The rigidity of infinite graphs

A rigidity theory is developed for the Euclidean and non-Euclidean placements of countably infinite simple graphs in R^d with respect to the classical l^p norms, for d>1 and 1<p<\infty. Generalisations are obtained for the Laman and Henneberg combinatorial characterisations of generic infinitesimal rigidity for finite graphs in the Euclidean plane. Also Tay's multi-graph characterisation of the rigidity of generic finite body-bar frameworks in d-dimensional Euclidean space is generalised to the non-Euclidean l^p norms and to countably infinite graphs. For all dimensions and norms it is shown that a generically rigid countable simple graph is the direct limit of an inclusion tower of finite graphs for which the inclusions satisfy a relative rigidity property. For d>2 a countable graph which is rigid for generic placements in R^d may fail the stronger property of sequential rigidity, while for d=2 the equivalence with sequential rigidity is obtained from the generalised Laman characterisations. Applications are given to the flexibility of non-Euclidean convex polyhedra and to the infinitesimal and continuous rigidity of compact infinitely-faceted simplicial polytopes.Comment: 51 page

Digitization of multistep organic synthesis in reactionware for on-demand pharmaceuticals

Chemical manufacturing is often done at large facilities that require a sizable capital investment and then produce key compounds for a finite period. We present an approach to the manufacturing of fine chemicals and pharmaceuticals in a self-contained plastic reactionware device. The device was designed and constructed by using a chemical to computer-automated design (ChemCAD) approach that enables the translation of traditional bench-scale synthesis into a platform-independent digital code. This in turn guides production of a three-dimensional printed device that encloses the entire synthetic route internally via simple operations. We demonstrate the approach for the γ-aminobutyric acid receptor agonist, (±)-baclofen, establishing a concept that paves the way for the local manufacture of drugs outside of specialist facilities

Topology and Bistability in liquid crystal devices

We study nematic liquid crystal configurations in a prototype bistable device - the Post Aligned Bistable Nematic (PABN) cell. Working within the Oseen-Frank continuum model, we describe the liquid crystal configuration by a unit-vector field, in a model version of the PABN cell. Firstly, we identify four distinct topologies in this geometry. We explicitly construct trial configurations with these topologies which are used as initial conditions for a numerical solver, based on the finite-element method. The morphologies and energetics of the corresponding numerical solutions qualitatively agree with experimental observations and suggest a topological mechanism for bistability in the PABN cell geometry

The rigidity of infinite graphs

A rigidity theory is developed for the Euclidean and non-Euclidean placements of countably infinite simple graphs in the normed spaces (\bR^d,\|\cdot \|_q), for $d\geq 2$ and $1 <q < \infty$. Generalisations are obtained for the Laman combinatorial characterisation of generic infinitesimal rigidity for  finite graphs in  (\bR^2,\|\cdot \|_2).  Also Tay's multi-graph characterisation of generic infinitesimal rigidity for finite body-bar frameworks in (\bR^d,\|\cdot\|_2) is generalised to the non-Euclidean norms and to countably infinite graphs. For all dimensions and norms  it is shown that a generically rigid countable simple graph is the direct limit $G= \varinjlim G_k$ of an inclusion tower of finite graphs $G_1 \subseteq G_2 \subseteq  \dots$ for which the inclusions satisfy a relative rigidity property. For $d\geq 3$ a countable graph which is rigid for generic placements in  \bR^d may fail the stronger property of  sequential rigidity, while for $d=2$ the properties are equivalent

The challenges of communicating research evidence in practice: perspectives from UK health visitors and practice nurses

&lt;p&gt;Background: Health practitioners play a pivotal role in providing patients with up-to-date evidence and health information. Evidence-based practice and patient-centred care are transforming the delivery of healthcare in the UK. Health practitioners are increasingly balancing the need to provide evidence-based information against that of facilitating patient choice, which may not always concur with the evidence base. There is limited research exploring how health practitioners working in the UK, and particularly those more autonomous practitioners such as health visitors and practice nurses working in community practice settings, negotiate this challenge. This research provides a descriptive account of how health visitors and practice nurses negotiate the challenges of communicating health information and research evidence in practice.&lt;/p&gt; &lt;p&gt;Methods: A total of eighteen in-depth telephone interviews were conducted in the UK between September 2008 and May 2009. The participants comprised nine health visitors and nine practice nurses, recruited via adverts on a nursing website, posters at a practitioner conference and through recommendation. Thematic analysis, with a focus on constant comparative method, was used to analyse the data.&lt;/p&gt; &lt;p&gt;Results: The data were grouped into three main themes: communicating evidence to the critically-minded patient; confidence in communicating evidence; and maintaining the integrity of the patient-practitioner relationship. These findings highlight some of the daily challenges that health visitors and practice nurses face with regard to the complex and dynamic nature of evidence and the changing attitudes and expectations of patients. The findings also highlight the tensions that exist between differing philosophies of evidence-based practice and patient-centred care, which can make communicating about evidence a daunting task.&lt;/p&gt; &lt;p&gt;Conclusions: If health practitioners are to be effective at communicating research evidence, we suggest that more research and resources need to be focused on contextual factors, such as how research evidence is negotiated, appraised and communicated within the dynamic patient-practitioner relationship.&lt;/p&gt

Targeting danger molecules in tendinopathy: the HMGB1/TLR4 axis

Objectives: To seek evidence of the danger molecule, high-mobility group protein B1 (HMGB1) expression in human tendinopathy and thereafter, to explore mechanisms where HMGB1 may regulate inflammatory mediators and matrix regulation in human tendinopathy. Methods: Torn supraspinatus tendon (established pathology) and matched intact subscapularis tendon (representing ‘early pathology’) biopsies were collected from patients undergoing arthroscopic shoulder surgery. Control samples of subscapularis tendon were collected from patients undergoing arthroscopic stabilisation surgery. Markers of inflammation and HMGB1 were quantified by reverse transcriptase PCR (RT-PCR) and immunohistochemistry. Human tendon-derived primary cells were derived from hamstring tendon tissue obtained during hamstring tendon anterior cruciate ligament reconstruction and used through passage 3. In vitro effects of recombinant HMGB1 on tenocyte matrix and inflammatory potential were measured using quantitative RT-PCR, ELISA and immunohistochemistry staining. Results: Tendinopathic tissues demonstrated significantly increased levels of the danger molecule HMGB1 compared with control tissues with early tendinopathy tissue showing the greatest expression. The addition of recombinant human HMGB1 to tenocytes led to significant increase in expression of a number of inflammatory mediators, including interleukin 1 beta (IL-1β), IL-6, IL-33, CCL2 and CXCL12, in vitro. Further analysis demonstrated rhHMGB1 treatment resulted in increased expression of genes involved in matrix remodelling. Significant increases were observed in Col3, Tenascin-C and Decorin. Moreover, blocking HMGB1 signalling via toll-like receptor 4 (TLR4) silencing reversed these key inflammatory and matrix changes. Conclusion: HMGB1 is present in human tendinopathy and can regulate inflammatory cytokines and matrix changes. We propose HMGB1 as a mediator driving the inflammatory/matrix crosstalk and manipulation of the HMGB1/TLR4 axis may offer novel therapeutic approaches targeting inflammatory mechanisms in the management of human tendon disorders

Boundary Shape and Casimir Energy

Casimir energy changes are investigated for geometries obtained by small but arbitrary deformations of a given geometry for which the vacuum energy is already known for the massless scalar field. As a specific case, deformation of a spherical shell is studied. From the deformation of the sphere we show that the Casimir energy is a decreasing function of the surface to volume ratio. The decreasing rate is higher for less smooth deformations.Comment: 12 page

Fluorescent dyes as a probe for the localized field of coupled surface plasmon-related resonances

M. Kreiter, T. Neumann, S. Mittler, W. Knoll, and J. Roy Sambles, Physical Review B, Vol. 64, article 075406 (2001). "Copyright © 2001 by the American Physical Society."The fluorescence light of Cy5 dye molecules in the vicinity of a metal grating is studied for varying directions of both the exciting and the emitted light. A different angular dependence of the intensity of the emitted light is observed for different directions of excitation. Model calculations that take into account the localization of the electrical field of grating-coupled surface plasmon-related resonances are in good agreement with the experimental observations. In addition, the spatially inhomogenous photobleaching of the dye in the field of the coupled resonances is experimentally observed. These results can be viewed both as a way to use chromophores as molecular probes for the localized electrical near field of coupled surface plasmon-related resonances and as a way to manipulate dye molecules on a submicron scale

Single photon generation by pulsed excitation of a single dipole

The fluorescence of a single dipole excited by an intense light pulse can lead to the generation of another light pulse containing a single photon. The influence of the duration and energy of the excitation pulse on the number of photons in the fluorescence pulse is studied. The case of a two-level dipole with strongly damped coherences is considered. The presence of a metastable state leading to shelving is also investigated.Comment: 17 pages, 4 figures, submitted to PR

Surface plasmons on zig-zag gratings

publication-status: Publishedtypes: ArticleThis paper was published in Optics Express and is made available as an electronic reprint with the permission of OSA. The paper can be found at the following URL on the OSA website: http://dx.doi.org/10.1364/OE.20.023921 Systematic or multiple reproduction or distribution to multiple locations via electronic or other means is prohibited and is subject to penalties under law.© Copyright 2012 Optical Society of Americ