Uniqueness of Petrov type D spatially inhomogeneous irrotational silent models

The consistency of the constraint with the evolution equations for spatially inhomogeneous and irrotational silent (SIIS) models of Petrov type I, demands that the former are preserved along the timelike congruence represented by the velocity of the dust fluid, leading to \emph{new} non-trivial constraints. This fact has been used to conjecture that the resulting models correspond to the spatially homogeneous (SH) models of Bianchi type I, at least for the case where the cosmological constant vanish. By exploiting the full set of the constraint equations as expressed in the 1+3 covariant formalism and using elements from the theory of the spacelike congruences, we provide a direct and simple proof of this conjecture for vacuum and dust fluid models, which shows that the Szekeres family of solutions represents the most general class of SIIS models. The suggested procedure also shows that, the uniqueness of the SIIS of the Petrov type D is not, in general, affected by the presence of a non-zero pressure fluid. Therefore, in order to allow a broader class of Petrov type I solutions apart from the SH models of Bianchi type I, one should consider more general ``silent'' configurations by relaxing the vanishing of the vorticity and the magnetic part of the Weyl tensor but maintaining their ``silence'' properties i.e. the vanishing of the curls of $E_{ab},H_{ab}$ and the pressure $p$.Comment: Latex, 19 pages, no figures;(v2) some clarification remarks and an appendix are added; (v3) minor changes to match published versio

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

Comment on Ricci Collineations for type B warped space-times

We present two counterexamples to the paper by Carot et al. in Gen. Rel. Grav. 1997, 29, 1223 and show that the results obtained are correct but not general.Comment: LaTex, 3 pages, Eq. (9) and reference added, typos corrected; Gen. Rel. Grav (to appear

Fluence and polarisation dependence of GaAs based Lateral Photo-Dember terahertz emitters

We characterise THz output of lateral photo-Dember (LPD) emitters based on semi-insulating (SI), unannealed and annealed low temperature grown (LTG) GaAs. Saturation of THz pulse power with optical fluence is observed, with unannealed LTG GaAs showing highest saturation fluence at 1.1 ± 0.1 mJ cm-2. SI-GaAs LPD emitters show a flip in signal polarity with optical fluence that is attributed to THz emission from the metal-semiconductor contact. Variation in optical polarisation affects THz pulse power that is attributed to a local optical excitation near the metal contact

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

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

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