The Mixmaster Spacetime, Geroch's Transformation and Constants of Motion

We show that for $U(1)$-symmetric spacetimes on $S^3 \times R$ a constant of motion associated with the well known Geroch transformation, a functional $K[h_{ij},\pi^{ij}]$, quadratic in gravitational momenta, is strictly positive in an open subset of the set of all $U(1)$-symmetric initial data, and therefore not weakly zero. The Mixmaster initial data appear to be on the boundary of that set. We calculate the constant of motion perturbatively for the Mixmaster spacetime and find it to be proportional to the minisuperspace Hamiltonian to the first order in the Misner anisotropy variables, i.e. weakly zero. Assuming that $K$ is exactly zero for the Mixmaster spacetime, we show that Geroch's transformation, when applied to the Mixmaster spacetime, gives a new \mbox{$U(1)$-symmetric} solution of the vacuum Einstein equations, globally defined on \mbox{$S^2 \times S^1 \times R$},which is non-homogeneous and presumably exhibits Mixmaster-like complicated dynamical behavior.Comment: 25 pages, preprint YCTP-20-93, Revte

High velocity spikes in Gowdy spacetimes

We study the behavior of spiky features in Gowdy spacetimes. Spikes with velocity initially high are, generally, driven to low velocity. Let n be any integer greater than or equal to 1. If the initial velocity of an upward pointing spike is between 4n-3 and 4n-1 the spike persists with final velocity between 1 and 2, while if the initial velocity is between 4n-1 and 4n+1, the spiky feature eventually disappears. For downward pointing spikes the analogous rule is that spikes with initial velocity between 4n-4 and 4n-2 persist with final velocity between 0 and 1, while spikes with initial velocity between 4n-2 and 4n eventually disappear.Comment: discussion of constraints added. Accepted for publication in Phys. Rev.

Potential of Microalgae for the Production of Different Biotechnological Products

Microalgae have been recognized as powerful phototrophic cell-factories whose applications range from biomass production for food and feed purposes to the production of high-value products and biofuels. Microalgae have been considered a source of functional ingredients, such as polyunsaturated fatty acids, polysaccharides, essential minerals, vitamins and bioactive peptides that can have positive effects on human and animal health. Besides having high nutritional value due to the high percentage of proteins in their composition, microalgae generate high-value products, such as pigments, polysaccharides, bio-hydrogen, and even bio-polyesters with plastic-like properties. Algal biomass that remains after product recovery can be used as forage, biofertilizer or feedstock for biogas production. This step in overall algal production is important from an economic point of view due to the reduction in production costs. This paper presents the detailed study of the biotechnologically most important microalgae strains, and the design principles of photobioreactors for their cultivation. In addition, the main existing and potential high-value products derivable from microalgae, as well as utilization of microalgae for phytoremediation and biogas production, were reviewed. This work is licensed under a Creative Commons Attribution 4.0 International License

Bioethanol Production from Dilute-acid Pre-treated Wheat Straw Liquor Hydrolysate by Genetically Engineered Saccharomyces cerevisiae

Sustainable recycling of lignocellulosic biomass includes utilization of all carbohydrates present in its hydrolysates. Since wheat straw is a xylose-rich raw material, utilization of xylose from obtained liquid part (liquor) of hydrolysates improves overall bioprocess efficiency. In this work, dilute acid pre-treatment of wheat straw was performed in high-pressure reactor at different temperatures (160 °C – 200 °C), residence times (1 min – 10 min), and acids (H2SO4 and H3PO4) concentrations. During dilute acid pre-treatment, hemicellulose is degraded to pentose sugars that cannot be used by industrial ethanol-producing yeasts. Therefore, genetically engineered Saccharomyces cerevisiae strain that can utilize xylose was used. Fermentations were performed on different xylose-rich liquor wheat straw hydrolysates in shake-flasks and in horizontal rotating tubular bioreactor. The efficiency of fermentations carried out in shake flasks using xylose-rich liquor wheat straw hydrolysates were in the range of 19.61 – 74.51 %. However, the maximum bioprocess efficiency (88.24 %) was observed during fermentation in the HRTB on the liquor wheat straw hydrolysate obtained by pre-treatment with 2 % w/w phosphoric acid

The effect of Nepeta rtanjensis essential oil on test micromycetes mycelia growth

The antifungal activity of Nepeta rtanjensis Diklić et Milojević essential oil on mycelia growth has been performed by macrodilution method. The most efficient impact of N. rtanjensis essential oil on mycelia growth in vitro was found in Alternaria species with the same value of minimal inhibitory quantity (MIQ) of 0.6 μl/ml. Bipolaris spicifera and Cladosporium cladosporoioides had MIQ values of 1.0 μl/ml whereas Trichoderma viride with MIQ value of 1.6 μl/ml showed the most efficient defense against the essential oil examined. The values of minimal fungicidal quantity (MFQ) in Alternaria sp. 2, B. spicifera and C. cladosporioides match the MIQ values whereas MFQ values in Alternaria sp. 1 is 0.8 μl/ml, and in T. viride 1.8 μl/ml.Makrodilucionom metodom testiran je uticaj etarskog ulja endemične biljke Nepeta rtanjensis (Lamiaceae) na micelijalni rast mikromiceta: Alternaria sp. 1, Alternaria sp. 2, Bipolaris spicifera, Cladosporium cladosporioides i Trichoderma viride. Hemijska analiza etarskog ulja N. rtanjensis pokazala je apsolutnu dominaciju 4aα, 7α, 7aβ nepetalaktona (79.89%). Najefikasniji uticaj na rast micelije in vitro zabeležen je kod vrsta roda Alternaria sa istom vrednošću minimalne inhibitorne količine (MIK) od 0.6 μl/ml. Bipolaris spicifera i Cladosporium cladosporioides su imali MIK 1.0 μl/ml, dok je Trichoderma viride, sa vrednošću MIK od 1.6 μl/ml, pokazala najveću otpornost na dejstvo ispitivanog ulja. Vrednosti minimalne fungicidne količine (MFK) se kod Alternaria sp. 2 (0.6 μl/ml), B. spicifera (1.0 μl/ml) i C. cladosporioides (1.0 μl/ml) poklapaju sa vrednostima MIK, dok je kod Alternaria sp. 1 MFK 0.8 μl/ml, a kod T. viride 1.8 μl/ml. Etarsko ulje N. rtanjensis pokazalo je jako antifungalno dejstvo na rast micelije testiranih mikromiceta.nul

Numerical Approaches to Spacetime Singularities

This Living Review updates a previous version which its itself an update of a review article. Numerical exploration of the properties of singularities could, in principle, yield detailed understanding of their nature in physically realistic cases. Examples of numerical investigations into the formation of naked singularities, critical behavior in collapse, passage through the Cauchy horizon, chaos of the Mixmaster singularity, and singularities in spatially inhomogeneous cosmologies are discussed.Comment: 51 pages, 6 figures may be found in online version: Living Rev. Relativity 2002-1 at www.livingreviews.or

Numerical Investigation of Cosmological Singularities

Although cosmological solutions to Einstein's equations are known to be generically singular, little is known about the nature of singularities in typical spacetimes. It is shown here how the operator splitting used in a particular symplectic numerical integration scheme fits naturally into the Einstein equations for a large class of cosmological models and thus allows study of their approach to the singularity. The numerical method also naturally singles out the asymptotically velocity term dominated (AVTD) behavior known to be characteristic of some of these models, conjectured to describe others, and probably characteristic of a subclass of the rest. The method is first applied to the unpolarized Gowdy T$^3$ cosmology. Exact pseudo-unpolarized solutions are used as a code test and demonstrate that a 4th order accurate implementation of the numerical method yields acceptable agreement. For generic initial data, support for the conjecture that the singularity is AVTD with geodesic velocity (in the harmonic map target space) < 1 is found. A new phenomenon of the development of small scale spatial structure is also observed. Finally, it is shown that the numerical method straightforwardly generalizes to an arbitrary cosmological spacetime on $T^3 \times R$ with one spacelike U(1) symmetry.Comment: 37 pp +14 figures (not included, available on request), plain Te

The South Georgia Wave Experiment: a means for improved analysis of gravity waves and low-level wind impacts generated from mountainous islands

Gravity waves (GWs) play an important role in many atmospheric processes. However, the observation-based understanding of GWs is limited, and representing them in numerical models is difficult. Recent studies show that small islands can be intense sources of GWs, with climatologically significant effects on the atmospheric circulation. South Georgia, in the South Atlantic, is a notable source of such “small island” waves. GWs are usually too small scale to be resolved by current models, so their effects are represented approximately using resolved model fields (parameterization). However, the small-island waves are not well represented by such parameterizations, and the explicit representation of GWs in very-high-resolution models is still in its infancy. Steep islands such as South Georgia are also known to generate low-level wakes, affecting the flow hundreds of kilometers downwind. These wakes are also poorly represented in models. We present results from the South Georgia Wave Experiment (SG-WEX) for 5 July 2015. Analysis of GWs from satellite observations is augmented by radiosonde observations made from South Georgia. Simulations were also made using high-resolution configurations of the Met Office Unified Model (UM). Comparison with observations indicates that the UM performs well for this case, with realistic representation of GW patterns and low-level wakes. Examination of a longer simulation period suggests that the wakes generally are well represented by the model. The realism of these simulations suggests they can be used to develop parameterizations for use at coarser model resolutions