6,915 research outputs found
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 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 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
, is defined for 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 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 and VII)
with a perfect fluid and a linear barotropic -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 models. We prove the
important result that for non-inflationary Bianchi type VII models vacuum
plane-wave solutions are the only future attracting equilibrium points in the
Bianchi type VII 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 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 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 VI Universes
We study the asymptotic behaviour of the Bianchi type VI universes with a
tilted -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, , 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 .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
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