869 research outputs found

### Integrability of irrotational silent cosmological models

We revisit the issue of integrability conditions for the irrotational silent
cosmological models. We formulate the problem both in 1+3 covariant and 1+3
orthonormal frame notation, and show there exists a series of constraint
equations that need to be satisfied. These conditions hold identically for
FLRW-linearised silent models, but not in the general exact non-linear case.
Thus there is a linearisation instability, and it is highly unlikely that there
is a large class of silent models. We conjecture that there are no spatially
inhomogeneous solutions with Weyl curvature of Petrov type I, and indicate
further issues that await clarification.Comment: Minor corrections and improvements; 1 new reference; to appear Class.
Quantum Grav.; 16 pages Ioplpp

### 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

### Dynamical systems approach to G2 cosmology

In this paper we present a new approach for studying the dynamics of
spatially inhomogeneous cosmological models with one spatial degree of freedom.
By introducing suitable scale-invariant dependent variables we write the
evolution equations of the Einstein field equations as a system of autonomous
partial differential equations in first-order symmetric hyperbolic format,
whose explicit form depends on the choice of gauge. As a first application, we
show that the asymptotic behaviour near the cosmological initial singularity
can be given a simple geometrical description in terms of the local past
attractor on the boundary of the scale-invariant dynamical state space. The
analysis suggests the name ``asymptotic silence'' to describe the evolution of
the gravitational field near the cosmological initial singularity.Comment: 28 pages, 3 tables, 1 *.eps figure, LaTeX2e (10pt), matches version
accepted for publication by Classical and Quantum Gravit

### Weyssenhoff fluid dynamics in general relativity using a 1+3 covariant approach

The Weyssenhoff fluid is a perfect fluid with spin where the spin of the
matter fields is the source of torsion in an Einstein-Cartan framework. Obukhov
and Korotky showed that this fluid can be described as an effective fluid with
spin in general relativity. A dynamical analysis of such a fluid is performed
in a gauge invariant manner using the 1+3 covariant approach. This yields the
propagation and constraint equations for the set of dynamical variables. A
verification of these equations is performed for the special case of
irrotational flow with zero peculiar acceleration by evolving the constraints.Comment: 20 page

### Odors treatment : biological technologies

Physical-chemical waste gas cleaning techniques have proven their effi ciency and reliability and will continue to occupy their niche, but several disadvantages remain. Among them are high investment and operation costs and the possible generation of secondary waste streams. With biological waste treatment techniques, reactor engineering is often less complicated and consequently costs are less. In addition, usually no secondary wastes are produced. Biological methods are nonhazardous and benign for the environment. Possible drawbacks are restricted knowledge about the biodegradation processes, limited process control, and relatively slow reaction kinetics. Anyway, the biological methods for the removal of odors and volatile organic compounds (VOCs) from waste gases are cost-effective technologies, when low concentrations (below 1-10 g/m -3 ) are to be dealt with (Kosteltz et al., 1996). Therefore, decision making can be based merely on economical analysis. Like the treatment of liquid effl uents, gaseous streams will be more often considered for biological treatment. For organic compounds, the biological reaction can be described as: CHO + O 2 + nutrients C 5 H 7 O 2 N (cell dry weight) + CO 2 + H 2 O + heat When heteroatoms are present (e.g., chlorine, sulfur), end-products like HCl or H 2 SO 4 can be formed. For effi cient pollutant removal, target pollutants have to be suffi ciently biodegradable and bioavailable. A major advantage in the case of odor treatment is that biocatalysts have high affi nity for the substrates, which allows effi cient treatment of low infl uent concentrations. Biocatalysts also operate at room temperature and they have innocuous fi nal products (e.g., carbon dioxide and water). Provided that you have the right inocula, microorganisms can metabolize almost every compound there is. In general, odors consist of a very complex mixture of volatile organic as well as inorganic compounds. The most relevant compounds regarding odors in the food industry are nitrogencontaining compou(undefined

### 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

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