Linearisable third order ordinary differential equations and generalised Sundman transformations

We calculate in detail the conditions which allow the most general third order ordinary differential equation to be linearised in X'''(T)=0 under the transformation X(T)=F(x,t), dT=G(x,t)dt. Further generalisations are considered.Comment: 33 page

Self-assembly of a columnar polymeric calcium phosphinate derived from camphene

(2,2-Dimethylbicyclo[2.2.1] hept-3-ylmethyl)phosphinic acid (RPO₂H₂), readily prepared from camphene and hypophosphorous acid, formed a polymeric calcium salt [{Ca(RPO₂H) ₂ (RPO₂H₂)(H₂O)}n], with both terminal and triply bridging phosphinate groups, and an overall columnar structure with an inorganic core and a pseudo-close-packed sheath of terpene moieties

Lifetime Adherence to Physical Activity Recommendations and Fall Occurrence in Community-dwelling Older Adults: a Retrospective Cohort Study

Falling is a major health concern for community-dwelling older adults. Regular physical activity has been proposed to prevent falls. The aim of this study was to assess whether the achievement of the 2004 UK Department of Health physical activity recommendations over a lifetime had a protective effect against falling in older people. 313 community-dwelling older adults completed a questionnaire about lifetime physical activity and fall occurrence. There were significantly fewer falls in those who had led an active lifestyle compared to those who had not (χ2Yates=4.568, p=0.033), with a lower relative risk of fall occurrence for the active respondents (RR=0.671) compared to the inactive (RR=1.210). Of those who were sufficiently active in their early adulthood, the decade where there was the biggest decrease in remaining active enough was in the 60s. It is concluded that an active lifestyle may have decreased the likelihood of having a fall in older ag

Osteogenic preconditioning in perfusion bioreactors improves vascularization and bone formation by human bone marrow aspirates.

Cell-derived extracellular matrix (ECM) provides a niche to promote osteogenic differentiation, cell adhesion, survival, and trophic factor secretion. To determine whether osteogenic preconditioning would improve the bone-forming potential of unfractionated bone marrow aspirate (BMA), we perfused cells on ECM-coated scaffolds to generate naïve and preconditioned constructs, respectively. The composition of cells selected from BMA was distinct on each scaffold. Naïve constructs exhibited robust proangiogenic potential in vitro, while preconditioned scaffolds contained more mesenchymal stem/stromal cells (MSCs) and endothelial cells (ECs) and exhibited an osteogenic phenotype. Upon implantation into an orthotopic calvarial defect, BMA-derived ECs were present in vessels in preconditioned implants, resulting in robust perfusion and greater vessel density over the first 14 days compared to naïve implants. After 10 weeks, human ECs and differentiated MSCs were detected in de novo tissues derived from naïve and preconditioned scaffolds. These results demonstrate that bioreactor-based preconditioning augments the bone-forming potential of BMA

Physics 201: Modern Physics

Following the spirit of the new curriculum, it was decided to convert the Modern Physics course, Physics 201, into a course with a COLL200 attribute. The course covered the basics of relativity and quantum mechanics, and typically has 50-60 students. It was desired to include a substantial discussion of the historical and social significance of the material

Enterprise Requirements and Acquisition Model

In support of senior leadership emphasis on improving early systems engineering and analysis, the Enterprise Requirements and Acquisition Model (ERAM) is a quantitative discrete-event process simulation model that accounts for activities from the identification of a desired space capability early in the JCIDS process through Milestone C of the acquisition system resulting in a probabilistic schedule distribution for a given concept. This model of the DoD\u27s space capability development process will provide valuable decision making information for Concept Characterization and Technical Descriptions referenced during Analysis of Alternatives. The research focused on identifying activities, assigning historical triangular distributions and probabilities at each decision point. Data was collected through analysis of applicable policy, instructions, and journal articles as well as interviews with subject matter experts from the Air Staff, Air Force Space Command and the Space and Missile Systems Center. ERAM will be utilized at the Aerospace Concept Design Center providing decision-makers insight into timeline estimations and probabilities of success. ERAM has the potential to be used as a training tool for Air Staff, AFSPC and SMC personnel to better understand existing organizational interdependencies and required activities to successfully acquire a capability on schedule and within budget

Analytic Behaviour of Competition among Three Species

We analyse the classical model of competition between three species studied by May and Leonard ({\it SIAM J Appl Math} \textbf{29} (1975) 243-256) with the approaches of singularity analysis and symmetry analysis to identify values of the parameters for which the system is integrable. We observe some striking relations between critical values arising from the approach of dynamical systems and the singularity and symmetry analyses.Comment: 14 pages, to appear in Journal of Nonlinear Mathematical Physic

Spherically Symmetric Solutions to Fourth-Order Theories of Gravity

Gravitational theories generated from Lagrangians of the form f(R) are considered. The spherically symmetric solutions to these equations are discussed, paying particular attention to features that differ from the standard Schwarzschild solution. The asymptotic form of solutions is described, as is the lack of validity of Birkhoff's theorem. Exact solutions are presented which illustrate these points and their stability and geodesics are investigated.Comment: 10 pages, published versio

Modelling the Galactic Magnetic Field on the Plane in 2D

We present a method for parametric modelling of the physical components of the Galaxy's magnetised interstellar medium, simulating the observables, and mapping out the likelihood space using a Markov Chain Monte-Carlo analysis. We then demonstrate it using total and polarised synchrotron emission data as well as rotation measures of extragalactic sources. With these three datasets, we define and study three components of the magnetic field: the large-scale coherent field, the small-scale isotropic random field, and the ordered field. In this first paper, we use only data along the Galactic plane and test a simple 2D logarithmic spiral model for the magnetic field that includes a compression and a shearing of the random component giving rise to an ordered component. We demonstrate with simulations that the method can indeed constrain multiple parameters yielding measures of, for example, the ratios of the magnetic field components. Though subject to uncertainties in thermal and cosmic ray electron densities and depending on our particular model parametrisation, our preliminary analysis shows that the coherent component is a small fraction of the total magnetic field and that an ordered component comparable in strength to the isotropic random component is required to explain the polarisation fraction of synchrotron emission. We outline further work to extend this type of analysis to study the magnetic spiral arm structure, the details of the turbulence as well as the 3D structure of the magnetic field.Comment: 18 pages, 11 figures, updated to published MNRAS versio