166 research outputs found
New explicit spike solution -- non-local component of the generalized Mixmaster attractor
By applying a standard solution-generating transformation to an arbitrary
vacuum Bianchi type II solution, one generates a new solution with spikes
commonly observed in numerical simulations. It is conjectured that the spike
solution is part of the generalized Mixmaster attractor.Comment: Significantly revised. Colour figures simplified to accommodate
non-colour printin
Monotonic functions in Bianchi models: Why they exist and how to find them
All rigorous and detailed dynamical results in Bianchi cosmology rest upon
the existence of a hierarchical structure of conserved quantities and monotonic
functions. In this paper we uncover the underlying general mechanism and derive
this hierarchical structure from the scale-automorphism group for an
illustrative example, vacuum and diagonal class A perfect fluid models. First,
kinematically, the scale-automorphism group leads to a reduced dynamical system
that consists of a hierarchy of scale-automorphism invariant sets. Second, we
show that, dynamically, the scale-automorphism group results in
scale-automorphism invariant monotone functions and conserved quantities that
restrict the flow of the reduced dynamical system.Comment: 26 pages, replaced to match published versio
Conformal regularization of Einstein's field equations
To study asymptotic structures, we regularize Einstein's field equations by
means of conformal transformations. The conformal factor is chosen so that it
carries a dimensional scale that captures crucial asymptotic features. By
choosing a conformal orthonormal frame we obtain a coupled system of
differential equations for a set of dimensionless variables, associated with
the conformal dimensionless metric, where the variables describe ratios with
respect to the chosen asymptotic scale structure. As examples, we describe some
explicit choices of conformal factors and coordinates appropriate for the
situation of a timelike congruence approaching a singularity. One choice is
shown to just slightly modify the so-called Hubble-normalized approach, and one
leads to dimensionless first order symmetric hyperbolic equations. We also
discuss differences and similarities with other conformal approaches in the
literature, as regards, e.g., isotropic singularities.Comment: New title plus corrections and text added. To appear in CQ
Asymptotic silence-breaking singularities
We discuss three complementary aspects of scalar curvature singularities:
asymptotic causal properties, asymptotic Ricci and Weyl curvature, and
asymptotic spatial properties. We divide scalar curvature singularities into
two classes: so-called asymptotically silent singularities and non-generic
singularities that break asymptotic silence. The emphasis in this paper is on
the latter class which have not been previously discussed. We illustrate the
above aspects and concepts by describing the singularities of a number of
representative explicit perfect fluid solutions.Comment: 25 pages, 6 figure
Spherically symmetric relativistic stellar structures
We investigate relativistic spherically symmetric static perfect fluid models
in the framework of the theory of dynamical systems. The field equations are
recast into a regular dynamical system on a 3-dimensional compact state space,
thereby avoiding the non-regularity problems associated with the
Tolman-Oppenheimer-Volkoff equation. The global picture of the solution space
thus obtained is used to derive qualitative features and to prove theorems
about mass-radius properties. The perfect fluids we discuss are described by
barotropic equations of state that are asymptotically polytropic at low
pressures and, for certain applications, asymptotically linear at high
pressures. We employ dimensionless variables that are asymptotically homology
invariant in the low pressure regime, and thus we generalize standard work on
Newtonian polytropes to a relativistic setting and to a much larger class of
equations of state. Our dynamical systems framework is particularly suited for
numerical computations, as illustrated by several numerical examples, e.g., the
ideal neutron gas and examples that involve phase transitions.Comment: 23 pages, 25 figures (compressed), LaTe
Colour reconnections in Herwig++
We describe the implementation details of the colour reconnection model in
the event generator Herwig++. We study the impact on final-state observables in
detail and confirm the model idea from colour preconfinement on the basis of
studies within the cluster hadronization model. Moreover, we show that the
description of minimum bias and underlying event data at the LHC is improved
with this model and present results of a tune to available data.Comment: 19 pages, 21 figures, 2 tables. Matches with published versio
Bianchi type I models with two tilted fluids
In this paper we investigate expanding Bianchi type I models with two tilted
fluids with linear equations of state. Individually the fluids have non-zero
energy fluxes w.r.t. the symmetry surfaces, but these cancel each other because
of the Codazzi constraint. Asymptotically toward the past the solutions
approach Kasner states if the speeds of sound are less than that of light. If
one of the fluids has a speed of sound that is less or equal to 1/3 of the
speed of light (radiation) then the models isotropize toward the future, but if
both fluids are stiffer than radiation then the final state is anisotropic with
non-zero Hubble-normalized shear. The significance of these results is
discussed in a broader context.Comment: 19 pages, 2 figure
Alterations in rhythmic and non-rhythmic resting-state EEG activity and their link to cognition in older age
While many structural and biochemical changes in the brain have been previously associated with aging, the findings concerning electrophysiological signatures, reflecting functional properties of neuronal networks, remain rather controversial. To try resolve this issue, we took advantage of a large population study (N=1703) and comprehensively investigated the association of multiple EEG biomarkers (power of alpha and theta oscillations, individual alpha peak frequency (IAF), the slope of 1/f power spectral decay), aging, and aging and cognitive performance. Cognitive performance was captured with three factors representing processing speed, episodic memory, and interference resolution. Our results show that not only did IAF decline with age but it was also associated with interference resolution over multiple cortical areas. To a weaker extent, 1/f slope of the PSD showed age-related reductions, mostly in frontal brain regions. Finally, alpha power was negatively associated with the speed of processing in the right frontal lobe, despite the absence of age-related alterations. Our results thus demonstrate that multiple electrophysiological features, as well as their interplay, should be considered when investigating the association between age, neuronal activity, and cognitive performance
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