Theoretical Analysis of STM Experiments at Rutile TiO_2 Surfaces

A first-principles atomic orbital-based electronic structure method is used to investigate the low index surfaces of rutile Titanium Dioxide. The method is relatively cheap in computational terms, making it attractive for the study of oxide surfaces, many of which undergo large reconstructions, and may be governed by the presence of Oxygen vacancy defects. Calculated surface charge densities are presented for low-index surfaces of TiO$_2$, and the relation of these results to experimental STM images is discussed. Atomic resolution images at these surfaces tend to be produced at positive bias, probing states which largely consist of unoccupied Ti 3$d$ bands, with a small contribution from O 2$p$. These experiments are particularly interesting since the O atoms tend to sit up to 1 angstrom above the Ti atoms, so providing a play-off between electronic and geometric structure in image formation.Comment: 9 pages, Revtex, 3 postscript figures, accepted by Surf. Scienc

Linear Stability of Triangular Equilibrium Points in the Generalized Photogravitational Restricted Three Body Problem with Poynting-Robertson Drag

In this paper we have examined the linear stability of triangular equilibrium points in the generalised photogravitational restricted three body problem with Poynting-Robertson drag. We have found the position of triangular equilibrium points of our problem. The problem is generalised in the sense that smaller primary is supposed to be an oblate spheroid. The bigger primary is considered as radiating. The equations of motion are affected by radiation pressure force, oblateness and P-R drag. All classical results involving photogravitational and oblateness in restricted three body problem may be verified from this result. With the help of characteristic equation, we discussed the stability. Finally we conclude that triangular equilibrium points are unstable.Comment: accepted for publication in Journal of Dynamical Systems & Geometric Theories Vol. 4, Number 1 (2006

Invasive Allele Spread under Preemptive Competition

We study a discrete spatial model for invasive allele spread in which two alleles compete preemptively, initially only the "residents" (weaker competitors) being present. We find that the spread of the advantageous mutation is well described by homogeneous nucleation; in particular, in large systems the time-dependent global density of the resident allele is well approximated by Avrami's law.Comment: Computer Simulation Studies in Condensed Matter Physics XVIII, edited by D.P. Landau, S.P. Lewis, and H.-B. Schuttler, (Springer, Heidelberg, Berlin, in press

Is null-point reconnection important for solar flux emergence?

The role of null-point reconnection in a 3D numerical MHD model of solar emerging flux is investigated. The model consists of a twisted magnetic flux tube rising through a stratified convection zone and atmosphere to interact and reconnect with a horizontal overlying magnetic field in the atmosphere. Null points appear as the reconnection begins and persist throughout the rest of the emergence, where they can be found mostly in the model photosphere and transition region, forming two loose clusters on either side of the emerging flux tube. Up to 26 nulls are present at any one time, and tracking in time shows that there is a total of 305 overall, despite the initial simplicity of the magnetic field configuration. We find evidence for the reality of the nulls in terms of their methods of creation and destruction, their balance of signs, their long lifetimes, and their geometrical stability. We then show that due to the low parallel electric fields associated with the nulls, null-point reconnection is not the main type of magnetic reconnection involved in the interaction of the newly emerged flux with the overlying field. However, the large number of nulls implies that the topological structure of the magnetic field must be very complex and the importance of reconnection along separators or separatrix surfaces for flux emergence cannot be ruled out.Comment: 26 pages, 12 figures. Added one referenc

Advanced microscopy analysis of the micro-nanoscale architecture of human menisci

The complex inhomogeneous architecture of the human meniscal tissue at the micro and nano scale in the absence of artefacts introduced by sample treatments has not yet been fully revealed. The knowledge of the internal structure organization is essential to understand the mechanical functionality of the meniscus and its relationship with the tissue’s complex structure. In this work, we investigated human meniscal tissue structure using up-to-date non-invasive imaging techniques, based on multiphoton fluorescence and quantitative second harmonic generation microscopy complemented with Environmental Scanning Electron Microscopy measurements. Observations on 50 meniscal samples extracted from 6 human menisci (3 lateral and 3 medial) revealed fundamental features of structural morphology and allowed us to quantitatively describe the 3D organisation of elastin and collagen fibres bundles. 3D regular waves of collagen bundles are arranged in “honeycomb-like” cells that are comprised of pores surrounded by the collagen and elastin network at the micro-scale. This type of arrangement propagates from macro to the nanoscale

Predictors of Patient-Reported Pain and Functional Outcomes Over 10 Years After Primary Total Knee Arthroplasty: A Prospective Cohort Study.

Background This study aimed to identify preoperative predictors of patient-reported outcomes after total knee replacement (TKR) and to investigate their association with the outcomes over time. Methods We used data from 2,080 patients from the Knee Arthroplasty Trial (KAT) who received primary TKR in the UK between July 1999 and January 2003. The primary outcome measure was the Oxford Knee Score (OKS) collected annually over 10 years after TKR. Preoperative predictors included a range of patient characteristics and clinical conditions. Mixed-effects linear regression model analysis of repeated measurements was used to identify predictors of OKS overall score, pain and function subscale scores over 10 years, separately. Results Worse preoperative OKS score, worse mental well-being, BMI>35 kg/m^2, living in the most deprived areas, higher American Society of Anaesthesiologists grade, presence of comorbidities, and history of previous knee surgery were associated with worse OKS overall score over 10 years after surgery. The same predictors were identified for pain and function subscale scores, and for both long-term (10 years) and short-/mid-term outcomes (1 and 5 years). However, fitted models explained more variations in function and shorter-term outcomes than in pain and longer-term outcomes, respectively. Conclusion The same predictors were identified for pain and functional outcomes over both short-tomedium term and long term after TKR. Within the factors identified, functional and shorter-term outcomes were more predictable than pain and longer-term outcomes, respectively. Regardless of their preoperative characteristics, on average, patients achieved substantial improvement in pain over time, though improvement for function was less prominent. </p

Nonlinear Stability in the Generalised Photogravitational Restricted Three Body Problem with Poynting-Robertson Drag

The Nonlinear stability of triangular equilibrium points has been discussed in the generalised photogravitational restricted three body problem with Poynting-Robertson drag. The problem is generalised in the sense that smaller primary is supposed to be an oblate spheroid. The bigger primary is considered as radiating. We have performed first and second order normalization of the Hamiltonian of the problem. We have applied KAM theorem to examine the condition of non-linear stability. We have found three critical mass ratios. Finally we conclude that triangular points are stable in the nonlinear sense except three critical mass ratios at which KAM theorem fails.Comment: Including Poynting-Robertson Drag the triangular equilibrium points are stable in the nonlinear sense except three critical mass ratios at which KAM theorem fail