Geodesic equation in kk-Minkowski spacetime

In this paper, we derive corrections to the geodesic equation due to the $k$-deformation of curved space-time, up to the first order in the deformation parameter a. This is done by generalizing the method from our previous paper [31], to include curvature effects. We show that the effect of $k$-noncommutativity can be interpreted as an extra drag that acts on the particle while moving in this $k$-deformed curved space. We have derived the Newtonian limit of the geodesic equation and using this, we discuss possible bounds on the deformation parameter. We also derive the generalized uncertainty relations valid in the non-relativistic limit of the $k$-space-time.Comment: 11 pages, references adde

Noncommutative duality and fermionic quasinormal modes of the BTZ black hole

We analyze the fermionic quasinormal modes of the BTZ black hole in the presence of space-time noncommutativity. Our analysis exploits a duality between a spinless and spinning BTZ black hole, the spin being proportional to the noncommutative deformation parameter. Using the AdS/CFT correspondence we show that the horizon temperatures obtained from the dual CFT pick up noncommutative contributions. We demonstrate the equivalence between the quasinormal and non-quasinormal modes for the noncommutative fermionic probes, which provides further evidence of holography in the noncommutative setting. Finally we present an analysis of the emission of Dirac fermions and the corresponding tunneling amplitude within this noncommutative framework.Comment: 17 pages, 1 figure, minor corrections, published in JHE

Noncommutative scalar quasinormal modes and quantization of entropy of a BTZ black hole

We obtain an exact analytic expression for the quasinormal modes of a noncommutative massless scalar field in the background of a massive spinless BTZ black hole up to the first order in the deformation parameter. We also show that the equations of motion governing these quasinormal modes are identical in form to the equations of motion of a commutative massive scalar field in the background of a fictitious massive spinning BTZ black hole. This results hints at a duality between the commutative and noncommutative systems in the background of a BTZ black hole. Using the obtained results for quasinormal mode frequencies, the area and entropy spectra for the BTZ black hole in the presence of noncommutativity are calculated. In particular, the separations between the neighboring values of these spectra are determined and it is found that they are nonuniform. Therefore, it appears that the noncommutativity leads to a non-equispaced (discrete) area and entropy spectra.Comment: 11 pages, improved version published in JHE

Dynamical Origin of Extrasolar Planet Eccentricity Distribution

We explore the possibility that the observed eccentricity distribution of extrasolar planets arose through planet-planet interactions, after the initial stage of planet formation was complete. Our results are based on ~3250 numerical integrations of ensembles of randomly constructed planetary systems, each lasting 100 Myr. We find that for a remarkably wide range of initial conditions the eccentricity distributions of dynamically active planetary systems relax towards a common final equilibrium distribution, well described by the fitting formula dn ~ e exp[-1/2 (e/0.3)^2] de. This distribution agrees well with the observed eccentricity distribution for e > 0.2, but predicts too few planets at lower eccentricities, even when we exclude planets subject to tidal circularization. These findings suggest that a period of large-scale dynamical instability has occurred in a significant fraction of newly formed planetary systems, lasting 1--2 orders of magnitude longer than the ~1 Myr interval in which gas-giant planets are assembled. This mechanism predicts no (or weak) correlations between semimajor axis, eccentricity, inclination, and mass in dynamically relaxed planetary systems. An additional observational consequence of dynamical relaxation is a significant population of planets (>10%) that are highly inclined (>25deg) with respect to the initial symmetry plane of the protoplanetary disk; this population may be detectable in transiting planets through the Rossiter-McLaughlin effect.Comment: Accepted to ApJ, conclusions updated to reflect the current observational constraint

Flotation of ores and waste waters

World generally requires a very high standard of pollution control, and mining companies pride their organisations as being examples of excellence in this field. Hydrometallurgical mining processes decrease the production of gas and solid pollutants into the atmosphere and maximize the recirculation of solvents at every level of waste waters treatment. The extra electrowinning of metal using the circular hydrometallurgical process ensures that the maximum amount of mined metal is recovered. Reducing pollution helps to improve company profitability

The frequency of occurrence of aflatoxin M1 in milk on the territory of Vojvodina

Aflatoxin is one of the most common mycotoxins which can be found in milk. It represents a natural metabolite of aflatoxin B1 that occurs as a result of animal metabolism and the body's attempt to detoxificate it. It is excreted in milk, feces and urine of animals that consumed contaminated feed with aflatoxin B1. The carry-over from feed to milk depends on many factors, ranging from 0.3 to 6.2%. Aflatoxin M1 is in the first group of carcinogens according to the IRAC classification from 2002, but it is considered to have only 10% of carcinogenicity from its precursor aflatoxin B1. Legislation in member countries of European Union for this mycotoxin in milk intended for people is 0.05 μg/l, while the rest of the countries that also have legislation for this mycotoxin allow the concentration that is ten times higher, and that is 0.5 μg/l. In this paper, we have tried to provide on insight into the quality of milk, food often consumed by children, from the standpoint of mycotoxicology, and to compare the obtained data with data available from literature, from countries in the region that have similar climatic and agricultural conditions. From a total of 65 samples of processed milk, aflatoxin M1 was found in 18 samples and none of the samples exceeded the level of 0.05 μg/l, which is allowed by the legislation of the European Union

The Dark Disk of the Milky Way

Massive satellite accretions onto early galactic disks can lead to the deposition of dark matter in disk-like configurations that co-rotate with the galaxy. This phenomenon has potentially dramatic consequences for dark matter detection experiments. We utilize focused, high-resolution simulations of accretion events onto disks designed to be Galaxy analogues, and compare the resultant disks to the morphological and kinematic properties of the Milky Way's thick disk in order to bracket the range of co-rotating accreted dark matter. We find that the Milky Way's merger history must have been unusually quiescent compared to median LCDM expectations and therefore its dark disk must be relatively small: the fraction of accreted dark disk material near the Sun is about 20% of the host halo density or smaller and the co-rotating dark matter fraction near the Sun, defined as particles moving with a rotational velocity lag less than 50 km/s, is enhanced by about 30% or less compared to a standard halo model. Such a dark disk could contribute dominantly to the low energy (of order keV for a dark matter particle with mass 100 GeV) nuclear recoil event rate of direct dectection experiments, but it will not change the likelihood of detection significantly. These dark disks provide testable predictions of weakly-interacting massive particle dark matter models and should be considered in detailed comparisons to experimental data. Our findings suggest that the dark disk of the Milky Way may provide a detectable signal for indirect detection experiments, contributing up to about 25% of the dark matter self-annihilation signal in the direction of the center of the Galaxy, lending the signal a noticeably oblate morphology.Comment: 11 pages, 6 figures, 1 table; submitted to Ap

Electrodynamics on κ\kappa-Minkowski space-time

In this paper, we derive Lorentz force and Maxwell's equations on kappa-Minkowski space-time up to the first order in the deformation parameter. This is done by elevating the principle of minimal coupling to non-commutative space-time. We also show the equivalence of minimal coupling prescription and Feynman's approach. It is shown that the motion in kappa space-time can be interpreted as motion in a background gravitational field, which is induced by this non-commutativity. In the static limit, the effect of kappa deformation is to scale the electric charge. We also show that the laws of electrodynamics depend on the mass of the charged particle, in kappa space-time.Comment: 16 pages,minor changes, paragraph added on page 13, two new references added, to appear in Phys.Rev.