Self-similar Bianchi models: II. Class B models

In a companion article (referred hearafter as paper I) a detailed study of the simply transitive Spatially Homogeneous (SH) models of class A concerning the existence of a simply transitive similarity group has been given. The present work (paper II) continues and completes the above study by considering the remaining set of class B models. Following the procedure of paper I we find all SH models of class B subjected only to the minimal geometric assumption to admit a proper Homothetic Vector Field (HVF). The physical implications of the obtained geometric results are studied by specialising our considerations to the case of vacuum and $\gamma -$law perfect fluid models. As a result we regain all the known exact solutions regarding vacuum and non-tilted perfect fluid models. In the case of tilted fluids we find the \emph{general }self-similar solution for the exceptional type VI$_{-1/9}$ model and we identify it as equilibrium point in the corresponding dynamical state space. It is found that this \emph{new} exact solution belongs to the subclass of models $n_\alpha ^\alpha =0$, is defined for $\gamma \in (\frac 43,\frac 32)$ and although has a five dimensional stable manifold there exist always two unstable modes in the restricted state space. Furthermore the analysis of the remaining types, guarantees that tilted perfect fluid models of types III, IV, V and VII$_h$ cannot admit a proper HVF strongly suggesting that these models either may not be asymptotically self-similar (type V) or may be extreme tilted at late times. Finally for each Bianchi type, we give the extreme tilted equilibrium points of their state space.Comment: Latex, 15 pages, no figures; to appear in Classical Quantum Gravity (uses iopart style/class files); (v2) minor corrections to match published versio

THE INCIDENCE OF THE INFRAPATELLAR PLICAE IN THE ELDERLY WELSH POPULATION

There are several studies reporting the incidence of suprapatellar, medial and lateral plicae, but there is very limited information regarding the incidence of the infrapatellar plica. The purpose of our study was to record the incidence of the infrapatelar plicae in the elderly Welsh population suffering of knee osteoarthritis. A prospective study was performed and 90 knees with severe osteoarthritis of the knee joint (Kellgren-Lawrence type III and IV) were investigated during total knee arthroplasty surgery.  Documentation was performed at every total knee replacement surgery for the length of the study. Knee replacement was performed by one senior surgeon. Infrapatellar plica was investigated by a medial parapatellar approach and was classified into five types according to Kim’s classification. The overall incidence of the infrapatellar plicae was 37.7%. The most common type of plicae was the separate type (23.3 %). There was no significant difference found between male and female patients. The fenestra type was the least common (2.22%). The incidence of infrapatellar plicae in the elderly Welsh population suffering of knee osteoarthritis was significantly lower when compared to a study that recorded the incidence of infrapatellar plica in young patients. Possibly, the degenerative changes of the knee joint can cause the reabsorption of the infrapatellar plica decreasing by this way its incidence in the elderly population.Key words: infrapatellar plicae, incidence, knee osteoarthritis, elderl

Self-similar Bianchi models: I. Class A models

We present a study of Bianchi class A tilted cosmological models admitting a proper homothetic vector field together with the restrictions, both at the geometrical and dynamical level, imposed by the existence of the simply transitive similarity group. The general solution of the symmetry equations and the form of the homothetic vector field are given in terms of a set of arbitrary integration constants. We apply the geometrical results for tilted perfect fluids sources and give the general Bianchi II self-similar solution and the form of the similarity vector field. In addition we show that self-similar perfect fluid Bianchi VII$_0$ models and irrotational Bianchi VI$_0$ models do not exist.Comment: 14 pages, Latex; to appear in Classical and Quantum Gravit

A geometric description of the intermediate behaviour for spatially homogeneous models

A new approach is suggested for the study of geometric symmetries in general relativity, leading to an invariant characterization of the evolutionary behaviour for a class of Spatially Homogeneous (SH) vacuum and orthogonal $\gamma -$law perfect fluid models. Exploiting the 1+3 orthonormal frame formalism, we express the kinematical quantities of a generic symmetry using expansion-normalized variables. In this way, a specific symmetry assumption lead to geometric constraints that are combined with the associated integrability conditions, coming from the existence of the symmetry and the induced expansion-normalized form of the Einstein's Field Equations (EFE), to give a close set of compatibility equations. By specializing to the case of a \emph{Kinematic Conformal Symmetry} (KCS), which is regarded as the direct generalization of the concept of self-similarity, we give the complete set of consistency equations for the whole SH dynamical state space. An interesting aspect of the analysis of the consistency equations is that, \emph{at least} for class A models which are Locally Rotationally Symmetric or lying within the invariant subset satisfying $N_{\alpha}^{\alpha}=0$, a proper KCS \emph{always exists} and reduces to a self-similarity of the first or second kind at the asymptotic regimes, providing a way for the ``geometrization'' of the intermediate epoch of SH models.Comment: Latex, 15 pages, no figures (uses iopart style/class files); added one reference and minor corrections; (v3) improved and extended discussion; minor corrections and several new references are added; to appear in Class. Quantum Gra

Self-similar Bianchi type VIII and IX models

It is shown that in transitively self-similar spatially homogeneous tilted perfect fluid models the symmetry vector is not normal to the surfaces of spatial homogeneity. A direct consequence of this result is that there are no self-similar Bianchi VIII and IX tilted perfect fluid models. Furthermore the most general Bianchi VIII and IX spacetime which admit a four dimensional group of homotheties is given.Comment: 5 pages, Latex; One reference and minor clarifications added. To appear in General Relativity and Gravitatio

The influence of carbon on the resistivity recovery of proton irradiated Fe–11at.% Cr alloys

AbstractThe effect of carbon on the point defect migration properties in Fe–Cr alloys with a concentration of 11 at.% Cr is studied by means of resistivity recovery measurements after low temperature proton irradiation. The presence of carbon mainly affects features of the resistivity recovery spectra in the temperature ranges of (a) 150–200K, which are linked to self-interstitial defects, and (b) 400–500K, which are probably due to vacancy and vacancy-carbon complexes. The experimental results are discussed in terms of the possible interactions of carbon with radiation defects and its influence on solute atom re-ordering

Symmetries of Bianchi I space-times

All diagonal proper Bianchi I space-times are determined which admit certain important symmetries. It is shown that for Homotheties, Conformal motions and Kinematic Self-Similarities the resulting space-times are defined explicitly in terms of a set of parameters whereas Affine Collineations, Ricci Collineations and Curvature Collineations, if they are admitted, they determine the metric modulo certain algebraic conditions. In all cases the symmetry vectors are explicitly computed. The physical and the geometrical consequences of the results are discussed and a new anisitropic fluid, physically valid solution which admits a proper conformal Killing vector, is given.Comment: 19 pages, LaTex, Accepted for publication in Journal of Mathematical Physic

Structural Comparison of Allogeneic and Syngeneic T Cell Receptor–Peptide-Major Histocompatibility Complex Complexes: A Buried Alloreactive Mutation Subtly Alters Peptide Presentation Substantially Increasing Vβ Interactions

The crystal structures of the 2C/H-2Kbm3–dEV8 allogeneic complex at 2.4 Å and H-2Kbm3–dEV8 at 2.15 Å, when compared with their syngeneic counterparts, elucidate structural changes that induce an alloresponse. The Asp77Ser mutation that imbues H-2Kbm3–dEV8 with its alloreactive properties is located beneath the peptide and does not directly contact the T cell receptor (TCR). However, the buried mutation induces local rearrangement of the peptide itself to preserve hydrogen bonding interactions between the peptide and the α1 77 residue. The COOH terminus of the peptide main chain is tugged toward the α1-helix such that its presentation to the TCR is altered. These changes increase the stability of the allogeneic peptide-major histocompatibility complex (pMHC) complex and increase complementarity in the TCR–pMHC interface, placing greater emphasis on recognition of the pMHC by the TCR β-chain, evinced by an increase in shape complementarity, buried surface area, and number of TCR–pMHC contacting residues. A nearly fourfold increase in the number of β-chain–pMHC contacts is accompanied by a concomitant 64% increase in β-chain–pMHC shape complementarity. Thus, the allogeneic mutation causes the same peptide to be presented differently, temporally and spatially, by the allogeneic and syngeneic MHCs

Multi-level optical signal generation using a segmented-electrode InP IQ-MZM with integrated CMOS binary drivers

We present a segmented-electrode InP IQ-MZM, capable of multi-level optical signal generation (5-bit per I/Q arm) by employing direct digital drive from integrated, low-power (1W) CMOS binary drivers. Programmable, multi-level operation is demonstrated experimentally on one MZM of the device