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

Ruptures and repairs of group therapy alliance. an untold story in psychotherapy research

Although previous studies investigated the characteristics of therapeutic alliance in group treatments, there is still a dearth of research on group alliance ruptures and repairs. The model by Safran and Muran was originally developed to address therapeutic alliance in individual therapies, and the usefulness of this approach to group intervention needs to be demonstrated. Alliance ruptures are possible at member to therapist, member to member, member to group levels. Moreover, repairs of ruptures in group are quite complex, i.e., because other group members have to process the rupture even if not directly involved. The aim of the current study is to review the empirical research on group alliance, and to examine whether the rupture repair model can be a suitable framework for clinical understanding and research of the complexity of therapeutic alliance in group treatments. We provide clinical vignettes and commentary to illustrate theoretical and research aspects of therapeutic alliance rupture and repair in groups. Our colleague Jeremy Safran made a substantial contribution to research on therapeutic alliance, and the current paper illustrates the enduring legacy of this work and its potential application to the group therapy context

A dynamical systems approach to the tilted Bianchi models of solvable type

We use a dynamical systems approach to analyse the tilting spatially homogeneous Bianchi models of solvable type (e.g., types VI$_h$ and VII$_h$) with a perfect fluid and a linear barotropic $\gamma$-law equation of state. In particular, we study the late-time behaviour of tilted Bianchi models, with an emphasis on the existence of equilibrium points and their stability properties. We briefly discuss the tilting Bianchi type V models and the late-time asymptotic behaviour of irrotational Bianchi VII$_0$ models. We prove the important result that for non-inflationary Bianchi type VII$_h$ models vacuum plane-wave solutions are the only future attracting equilibrium points in the Bianchi type VII$_h$ invariant set. We then investigate the dynamics close to the plane-wave solutions in more detail, and discover some new features that arise in the dynamical behaviour of Bianchi cosmologies with the inclusion of tilt. We point out that in a tiny open set of parameter space in the type IV model (the loophole) there exists closed curves which act as attracting limit cycles. More interestingly, in the Bianchi type VII$_h$ models there is a bifurcation in which a set of equilibrium points turn into closed orbits. There is a region in which both sets of closed curves coexist, and it appears that for the type VII$_h$ models in this region the solution curves approach a compact surface which is topologically a torus.Comment: 29 page

Space-times admitting a three-dimensional conformal group

Perfect fluid space-times admitting a three-dimensional Lie group of conformal motions containing a two-dimensional Abelian Lie subgroup of isometries are studied. Demanding that the conformal Killing vector be proper (i.e., not homothetic nor Killing), all such space-times are classified according to the structure of their corresponding three-dimensional conformal Lie group and the nature of their corresponding orbits (that are assumed to be non-null). Each metric is then explicitly displayed in coordinates adapted to the symmetry vectors. Attention is then restricted to the diagonal case, and exact perfect fluid solutions are obtained in both the cases in which the fluid four-velocity is tangential or orthogonal to the conformal orbits, as well as in the more general "tilting" case.Comment: Latex 34 page

The Asymptotic Behaviour of Tilted Bianchi type VI0_0 Universes

We study the asymptotic behaviour of the Bianchi type VI$_0$ universes with a tilted $\gamma$-law perfect fluid. The late-time attractors are found for the full 7-dimensional state space and for several interesting invariant subspaces. In particular, it is found that for the particular value of the equation of state parameter, $\gamma=6/5$, there exists a bifurcation line which signals a transition of stability between a non-tilted equilibrium point to an extremely tilted equilibrium point. The initial singular regime is also discussed and we argue that the initial behaviour is chaotic for $\gamma<2$.Comment: 22 pages, 4 figures, to appear in CQ

Caustics of Compensated Spherical Lens Models

We consider compensated spherical lens models and the caustic surfaces they create in the past light cone. Examination of cusp and crossover angles associated with particular source and lens redshifts gives explicit lensing models that confirm previous claims that area distances can differ by substantial factors from angular diameter distances even when averaged over large angular scales. `Shrinking' in apparent sizes occurs, typically by a factor of 3 for a single spherical lens, on the scale of the cusp caused by the lens; summing over many lenses will still leave a residual effect.Comment: 21 pages, 5 ps figures, eps

Information-flux approach to multiple-spin dynamics

We introduce and formalize the concept of information flux in a many-body register as the influence that the dynamics of a specific element receive from any other element of the register. By quantifying the information flux in a protocol, we can design the most appropriate initial state of the system and, noticeably, the distribution of coupling strengths among the parts of the register itself. The intuitive nature of this tool and its flexibility, which allow for easily manageable numerical approaches when analytic expressions are not straightforward, are greatly useful in interacting many-body systems such as quantum spin chains. We illustrate the use of this concept in quantum cloning and quantum state transfer and we also sketch its extension to non-unitary dynamics.Comment: 7 pages, 4 figures, RevTeX

FOULING DURING THE USE OF ‘FRESH’ WATER AS COOLANT- THE DEVELOPMENT OF A ‘USER GUIDE’

IHS ESDU recently published its latest ‘User Guide’ to fouling in heat exchange systems, for systems with fresh water as the coolant. ESDU 07006 [1] is the third in a group, following the development of the Crude Oil Fouling User Guide [2] issued in 2000 and the Seawater Fouling User Guide [3] issued in 2004. ESDU 07006 was developed by IHS ESDU over a period of five years under the guidance of the Oil Industry Fouling Working Party, a collaborative team of oil refiners, heat transfer equipment and services suppliers and Universities. It provides designers and operators of cooling water facilities with a practical source of guidance on the occurrence, the mechanisms and the mitigation of fresh water fouling in these systems. IHS ESDU’s Oil Industry Fouling Working Party was formed in recognition of the huge economic and environmental importance of heat exchanger fouling and the potential benefits that can accrue from better understanding of mitigation strategies. Work is now underway on reboiler and FCCU fouling. The development of the User Guide ESDU 07006 is discussed in this paper and its technical content is summarized

The Mass Distribution of the Lens Galaxy in MG1131+0456

We present the results of modeling 5, 8 and 15 GHz maps of the gravitational lens MG1131+0456 using the LensClean algorithm. Two models for the mass distribution in the lens were fit: a de Vaucouleurs model and a model with the two-dimensional potential phi = b^{2-alpha}(r^2+s^2)^{alpha/2}/2alpha, both in an external shear field. The best fit de Vaucouleurs model has an effective radius of R_e = 0.83+-0.13 arcseconds, larger than that measured at optical wavelengths. The best fit ``alpha model'' has alpha=0.6+-0.2 and a core radius of s = 0.19 +- 0.07 arcseconds. An isothermal model (alpha=1) is inconsistent with the data. The best alpha model fits the 8 GHz map significantly better than the best de Vaucouleurs model. Although it is difficult to distinguish visually the original image and the reconstructions, none of the models is statistically consistent with the data. We believe the primary problem is that an external shear is an inadequate model for the angular structure of the lens galaxy. The finite core radius in the models is required by the structure of the extended ring, so we confirm that the central component in the 8 GHz map is a central, lensed image of the source rather than the lens galaxy. The model lens positions, the position angle of the shear, and the mass interior to the ring are determined very precisely by the lens models. The time delay between the compact components is predicted with an uncertainty we estimate to be at most +- 9%; the formal uncertainty is +- 4%.Comment: 47 pages. There are 2 Postscript files in the package

One-dimensional relativistic dissipative system with constant force and its quantization

For a relativistic particle under a constant force and a linear velocity dissipation force, a constant of motion is found. Problems are shown for getting the Hamiltoninan of this system. Thus, the quantization of this system is carried out through the constant of motion and using the quantization of the velocity variable. The dissipative relativistic quantum bouncer is outlined within this quantization approach.Comment: 11 pages, no figure