6,815 research outputs found
Asymptotic dynamics of the exceptional Bianchi cosmologies
In this paper we give, for the first time, a qualitative description of the
asymptotic dynamics of a class of non-tilted spatially homogeneous (SH)
cosmologies, the so-called exceptional Bianchi cosmologies, which are of
Bianchi type VI. This class is of interest for two reasons. Firstly,
it is generic within the class of non-tilted SH cosmologies, being of the same
generality as the models of Bianchi types VIII and IX. Secondly, it is the SH
limit of a generic class of spatially inhomogeneous cosmologies.
Using the orthonormal frame formalism and Hubble-normalized variables, we
show that the exceptional Bianchi cosmologies differ from the non-exceptional
Bianchi cosmologies of type VI in two significant ways. Firstly, the
models exhibit an oscillatory approach to the initial singularity and hence are
not asymptotically self-similar. Secondly, at late times, although the models
are asymptotically self-similar, the future attractor for the vacuum-dominated
models is the so-called Robinson-Trautman SH model instead of the vacuum SH
plane wave models.Comment: 15 pages, 6 figures, submitted to Class. Quantum Gra
Integrability and explicit solutions in some Bianchi cosmological dynamical systems
The Einstein field equations for several cosmological models reduce to
polynomial systems of ordinary differential equations. In this paper we shall
concentrate our attention to the spatially homogeneous diagonal G_2
cosmologies. By using Darboux's theory in order to study ordinary differential
equations in the complex projective plane CP^2 we solve the Bianchi V models
totally. Moreover, we carry out a study of Bianchi VI models and first
integrals are given in particular cases
Hydrological Investigations at Biafo Glacier, Karakoram Range, Himalaya; an Important Source of Water For the Indus River
Over 80% of the flow of the Upper Indus River is derived from less than 20% of its area: essentially from zones of heavy snowfall and glacierized basins above 3500 m elevation. The trans-Himalaya n contribution comes largely from an area of some 20000 km2 of glacierized basins, mostly along the axis of the Greater Karakoram range and especially from 20-30 of the largest glacier basins. Very few glaciological investigations have so far been undertaken in this the major glacierized region of Central Asia. Biafo Glacier, one of the largest of the Karakoram glaciers, drains south-eastwards from the central Karakoram crest. Its basin covers a total area of 853 km2 , 628 km2 of which are permanent snow and ice, with 68% of the glacier area forming the accumulation zone. This paper describes investigations of snow accumulation, ablation , glacier movement, and glacier depth undertaken in the period 1985-87 , set against a background of investigations carried out over the last 130 yea rs. Biafo Glacier differs from most of the other Karakoram glaciers in being nourished mainly by direct snowfall rather than by avalanching; this has the advantage of allowing extensive investigation of accumulation over a broad range of altitude. Snow-accumulation studies in the Biafo Glacier basin have indicated that annual accumulation varies from 0.9 to 1.9 m of water equivalent between 4650 and 5450 m a .. s.l. This suggests an annual moisture input above the equilibrium line of approximately 0.6 km3. Monopulse radar measurements indicate the presence of ice thickness as great as 1400 m at the equilibrium line, although these results may not be completely reliable . Mean surface velocity during the summer of 0.8 m d -I has been measured near to the equilibrium line. Calculations of annual ice flux through the vertical cross-profile at the equilibrium line indicate a throughput of 0.7 km3 a-I Estimates from stake ablation measurements also suggest that ice loss on Biafo Glacier is about 0.7 km3 a-I. The close agreement between these three sets of measurements is reassuring, indicating that the ablation zone of Biafo Glacier, whose area covers 0.09% of the whole Upper Indus basin, produces approximately 0.9% of the total run-off. However. it should be mentioned that this estimate does not include water originating from seasonal snow melt, e either above or below the equilibrium line, or from rainfall. Net annual ice losses due to wastage of the glacier since 1910 are probably of the order of 0.4-{).5 m a-I; this would represent between 12 and 15% of annual water yield from melting ice
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
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
Cosmic No Hair for Collapsing Universes
It is shown that all contracting, spatially homogeneous, orthogonal Bianchi
cosmologies that are sourced by an ultra-stiff fluid with an arbitrary and, in
general, varying equation of state asymptote to the spatially flat and
isotropic universe in the neighbourhood of the big crunch singularity. This
result is employed to investigate the asymptotic dynamics of a collapsing
Bianchi type IX universe sourced by a scalar field rolling down a steep,
negative exponential potential. A toroidally compactified version of M*-theory
that leads to such a potential is discussed and it is shown that the isotropic
attractor solution for a collapsing Bianchi type IX universe is supersymmetric
when interpreted in an eleven-dimensional context.Comment: Extended discussion to include Kantowski-Sachs universe. In press,
Classical and Quantum Gravit
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
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
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