Hyperboloidal slices for the wave equation of Kerr-Schild metrics and numerical applications

We present new results from two open source codes, using finite differencing and pseudo-spectral methods for the wave equations in (3+1) dimensions. We use a hyperboloidal transformation which allows direct access to null infinity and simplifies the control over characteristic speeds on Kerr-Schild backgrounds. We show that this method is ideal for attaching hyperboloidal slices or for adapting the numerical resolution in certain spacetime regions. As an example application, we study late-time Kerr tails of sub-dominant modes and obtain new insight into the splitting of decay rates. The involved conformal wave equation is freed of formally singular terms whose numerical evaluation might be problematically close to future null infinity.Comment: 15 pages, 12 figure

Isometric embeddings of 2-spheres by embedding flow for applications in numerical relativity

We present a numerical method for solving Weyl's embedding problem which consists of finding a global isometric embedding of a positively curved and positive-definite spherical 2-metric into the Euclidean three space. The method is based on a construction introduced by Weingarten and was used in Nirenberg's proof of Weyl's conjecture. The target embedding results as the endpoint of an embedding flow in R^3 beginning at the unit sphere's embedding. We employ spectral methods to handle functions on the surface and to solve various (non)-linear elliptic PDEs. Possible applications in 3+1 numerical relativity range from quasi-local mass and momentum measures to coarse-graining in inhomogeneous cosmological models.Comment: 18 pages, 14 figure

The spatial relation between the event horizon and trapping horizon

The relation between event horizons and trapping horizons is investigated in a number of different situations with emphasis on their role in thermodynamics. A notion of constant change is introduced that in certain situations allows the location of the event horizon to be found locally. When the black hole is accreting matter the difference in area between the two different horizons can be many orders of magnitude larger than the Planck area. When the black hole is evaporating the difference is small on the Planck scale. A model is introduced that shows how trapping horizons can be expected to appear outside the event horizon before the black hole starts to evaporate. Finally a modified definition is introduced to invariantly define the location of the trapping horizon under a conformal transformation. In this case the trapping horizon is not always a marginally outer trapped surface.Comment: 16 pages, 1 figur

Evaluation of brittle fracturing in the sedimentary rock through laboratory analysis and computer simulation

This is the final version. Available from Faculty of Mining, Ecology, Process Control and Geotechnologies (FBERG), Technical University of Kosice via the DOI in this record. Estimation of the mechanical responses of a sample of rock is a critical characteristic to estimate the responses of rock strata under stress. In this paper, laboratory tests analysis and numerical modelling are used to analyse and replicate intact rock materials. Laboratory and petrographical analyses were undertaken to characterise the brittle response to the uniaxial loading of selected sedimentary samples. Complementary numerical modelling of virtual uniaxial compression tests is carried out using 3DEC software. These models were developed through a Grain Based Model capable of reproducing brittle failure of rocks, for which Voronoi 3D tessellation was generated. Failure mechanisms observed in laboratory and non-linear behaviour due to fracture propagation have been reproduced. Virtual modelling of intact rock with Discrete Element Code would allow, in combination with Discrete Fracture Networks, the numerical analysis of rock mass scale effects and anisotropy through Synthetic Rock Mass (SRM) modelling.Research Fund for Coal and Steel (RFCS)Polish Ministry of Science and Higher Educatio

Intermediate behavior of Kerr tails

The numerical investigation of wave propagation in the asymptotic domain of Kerr spacetime has only recently been possible thanks to the construction of suitable hyperboloidal coordinates. The asymptotics revealed an apparent puzzle in the decay rates of scalar fields: the late-time rates seemed to depend on whether finite distance observers are in the strong field domain or far away from the rotating black hole, an apparent phenomenon dubbed "splitting". We discuss far-field "splitting" in the full field and near-horizon "splitting" in certain projected modes using horizon-penetrating, hyperboloidal coordinates. For either case we propose an explanation to the cause of the "splitting" behavior, and we determine uniquely decay rates that previous studies found to be ambiguous or immeasurable. The far-field "splitting" is explained by competition between projected modes. The near-horizon "splitting" is due to excitation of lower multipole modes that back excite the multipole mode for which "splitting" is observed. In both cases "splitting" is an intermediate effect, such that asymptotically in time strong field rates are valid at all finite distances. At any finite time, however, there are three domains with different decay rates whose boundaries move outwards during evolution. We then propose a formula for the decay rate of tails that takes into account the inter--mode excitation effect that we study.Comment: 16 page

Inteligentne sensory samozasilające w nowoczesnych systemach sterowania maszyn górniczych

Perspectives of development of control system dedicated for areas threatened by methane and/or coal dust explosion hazard are presented. Development of self-powered sensors, dedicated for operation in wireless network is one of the development directions. Such a solution will complement typical control systems and it can be used in the places, where there is no possibility of using the typical sensors, in close vicinity to the machine – due to lack of wired connection. General concept of the self-powered sensors with use of two methods of power supply – piezoelectric energy harvester and thermoelectric generator, is given. Perspective of using the methods of artificial intelligence in automatic configuration of sensors network is suggested.W artykule przedstawiono perspektywy rozwoju systemów sterowania dedykowanych do przestrzeni zagrożonych wybuchem metanu i/lub pyłu węglowego. Jednym z kierunków rozwoju tych systemów jest opracowanie systemu czujników samozasilających, dedykowanych do pracy w sieciach bezprzewodowych. Rozwiązanie takie będzie stanowić uzupełnienie typowych układów sterowania, możliwe do zastosowania w miejscach, w których nie istnieje możliwość zainstalowania czujników konwencjonalnych lub w bezpośrednim otoczeniu maszyny, w przypadku braku możliwości połączenia przewodowego. W artykule została przedstawiona ogólna koncepcja sieci czujników samozasilających z uwzględnieniem dwóch metod zasilania – z zastosowaniem piezoelectric energy harvester (odzysk energii z użyciem piezoelektryków) oraz termogeneratorów. Przedstawiona została również perspektywa zastosowania metod sztucznej inteligencji w automatycznej konfiguracji złożonej sieci komunikacyjnej obejmującej przedmiotowe oczujnikowanie

M - SmartGRID, the mine smart power grid

Ciągłość dostaw energii elektrycznej jest podstawowym czynnikiem warunkującym prowadzenie działalności w zakładach górniczych i jest podstawą bezpieczeństwa pracy ludzi oraz ochrony środków produkcji. Przerwy w dostawach energii stwarzają zagrożenie dla takich procesów jak: przewietrzanie wyrobisk podziemnych, transport załogi z i na powierzchnię kopalni. Instalacje elektryczne są często bardzo złożone i przesyłają dużą ilości energii, zwłaszcza, gdy szczytowe wartości mocy obciążenia są kilka razy wyższe niż jego średnia moc. Stąd istotne jest zarządzanie kopalnianą siecią elektroenergetyczną i jej monitorowanie oraz prognozowanie obciążeń i wspomaganie podejmowania decyzji w różnych warunkach funkcjonowania sieci. W niniejszym artykule przedstawiono oprogramowanie opracowane w ITG KOMAG.Reliability of energy supply is essential for operation of mining plants. Lack of supply poses a risks to such processes as: ventilation of workings, personnel transportation from and to the mine surface, and is fundamental for personnel safety and protection of means of production. Electrical installations are often very complex, they distribute large amount of power, especially when the peak power is a few times greater than the average power consumption. That is why it is essential to manage the mining power grid and its monitoring as well as forecasting the loads and assisting in making decisions at different conditions of the grid operation. Software developed by KOMAG is presented

Systems for monitoring, diagnostics and control of mining machines

Systemy monitoringu, sterowania i automatyzacji, zdolne do adaptacji i uczenia się, są co raz szerzej stosowane w praktyce przemysłowej. Wzrasta również obszar zastosowań systemów inteligentnych w polskim górnictwie węgla kamiennego. W artykule przedstawiono wybrane prace realizowane w Instytucie Techniki Górniczej KOMAG, we współpracy z KOPEX MACHINERY S.A., KWK Budryk i Gabrypol Sp. J. Z. i R. Juszczyk, w powyższym zakresie, które podnoszą wydajność maszyn i procesów technologicznych oraz zwiększają bezpieczeństwo pracy w górnictwie. Zaprezentowano modułowy, iskrobezpieczny system sterowania KOGAster, zintegrowany system sterowania węzłem osadzarkowym KOGA, system wibrodiagnostyczny maszyn górniczych VITO oraz system elektronicznej identyfikacji i ewidencji części maszyn Iris jako przykłady prac nad inteligentnymi maszynami górniczymi.The control and automation systems, i.e. the systems capable for adaptation and learning, gain wider group of users. The area of implementation of intelligent systems in the Polish hard coal mining industry also extends. Selected projects realized at the KOMAG Institute of Mining Technology in cooperation with KOPEX MACHINERY S.A., KWK Budryk and Gabrypol Sp. J. Z. i R. Juszczyk, as regards state-of-the-art, intelligent mechatronic systems, which increase the safety in the mining industry and which reduce energy consumption of technological process of coal production, are presented in the paper. Discussed projects include the modular, intrinsically safe KOGAster control system, the KOGA - integrated control system of jig’s cell, the vibro-diagnostics system VITO dedicated for mining machinery and an iRIS - electronic system of identification and registration of machine parts