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