. van der Heijden

Guidelines for the management of adult lower respiratory tract infections ‐ Full version

Abstract This document is an update of Guidelines published in 2005 and now includes scientific publications through to May 2010. It provides evidence-based recommendations for the most common management questions occurring in routine clinical practice in the management of adult patients with LRTI. Topics include management outside hospital, management inside hospital (including community-acquired pneumonia (CAP), acute exacerbations of COPD (AECOPD), acute exacerbations of bronchiectasis) and prevention. Background sections and graded evidence tables are also included. The target audience for the Guideline is thus all those whose routine practice includes the management of adult LRTI.

Guidelines for the management of adult lower respiratory tract infections - Summary

This document is an update of Guidelines published in 2005 and now includes scientific publications through to May 2010. It provides evidence-based recommendations for the most common management questions occurring in routine clinical practice in the management of adult patients with LRTI. Topics include management outside hospital, management inside hospital (including community-acquired pneumonia (CAP), acute exacerbations of COPD (AECOPD), acute exacerbations of bronchiectasis) and prevention. The target audience for the Guideline is thus all those whose routine practice includes the management of adult LRTI.

Instability and self-contact phenomena in the writhing of clamped rods

We use the Cosserat rod theory to present a unified picture of jump phenomena, associated with looping, snap-through, pop-out, etc., in twisted clamped rods undergoing large deflections. Both contact-free rods and rods with isolated points of self-contact are considered. Taking proper account of the symmetries of the problem we find that an arbitrary contact-free solution is fully characterised by four parameters; each point contact adds another two. A shooting method is used for solving the boundary value problem. An intricate bifurcation picture emerges with a strong interplay between planar and spatial rod configurations. We find new jump phenomena by treating the ratio of torsional to bending stiffness of the rod as a bifurcation parameter. Load-deflection curves are computed and compared with results from carefully conducted experiments on contact-free as well as self-contacting metal-alloy rods.

Helical and Localised Buckling in Twisted Rods: A Unified Analysis of the Symmetric Case

We review the geometric rod theory for the case of a naturallystraight, linearly elastic, inextensible, circular rod suffering bendingand torsion but no shear. Our primary focus is on the post-bucklingbehaviour of such rods when subjected to end moment and tension.Although this is a classic problem with an extensive literature, datingback to Kirchhoff, the usual approach tends to neglect the physicalinterpretation of solutions (i.e., rod configurations) to the modelsproposed. Here, we explicitly compute geometrical properties of buckledrods. In a unified approach, making use of Kirchhoffs dynamic analogy,both the classical helical and the more recently investigated localisedbuckling are considered. Special attention is given to a consistenttreatment of concepts of link, twist and writhe.

Supercoiling of DNA plasmids: mechanics of the generalized ply

In this paper we address the mechanics of ply formation in DNA supercoils. We extend the variable ply formulation of Coleman & Swigon to include end loads, and the derived constitutive relations of this generalized ply are shown to be in excellent agreement with experiments. We make a careful physical examination of the uniform ply in which two strands coil around one another in the form of a helix. We next address the problem of determining the link (Lk), twist (Tw) and writhe (Wr) of a closed DNA plasmid from an inspection of its electron micrograph. Previous work has made use of the topological relation, Lk= Tw+ Wr, but we show how this kinematic result can be augmented by the mechanics solutions. A very precise result is achieved in a trial calculation.

Geometry and Mechanics of Uniform n-Plies: from Engineering Ropes to Biological Filaments

We study the mechanics of uniform n-plies, correcting and extending previous work in the literature. An n-ply is the structure formed when n pretwisted strands coil around one another in helical fashion. Such structures are encountered widely in engineering (mooring ropes, power lines) and biology (DNA, proteins). We first show that the well-known lock-up phenomenon for n=2, described by a pitchfork bifurcation, gets unfolded for higher n. Geometrically, n-plies with n>2 are all found to behave qualitatively the same. Next, using elastic rod theory, we consider the mechanics of n-plies, allowing for axial end forces and end moments while ignoring friction. An exact expression for the interstrand pressure force is derived, which is used to investigate the onset of strand separation in plied structures. After defining suitable displacements we also give an alternative variational formulation and derive (nonlinear) constitutive relationships for torsion and extension (including their coupling) of the overall ply. For a realistic loading problem in which the ends are not free to rotate one needs to consider the topological conservation law, and we show how the concepts of link and writhe can be extended to n-plies.

The static deformation of a twisted elastic rod constrained to lie on a cylinder

The Cosserat director theory is used to formulate the problem of a long thin weightless rod constrained, by suitable distributed forces, to lie on a cylinder while being held by end tension and twisting moment. Applications of this problem are found, for instance, in the buckling of drill strings inside a cylindrical hole. In the case of a rod of isotropic cross-section the equilibrium equations can be reduced to those of a one-degree-of-freedom oscillator in terms of the angle that the local tangent to the rod makes with the axis of the cylinder. Depending on the radius of the cylinder and the applied load, the oscillator has several fixed points, each of which corresponds to a different helical solution of the rod. More complicated shapes are also possible, and special attention is given to localized configurations described by homoclinic orbits of the oscillator. Heteroclinic saddle connections are found to play an important role in the post-buckling behaviour by defining critical loads at which a straight rod may coil up into a helix.

Experiments on snap buckling, hysteresis and loop formation in twisted rods

We give the results of large deflection experiments involving the bending and twisting of 1 mm diameter nickel-titanium alloy rods, up to 2 m in length. These results are compared to calculations based on the Cosserat theory of rods. We present details of this theory, formulated as a boundary value problem. The mathematical boundary conditions model the experimental setup. The rods are clamped in aligned chucks and the experiments are carried out under rigid loading conditions. An experiment proceeds by either twisting the ends of the rod by a certain amount and then adjusting the slack, or fixing the slack and varying the amount of twist. In this way, commonly encountered phenomena are investigated, such as snap buckling, the formation of loops, and buckling into and out of planar configurations. The effect of gravity is discussed.

Spatially complex localization after one-twist-per-wave equilibria in twisted circular rods with initial curvature

In experiments on long rubber rods subject to end tension and moment, a one–twist–per–wave deformation is often observed on the fundamental path prior to the onset of localized buckling. An analysis is undertaken here to account for this observed behaviour. First we derive general equilibrium equations using the Cosserat theory, incorporating the effects of non–symmetric cross–section, shear deformation, gravity and a uniform initial curvature of the unstressed rod. Each of these effects in turn can be expressed as a perturbation of the classical completely integrable Kirchhoff–Love differential equations which are equivalent to those describing a spinning symmetric top. Non–symmetric cross–section was dealt with in earlier papers. Here, after demonstrating that shear deformation alone makes little qualitative difference, the case of initial curvature is examined in some detail. It is shown that the straight configuration of the rod is replaced by a one–twist–per–wave equilibrium whose amplitude varies with pre–buckling load. Superimposed on this equilibrium is a localized buckling mode, which can be described as a homoclinic orbit to the new fundamental path. The dependence is measured of the pre–buckled state and critical buckling load on the amount of initial curvature. Numerical techniques are used to explore the multiplicity of localized buckling modes, given that non–zero initial curvature breaks the complete integrability of the differential equations, and also one of a pair of reversibilities. Finally, the physical implications of the results are assessed and are shown to match qualitatively what is observed in an experiment.

Lock-on to tape-like behaviour in the torsional buckling of anisotropic rods

Abstract Through nonlinear normal form analysis of the equilibrium equations developed in a neighbourhood of the straight rod solution we show the existence of a ‘phase transition’ from mildly anisotropic to full ‘tape-like’ buckling in non-symmetric rods subject to terminal loads, provided the material has a sufficiently low Poissons ratio. For a solid elliptical rod with a Poissons ratio of 0.2 the critical point is found to occur at a cross-sectional aspect ratio of just over 3. For larger aspect ratios the rod locks on to a one-twist-per-wave buckling mode with no internal twist. In the mildly anisotropic regime there turn out to be two physically distinct pairs of symmetric so-called primary localised buckling modes, differing in the phase of the internal twist. These four modes (homoclinic orbits) remain of the full circle of localised buckling modes existing in the symmetric case after breaking of the circular symmetry of the rods cross-section. In the strongly anisotropic regime only the energetically favourable pair of ‘flat’ buckling modes survives.